[ { "id": "https://authors.library.caltech.edu/records/fm28z-4ed64", "eprint_status": "archive", "datestamp": "2026-04-22 20:30:20", "lastmod": "2026-04-22 20:30:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ryoo-Seung-Yeon", "name": { "family": "Ryoo", "given": "Seung-Yeon" }, "orcid": "0000-0002-0650-4854" } ] }, "title": "Quantitative nonembeddability of groups of polynomial growth into uniformly convex spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Groups of polynomial growth; Uniform convexity; Vector-valued Littlewood\u2013Paley\u2013Stein theory; Dorronsoro's theorem", "note": "

© 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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Part of this work appeared in my doctoral dissertation under the supervision of Professor Assaf Naor at Princeton University. I thank him, Professors Tuomas Orponen and Robert Young, and Ian Fleschler and Petr Kosenko for helpful discussions and suggestions. I am indebted to the anonymous referee for an extremely thorough reading of the manuscript, many useful corrections, and suggested improvements. This work was partially supported by the Overseas PhD Scholarship Program of the Korea Foundation for Advanced Studies, and an AMS–Simons Travel Grant.

", "abstract": "

Nonabelian simply connected nilpotent Lie groups and not virtually abelian finitely generated groups of polynomial growth do not quasi-isometrically embed into uniformly convex Banach spaces. We quantify this fact by showing that a ball of radius r ≥ 2 in the aforementioned groups must incur bilipschitz distortion at least a constant multiple of ( log \u2061 r ) 1 / q into a q ( ≥ 2 ) -uniformly convex Banach space. This bound is sharp for the L p ( 1 < p < ∞ ) spaces. We prove this by establishing \"vertical versus horizontal inequalities\" for functions from the aforementioned groups into uniformly convex spaces, using the vector-valued Littlewood–Paley–Stein theory approach of Lafforgue and Naor (2012). These inequalities are quantitative nonembeddability statements that any Lipschitz mapping from the aforementioned groups into a uniformly convex space quantitatively collapses along certain central subgroups. In the special case of mappings of Carnot groups into the L p ( 1 < p < ∞ ) spaces, we prove that the quantitative collapse occurs on the commutator subgroup; this is in line with the qualitative Pansu–Semmes nonembeddability argument given by Cheeger and Kleiner (2006) and Lee and Naor (2006). We prove this by establishing a version of the classical Dorronsoro theorem on Carnot groups. Previously, in the setting of Heisenberg groups, Fässler and Orponen (2019) established a one-sided Dorronsoro theorem with a restriction 0 < α < 2 on the range of exponents α of the Laplacian; this restriction does not appear in the commutative setting and is caused by their use of horizontal polynomials as approximants. We identify the correct class of approximant polynomials and prove the two-sided Dorronsoro theorem with the full range 0 < α < ∞ of exponents in the general setting of Carnot groups, thus strengthening and extending the work of Fässler and Orponen.

", "date": "2026-08-01", "date_type": "published", "publication": "Journal of Functional Analysis", "publisher": "Elsevier", "pagerange": "111491", "issn": "0022-1236", "official_url": "https://authors.library.caltech.edu/records/fm28z-4ed64", "funders": { "items": [ {}, {} ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1016/j.jfa.2026.111491", "pub_year": "2026", "author_list": "Ryoo, Seung-Yeon" }, { "id": "https://authors.library.caltech.edu/records/b06cw-mmv44", "eprint_status": "archive", "datestamp": "2026-04-08 16:38:53", "lastmod": "2026-04-08 16:38:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Laptev", "given": "Ari" }, "orcid": "0000-0002-1286-8670" }, { "name": { "family": "Suragan", "given": "Durvudkhan" }, "orcid": "0000-0003-4789-1982" } ] }, "title": "Eigenvalue lower bounds through a generalized inradius", "ispublished": "pub", "full_text_status": "public", "keywords": "Robin Laplacian; Polyharmonic operator; Heisenberg group; Lowest eigenvalue", "note": "

© 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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The authors were supported in parts by US National Science Foundation grant DMS-1954995 (R.L.F.) and the German Research Foundation grants EXC-2111-390814868 and TRR 352-Project-ID 470903074 (R.L.F.). This research is funded by Nazarbayev University under the FDCRGP 110326FD3205 (D.S.).

", "abstract": "

Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian on the Heisenberg group. We propose a method based on Hardy inequalities that is different from Lieb's approach.

", "date": "2026-07-01", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "291", "number": "1", "publisher": "Elsevier", "pagerange": "111473", "issn": "0022-1236", "official_url": "https://authors.library.caltech.edu/records/b06cw-mmv44", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "TRR 352-Project-ID 470903074" }, { "grant_number": "110326FD3205" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2026.111473", "pub_year": "2026", "author_list": "Frank, Rupert L.; Laptev, Ari; et al." }, { "id": "https://authors.library.caltech.edu/records/xen46-etw49", "eprint_status": "archive", "datestamp": "2026-06-03 22:34:45", "lastmod": "2026-06-03 22:34:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Huang", "given": "Jiaoyang" }, "orcid": "0000-0001-8266-1301" }, { "id": "Zhang-Lingfu", "name": { "family": "Zhang", "given": "Lingfu" }, "orcid": "0000-0002-4794-7678" } ] }, "title": "A convergence framework for Airy\u03b2 line ensemble via pole evolution", "ispublished": "pub", "full_text_status": "public", "keywords": "Random matrices; Dyson Brownian motion; Airy line ensemble; Interacting particle system", "note": "

© 2026 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

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Part of this project was done when L.Z. was visiting University of Pennsylvania in the spring of 2023, and he thanks them for their hospitality. The authors would like to thank Paul Bourgade, Vadim Gorin, Benjamin Landon, and Bálint Virág for helpful discussions, and the referees for their careful reading of the manuscript and constructive suggestions.

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The research of J.H. is supported by NSF grant DMS-2331096 and DMS-2337795, and the Sloan research award. The research of L.Z. is supported by NSF grant DMS-2505625, the Miller Institute for Basic Research in Science, and the Sloan research award.

", "abstract": "

The Airy β line ensemble is an infinite sequence of random curves. It is a natural extension of the Tracy-Widom β distributions, and is expected to be the universal edge scaling limit of a range of models in random matrix theory and statistical mechanics. In this work, we provide a framework of proving convergence to the Airy β line ensemble, via a characterization through the pole evolution of meromorphic functions satisfying certain stochastic differential equations. Our framework is then applied to prove the universality of the Airy β line ensemble as the edge limit of various continuous time processes, including Dyson Brownian motions with general β and potentials, Laguerre processes and Jacobi processes.

", "date": "2026-07", "date_type": "published", "publication": "Advances in Mathematics", "volume": "498", "publisher": "Elsevier", "pagerange": "111028", "issn": "0001-8708", "official_url": "https://authors.library.caltech.edu/records/xen46-etw49", "funders": { "items": [ { "grant_number": "DMS-2331096" }, { "grant_number": "DMS-2337795" }, {}, { "grant_number": "DMS-2505625" }, {} ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1016/j.aim.2026.111028", "primary_object": { "basename": "1-s2.0-S0001870826002501-main.pdf", "url": "https://authors.library.caltech.edu/records/xen46-etw49/files/1-s2.0-S0001870826002501-main.pdf" }, "pub_year": "2026", "author_list": "Huang, Jiaoyang and Zhang, Lingfu" }, { "id": "https://authors.library.caltech.edu/records/gmvhx-q6s56", "eprint_status": "archive", "datestamp": "2026-02-26 16:51:07", "lastmod": "2026-02-26 16:51:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Noguchi", "given": "Kimihiro" }, "orcid": "0000-0002-5904-9568" }, { "name": { "family": "Lukken", "given": "Cayden" } }, { "id": "Ward-Mayla-C", "name": { "family": "Ward", "given": "Mayla C." }, "orcid": "0009-0002-2530-8370" } ] }, "title": "Asymptotic optimality of the Wilson-Hilferty cube-root transformation on the gamma distribution for higher-order odd central moments", "ispublished": "pub", "full_text_status": "public", "keywords": "Hyperskewness; Incomplete gamma function; Normality; Power transformation; Stirling numbers of the second kind; Superskewness", "note": "

© 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors are grateful to the anonymous reviewers and Branko \u0106urgus for their valuable comments.
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MMC S1. The online supplementary material provides detailed derivations for both the odd and even central moment cases.

", "abstract": "The Wilson-Hilferty cube-root transformation is often applied to the gamma distribution to achieve approximate normality. Its asymptotic optimality was originally derived by expanding the third central moment of the scaled and power-transformed chi-squared distribution as the degrees of freedom approaches infinity. However, the original approach does not easily generalize to higher-order odd central moments of the power-transformed gamma distribution due to the increasing complexity of the resulting mathematical expression. To overcome the difficulty, we provide a novel efficient quantile-based approach to demonstrate that the cube-root transformation remains asymptotically optimal when any odd central moment of order three or higher is used as a criterion for approximate symmetry of the power-transformed gamma distribution. Unlike the previous approaches, the quantile-based approach provides a theoretical justification for the cube-root transformation on the tails of the gamma distribution, which is crucial for the normal-based inference on gamma-distributed data.", "date": "2026-06", "date_type": "published", "publication": "Statistics & Probability Letters", "volume": "233", "publisher": "Elsevier", "pagerange": "110680", "issn": "0167-7152", "official_url": "https://authors.library.caltech.edu/records/gmvhx-q6s56", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1016/j.spl.2026.110680", "primary_object": { "basename": "1-s2.0-S0167715226000441-mmc1.pdf", "url": "https://authors.library.caltech.edu/records/gmvhx-q6s56/files/1-s2.0-S0167715226000441-mmc1.pdf" }, "pub_year": "2026", "author_list": "Noguchi, Kimihiro; Lukken, Cayden; et al." }, { "id": "https://authors.library.caltech.edu/records/7hg56-9kr84", "eprint_status": "archive", "datestamp": "2026-05-21 19:56:25", "lastmod": "2026-05-21 19:56:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Agus", "given": "Syamsul B." }, "orcid": "0000-0002-9562-3790" }, { "name": { "family": "Pasaribu", "given": "Martines" }, "orcid": "0009-0001-2555-4873" }, { "name": { "family": "Yulius" }, "orcid": "0000-0002-2643-4240" }, { "name": { "family": "Salim", "given": "Hadiwijaya L." }, "orcid": "0000-0002-7045-4302" }, { "name": { "family": "Arifin", "given": "Taslim" }, "orcid": "0000-0001-5587-888X" }, { "name": { "family": "Kusumaningtyas", "given": "Mariska A." }, "orcid": "0000-0003-3538-4959" }, { "name": { "family": "Hartati", "given": "Sri T." }, "orcid": "0009-0005-1119-3789" }, { "name": { "family": "Akhwady", "given": "Rudhy" } }, { "name": { "family": "Suryono", "given": "Devi D." }, "orcid": "0009-0001-3429-7805" }, { "name": { "family": "Putra", "given": "Aprizon" }, "orcid": "0000-0002-4619-4117" }, { "name": { "family": "Sufyan", "given": "Agus" }, "orcid": "0000-0002-2540-6379" }, { "name": { "family": "Ramdhan", "given": "Muhammad" }, "orcid": "0000-0002-6921-6024" }, { "name": { "family": "Wahyono", "given": "Ari" }, "orcid": "0009-0008-5014-085X" }, { "name": { "family": "Rahmania", "given": "Rinny" }, "orcid": "0000-0002-1935-8294" }, { "name": { "family": "Zulfiandi" } }, { "name": { "family": "Kurniawan", "given": "Fery" }, "orcid": "0000-0003-4342-2169" }, { "id": "Reeves-Lily", "name": { "family": "Reeves", "given": "Lily" } } ] }, "title": "Mapping and analyzing mangrove canopy density in East Belitung using Pleiades satellite imagery and hemispherical photography", "ispublished": "pub", "full_text_status": "public", "keywords": "Canopy density; Coastal management; East Belitung; Fisheye photos; Mangroves; Satellite data", "note": "

© 2026 The Authors. Published by Elsevier B.V. on behalf of National Authority of Remote Sensing & Space Science. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

", "abstract": "
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Mangrove ecosystems face growing threats from human activity and erosion. This study aims to map mangrove distribution and canopy density and to evaluate the relationship between Normalized Difference Vegetation Index (NDVI) and field-measured canopy cover in East Belitung, Indonesia, by integrating high-resolution Pleiades imagery, NDVI, and hemispherical photography. A total of 50 field plots were used to assess canopy cover through hemispherical photography, while Object-Based Image Analysis (OBIA) with Support Vector Machine (SVM) classification was applied to map mangrove distribution and density. Results show that very dense canopies were largely associated with stands dominated by Rhizophora spp. along riverbanks and estuaries, especially in the northern and southern parts of the study area, with favorable hydrological conditions. Classification accuracy reached 83.3% (Kappa = 0.71), and canopy cover was strongly correlated with NDVI (r = 0.855), validating the method. The regression analysis further showed that canopy cover explained a substantial proportion of NDVI variation (R2 = 0.731). Combining satellite data with field validation offers a scalable framework for mangrove monitoring and supports coastal resilience and sustainable management.
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", "date": "2026-06", "date_type": "published", "publication": "The Egyptian Journal of Remote Sensing and Space Sciences", "volume": "29", "number": "2", "publisher": "Elsevier", "pagerange": "357-368", "issn": "1110-9823", "official_url": "https://authors.library.caltech.edu/records/7hg56-9kr84", "funders": { "items": [ {} ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1016/j.ejrs.2026.04.002", "primary_object": { "basename": "1-s2.0-S111098232600027X-main.pdf", "url": "https://authors.library.caltech.edu/records/7hg56-9kr84/files/1-s2.0-S111098232600027X-main.pdf" }, "pub_year": "2026", "author_list": "Agus, Syamsul B.; Pasaribu, Martines; et al." }, { "id": "https://authors.library.caltech.edu/records/v19pp-e7j03", "eprint_status": "archive", "datestamp": "2026-05-12 16:18:00", "lastmod": "2026-05-12 16:18:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Hsin", "given": "Po-Shen" }, "orcid": "0000-0002-4764-1476" }, { "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" } ] }, "title": "Generalized global symmetries of T[M] theories. Part II", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories; Field Theories in Higher Dimensions; Topological Field Theories; Supersymmetric Effective Theories", "note": "

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3.

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We thank Cyril Closset, Thomas Dumitrescu, Anton Kapustin, Hiraku Nakajima, Pavel Putrov, Nathan Seiberg, Dan Xie, Tian Yang, and Bingyu Zhang for discussions. We thank the audience of our talks based on this work given on various occasions throughout the past five years for their feedback and encouragements. SG was supported by the Simons Collaboration Grant on “New Structures in Low-Dimensional Topology,” by the NSF grant DMS-2245099, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of P.-S. H. was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award, by the Simons Collaboration of Global Categorical Symmetry, and also by Department of Mathematics King’s College London. The work of D.P. is partly supported by research grant 42125 from Villum Fonden, ERC-SyG project No. 810573 “Recursive and Exact New Quantum Theory,” and Simons Collaboration on “New Structures in Low-Dimensional Topology.” D.P. also want to thank the Yau Center for Mathematical Sciences at Tsinghua University for hospitality during his visits.

", "abstract": "

We continue the investigation of symmetries and anomalies of T[M] theories obtained by compactifying 6d SCFTs on an internal manifold M. We extend the notion of “polarizations on a manifold M” to cases where M may have boundaries or defects. Through examples with M of dimension two, three, and four, we illustrate recurring themes in compactifications — for instance, the important roles played by Kaluza-Klein modes, and how the generalized symmetries (including higher-group and non-invertible ones) of T[M], together with their anomalies, arise from non-trivial combinations of the parent 6d symmetries and the geometric structures of the internal manifold. For each dimension, we also focus on several topics that are especially interesting in that setting. These include: for 2-manifolds, the geometry of the “full moduli space” of T[M2] and its interaction with polarizations and symmetries; for 3-manifolds, the effect of torsion in homology on the spectrum of line operators in T[M3], together with applications to the study of quantum invariants such as Z_a (M\u2083, q); and for 4-manifolds, predictions for VOA[M4] following from symmetries of T[M4], as well as the construction of a new invariant of 4-manifolds that depends on two “q-parameters.” Along the way, we discuss a range of topics that are of independent interest, such as how non-invertible symmetries in higher dimensions can become invertible under compactification, how to classify defects in quantum field theory via their response to a change of framing, and the interplay between Z_a and volume conjectures.

", "date": "2026-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2026", "number": "5", "publisher": "Springer Science and Business Media LLC", "pagerange": "87", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/v19pp-e7j03", "funders": { "items": [ {}, { "agency": "National Science Foundation", "grant_number": "DMS-2245099" }, { "grant_number": "DE-SC0011632" }, {}, { "agency": "Villum Fonden", "grant_number": "42125" }, { "agency": "European Research Council", "grant_number": "810573" }, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep05(2026)087", "primary_object": { "basename": "JHEP05(2026)087.pdf", "url": "https://authors.library.caltech.edu/records/v19pp-e7j03/files/JHEP05(2026)087.pdf" }, "pub_year": "2026", "author_list": "Gukov, Sergei; Hsin, Po-Shen; et al." }, { "id": "https://authors.library.caltech.edu/records/5k26m-b1s32", "eprint_status": "archive", "datestamp": "2026-04-23 19:57:09", "lastmod": "2026-04-23 19:57:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Cant", "given": "Dylan" }, "orcid": "0000-0002-6894-0504" }, { "id": "Chen-Daren", "name": { "family": "Chen", "given": "Daren" }, "orcid": "0000-0002-5637-447X" } ] }, "title": "Adiabatic compactness for holomorphic curves with boundary on nearby Lagrangians", "ispublished": "pub", "full_text_status": "public", "keywords": "adiabatic compactness; holomorphic curves with Lagrangian boundary conditions; Morse flow trees", "note": "

© 2026 by Kyoto University.

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This work was completed while the authors were graduate students at Stanford University. Both authors benefited greatly from interactions with Yasha Eliashberg, Eleny Ionel, Umut Varolgunes, and other graduate students in our field. The authors also thank Yong-Geun Oh, Ke Zhu, Octav Cornea, and the anonymous referee for useful comments during the preparation of the text.

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", "abstract": "

In a 1989 paper [14], Floer established a connection between holomorphic strips with boundary on a Lagrangian L and a small Hamiltonian push-off Lf and gradient flow lines for the function f. The present paper studies the compactness theory for holomorphic curves un whose boundary components lie on Hamiltonian perturbations Ln1,…,LnN of a fixed Lagrangian L, where each sequence of nearby Lagrangians Lnj converges to L as n→∞. Generalizing earlier work of Oh, Fukaya, Ekholm, and Zhu, we prove that the limit of a sequence of such holomorphic maps is a configuration consisting of holomorphic curves with boundary on L joined by gradient flow lines connecting points on the boundary of holomorphic pieces. The key new result is an exponential estimate analyzing the interface between the holomorphic parts and the gradient flow line parts.

", "date": "2026-05", "date_type": "published", "publication": "Kyoto Journal of Mathematics", "volume": "66", "number": "2", "publisher": "Duke University Press", "issn": "2156-2261", "official_url": "https://authors.library.caltech.edu/records/5k26m-b1s32", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1215/21562261-2024-0043", "pub_year": "2026", "author_list": "Cant, Dylan and Chen, Daren" }, { "id": "https://authors.library.caltech.edu/records/br2zc-wmx83", "eprint_status": "archive", "datestamp": "2026-04-23 21:22:57", "lastmod": "2026-04-23 21:22:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Chang", "given": "Kevin" }, "orcid": "0009-0003-6920-8897" }, { "name": { "family": "Dragutinovi\u0107", "given": "Du\u0161an" }, "orcid": "0009-0009-5187-7033" }, { "name": { "family": "Groen", "given": "Steven" }, "orcid": "0000-0001-8595-4281" }, { "id": "Lin-Yuxin", "name": { "family": "Lin", "given": "Yuxin" }, "orcid": "0000-0001-9230-7728" }, { "name": { "family": "Pacheco-Tallaj", "given": "Natalia" }, "orcid": "0000-0003-1637-9492" }, { "name": { "family": "Singhal", "given": "Deepesh" }, "orcid": "0000-0003-1317-5523" } ] }, "title": "The p-rank stratification of the moduli space of double covers of a fixed elliptic curve", "ispublished": "pub", "full_text_status": "public", "keywords": "curves; moduli spaces; positive characteristic; Jacobians; p-rank", "note": "

© The Author(s), 2026. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.

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This project originated at the Arizona Winter School in 2024, of which we would like to thank the organizers cordially. In particular, we would like to thank Rachel Pries for organizing the lecture series on the Torelli locus, suggesting this project topic and for many helpful conversations and instructions. We would like to thank George Nicolas Diaz-Wahl, Caleb Ji, Rose Lopez, and Isaiah Mindich for contributions to this project during the Arizona Winter School. We would also like to thank Ben Moonen for his helpful remark.

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It is our pleasure to thank an anonymous referee for helpful comments.

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D.D. is supported by the Mathematical Institute of Utrecht University. N.P.-T. is supported by the National Science Foundation under Grant No. DGE-2141064.

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", "abstract": "

In this article, we investigate the p-rank stratification of the moduli space of curves of genus g that admit a double cover to a fixed elliptic curve E in characteristic \ud835\udc5d >2. We show that the closed p-rank strata of this moduli space are equidimensional of the expected dimension. We also show the existence of a smooth double cover of E of all the possible values of the p-rank on this moduli space.

", "date": "2026-04-06", "date_type": "published", "publication": "Nagoya Mathematical Journal", "volume": "261", "publisher": "Cambridge University Press (CUP)", "pagerange": "e26", "issn": "0027-7630", "official_url": "https://authors.library.caltech.edu/records/br2zc-wmx83", "funders": { "items": [ {}, { "grant_number": "DGE-2141064" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1017/nmj.2026.10107", "primary_object": { "basename": "the-p-rank-stratification-of-the-moduli-space-of-double-covers-of-a-fixed-elliptic-curve.pdf", "url": "https://authors.library.caltech.edu/records/br2zc-wmx83/files/the-p-rank-stratification-of-the-moduli-space-of-double-covers-of-a-fixed-elliptic-curve.pdf" }, "pub_year": "2026", "author_list": "Chang, Kevin; Dragutinovi\u0107, Du\u0161an; et al." }, { "id": "https://authors.library.caltech.edu/records/n4v7p-6jw96", "eprint_status": "archive", "datestamp": "2026-01-27 19:18:35", "lastmod": "2026-03-09 21:42:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Boateng", "given": "Luisa" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Formal languages and TQFTs with defects", "ispublished": "pub", "full_text_status": "public", "keywords": "1D Boolean TQFT with defects; Formal languages; Context-free grammars; Cobordism; Operads of spliced arrows", "note": "

© 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

", "abstract": "

A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite state automata with transducers as morphisms. Certain classes of subregular languages correspond to additional cohomological structures on the associated TQFTs. We also show that the construction generalizes to context-free grammars through a categorical version of the Chomsky–Schützenberger representation theorem, due to Melliès and Zeilberger. The corresponding TQFTs are then described as morphisms of colored operads on an operad of cobordisms with defects.

", "date": "2026-04", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "222", "publisher": "Elsevier", "pagerange": "105771", "issn": "0393-0440", "official_url": "https://authors.library.caltech.edu/records/n4v7p-6jw96", "funders": { "items": [ {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2026.105771", "pub_year": "2026", "author_list": "Boateng, Luisa and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/a0ybm-q3j41", "eprint_status": "archive", "datestamp": "2026-04-14 21:25:46", "lastmod": "2026-04-14 21:25:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Allemand", "given": "Allan" } }, { "name": { "family": "Kanel-Belov", "given": "Alexey" } }, { "id": "Zaytsev-Rodion", "name": { "family": "Zaytsev", "given": "Rodion" } } ] }, "title": "Monodromy Groups and the Insolvability of Transcendental Equations in Quadratures", "ispublished": "pub", "full_text_status": "public", "keywords": "Topological Galois theory; monodromy group; unsolvability in quadratures; transcendental equations; braid group", "note": "

© 2026 Association for Mathematical Research.

", "abstract": "
This paper presents the authors’ results in applying Arnold’s method to compute the monodromy groups of certain trigonometric complex equations, and also provides a survey of other results in this area.
", "date": "2026-03-29", "date_type": "published", "publication": "Arnold Mathematical Journal", "volume": "012", "number": "001", "publisher": "Association for Mathematical Research", "pagerange": "004", "issn": "2199-6792", "official_url": "https://authors.library.caltech.edu/records/a0ybm-q3j41", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.56994/armj.012.001.004", "pub_year": "2026", "author_list": "Allemand, Allan; Kanel-Belov, Alexey; et al." }, { "id": "https://authors.library.caltech.edu/records/ww1dv-bre08", "eprint_status": "archive", "datestamp": "2025-09-08 18:02:25", "lastmod": "2026-03-08 17:37:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "He", "given": "Xiaoyu" } }, { "name": { "family": "Mubayi", "given": "Dhruv" } }, { "name": { "family": "Suk", "given": "Andrew" } }, { "name": { "family": "Verstra\u00ebte", "given": "Jacques" } } ] }, "title": "Big line or big convex polygon", "ispublished": "pub", "full_text_status": "public", "keywords": "Erd\u0151s-Szekeres; Convex polygon; Collinear points", "note": "

© 2025 Published by Elsevier B.V.

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This research was initiated during a visit to the American Institute of Mathematics under their SQuaREs program. We are grateful to Sam Spiro for pointing out a typographical error in a previous version of this paper.
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Research supported by NSF Awards DMS-2054452 and DMS-2348859.
Research supported by NSF Award DMS-2154129.
Research supported by NSF Award DMS-2103154.
Research partially supported by NSF Awards DMS-1952767 and DMS-2153576.
Research supported by an NSF CAREER Award and by NSF Awards DMS-1952786 and DMS-2246847.
Research supported by NSF Award DMS-1800332.

", "abstract": "

Let ES\u2113(n) be the minimum N such that every N-element point set in the plane contains either \u2113 collinear members or n points in convex position. We prove that there is a constant C > 0 such that, for each \u2113, n ≥ 3, (3\u2113 − 1) ⋅ 2^(n − 5) < ES\u2113(n) < \u2113² ⋅ 2^(n + C √n log n). A similar extension of the well-known Erd\u0151s–Szekeres cups-caps theorem is also proved.

", "date": "2026-03", "date_type": "published", "publication": "Computational Geometry", "volume": "131", "publisher": "Elsevier", "pagerange": "102218", "issn": "0925-7721", "official_url": "https://authors.library.caltech.edu/records/ww1dv-bre08", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, { "grant_number": "DMS-2154129" }, { "grant_number": "DMS-2103154" }, { "grant_number": "DMS-1952767" }, { "grant_number": "DMS-2153576" }, { "grant_number": "DMS-1952786" }, { "grant_number": "DMS-2246847" }, { "grant_number": "DMS-1800332" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.comgeo.2025.102218", "pub_year": "2026", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/ntdcd-7xp35", "eprint_status": "archive", "datestamp": "2026-01-29 17:33:06", "lastmod": "2026-03-08 17:37:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "F\u00fchrer", "given": "Jakob" }, "orcid": "0009-0009-4793-0356" } ] }, "title": "Non-spherical sets versus lines in Euclidean Ramsey theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Euclidean Ramsey theory; spherical sets; equidistribution", "note": "
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© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society.

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The authors thank Manuel Hauke for helpful conversations regarding equidistribution.

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D.C. was supported by NSF Awards DMS-2054452 and DMS-2348859. J.F. was supported by the Austrian Science Fund (FWF) under the project W1230.

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", "abstract": "

We show that for every non-spherical set X in E^d, there exists a natural number m and a red/blue-coloring of E^n for every n such that there is no red copy of X and no blue progression of length m with each consecutive point at distance 1. This verifies a conjecture of Wu and the first author.

", "date": "2026-03", "date_type": "published", "publication": "Canadian Mathematical Bulletin", "volume": "69", "number": "1", "publisher": "Canadian Mathematical Society", "pagerange": "179-183", "issn": "0008-4395", "official_url": "https://authors.library.caltech.edu/records/ntdcd-7xp35", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, { "grant_number": "W1230" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4153/s0008439525101082", "pub_year": "2026", "author_list": "Conlon, David and F\u00fchrer, Jakob" }, { "id": "https://authors.library.caltech.edu/records/ywbjj-n1p25", "eprint_status": "archive", "datestamp": "2026-01-19 22:38:43", "lastmod": "2026-03-09 20:41:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Arant", "given": "Tyler" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "name": { "family": "Lutz", "given": "Patrick" } } ] }, "title": "Borel graphable equivalence relations", "ispublished": "pub", "full_text_status": "public", "keywords": "Effective descriptive set theory; Polish group; Church-Kleene ordinal; Kumabe-Slaman forcing; Analytic equivalence relation; Invariant descriptive set theory", "note": "

Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Thanks to Gabe Goldberg for pointing out the absoluteness argument in Section 2, to Jan Grebík for several helpful conversations and to an anonymous reviewer for pointing out a simplified proof of Theorem 45. A special thanks to Andrew Marks for many useful comments and insights when the notion of Borel graphability was first considered.

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Research partially supported by NSF Grant DMS-1950475.

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Research partially supported by NSF Grant DMS-203072.

", "abstract": "

This paper is devoted to the study of analytic equivalence relations which are Borel graphable, i.e. which can be realized as the connectedness relation of a Borel graph. Our main focus is the question of which analytic equivalence relations are Borel graphable. First, we study an equivalence relation arising from the theory of countable admissible ordinals and show that it is Borel graphable if and only if there is a non-constructible real. As a corollary of the proof, we construct an analytic equivalence relation which is (provably in ZFC) not Borel graphable and an effectively analytic equivalence relation which is Borel graphable but not effectively Borel graphable. Next, we study analytic equivalence relations given by the isomorphism relation for some class of countable structures. We show that all such equivalence relations are Borel graphable, which implies that for every Borel action of S ∞, the associated orbit equivalence relation is Borel graphable. This leads us to study the class of Polish groups whose Borel actions always give rise to Borel graphable orbit equivalence relations; we refer to such groups as graphic groups. We show that besides S ∞, the class of graphic groups includes all connected Polish groups and is closed under countable products. We finish by studying structural properties of the class of Borel graphable analytic equivalence relations and by considering two variations on Borel graphability: a generalization with hypergraphs instead of graphs and an analogue of Borel graphability in the setting of computably enumerable equivalence relations.

", "date": "2026-03", "date_type": "published", "publication": "Advances in Mathematics", "volume": "487", "publisher": "Elsevier", "pagerange": "110765", "issn": "0001-8708", "official_url": "https://authors.library.caltech.edu/records/ywbjj-n1p25", "funders": { "items": [ { "grant_number": "DMS-1950475" }, { "grant_number": "DMS-203072" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2025.110765", "primary_object": { "basename": "1-s2.0-S0001870825006632-main.pdf", "url": "https://authors.library.caltech.edu/records/ywbjj-n1p25/files/1-s2.0-S0001870825006632-main.pdf" }, "pub_year": "2026", "author_list": "Arant, Tyler; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/m5v31-zjd38", "eprint_status": "archive", "datestamp": "2025-12-05 01:16:46", "lastmod": "2026-04-09 21:53:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-Rupert-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Larson-Simon", "name": { "family": "Larson", "given": "Simon" }, "orcid": "0000-0002-0057-8211" } ] }, "title": "Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025 The Author(s). Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

\n\n", "abstract": "

We are interested in inequalities that bound the Riesz means of the eigenvalues of the Dirichlet and Neumann Laplacians in terms of their semiclassical counterpart. We show that the classical inequalities of Berezin–Li–Yau and Kröger, valid for Riesz exponents γ ≥ 1, extend to certain values γ < 1 , provided the underlying domain is convex. We also study the corresponding optimization problems and describe the implications of a possible failure of Pólya's conjecture for convex sets in terms of Riesz means. These findings allow us to describe the asymptotic behavior of solutions of a spectral shape optimization problem for convex sets.

", "date": "2026-03", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "79", "number": "3", "publisher": "Wiley", "pagerange": "762-822", "issn": "0010-3640", "official_url": "https://authors.library.caltech.edu/records/m5v31-zjd38", "funders": { "items": [ { "grant_number": "DMS\u20101954995" }, { "grant_number": "EXC\u20102111\u2010390814868" }, { "grant_number": "TRR 352\u2010Project\u2010ID 470903074" }, { "grant_number": "KAW 2017.0295" }, { "grant_number": "2023\u201003985" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1002/cpa.70019", "primary_object": { "basename": "Comm Pure Appl Math - 2025 - Frank - Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains.pdf", "url": "https://authors.library.caltech.edu/records/m5v31-zjd38/files/Comm Pure Appl Math - 2025 - Frank - Semiclassical inequalities for Dirichlet and Neumann Laplacians on convex domains.pdf" }, "pub_year": "2026", "author_list": "Frank, Rupert L. and Larson, Simon" }, { "id": "https://authors.library.caltech.edu/records/0c74v-ax784", "eprint_status": "archive", "datestamp": "2026-02-27 23:32:25", "lastmod": "2026-02-27 23:32:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Larson", "given": "Simon" }, "orcid": "0000-0002-0057-8211" }, { "name": { "family": "Pfeiffer", "given": "Paul" }, "orcid": "0009-0009-2433-4180" } ] }, "title": "Improved semiclassical eigenvalue estimates for the Laplacian and the Landau Hamiltonian", "ispublished": "pub", "full_text_status": "public", "keywords": "eigenvalue estimates; Laplace operator; Landau Hamiltonian; semiclassical analysis; uncertainty principle", "note": "

© 2025 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license.

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Partial support through US National Science Foundation grant DMS1954995 (R.L.F.), the German Research Foundation through EXC-2111-390814868 (R.L.F.) and TRR 352-Project-ID 470903074 (R.L.F. & P.P.), as well as the Swedish Research Council grant no. 2023-03985 (S.L.) is acknowledged.

", "abstract": "

The Berezin–Li–Yau and the Kröger inequalities show that Riesz means of order ≥1 of the eigenvalues of the Laplacian on a domain Ω of finite measure are bounded in terms of their semiclassical limit expressions. We show that these inequalities can be improved by a multiplicative factor that depends only on the dimension and the product Λ\u2223Ω\u22231/d, where Λ is the eigenvalue cut-off parameter in the definition of the Riesz mean. The same holds when \u2223Ω\u22231/d is replaced by a generalized inradius of Ω. Finally, we show similar inequalities in two dimensions in the presence of a constant magnetic field.

", "date": "2026-02-17", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "16", "number": "1", "publisher": "European Mathematical Society - EMS - Publishing House GmbH", "pagerange": "243-270", "issn": "1664-039X", "official_url": "https://authors.library.caltech.edu/records/0c74v-ax784", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "470903074" }, { "grant_number": "2023-03985" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.4171/jst/589", "primary_object": { "basename": "10.4171-jst-589.pdf", "url": "https://authors.library.caltech.edu/records/0c74v-ax784/files/10.4171-jst-589.pdf" }, "pub_year": "2026", "author_list": "Frank, Rupert L.; Larson, Simon; et al." }, { "id": "https://authors.library.caltech.edu/records/vrq63-tpg96", "eprint_status": "archive", "datestamp": "2026-02-10 18:02:06", "lastmod": "2026-03-10 03:30:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Haghighat", "given": "Babak" }, "orcid": "0000-0002-6688-7076" }, { "name": { "family": "Liu", "given": "Yihua" }, "orcid": "0009-0009-0493-7347" }, { "name": { "family": "Reshetikhin", "given": "Nicolai" }, "orcid": "0000-0002-5352-2676" } ] }, "title": "Irregular KZ equations and Kac\u2013Moody representations", "ispublished": "pub", "full_text_status": "public", "keywords": "Knizhnik\u2013Zamolodchikov equation; Kac\u2013Moody algebra; Liouville theory; Argyres\u2013Douglas theory; Rozansky\u2013Witten theory; Lefschetz thimble", "note": "

© 2026 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.

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It is our pleasure to thank Boris Feigin, Xia Gu, Pavel Putrov and Xiaomeng Xu for helpful discussions and suggestions. The work of S G is supported by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology, by the NSF Grant DMS-2245099, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of B H and Y L is supported by NSFC Grant 12250610187. The work of N R was supported by the Simons Collaboration ‘Categorical symmetries’, by the grant BMSTC and ACZSP (Grant No. Z221100002722017), by the Changjiang fund, and by the Project No 075-15-2024-631 funded by the ministery of Science and Higher Education of the Russian Federation.

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All data that support the findings of this study are included within the article (and any supplementary files).

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", "abstract": "

In this paper we construct irregular representations of the affine Kac–Moody algebra sl (2, \u2102). We show how such irregular representations correspond to irregular Gaiotto–Teschner representations of the Virasoro algebra. The intertwiners for such representations satisfy a version of Knizhnik–Zamolodchikov (KZ) equations which we call irregular KZ equations. By connecting to 2d Liouville theory, we show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres–Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve.

", "date": "2026-02-06", "date_type": "published", "publication": "Journal of Physics A: Mathematical and Theoretical", "volume": "59", "number": "5", "publisher": "IOP Publishing", "pagerange": "055202", "issn": "1751-8113", "official_url": "https://authors.library.caltech.edu/records/vrq63-tpg96", "funders": { "items": [ { "grant_number": "DMS-2245099" }, { "grant_number": "DE-SC0011632" }, { "grant_number": "12250610187" }, {}, { "agency": "Changjiang fund" }, { "grant_number": "075-15-2024-631" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1088/1751-8121/ae35ec", "pub_year": "2026", "author_list": "Gukov, Sergei; Haghighat, Babak; et al." }, { "id": "https://authors.library.caltech.edu/records/g4yht-egb96", "eprint_status": "archive", "datestamp": "2026-02-09 22:29:04", "lastmod": "2026-03-10 03:30:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Adams-Griffen", "name": { "family": "Adams", "given": "Griffen" }, "orcid": "0009-0009-0535-4469" }, { "id": "Costin-Ovidiu", "name": { "family": "Costin", "given": "Ovidiu" }, "orcid": "0000-0001-7105-7379" }, { "id": "Dunne-Gerald-V", "name": { "family": "Dunne", "given": "Gerald V." }, "orcid": "0000-0003-1338-339X" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "\u00d6ner-O\u011fuz", "name": { "family": "\u00d6ner", "given": "O\u011fuz" }, "orcid": "0009-0002-3620-6783" } ] }, "title": "c_(eff) from resurgence at the Stokes line", "ispublished": "pub", "full_text_status": "public", "keywords": "Nonperturbative Effects; Chern-Simons Theories; Topological Field Theories", "note": "

© The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Thanks to John Chae, Miranda C. N. Cheng, Daniele Dorigoni, Jean Écalle, Shimal Harichurn, Mrunmay Jagadale, Albrecht Klemm, Dmitry Noshchenko, Davide Passaro, and Don Zagier for discussions, ideas, help, advice, support and inspiration that have greatly benefited this project. We are especially grateful to Shimal Harichurn, Mrunmay Jagadale, Dmitry Noshchenko and Davide Passaro for sharing their results in [13]... GD thanks the Max Planck Institute for Mathematics, Bonn, for support during the program “Combinatorics, Resurgence and Algebraic Geometry in Quantum Field Theory”, August 2024. GA and OÖ thank L’École de Physique des Houches for support during the 2024 Summer School “Quantum Geometry”.

", "abstract": "

In recent papers [1, 2], a new method to cross the natural boundary has been proposed, and applied to Mordell-Borel integrals arising in the study of Chern-Simons theory, based on decompositions into resurgent cyclic orbits . Resurgent analysis on the Stokes line leads to a unique transseries decomposition in terms of unary false theta functions, which can be continued across the natural boundary to produce dual q -series whose integer-valued coefficients enumerate BPS states. This constitutes a deeper new manifestation of resurgence in quantum field theoretic path integrals. In this paper we show that the algebraic structure of the resurgent cyclic orbits , combined with just the leading term of the q -series, completely determines the large order rate of growth of the dual q -series coefficients. The essential exponent of this asymptotic growth has a Cardy-like interpretation [12] of an effective central charge in a 3 dimensional quantum field theory with N = 2 supersymmetry related to the Chern-Simons theory through the 3d -3d correspondence.

", "date": "2026-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2026", "number": "2", "publisher": "Springer Science and Business Media LLC", "pagerange": "75", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/g4yht-egb96", "funders": { "items": [ { "grant_number": "DMS-2206241" }, { "grant_number": "DE-SC0010339" }, { "grant_number": "DMS-2245099" }, { "grant_number": "DE-SC0011632" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep02(2026)075", "primary_object": { "basename": "JHEP02(2026)075.pdf", "url": "https://authors.library.caltech.edu/records/g4yht-egb96/files/JHEP02(2026)075.pdf" }, "pub_year": "2026", "author_list": "Adams, Griffen; Costin, Ovidiu; et al." }, { "id": 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L." } }, { "name": { "family": "Zhu", "given": "Kelin" } }, { "name": { "family": "Bartolo", "given": "Max" } }, { "name": { "family": "Wheeler", "given": "Richard" } }, { "name": { "family": "Stehberger", "given": "Martin" } }, { "name": { "family": "Bradshaw", "given": "Peter" } }, { "name": { "family": "Heimonen", "given": "JP" } }, { "name": { "family": "Sridhar", "given": "Kaustubh" } }, { "name": { "family": "Akov", "given": "Ido" } }, { "name": { "family": "Sandlin", "given": "Jennifer" } }, { "name": { "family": "Makarychev", "given": "Yury" } }, { "name": { "family": "Tam", "given": "Joanna" } }, { "name": { "family": "Hoang", "given": "Hieu" } }, { "name": { "family": "Cunningham", "given": "David M." } }, { "name": { "family": "Goryachev", "given": "Vladimir" } }, { "name": { "family": "Patramanis", "given": "Demosthenes" } }, { "name": { "family": "Krause", "given": "Michael" } }, { "name": { "family": "Redenti", "given": "Andrew" } }, { "name": { "family": "Aldous", "given": "David" } }, { "name": { "family": "Lai", "given": "Jesyin" } }, { "name": { "family": "Coleman", "given": "Shannon" } }, { "name": { "family": "Xu", "given": "Jiangnan" } }, { "name": { "family": "Lee", "given": "Sangwon" } }, { "name": { "family": "Magoulas", "given": "Ilias" } }, { "name": { "family": "Zhao", "given": "Sandy" } }, { "name": { "family": "Tang", "given": "Ning" } }, { "name": { "family": "Cohen", "given": "Michael K." } }, { "name": { "family": "Paradise", "given": "Orr" } }, { "name": { "family": "Kirchner", "given": "Jan Hendrik" } }, { "name": { "family": "Ovchynnikov", "given": "Maksym" } }, { "name": { "family": "Matos", "given": "Jason O." } }, { "name": { "family": "Shenoy", "given": "Adithya" } }, { "name": { "family": "Wang", "given": "Michael" } }, { "name": { "family": "Nie", "given": "Yuzhou" } }, { "name": { "family": "Sztyber-Betley", "given": "Anna" } }, { "name": { "family": "Faraboschi", "given": "Paolo" } }, { "name": { "family": "Riblet", "given": "Robin" } }, { "name": { "family": "Crozier", "given": "Jonathan" } }, { "name": { "family": "Halasyamani", "given": "Shiv" } }, { "name": { "family": "Verma", "given": "Shreyas" } }, { "name": { "family": "Joshi", "given": "Prashant" } }, { "name": { "family": "Meril", "given": "Eli" } }, { "name": { "family": "Ma", "given": "Ziqiao" } }, { "name": { "family": "Andr\u00e9oletti", "given": "J\u00e9r\u00e9my" } }, { "name": { "family": "Singhal", "given": "Raghav" } }, { "name": { "family": "Platnick", "given": "Jacob" } }, { "name": { "family": "Nevirkovets", "given": "Volodymyr" } }, { "name": { "family": "Basler", "given": "Luke" } }, { "name": { "family": "Ivanov", "given": "Alexander" } }, { "name": { "family": "Khoury", "given": "Seri" } }, { "name": { "family": "Gustafsson", "given": "Nils" } }, { "name": { "family": "Piccardo", "given": "Marco" } }, { "name": { "family": "Mostaghimi", "given": "Hamid" } }, { "name": { "family": "Chen", "given": "Qijia" } }, { "name": { "family": "Singh", "given": "Virendra" } }, { "name": { "family": "Kh\u00e1nh", "given": "Tran Quoc" } }, { "name": { "family": "Rosu", "given": "Paul" } }, { "name": { "family": "Szlyk", "given": "Hannah" } }, { "name": { "family": "Brown", "given": "Zachary" } }, { "name": { "family": "Narayan", "given": "Himanshu" } }, { "name": { "family": "Menezes", "given": "Aline" } }, { "name": { "family": "Roberts", "given": "Jonathan" } }, { "name": { "family": "Alley", "given": "William" } }, { "name": { "family": "Sun", "given": "Kunyang" } }, { "name": { "family": "Patel", "given": "Arkil" } }, { "name": { "family": "Lamparth", "given": "Max" } }, { "name": { "family": "Reuel", "given": "Anka" } }, { "name": { "family": "Xin", "given": "Linwei" } }, { "name": { "family": "Xu", "given": "Hanmeng" } }, { "name": { "family": "Loader", "given": "Jacob" } }, { "name": { "family": "Martin", "given": "Freddie" } }, { "name": { "family": "Wang", "given": "Zixuan" } }, { "name": { "family": "Achilleos", "given": "Andrea" } }, { "name": { "family": "Preu", "given": "Thomas" } }, { "name": { "family": "Korbak", "given": "Tomek" } }, { "name": { "family": "Bosio", "given": "Ida" } }, { "name": { "family": "Kazemi", "given": "Fereshteh" } }, { "name": { "family": "Chen", "given": "Ziye" } }, { "name": { "family": "B\u00e1lint", "given": "Bir\u00f3" } }, { "name": { "family": "Lo", "given": "Eve J. Y." } }, { "name": { "family": "Wang", "given": "Jiaqi" } }, { "name": { "family": "Nunes", "given": "Maria In\u00eas S." } }, { "name": { "family": "Milbauer", "given": "Jeremiah" } }, { "name": { "family": "Bari", "given": "M. Saiful" } }, { "name": { "family": "Wang", "given": "Zihao" } }, { "name": { "family": "Ansarinejad", "given": "Behzad" } }, { "name": { "family": "Sun", "given": "Yewen" } }, { "name": { "family": "Durand", "given": "Stephane" } }, { "name": { "family": "Elgnainy", "given": "Hossam" } }, { "name": { "family": "Douville", "given": "Guillaume" } }, { "name": { "family": "Tordera", "given": "Daniel" } }, { "name": { "family": "Balabanian", "given": "George" } }, { "name": { "family": "Wolff", "given": "Hew" } }, { "name": { "family": "Kvistad", "given": "Lynna" } }, { "name": { "family": "Milliron", "given": "Hsiaoyun" } }, { "name": { "family": "Sakor", "given": "Ahmad" } }, { "name": { "family": "Eron", "given": "Murat" } }, { "name": { "family": "Andrew Favre", "given": "D. O." } }, { "name": { "family": "Shah", "given": "Shailesh" } }, { "name": { "family": "Zhou", "given": "Xiaoxiang" } }, { "name": { "family": "Kamalov", "given": "Firuz" } }, { "name": { "family": "Abdoli", "given": "Sherwin" } }, { "name": { "family": "Santens", "given": "Tim" } }, { "name": { "family": "Barkan", "given": "Shaul" } }, { "name": { "family": "Tee", "given": "Allison" } }, { "name": { "family": "Zhang", "given": "Robin" } }, { "name": { "family": "Tomasiello", "given": "Alessandro" } }, { "name": { "family": "De Luca", "given": "G. 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"name": { "family": "Ciob\u00e2c\u0103", "given": "Stefan" } }, { "name": { "family": "Gross", "given": "Jason" } }, { "name": { "family": "Pandey", "given": "Rohan" } }, { "name": { "family": "Gusev", "given": "Ilya" } }, { "name": { "family": "Jones", "given": "Adam" } }, { "name": { "family": "Agnihotri", "given": "Shashank" } }, { "name": { "family": "Zhelnov", "given": "Pavel" } }, { "name": { "family": "Mofayezi", "given": "Mohammadreza" } }, { "name": { "family": "Piperski", "given": "Alexander" } }, { "name": { "family": "Zhang", "given": "David K." } }, { "name": { "family": "Dobarskyi", "given": "Kostiantyn" } }, { "name": { "family": "Leventov", "given": "Roman" } }, { "name": { "family": "Soroko", "given": "Ignat" } }, { "name": { "family": "Duersch", "given": "Joshua" } }, { "name": { "family": "Taamazyan", "given": "Vage" } }, { "name": { "family": "Ho", "given": "Andrew" } }, { "name": { "family": "Ma", "given": "Wenjie" } }, { "name": { "family": "Held", "given": "William" } }, { "name": { "family": "Xian", "given": "Ruicheng" } }, { "name": { "family": "Zebaze", "given": "Armel Randy" } }, { "name": { "family": "Mohamed", "given": "Mohanad" } }, { "name": { "family": "Leser", "given": "Julian Noah" } }, { "name": { "family": "Yuan", "given": "Michelle X." } }, { "name": { "family": "Yacar", "given": "Laila" } }, { "name": { "family": "Lengler", "given": "Johannes" } }, { "name": { "family": "Olszewska", "given": "Katarzyna" } }, { "name": { "family": "Di Fratta", "given": "Claudio" } }, { "name": { "family": "Oliveira", "given": "Edson" } }, { "name": { "family": "Jackson", "given": "Joseph W." } }, { "name": { "family": "Zou", "given": "Andy" } }, { "name": { "family": "Chidambaram", "given": "Muthu" } }, { "name": { "family": "Manik", "given": "Timothy" } }, { "name": { "family": "Haffenden", "given": "Hector" } }, { "name": { "family": "Stander", "given": "Dashiell" } }, { "name": { "family": "Dasouqi", "given": "Ali" } }, { "name": { "family": "Shen", "given": "Alexander" } }, { "name": { "family": "Golshani", "given": "Bita" } }, { "name": { "family": "Stap", "given": "David" } }, { "name": { "family": "Kretov", "given": "Egor" } }, { "name": { "family": "Uzhou", "given": "Mikalai" } }, { "name": { "family": "Zhidkovskaya", "given": "Alina Borisovna" } }, { "name": { "family": "Winter", "given": "Nick" } }, { "name": { "family": "Rodriguez", "given": "Miguel Orbegozo" } }, { "name": { "family": "Lauff", "given": "Robert" } }, { "name": { "family": "Wehr", "given": "Dustin" } }, { "name": { "family": "Tang", "given": "Colin" } }, { "name": { "family": "Hossain", "given": "Zaki" } }, { "name": { "family": "Phillips", "given": "Shaun" } }, { "name": { "family": "Samuele", "given": "Fortuna" } }, { "name": { "family": "Ekstr\u00f6m", "given": "Fredrik" } }, { "name": { "family": "Hammon", "given": "Angela" } }, { "name": { "family": "Patel", "given": "Oam" } }, { "name": { "family": "Farhidi", "given": "Faraz" } }, { "name": { "family": "Medley", "given": "George" } }, { "name": { "family": "Mohammadzadeh", "given": "Forough" } }, { "name": { "family": "Pe\u00f1aflor", "given": "Madellene" } }, { "name": { "family": "Kassahun", "given": "Haile" } }, { "name": { "family": "Friedrich", "given": "Alena" } }, { "name": { "family": "Perez", "given": "Rayner Hernandez" } }, { "name": { "family": "Pyda", "given": "Daniel" } }, { "name": { "family": "Sakal", "given": "Taom" } }, { "name": { "family": "Dhamane", "given": "Omkar" } }, { "name": { "family": "Mirabadi", "given": "Ali Khajegili" } }, { "name": { "family": "Hallman", "given": "Eric" } }, { "name": { "family": "Okutsu", "given": "Kenchi" } }, { "name": { "family": "Battaglia", "given": "Mike" } }, { "name": { "family": "Maghsoudimehrabani", "given": "Mohammad" } }, { "name": { "family": "Amit", "given": "Alon" } }, { "name": { "family": "Hulbert", "given": "Dave" } }, { "name": { "family": "Pereira", "given": "Roberto" } }, { "name": { "family": "Weber", "given": "Simon" } }, { "name": { "family": "Handoko" } }, { "name": { "family": "Peristyy", "given": "Anton" } }, { "name": { "family": "Malina", "given": "Stephen" } }, { "name": { "family": "Mehkary", "given": "Mustafa" } }, { "name": { "family": "Aly", "given": "Rami" } }, { "name": { "family": "Reidegeld", "given": "Frank" } }, { "name": { "family": "Dick", "given": "Anna-Katharina" } }, { "name": { "family": "Friday", "given": "Cary" } }, { "name": { "family": "Singh", "given": "Mukhwinder" } }, { "name": { "family": "Shapourian", "given": "Hassan" } }, { "name": { "family": "Kim", "given": "Wanyoung" } }, { "name": { "family": "Costa", "given": "Mariana" } }, { "name": { "family": "Gurdogan", "given": "Hubeyb" } }, { "name": { "family": "Kumar", "given": "Harsh" } }, { "name": { "family": "Ceconello", "given": "Chiara" } }, { "name": { "family": "Zhuang", "given": "Chao" } }, { "name": { "family": "Park", "given": "Haon" } }, { "name": { "family": "Carroll", "given": "Micah" } }, { "name": { "family": "Tawfeek", "given": "Andrew R." } }, { "name": { "family": "Steinerberger", "given": "Stefan" } }, { "name": { "family": "Aggarwal", "given": "Daattavya" } }, { "name": { "family": "Kirchhof", "given": "Michael" } }, { "name": { "family": "Dai", "given": "Linjie" } }, { "name": { "family": "Kim", "given": "Evan" } }, { "name": { "family": "Ferret", "given": "Johan" } }, { "name": { "family": "Shah", "given": "Jainam" } }, { "name": { "family": "Wang", "given": "Yuzhou" } }, { "name": { "family": "Yan", "given": "Minghao" } }, { "name": { "family": "Burdzy", "given": "Krzysztof" } }, { "name": { "family": "Zhang", "given": "Lixin" } }, { "name": { "family": "Franca", "given": "Antonio" } }, { "name": { "family": "Pham", "given": "Diana T." } }, { "name": { "family": "Loh", "given": "Kang Yong" } }, { "name": { "family": "Robinson", "given": "Joshua" } }, { "name": { "family": "Jackson", "given": "Abram" } }, { "name": { "family": "Giordano", "given": "Paolo" } }, { "name": { "family": "Petersen", "given": "Philipp" } }, { "name": { "family": "Cosma", "given": "Adrian" } }, { "name": { "family": "Colino", "given": "Jesus" } }, { "name": { "family": "White", "given": "Colin" } }, { "name": { "family": "Votava", "given": "Jacob" } }, { "name": { "family": "Vinnikov", "given": "Vladimir" } }, { "name": { "family": "Delaney", "given": "Ethan" } }, { "name": { "family": "Spelda", "given": "Petr" } }, { "name": { "family": "Stritecky", "given": "Vit" } }, { "name": { "family": "Shahid", "given": "Syed M." } }, { "name": { "family": "Mourrat", "given": "Jean-Christophe" } }, { "name": { "family": "Vetoshkin", "given": "Lavr" } }, { "name": { "family": "Sponselee", "given": "Koen" } }, { "name": { "family": "Bacho", "given": "Renas" } }, { "name": { "family": "Yong", "given": "Zheng-Xin" } }, { "name": { "family": "de la Rosa", "given": "Florencia" } }, { "name": { "family": "Cho", "given": "Nathan" } }, { "name": { "family": "Li", "given": "Xiuyu" } }, { "name": { "family": "Malod", "given": "Guillaume" } }, { "name": { "family": "Weller", "given": "Orion" } }, { "name": { "family": "Albani", "given": "Guglielmo" } }, { "name": { "family": "Lang", "given": "Leon" } }, { "name": { "family": "Laurendeau", "given": "Julien" } }, { "name": { "family": "Kazakov", "given": "Dmitry" } }, { "name": { "family": "Adesanya", "given": "Fatimah" } }, { "name": { "family": "Portier", "given": "Julien" } }, { "name": { "family": "Hollom", "given": "Lawrence" } }, { "name": { "family": "Souza", "given": "Victor" } }, { "name": { "family": "Zhou", "given": "Yuchen Anna" } }, { "name": { "family": "Degorre", "given": "Julien" } }, { "name": { "family": "Yaln", "given": "Yi\u011fit" } }, { "name": { "family": "Obikoya", "given": "Gbenga Daniel" } }, { "name": { "family": "Michael Pokorny", "given": "Rai" } }, { "name": { "family": "Bigi", "given": "Filippo" } }, { "name": { "family": "Bosc\u00e1", "given": "M. C." } }, { "name": { "family": "Shumar", "given": "Oleg" } }, { "name": { "family": "Bacho", "given": "Kaniuar" } }, { "name": { "family": "Recchia", "given": "Gabriel" } }, { "name": { "family": "Popescu", "given": "Mara" } }, { "name": { "family": "Shulga", "given": "Nikita" } }, { "name": { "family": "Tanwie", "given": "Ngefor Mildred" } }, { "name": { "family": "Lux", "given": "Thomas C. H." } }, { "name": { "family": "Rank", "given": "Ben" } }, { "name": { "family": "Ni", "given": "Colin" } }, { "name": { "family": "Brooks", "given": "Matthew" } }, { "name": { "family": "Yakimchyk", "given": "Alesia" } }, { "name": { "family": "Quinn Liu", "given": "Huanxu" } }, { "name": { "family": "Cavalleri", "given": "Stefano" } }, { "name": { "family": "H\u00e4ggstr\u00f6m", "given": "Olle" } }, { "name": { "family": "Verkama", "given": "Emil" } }, { "name": { "family": "Newbould", "given": "Joshua" } }, { "name": { "family": "Gundlach", "given": "Hans" } }, { "name": { "family": "Brito-Santana", "given": "Leonor" } }, { "name": { "family": "Amaro", "given": "Brian" } }, { "name": { "family": "Vajipey", "given": "Vivek" } }, { "name": { "family": "Grover", "given": "Rynaa" } }, { "name": { "family": "Wang", "given": "Ting" } }, { "name": { "family": "Kratish", "given": "Yosi" } }, { "name": { "family": "Li", "given": "Wen-Ding" } }, { "name": { "family": "Gopi", "given": "Sivakanth" } }, { "name": { "family": "Caciolai", "given": "Andrea" } }, { "name": { "family": "de Witt", "given": "Christian Schroeder" } }, { "name": { "family": "Hern\u00e1ndez-C\u00e1mara", "given": "Pablo" } }, { "name": { "family": "Rodol\u00e0", "given": "Emanuele" } }, { "name": { "family": "Robins", "given": "Jules" } }, { "name": { "family": "Williamson", "given": "Dominic" } }, { "name": { "family": "Raynor", "given": "Brad" } }, { "name": { "family": "Qi", "given": "Hao" } }, { "name": { "family": "Segev", "given": "Ben" } }, { "name": { "family": "Fan", "given": "Jingxuan" } }, { "name": { "family": "Martinson", "given": "Sarah" } }, { "name": { "family": "Wang", "given": "Erik Y." } }, { "name": { "family": "Hausknecht", "given": "Kaylie" } }, { "name": { "family": "Brenner", "given": "Michael P." } }, { "name": { "family": "Mao", "given": "Mao" } }, { "name": { "family": "Demian", "given": "Christoph" } }, { "name": { "family": "Kassani", "given": "Peyman" } }, { "name": { "family": "Zhang", "given": "Xinyu" } }, { "name": { "family": "Avagian", "given": "David" } }, { "name": { "family": "Scipio", "given": "Eshawn Jessica" } }, { "name": { "family": "Ragoler", "given": "Alon" } }, { "name": { "family": "Tan", "given": "Justin" } }, { "name": { "family": "Sims", "given": "Blake" } }, { "name": { "family": "Plecnik", "given": "Rebeka" } }, { "name": { "family": "Kirtland", "given": "Aaron" } }, { "name": { "family": "Bodur", "given": "Omer Faruk" } }, { "name": { "family": "Shinde", "given": "D. P." } }, { "name": { "family": "Labrador", "given": "Yan Carlos Leyva" } }, { "name": { "family": "Adoul", "given": "Zahra" } }, { "name": { "family": "Zekry", "given": "Mohamed" } }, { "name": { "family": "Karakoc", "given": "Ali" } }, { "name": { "family": "Santos", "given": "Tania C. B." } }, { "name": { "family": "Shamseldeen", "given": "Samir" } }, { "name": { "family": "Karim", "given": "Loukmane" } }, { "name": { "family": "Liakhovitskaia", "given": "Anna" } }, { "name": { "family": "Resman", "given": "Nate" } }, { "name": { "family": "Farina", "given": "Nicholas" } }, { "name": { "family": "Gonzalez", "given": "Juan Carlos" } }, { "name": { "family": "Maayan", "given": "Gabe" } }, { "name": { "family": "Anderson", "given": "Earth" } }, { "name": { "family": "De Oliveira Pena", "given": "Rodrigo" } }, { "name": { "family": "Kelley", "given": "Elizabeth" } }, { "name": { "family": "Mariji", "given": "Hodjat" } }, { "name": { "family": "Pouriamanesh", "given": "Rasoul" } }, { "name": { "family": "Wu", "given": "Wentao" } }, { "name": { "family": "Finocchio", "given": "Ross" } }, { "name": { "family": "Alarab", "given": "Ismail" } }, { "name": { "family": "Cole", "given": "Joshua" } }, { "name": { "family": "Ferreira", "given": "Danyelle" } }, { "name": { "family": "Johnson", "given": "Bryan" } }, { "name": { "family": "Safdari", "given": "Mohammad" } }, { "name": { "family": "Dai", "given": "Liangti" } }, { "name": { "family": "Arthornthurasuk", "given": "Siriphan" } }, { "name": { "family": "McAlister", "given": "Isaac C." } }, { "name": { "family": "Moyano", "given": "Alejandro Jos\u00e9" } }, { "name": { "family": "Pronin", "given": "Alexey" } }, { "name": { "family": "Fan", "given": "Jing" } }, { "name": { "family": "Ramirez-Trinidad", "given": "Angel" } }, { "name": { "family": "Malysheva", "given": "Yana" } }, { "name": { "family": "Pottmaier", "given": "Daphiny" } }, { "name": { "family": "Taheri", "given": "Omid" } }, { "name": { "family": "Stepanic", "given": "Stanley" } }, { "name": { "family": "Perry", "given": "Samuel" } }, { "name": { "family": "Askew", "given": "Luke" } }, { "name": { "family": "Rodrguez", "given": "Ra\u00fal Adri\u00e1n Huerta" } }, { "name": { "family": "Minissi", "given": "Ali M. R." } }, { "name": { "family": "Lorena", "given": "Ricardo" } }, { "name": { "family": "Iyer", "given": "Krishnamurthy" } }, { "name": { "family": "Fasiludeen", "given": "Arshad Anil" } }, { "name": { "family": "Clark", "given": "Ronald" } }, { "name": { "family": "Ducey", "given": "Josh" } }, { "name": { "family": "Piza", "given": "Matheus" } }, { "name": { "family": "Somrak", "given": "Maja" } }, { "name": { "family": "Vergo", "given": "Eric" } }, { "name": { "family": "Qin", "given": "Juehang" } }, { "name": { "family": "Borb\u00e1s", "given": "Benj\u00e1min" } }, { "name": { "family": "Chu", "given": "Eric" } }, { "name": { "family": "Lindsey", "given": "Jack" } }, { "name": { "family": "Jallon", "given": "Antoine" } }, { "name": { "family": "McInnis", "given": "I. M. J." } }, { "name": { "family": "Chen", "given": "Evan" } }, { "name": { "family": "Semler", "given": "Avi" } }, { "name": { "family": "Gloor", "given": "Luk" } }, { "name": { "family": "Shah", "given": "Tej" } }, { "name": { "family": "Carauleanu", "given": "Marc" } }, { "name": { "family": "Lauer", "given": "Pascal" } }, { "name": { "family": "Huy", "given": "Tran Duc" } }, { "name": { "family": "Shahrtash", "given": "Hossein" } }, { "name": { "family": "Duc", "given": "Emilien" } }, { "name": { "family": "Lewark", "given": "Lukas" } }, { "name": { "family": "Brown", "given": "Assaf" } }, { "name": { "family": "Albanie", "given": "Samuel" } }, { "name": { "family": "Weber", "given": "Brian" } }, { "name": { "family": "Vaz", "given": "Warren S." } }, { "name": { "family": "Clavier", "given": "Pierre" } }, { "name": { "family": "Fan", "given": "Yiyang" } }, { "name": { "family": "Poesia Reis e Silva", "given": "Gabriel" } }, { "name": { "family": "Tony Lian", "given": "Long" } }, { "name": { "family": "Abramovitch", "given": "Marcus" } }, { "name": { "family": "Jiang", "given": "Xi" } }, { "name": { "family": "Mendoza", "given": "Sandra" } }, { "name": { "family": "Islam", "given": "Murat" } }, { "name": { "family": "Gonzalez", "given": "Juan" } }, { "name": { "family": "Mavroudis", "given": "Vasilios" } }, { "name": { "family": "Xu", "given": "Justin" } }, { "name": { "family": "Kumar", "given": "Pawan" } }, { "name": { "family": "Goswami", "given": "Laxman Prasad" } }, { "name": { "family": "Bugas", "given": "Daniel" } }, { "name": { "family": "Heydari", "given": "Nasser" } }, { "name": { "family": "Jeanplong", "given": "Ferenc" } }, { "name": { "family": "Jansen", "given": "Thorben" } }, { "name": { "family": "Pinto", "given": "Antonella" } }, { "name": { "family": "Apronti", "given": "Archimedes" } }, { "name": { "family": "Galal", "given": "Abdallah" } }, { "name": { "family": "Ze-An", "given": "Ng" } }, { "name": { "family": "Singh", "given": "Ankit" } }, { "name": { "family": "Jiang", "given": "Tong" } }, { "name": { "family": "of Arc Xavier", "given": "Joan" } }, { "name": { "family": "Agarwal", "given": "Kanu Priya" } }, { "name": { "family": "Berkani", "given": "Mohammed" } }, { "name": { "family": "Zhang", "given": "Gang" } }, { "name": { "family": "Du", "given": "Zhehang" } }, { "name": { "family": "de Oliveira Junior", "given": "Benedito Alves" } }, { "name": { "family": "Malishev", "given": "Dmitry" } }, { "name": { "family": "Remy", "given": "Nicolas" } }, { "name": { "family": "Hartman", "given": "Taylor D." } }, { "name": { "family": "Tarver", "given": "Tim" } }, { "name": { "family": "Mensah", "given": "Stephen" } }, { "name": { "family": "Loume", "given": "Gautier Abou" } }, { "name": { "family": "Morak", "given": "Wiktor" } }, { "name": { "family": "Habibi", "given": "Farzad" } }, { "name": { "family": "Hoback", "given": "Sarah" } }, { "name": { "family": "Cai", "given": "Will" } }, { "name": { "family": "Gimenez", "given": "Javier" } }, { "name": { "family": "Montecillo", "given": "Roselynn Grace" } }, { "name": { "family": "\u0141ucki", "given": "Jakub" } }, { "name": { "family": "Campbell", "given": "Russell" } }, { "name": { "family": "Sharma", "given": "Asankhaya" } }, { "name": { "family": "Meer", "given": "Khalida" } }, { "name": { "family": "Gul", "given": "Shreen" } }, { "name": { "family": "Gonzalez", "given": "Daniel Espinosa" } }, { "name": { "family": "Alapont", "given": "Xavier" } }, { "name": { "family": "Hoover", "given": "Alex" } }, { "name": { "family": "Chhablani", "given": "Gunjan" } }, { "name": { "family": "Vargus", "given": "Freddie" } }, { "name": { "family": "Agarwal", "given": "Arunim" } }, { "name": { "family": "Jiang", "given": "Yibo" } }, { "name": { "family": "Patil", "given": "Deepakkumar" } }, { "name": { "family": "Outevsky", "given": "David" } }, { "name": { "family": "Scaria", "given": "Kevin Joseph" } }, { "name": { "family": "Maheshwari", "given": "Rajat" } }, { "name": { "family": "Dendane", "given": "Abdelkader" } }, { "name": { "family": "Shukla", "given": "Priti" } }, { "name": { "family": "Cartwright", "given": "Ashley" } }, { "name": { "family": "Bogdanov", "given": "Sergei" } }, { "name": { "family": "M\u00fcndler", "given": "Niels" } }, { "name": { "family": "M\u00f6ller", "given": "S\u00f6ren" } }, { "name": { "family": "Arnaboldi", "given": "Luca" } }, { "name": { "family": "Thaman", "given": "Kunvar" } }, { "name": { "family": "Siddiqi", "given": "Muhammad Rehan" } }, { "name": { "family": "Saxena", "given": "Prajvi" } }, { "name": { "family": "Gupta", "given": "Himanshu" } }, { "name": { "family": "Fruhauff", "given": "Tony" } }, { "name": { "family": "Sherman", "given": "Glen" } }, { "name": { "family": "Vincze", "given": "M\u00e1ty\u00e1s" } }, { "name": { "family": "Usawasutsakorn", "given": "Siranut" } }, { "name": { "family": "Ler", "given": "Dylan" } }, { "name": { "family": "Radhakrishnan", "given": "Anil" } }, { "name": { "family": "Enyekwe", "given": "Innocent" } }, { "name": { "family": "Salauddin", "given": "Sk Md" } }, { "name": { "family": "Muzhen", "given": "Jiang" } }, { "name": { "family": "Maksapetyan", "given": "Aleksandr" } }, { "name": { "family": "Rossbach", "given": "Vivien" } }, { "name": { "family": "Harjadi", "given": "Chris" } }, { "name": { "family": "Bahaloohoreh", "given": "Mohsen" } }, { "name": { "family": "Sparrow", "given": "Claire" } }, { "name": { "family": "Sidhu", "given": "Jasdeep" } }, { "name": { "family": "Ali", "given": "Sam" } }, { "name": { "family": "Bian", "given": "Song" } }, { "name": { "family": "Lai", "given": "John" } }, { "name": { "family": "Singer", "given": "Eric" } }, { "name": { "family": "Uro", "given": "Justine Leon" } }, { "name": { "family": "Bateman", "given": "Greg" } }, { "name": { "family": "Sayed", "given": "Mohamed" } }, { "name": { "family": "Menshawy", "given": "Ahmed" } }, { "name": { "family": "Duclosel", "given": "Darling" } }, { "name": { "family": "Bezzi", "given": "Dario" } }, { "name": { "family": "Jain", "given": "Yashaswini" } }, { "name": { "family": "Aaron", "given": "Ashley" } }, { "name": { "family": "Tiryakioglu", "given": "Murat" } }, { "name": { "family": "Siddh", "given": "Sheeshram" } }, { "name": { "family": "Krenek", "given": "Keith" } }, { "name": { "family": "Shah", "given": "Imad Ali" } }, { "name": { "family": "Jin", "given": "Jun" } }, { "name": { "family": "Creighton", "given": "Scott" } }, { "name": { "family": "Peskoff", "given": "Denis" } }, { "name": { "family": "EL-Wasif", "given": "Zienab" } }, { "name": { "family": "P", "given": "Ragavendran" } }, { "name": { "family": "Richmond", "given": "Michael" } }, { "name": { "family": "McGowan", "given": "Joseph" } }, { "name": { "family": "Patwardhan", "given": "Tejal" } }, { "name": { "family": "Sun", "given": "Hao-Yu" } }, { "name": { "family": "Sun", "given": "Ting" } }, { "name": { "family": "Zubi\u0107", "given": "Nikola" } }, { "name": { "family": "Sala", "given": "Samuele" } }, { "name": { "family": "Ebert", "given": "Stephen" } }, { "name": { "family": "Kaddour", "given": "Jean" } }, { "name": { "family": "Schottdorf", "given": "Manuel" } }, { "name": { "family": "Wang", "given": "Dianzhuo" } }, { "name": { "family": "Petruzella", "given": "Gerol" } }, { "name": { "family": "Meiburg", "given": "Alex" } }, { "name": { "family": "Medved", "given": "Tilen" } }, { "name": { "family": "ElSheikh", "given": "Ali" } }, { "name": { "family": "Hebbar", "given": "S. Ashwin" } }, { "name": { "family": "Vaquero", "given": "Lorenzo" } }, { "name": { "family": "Yang", "given": "Xianjun" } }, { "name": { "family": "Poulos", "given": "Jason" } }, { "name": { "family": "Zouhar", "given": "Vil\u00e9m" } }, { "name": { "family": "Bogdanik", "given": "Sergey" } }, { "name": { "family": "Zhang", "given": "Mingfang" } }, { "name": { "family": "Sanz-Ros", "given": "Jorge" } }, { "name": { "family": "Anugraha", "given": "David" } }, { "name": { "family": "Dai", "given": "Yinwei" } }, { "name": { "family": "Nhu", "given": "Anh N." } }, { "name": { "family": "Wang", "given": "Xue" } }, { "name": { "family": "Demircali", "given": "Ali Anil" } }, { "name": { "family": "Jia", "given": "Zhibai" } }, { "name": { "family": "Zhou", "given": "Yuyin" } }, { "name": { "family": "Wu", "given": "Juncheng" } }, { "name": { "family": "He", "given": "Mike" } }, { "name": { "family": "Chandok", "given": "Nitin" } }, { "name": { "family": "Sinha", "given": "Aarush" } }, { "name": { "family": "Luo", "given": "Gaoxiang" } }, { "name": { "family": "Le", "given": "Long" } }, { "name": { "family": "Noy\u00e9", "given": "Micka\u00ebl" } }, { "name": { "family": "Pere\u0142kiewicz", "given": "Micha\u0142" } }, { "name": { "family": "Pantidis", "given": "Ioannis" } }, { "name": { "family": "Qi", "given": "Tianbo" } }, { "name": { "family": "Purohit", "given": "Soham Sachin" } }, { "name": { "family": "Parcalabescu", "given": "Letitia" } }, { "name": { "family": "Nguyen", "given": "Thai-Hoa" } }, { "name": { "family": "Winata", "given": "Genta Indra" } }, { "name": { "family": "Ponti", "given": "Edoardo M." } }, { "name": { "family": "Li", "given": "Hanchen" } }, { "name": { "family": "Dhole", "given": "Kaustubh" } }, { "name": { "family": "Park", "given": "Jongee" } }, { "name": { "family": "Abbondanza", "given": "Dario" } }, { "name": { "family": "Wang", "given": "Yuanli" } }, { "name": { "family": "Nayak", "given": "Anupam" } }, { "name": { "family": "Caetano", "given": "Diogo M." } }, { "name": { "family": "Wong", "given": "Antonio A. W. L." } }, { "name": { "family": "del Rio-Chanona", "given": "Maria" } }, { "name": { "family": "Kondor", "given": "D\u00e1niel" } }, { "name": { "family": "Francois", "given": "Pieter" } }, { "name": { "family": "Chalstrey", "given": "Ed" } }, { "name": { "family": "Zsambok", "given": "Jakob" } }, { "name": { "family": "Hoyer", "given": "Dan" } }, { "name": { "family": "Reddish", "given": "Jenny" } }, { "name": { "family": "Hauser", "given": "Jakob" } }, { "name": { "family": "Rodrigo-Gin\u00e9s", "given": "Francisco-Javier" } }, { "name": { "family": "Datta", "given": "Suchandra" } }, { "name": { "family": "Shepherd", "given": "Maxwell" } }, { "name": { "family": "Kamphuis", "given": "Thom" } }, { "name": { "family": "Zhang", "given": "Qizheng" } }, { "name": { "family": "Kim", "given": "Hyunjun" } }, { "name": { "family": "Sun", "given": "Ruiji" } }, { "name": { "family": "Yao", "given": "Jianzhu" } }, { "name": { "family": "Dernoncourt", "given": "Franck" } }, { "name": { "family": "Krishna", "given": "Satyapriya" } }, { "name": { "family": "Rismanchian", "given": "Sina" } }, { "name": { "family": "Pu", "given": "Bonan" } }, { "name": { "family": "Pinto", "given": "Francesco" } }, { "name": { "family": "Wang", "given": "Yingheng" } }, { "name": { "family": "Shridhar", "given": "Kumar" } }, { "name": { "family": "Overholt", "given": "Kalon J." } }, { "name": { "family": "Briia", "given": "Glib" } }, { "name": { "family": "Nguyen", "given": "Hieu" } }, { "name": { "family": "Quod Soler Bartomeu", "given": "David" } }, { "name": { "family": "Pang", "given": "Tony CY" } }, { "name": { "family": "Wecker", "given": "Adam" } }, { "name": { "family": "Xiong", "given": "Yifan" } }, { "name": { "family": "Li", "given": "Fanfei" } }, { "name": { "family": "Huber", "given": "Lukas S." } }, { "name": { "family": "Jaeger", "given": "Joshua" } }, { "name": { "family": "De Maddalena", "given": "Romano" } }, { "name": { "family": "L\u00f9", "given": "Xing Han" } }, { "name": { "family": "Zhang", "given": "Yuhui" } }, { "name": { "family": "Beger", "given": "Claas" } }, { "name": { "family": "Kon", "given": "Patrick Tser Jern" } }, { "name": { "family": "Li", "given": "Sean" } }, { "name": { "family": "Sanker", "given": "Vivek" } }, { "name": { "family": "Yin", "given": "Ming" } }, { "name": { "family": "Liang", "given": "Yihao" } }, { "name": { "family": "Zhang", "given": "Xinlu" } }, { "name": { "family": "Agrawal", "given": "Ankit" } }, { "name": { "family": "Yifei", "given": "Li S." } }, { "name": { "family": "Zhang", "given": "Zechen" } }, { "name": { "family": "Cai", "given": "Mu" } }, { "name": { "family": "Sonmez", "given": "Yasin" } }, { "name": { "family": "Cozianu", "given": "Costin" } }, { "name": { "family": "Li", "given": "Changhao" } }, { "name": { "family": "Slen", "given": "Alex" } }, { "name": { "family": "Yu", "given": "Shoubin" } }, { "name": { "family": "Park", "given": "Hyun Kyu" } }, { "name": { "family": "Sarti", "given": "Gabriele" } }, { "name": { "family": "Bria\u0144ski", "given": "Marcin" } }, { "name": { "family": "Stolfo", "given": "Alessandro" } }, { "name": { "family": "Nguyen", "given": "Truong An" } }, { "name": { "family": "Zhang", "given": "Mike" } }, { "name": { "family": "Perlitz", "given": "Yotam" } }, { "name": { "family": "Hernandez-Orallo", "given": "Jose" } }, { "name": { "family": "Li", "given": "Runjia" } }, { "name": { "family": "Shabani", "given": "Amin" } }, { "name": { "family": "Juefei-Xu", "given": "Felix" } }, { "name": { "family": "Dhingra", "given": "Shikhar" } }, { "name": { "family": "Zohar", "given": "Orr" } }, { "name": { "family": "Nguyen", "given": "My Chiffon" } }, { "name": { "family": "Pondaven", "given": "Alexander" } }, { "name": { "family": "Yilmaz", "given": "Abdurrahim" } }, { "name": { "family": "Zhao", "given": "Xuandong" } }, { "name": { "family": "Jin", "given": "Chuanyang" } }, { "name": { "family": "Jiang", "given": "Muyan" } }, { "name": { "family": "Todoran", "given": "Stefan" } }, { "name": { "family": "Han", "given": "Xinyao" } }, { "name": { "family": "Kreuer", "given": "Jules" } }, { "name": { "family": "Rabern", "given": "Brian" } }, { "name": { "family": "Plassart", "given": "Anna" } }, { "name": { "family": "Maggetti", "given": "Martino" } }, { "name": { "family": "Yap", "given": "Luther" } }, { "name": { "family": "Geirhos", "given": "Robert" } }, { "name": { "family": "Kean", "given": "Jonathon" } }, { "name": { "family": "Wang", "given": "Dingsu" } }, { "name": { "family": "Mollaei", "given": "Sina" } }, { "name": { "family": "Sun", "given": "Chenkai" } }, { "name": { "family": "Yin", "given": "Yifan" } }, { "name": { "family": "Wang", "given": "Shiqi" } }, { "name": { "family": "Li", "given": "Rui" } }, { "name": { "family": "Chang", "given": "Yaowen" } }, { "name": { "family": "Wei", "given": "Anjiang" } }, { "name": { "family": "Bizeul", "given": "Alice" } }, { "name": { "family": "Wang", "given": "Xiaohan" } }, { "name": { 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{ "name": { "family": "Malusare", "given": "Aditya" } }, { "name": { "family": "Tang", "given": "Maosen" } }, { "name": { "family": "Gupta", "given": "Isha" } }, { "name": { "family": "Fosin", "given": "Ivan" } }, { "name": { "family": "Kang", "given": "Timothy" } }, { "name": { "family": "Dworakowska", "given": "Barbara" } }, { "name": { "family": "Matsumoto", "given": "Kazuki" } }, { "name": { "family": "Zheng", "given": "Guangyao" } }, { "name": { "family": "Sewuster", "given": "Gerben" } }, { "name": { "family": "Villanueva", "given": "Jorge Pretel" } }, { "name": { "family": "Rannev", "given": "Ivan" } }, { "name": { "family": "Chernyavsky", "given": "Igor" } }, { "name": { "family": "Chen", "given": "Jiale" } }, { "name": { "family": "Banik", "given": "Deepayan" } }, { "name": { "family": "Racz", "given": "Ben" } }, { "name": { "family": "Dong", "given": "Wenchao" } }, { "name": { "family": "Wang", "given": "Jianxin" } }, { "name": { "family": "Bashmal", "given": "Laila" } }, { "name": { "family": "Gon\u00e7alves", "given": "Duarte V." } }, { "name": { "family": "Hu", "given": "Wei" } }, { "name": { "family": "Bar", "given": "Kaushik" } }, { "name": { "family": "Bohdal", "given": "Ondrej" } }, { "name": { "family": "Patlan", "given": "Atharv Singh" } }, { "name": { "family": "Dhuliawala", "given": "Shehzaad" } }, { "name": { "family": "Geirhos", "given": "Caroline" } }, { "name": { "family": "Wist", "given": "Julien" } }, { "name": { "family": "Kansal", "given": "Yuval" } }, { "name": { "family": "Chen", "given": "Bingsen" } }, { "name": { "family": "Tire", "given": "Kutay" } }, { "name": { "family": "Y\u00fccel", "given": "Atak Talay" } }, { "name": { "family": "Christof", "given": "Brandon" } }, { "name": { "family": "Singla", "given": "Veerupaksh" } }, { "name": { "family": "Song", "given": "Zijian" } }, { "name": { "family": "Chen", "given": "Sanxing" } }, { "name": { "family": "Ge", "given": "Jiaxin" } }, { "name": { "family": "Ponkshe", "given": "Kaustubh" } }, { "name": { "family": "Park", "given": "Isaac" } }, { "name": { "family": "Shi", "given": "Tianneng" } }, { "name": { "family": "Ma", "given": "Martin Q." } }, { "name": { "family": "Mak", "given": "Joshua" } }, { "name": { "family": "Lai", "given": "Sherwin" } }, { "name": { "family": "Moulin", "given": "Antoine" } }, { "name": { "family": "Cheng", "given": "Zhuo" } }, { "name": { "family": "Zhu", "given": "Zhanda" } }, { "name": { "family": "Zhang", "given": "Ziyi" } }, { "name": { "family": "Patil", "given": "Vaidehi" } }, { "name": { "family": "Jha", "given": "Ketan" } }, { "name": { "family": "Men", "given": "Qiutong" } }, { "name": { "family": "Wu", "given": "Jiaxuan" } }, { "name": { "family": "Zhang", "given": "Tianchi" } }, { "name": { "family": "Vieira", "given": "Bruno Hebling" } }, { "name": { "family": "Aji", "given": "Alham Fikri" } }, { "name": { "family": "Chung", "given": "Jae-Won" } }, { "name": { "family": "Mahfoud", "given": "Mohammed" } }, { "name": { "family": "Thi Hoang", "given": "Ha" } }, { "name": { "family": "Sperzel", "given": "Marc" } }, { "name": { "family": "Hao", "given": "Wei" } }, { "name": { "family": "Meding", "given": "Kristof" } }, { "name": { "family": "Xu", "given": "Sihan" } }, { "name": { "family": "Kostakos", "given": "Vassilis" } }, { "name": { "family": "Manini", "given": "Davide" } }, { "name": { "family": "Liu", "given": "Yueying" } }, { "name": { "family": "Toukmaji", "given": "Christopher" } }, { "name": { "family": "Yu", "given": "Eunmi" } }, { "name": { "family": "Demircali", "given": "Arif Engin" } }, { "name": { "family": "Sun", "given": "Zhiyi" } }, { "name": { "family": "Dewerpe", "given": "Ivan" } }, { "name": { "family": "Qin", "given": "Hongsen" } }, { "name": { "family": "Pflugfelder", "given": "Roman" } }, { "name": { "family": "Bailey", "given": "James" } }, { "name": { "family": "Morris", "given": "Johnathan" } }, { "name": { "family": "Heilala", "given": "Ville" } }, { "name": { "family": "Rosset", "given": "Sybille" } }, { "name": { "family": "Yu", "given": "Zishun" } }, { "name": { "family": "Chen", "given": "Peter E." } }, { "name": { "family": "Yeo", "given": "Woongyeong" } }, { "name": { "family": "Jain", "given": "Eeshaan" } }, { "name": { "family": "Chigurupati", "given": "Sreekar" } }, { "name": { "family": "Chernyavsky", "given": "Julia" } }, { "name": { "family": "Reddy", "given": "Sai Prajwal" } }, { "name": { "family": "Venugopalan", "given": "Subhashini" } }, { "name": { "family": "Batra", "given": "Hunar" } }, { "name": { "family": "Park", "given": "Core Francisco" } }, { "name": { "family": "Tran", "given": "Hieu" } }, { "name": { "family": "Maximiano", "given": "Guilherme" } }, { "name": { "family": "Zhang", "given": "Genghan" } }, { "name": { "family": "Liang", "given": "Yizhuo" } }, { "name": { "family": "Shiyu", "given": "Hu" } }, { "name": { "family": "Xu", "given": "Rongwu" } }, { "name": { "family": "Pan", "given": "Rui" } }, { "name": { "family": "Suresh", "given": "Siddharth" } }, { "name": { "family": "Liu", "given": "Ziqi" } }, { "name": { "family": "Gulati", "given": "Samaksh" } }, { "name": { "family": "Zhang", "given": "Songyang" } }, { "name": { "family": "Turchin", "given": "Peter" } }, { "name": { "family": "Bartlett", "given": "Christopher W." } }, { "name": { "family": "Scotese", "given": "Christopher R." } }, { "name": { "family": "Cao", "given": "Phuong M." } }, { "name": { "family": "Wu", "given": "Ben" } }, { "name": { "family": "Karwowski", "given": "Jacek" } }, { "name": { "family": "Scaramuzza", "given": "Davide" } } ] }, "title": "A benchmark of expert-level academic questions to assess AI capabilities", "ispublished": "pub", "full_text_status": "public", "keywords": "Computer science; Scientific data", "note": "

© 2026, The Author(s). Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

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The research is supported by Center for AI Safety and Scale AI.

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The HLE dataset is open-source and available at https://huggingface.co/datasets/cais/hle. Important updates to the project and dataset will be announced at https://lastexam.ai.

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The inference script for benchmarking AI systems on HLE is available at GitHub (https://github.com/centerforaisafety/hle).

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See attached - Supplementary Information containing the contributor guidelines and human review instructions.

", "abstract": "

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve more than 90% accuracy on popular benchmarks such as Measuring Massive Multitask Language Understanding1, limiting informed measurement of state-of-the-art LLM capabilities. Here, in response, we introduce Humanity’s Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be an expert-level closed-ended academic benchmark with broad subject coverage. HLE consists of 2,500 questions across dozens of subjects, including mathematics, humanities and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable but cannot be quickly answered by internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a marked gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai.

", "date": "2026-01-29", "date_type": "published", "publication": "Nature", "volume": "649", "number": "8099", "publisher": "Nature Publishing Group", "pagerange": "1139-1146", "issn": "0028-0836", "official_url": "https://authors.library.caltech.edu/records/qn54q-fdc47", "local_group": { "items": [ { "id": "Division-of-Engineering-and-Applied-Science" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/s41586-025-09962-4", "pmcid": "PMC12851929", "primary_object": { "basename": "s41586-025-09962-4.pdf", "url": "https://authors.library.caltech.edu/records/qn54q-fdc47/files/s41586-025-09962-4.pdf" }, "related_objects": [ { "basename": "41586_2025_9962_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/qn54q-fdc47/files/41586_2025_9962_MOESM1_ESM.pdf" } ], "pub_year": "2026", "author_list": "Phan, Long; Gatti, Alice; et al." }, { "id": "https://authors.library.caltech.edu/records/jrvfp-hg829", "eprint_status": "archive", "datestamp": "2026-01-09 22:05:02", "lastmod": "2026-03-10 03:36:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Looi-Shi-Zhuo", "name": { "family": "Looi", "given": "Shi-Zhuo" } }, { "name": { "family": "Tohaneanu", "given": "Mihai" } } ] }, "title": "Global existence and pointwise decay for nonlinear waves under the null condition", "ispublished": "pub", "full_text_status": "public", "keywords": "Nonlinear wave equations; null condition; global existence; pointwise decay; local energy decay; asymptotically flat spacetimes", "note": "

© 2025 International Press of Boston, Inc.

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Part of this work was conducted while S . Looi was at UC Berkeley and he thanks UC Berkeley for its hospitality.

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", "abstract": "

This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, asymptotically flat, and notably, non-stationary spacetimes. We consider nonlinearities satisfying a generalized null condition which does not necessarily retain its structure when commuted with vector fields. For sufficiently small initial data, and under the assumption that the underlying linear operator satisfies an integrated local energy decay estimate, we prove that solutions exist for all time and we establish sharp pointwise decay estimates for the solution \u03d5 and its vector-fields. The solution itself decays as |\u03d5(t,x) \u227e\u3008t + r\u3009\u207b¹\u3008t - r\u3009\u207b¹. This rate matches that of the nonlinear equation on a flat background. This rate is sharp, as this behavior holds already for certain time-dependent perturbations of the classical null form on Minkowski space, which we specify.

", "date": "2026-01-02", "date_type": "published", "publication": "Dynamics of Partial Differential Equations", "volume": "23", "number": "3", "publisher": "International Press of Boston", "pagerange": "225-268", "issn": "1548-159X", "official_url": "https://authors.library.caltech.edu/records/jrvfp-hg829", "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4310/dpde.260103064042", "pub_year": "2026", "author_list": "Looi, Shi-Zhuo and Tohaneanu, Mihai" }, { "id": "https://authors.library.caltech.edu/records/d1v9a-wh814", "eprint_status": "archive", "datestamp": "2025-12-23 02:05:56", "lastmod": "2026-03-09 02:14:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "R. L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Mateu", "given": "J." } }, { "name": { "family": "Mora", "given": "M. G." }, "orcid": "0000-0002-7456-0065" }, { "name": { "family": "Rondi", "given": "L." } }, { "name": { "family": "Scardia", "given": "L." } }, { "name": { "family": "Verdera", "given": "J." } } ] }, "title": "Explicit minimisers for anisotropic Riesz energies", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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RLF was partially supported through US National Science Foundation grant DMS-1954995, as well as through the German Research Foundation through EXC-2111-390814868 and TRR 352-Project-ID 470903074. JM and JV have been partially supported by 2021SGR-00071 (Catalonia) and PID2024-155320NB-I00 (Mineco, Spain). MGM is a member of GNAMPA–INdAM. MGM acknowledges support from PRIN 2022 (Project no. 2022J4FYNJ), funded by MUR, Italy, and the European Union – Next Generation EU, Mission 4 Component 1 CUP F53D23002760006. LR is supported by the Italian MUR through the PRIN 2022 project n.2022B32J5C, under the National Recovery and Resilience Plan (PNRR), Italy, funded by the European Union - Next Generation EU, Mission 4 Component 1 CUP F53D23002710006, and by GNAMPA-INdAM through 2025 projects. LS acknowledges support by the EPSRC under the grants EP/V00204X/1 and EP/V008897/1. Part of this work was done during a visit of JM, MGM, LR, and JV to Heriot-Watt University, whose kind hospitality is gratefully acknowledged.

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Open access funding provided by Università degli Studi di Pavia within the CRUI-CARE Agreement.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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", "abstract": "

In this paper we characterise the energy minimisers of a class of nonlocal interaction energies where the attraction is quadratic, and the repulsion is Riesz-like and anisotropic. In particular we show that, if the Fourier transform of the repulsive potential is positive, the minimiser is supported on a fully-dimensional ellipsoid, and its density is given by a Barenblatt-type profile. Our technique of proof is based on a Fourier representation of the potential of such measures, that extends a previous formula established by some of the authors in the Coulomb case.

", "date": "2026-01", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "65", "number": "1", "publisher": "Springer Science and Business Media LLC", "pagerange": "34", "issn": "0944-2669", "official_url": "https://authors.library.caltech.edu/records/d1v9a-wh814", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft", "grant_number": "EXC-2111-390814868" }, { "grant_number": "470903074" }, { "agency": "Generalitat de Catalunya", "grant_number": "2021SGR-00071" }, { "grant_number": "PID2024-155320NB-I00" }, { "agency": "Ministero dell'Universit\u00e0 e della Ricerca", "grant_number": "PRIN 2022J4FYNJ" }, { "agency": "Ministero dell'Universit\u00e0 e della Ricerca", "grant_number": "PRIN 2022B32J5C" }, { "agency": "Engineering and Physical Sciences Research Council", "grant_number": "EP/V00204X/1" }, { "agency": "Engineering and Physical Sciences Research Council", "grant_number": "EP/V008897/1" }, { "agency": "Universit\u00e0 degli Studi di Pavia" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-025-03185-1", "primary_object": { "basename": "s00526-025-03185-1.pdf", "url": "https://authors.library.caltech.edu/records/d1v9a-wh814/files/s00526-025-03185-1.pdf" }, "pub_year": "2026", "author_list": "Frank, R. L.; Mateu, J.; et al." }, { "id": "https://authors.library.caltech.edu/records/q9yht-4t331", "eprint_status": "archive", "datestamp": "2026-01-29 16:21:01", "lastmod": "2026-03-09 22:48:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Polishchuk", "given": "Alexander" }, "orcid": "0000-0001-5852-7663" }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Exceptional Pairs On Del Pezzo Surfaces And Spaces Of Compatible Feigin-Odesskii Brackets", "ispublished": "pub", "full_text_status": "public", "keywords": "14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli; 14F05: Sheaves, derived categories of sheaves and related constructions; 53D17: Poisson manifolds; Poisson groupoids and algebroids", "note": "
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© The Author(s), 2025. Published by Cambridge University Press.
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We are grateful to the anonymous referee for many useful comments and especially for suggesting a more conceptual approach to studying exceptional pairs (O,V) on a del Pezzo surface of degree 4 , using the connection with weighted projective lines. This material is based upon work supported by the National Science Foundation under grant No. DMS-1928930 and by the Alfred P. Sloan Foundation under grant G-2021-16778, while both authors were in residence at the Simons Laufer Mathematical Sciences Institute (formerly MSRI) in Berkeley, California, during the Spring 2024 semester. In addition, A.P. is partially supported by the NSF grant DMS-2349388, by the Simons Travel grant MPS-TSM-00002745, and within the framework of the HSE University Basic Research Program. A.P. is also grateful to the IHES, where part of this work was done, for hospitality and excellent working conditions.

", "abstract": "

We prove that for every relatively prime pair of integers (d,r) with r > 0, there exists an exceptional pair (O ,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be included into a 5-dimensional linear space of compatible Poisson brackets. We also construct new examples of linear spaces of compatible Feigin-Odesskii Poisson brackets of dimension >5, coming from del Pezzo surfaces of degree >4.

", "date": "2026-01", "date_type": "published", "publication": "Journal of the Institute of Mathematics of Jussieu", "volume": "25", "number": "1", "publisher": "Cambridge University Press (CUP)", "pagerange": "339-373", "issn": "1474-7480", "official_url": "https://authors.library.caltech.edu/records/q9yht-4t331", "funders": { "items": [ { "grant_number": "DMS-1928930" }, { "grant_number": "G-2021-16778" }, { "grant_number": "DMS-2349388" }, { "grant_number": "MPS-TSM-00002745" }, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s1474748025101333", "pub_year": "2026", "author_list": "Polishchuk, Alexander and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/xvzd6-kyz76", "eprint_status": "archive", "datestamp": "2026-01-13 16:07:23", "lastmod": "2026-03-08 17:37:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "Fox", "given": "Jacob" }, "orcid": "0000-0002-0664-497X" }, { "name": { "family": "He", "given": "Xiaoyu" }, "orcid": "0000-0003-2958-6845" }, { "name": { "family": "Mubayi", "given": "Dhruv" }, "orcid": "0000-0002-4709-8768" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Suk", "given": "Andrew" } }, { "name": { "family": "Verstraete", "given": "Jacques" } } ] }, "title": "A question of Erd\u0151s and Graham on Egyptian fractions", "ispublished": "pub", "full_text_status": "public", "keywords": "Egyptian fractions; entropy methods; subset sums", "note": "

© 2025 David Conlon, Jacob Fox, Xiaoyu He, Dhruv Mubayi, Huy Tuan Pham, Andrew Suk, and Jacques Verstraete. Licensed under a Creative Commons Attribution License (CC-BY)

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We are grateful to the American Institute of Mathematics for hosting the SQuaREs project at which this work was initiated. We are also indebted to Zachary Chase and the user Lucia for bringing the MathOverflow post [11] to our attention.

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Supported by NSF Awards DMS-2054452 and DMS-2348859.
Supported by NSF Awards DMS-2154129 and DMS-2452737.
Supported by NSF Award DMS-2103154.
Supported by NSF Awards DMS-1952767 and DMS-2153576.
Supported by a Clay Research Fellowship and a Stanford Science Fellowship.
Supported by an NSF CAREER Award and NSF Awards DMS-1952786 and DMS-2246847.
Supported by NSF Awards DMS-1800332 and DMS-2347832.

", "abstract": "

Answering a question of Erd\u0151s and Graham, we show that for each fixed positive rational number x the number of ways to write x as a sum of reciprocals of distinct positive integers each at most n is 2(cx + o(1))n for an explicit constant cx increasing with x.

", "date": "2025-12-19", "date_type": "published", "publication": "Discrete Analysis", "volume": "2025", "publisher": "Alliance of Diamond Open Access Journals", "pagerange": "28", "issn": "2397-3129", "official_url": "https://authors.library.caltech.edu/records/xvzd6-kyz76", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, { "grant_number": "DMS-2154129" }, { "grant_number": "DMS-2452737" }, { "grant_number": "DMS-2103154" }, { "grant_number": "DMS-1952767" }, { "grant_number": "DMS-2153576" }, {}, {}, { "grant_number": "DMS-1952786" }, { "grant_number": "DMS-2246847" }, { "grant_number": "DMS-1800332" }, { "grant_number": "DMS-2347832" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.19086/da.154329", "primary_object": { "basename": "2404.16016v2.pdf", "url": "https://authors.library.caltech.edu/records/xvzd6-kyz76/files/2404.16016v2.pdf" }, "pub_year": "2025", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/9j8v9-dvk17", "eprint_status": "archive", "datestamp": "2026-01-13 14:52:52", "lastmod": "2026-03-09 22:10:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Balogh", "given": "J\u00f3zsef" } }, { "name": { "family": "Bernshteyn", "given": "Anton" }, "orcid": "0000-0001-9573-5357" }, { "name": { "family": "Delcourt", "given": "Michelle" } }, { "name": { "family": "Ferber", "given": "Asaf" }, "orcid": "0000-0002-0568-4523" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "Sunflowers in Set Systems with Small VC-Dimension", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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The first four authors sincerely thank the American Institute of Mathematics for hosting the SQuaREs program “Containers from Different Angles,” where most of their work on this project was done. They also thank Caroline Terry and Anush Tserunyan for useful discussions on the project. The first author is grateful to Robert Krueger for fruitful discussions on the Kahn–Kalai conjecture/Park–Pham theorem. The third author would like to thank Luke Postle and Tom Kelly for a number of enlightening conversations on related topics. The fourth author is grateful to Marcelo Sales for fruitful discussions. Finally, we are thankful to the anonymous referees for carefully reading the manuscript and providing helpful comments.

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J. Balogh: Research supported in part by NSF grants DMS-1764123 and RTG DMS-1937241, FRG DMS-2152488, the Arnold O. Beckman Research Award (UIUC Campus Research Board RB 24012), and the Simons Fellowship. 

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A. Bernshteyn: Research supported in part by NSF CAREER grant DMS-2239187 and the Sloan Research Fellowship (2025).

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M. Delcourt: Research supported by NSERC under Discovery Grant No. 2019-042 and the Sloan Research Fellowship (2025).

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A. Ferber: Research is supported in part by NSF grant DMS-1953799, NSF CAREER grant DMS-2146406, the Sloan Research Fellowship (2022), and Air Force grant FA9550-23-1-0298.

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H. T. Pham: Research supported by a Two Sigma Fellowship, a Clay Research Fellowship, and a Stanford Science Fellowship.

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", "abstract": "

A family of r distinct sets {A\u2081,...,Ar} is an r-sunflower if for all 1 \u2a7d i < j \u2a7d r and 1 \u2a7d i' < j' \u2a7d r, we have Ai ∩ Aj = Ai' ∩ Aj'. Erd\u0151s and Rado conjectured in 1960 that every family H of \u2113-element sets of size at least K(r)\u2113 contains an r-sunflower, where K(r) is some function that depends only on r. We prove that if H is a family of \u2113-element sets of VC-dimension at most d and |H| > (Cr(log d + log*\u2113))\u2113 for some absolute constant C > 0, then H contains an r-sunflower. This improves a recent result of Fox, Pach, and Suk. When d = 1, we obtain a sharp bound, namely that |H| > (r -1)\u2113 is sufficient. Along the way, we establish a strengthening of the Kahn–Kalai conjecture for set families of bounded VC-dimension, which is of independent interest.

", "date": "2025-12", "date_type": "published", "publication": "Combinatorica", "volume": "45", "number": "6", "publisher": "Springer Science and Business Media LLC", "pagerange": "58", "issn": "0209-9683", "official_url": "https://authors.library.caltech.edu/records/9j8v9-dvk17", "funders": { "items": [ { "grant_number": "DMS-1764123" }, { "grant_number": "RTG DMS-1937241" }, { "grant_number": "FRG DMS-2152488" }, { "grant_number": "RB 24012" }, {}, { "grant_number": "DMS-2239187" }, {}, { "grant_number": "2019-042" }, { "grant_number": "DMS-1953799" }, { "grant_number": "DMS-2146406" }, { "grant_number": "FA9550-23-1-0298" }, {}, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-025-00186-8", "primary_object": { "basename": "s00493-025-00186-8.pdf", "url": "https://authors.library.caltech.edu/records/9j8v9-dvk17/files/s00493-025-00186-8.pdf" }, "pub_year": "2025", "author_list": "Balogh, J\u00f3zsef; Bernshteyn, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/xtea2-gmn29", "eprint_status": "archive", "datestamp": "2025-12-11 19:17:19", "lastmod": "2026-03-09 22:10:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Zakharov", "given": "Dmitrii" } } ] }, "title": "Sharp Bound for the Erd\u0151s\u2013Straus Non-averaging Set Problem", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

\n\n

Pham’s research is supported by a Clay Research Fellowship. Zakharov’s research was supported by the Jane Street Graduate Fellowship. 

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Open Access funding provided by the MIT Libraries.

", "abstract": "

A set of integers A is non-averaging if there is no element a in A which can be written as an average of a subset of A not containing a. We show that the largest non-averaging subset of {1,…,n} has size n^(1/4+o(1)), thus solving the Erd\u0151s–Straus problem. We also determine the largest size of a non-averaging set in a d-dimensional box for any fixed d. Our main tool includes the structure theorem for the set of subset sums due to Conlon, Fox and the first author, together with a result about the structure of a point set in nearly convex position.

", "date": "2025-12", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "35", "number": "6", "publisher": "Springer Science and Business Media LLC", "pagerange": "1712-1738", "issn": "1016-443X", "official_url": "https://authors.library.caltech.edu/records/xtea2-gmn29", "funders": { "items": [ {}, { "agency": "Massachusetts Institute of Technology" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-025-00728-8", "primary_object": { "basename": "s00039-025-00728-8.pdf", "url": "https://authors.library.caltech.edu/records/xtea2-gmn29/files/s00039-025-00728-8.pdf" }, "pub_year": "2025", "author_list": "Pham, Huy Tuan and Zakharov, Dmitrii" }, { "id": "https://authors.library.caltech.edu/records/q6ry1-7x950", "eprint_status": "archive", "datestamp": "2026-01-13 15:07:31", "lastmod": "2026-03-09 22:10:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "Nenadov", "given": "Rajko" }, "orcid": "0009-0003-3777-021X" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "The Largest Subgraph Without A Forbidden Induced Subgraph", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s), under exclusive licence to János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2025.

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Part of this work was completed while the second author was visiting Stanford University. We would also like to thank Matija Buci\u0107 for helpful discussions on connections to the recent works on induced Turán numbers. We thank Jakob Zimmermann for carefully reading the paper and suggesting improvements. We also thank Maria Axenovich for helpful comments.

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Research supported by NSF Awards DMS-2154129 and DMS-2452737.

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Research supported by the New Zealand Marsden Fund.

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Research supported by a Clay Research Fellowship and a Stanford Science Fellowship.

", "abstract": "

We initiate the systematic study of the following Turán-type question. Suppose Γ is a graph with n vertices such that the edge density between any pair of subsets of vertices of size at least t is at most 1 - c, for some t and c > 0. What is the largest number of edges in a subgraph G ⊆ Γ which does not contain a fixed graph H as an induced subgraph or, more generally, which belongs to a hereditary property P? This provides a common generalization of two recently studied cases, namely Γ being a (pseudo-)random graph and a graph without a large complete bipartite subgraph. We focus on the interesting case where H is a bipartite graph. We determine the answer up to a constant factor with respect to n and t, for certain bipartite H and for Γ either a dense random graph or a Paley graph with a square number of vertices. In particular, our bounds match if H is a tree, or if one part of H has d vertices complete to the other part, all other vertices in that part have degree at most d, and the other part has sufficiently many vertices. As applications of the latter result, we answer a question of Alon, Krivelevich, and Samotij on the largest subgraph with a hereditary property which misses a bipartite graph, and determine up to a constant factor the largest number of edges in a string subgraph of Γ. The proofs are based on a variant of the dependent random choice and a novel approach for finding induced copies by inductively defining probability distributions supported on induced copies of smaller subgraphs.

", "date": "2025-12", "date_type": "published", "publication": "Combinatorica", "volume": "45", "number": "6", "publisher": "Springer Science and Business Media LLC", "pagerange": "60", "issn": "0209-9683", "official_url": "https://authors.library.caltech.edu/records/q6ry1-7x950", "funders": { "items": [ { "grant_number": "DMS-2154129" }, { "grant_number": "DMS-2452737" }, { "grant_number": "-" }, {}, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-025-00190-y", "pub_year": "2025", "author_list": "Fox, Jacob; Nenadov, Rajko; et al." }, { "id": "https://authors.library.caltech.edu/records/f10dk-0hb09", "eprint_status": "archive", "datestamp": "2025-08-14 03:38:58", "lastmod": "2026-03-08 18:13:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Lim-Jeck", "name": { "family": "Lim", "given": "Jeck" } } ] }, "title": "Everywhere unbalanced configurations", "ispublished": "pub", "full_text_status": "public", "keywords": "Pseudolines; Allowable sequences", "note": "
© 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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Research supported by NSF Awards DMS-2054452 and DMS-2348859. Research partially supported by an NUS Overseas Graduate Scholarship.

", "abstract": "

An old problem in discrete geometry, originating with Kupitz, asks whether there is a fixed natural number k such that every finite set of points in the plane has a line through at least two of its points where the number of points on either side of this line differ by at most k. We give a negative answer to a natural variant of this problem, showing that for every natural number k there exists a finite set of points in the plane together with a pseudoline arrangement such that each pseudoline contains at least two points and there is a pseudoline through any pair of points where the number of points on either side of each pseudoline differ by at least k. Moreover, we may find such a configuration with at most 2²ck points, which, by a result of Pinchasi, is best possible up to the value of the constant c.

", "date": "2025-11", "date_type": "published", "publication": "Advances in Mathematics", "volume": "480", "publisher": "Elsevier", "pagerange": "110445", "issn": "0001-8708", "official_url": "https://authors.library.caltech.edu/records/f10dk-0hb09", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2025.110445", "pub_year": "2025", "author_list": "Conlon, David and Lim, Jeck" }, { "id": "https://authors.library.caltech.edu/records/tqsge-ky711", "eprint_status": "archive", "datestamp": "2026-01-13 21:20:41", "lastmod": "2026-03-08 17:37:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "Gunby", "given": "Benjamin" } }, { "name": { "family": "He", "given": "Xiaoyu" }, "orcid": "0000-0003-2958-6845" }, { "name": { "family": "Mubayi", "given": "Dhruv" }, "orcid": "0000-0002-4709-8768" }, { "name": { "family": "Suk", "given": "Andrew" } }, { "name": { "family": "Verstra\u00ebte", "given": "Jacques" } }, { "name": { "family": "Yu", "given": "Hung-Hsun" }, "orcid": "0009-0000-8173-6148" } ] }, "title": "When are off-diagonal hypergraph Ramsey numbers polynomial?", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025 American Mathematical Society.

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We are grateful to Jiaxi Nie, Maya Sankar and Yuval Wigderson for stimulating conversations. We are also grateful to the anonymous reviewers for several helpful remarks.

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The first author was supported by NSF Awards DMS-2054452 and DMS-2348859.
The second author was supported by NSF Award DMS-2154129.
The fourth author was supported by NSF Award DMS-2103154.
The fifth author was supported by NSF Awards DMS-1763317, DMS-1952767 and DMS2153576, by a Humboldt Research Award and by a Simons Fellowship.
The sixth author was supported by an NSF CAREER Award and by NSF Awards DMS1952786 and DMS-2246847.
The seventh author was supported by NSF Award DMS-1800332.

", "abstract": "

A natural open problem in Ramsey theory is to determine those 3-graphs H for which the off-diagonal Ramsey number r(H, Kn(3)) grows polynomially with n. We make substantial progress on this question by showing that if H is tightly connected or has at most two tight components, then r(H,Kn(3))  grows polynomially if and only if H is contained in an iterated blowup of an edge.

", "date": "2025-11", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "153", "number": "11", "publisher": "American Mathematical Society (AMS)", "pagerange": "4605-4617", "issn": "1088-6826", "official_url": "https://authors.library.caltech.edu/records/tqsge-ky711", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, { "grant_number": "DMS-2154129" }, { "grant_number": "DMS-2103154" }, { "grant_number": "DMS-1763317" }, { "grant_number": "DMS-1952767" }, { "grant_number": "DMS-2153576" }, {}, {}, { "grant_number": "DMS-1952786" }, { "grant_number": "DMS-2246847" }, { "grant_number": "DMS-1800332" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1090/proc/17321", "pub_year": "2025", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/9mpsw-88x77", "eprint_status": "archive", "datestamp": "2026-01-13 16:48:09", "lastmod": "2026-03-09 22:09:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Jain", "given": "Vishesh" }, "orcid": "0000-0002-7275-3218" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Sawhney", "given": "Mehtaab" } }, { "name": { "family": "Zakharov", "given": "Dmitrii" } } ] }, "title": "An explicit economical additive basis", "ispublished": "pub", "full_text_status": "public", "keywords": "Additive number theory; additive bases", "note": "

© The Author(s), 2025. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.

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We thank Zach Hunter and Sándor Kiss for carefully reading the manuscript and suggesting improvements and references.

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V.J. is supported by NSF CAREER award DMS-2237646. H.P. is supported by a Clay Research Fellowship and a Stanford Science Fellowship. M.S. is supported by NSF Graduate Research Fellowship Programme DGE-2141064. D.Z. is supported by the Jane Street Graduate Fellowship.

", "abstract": "

We present an explicit subset A ⊆ N = {0,1,…} such that A + A = N and for all ε >0,

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lim/N→∞ \u2223\u2223{(n\u2081,n\u2082):n\u2081+n\u2082 = N,(n\u2081,n\u2082) ∈ A²}\u2223\u2223 Nε = 0. This answers a question of Erd\u0151s.
\n
", "date": "2025-11", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "34", "number": "6", "publisher": "Cambridge University Press (CUP)", "pagerange": "815-820", "issn": "0963-5483", "official_url": "https://authors.library.caltech.edu/records/9mpsw-88x77", "funders": { "items": [ { "grant_number": "DMS-2237646" }, {}, {}, { "grant_number": "DGE-2141064" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s096354832510014x", "primary_object": { "basename": "an-explicit-economical-additive-basis.pdf", "url": "https://authors.library.caltech.edu/records/9mpsw-88x77/files/an-explicit-economical-additive-basis.pdf" }, "pub_year": "2025", "author_list": "Jain, Vishesh; Pham, Huy Tuan; et al." }, { "id": "https://authors.library.caltech.edu/records/ha75m-85865", "eprint_status": "archive", "datestamp": "2025-10-20 20:29:32", "lastmod": "2026-03-10 00:02:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Janda", "given": "Felix" } }, { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Gromov\u2013Witten Invariants with Naive Tangency Conditions", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) 2025. Published by Oxford University Press. All rights reserved.

\n\n

We are grateful to M. Kontsevich who initially suggested a possible relationship between naive tangencies and descendent invariants. Discussions with Q. Chen, S. Guo, E. Ionel, D. Maulik, R. Pandharipande, and M. Porta were very helpful. Special thanks to A. Polishchuk and Y. Shen for organizing the workshop “Topics in Enumerative Geometry” at the University of Oregon in May 2022, during which we first exchanged ideas.

\n

Communicated by Prof. Dragos Oprea

\n\n

F.J. was partially supported by NSF grants DMS-2054830 and DMS-2239320. T.Y.Y. was partially supported by NSF grants DMS-2302095 and DMS-2245099.

", "abstract": "

We introduce Gromov–Witten invariants with naive tangency conditions at the marked points of the source curve. We then establish an explicit formula which expresses Gromov–Witten invariants with naive tangency conditions in terms of descendent Gromov–Witten invariants. Several examples of genus zero Gromov–Witten invariants with naive tangencies are computed in the case of curves and surfaces. In particular, the counts of rational curves naively tangent to an anticanonical divisor on a del Pezzo surface are studied, and via mirror symmetry, we obtain a relation to the local Gromov–Witten invariants.

", "date": "2025-10", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2025", "number": "20", "publisher": "Oxford University Press (OUP)", "pagerange": "rnaf310", "issn": "1073-7928", "official_url": "https://authors.library.caltech.edu/records/ha75m-85865", "funders": { "items": [ { "grant_number": "DMS-2054830" }, { "grant_number": "DMS-2239320" }, { "grant_number": "DMS-2302095" }, { "grant_number": "DMS-2245099" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnaf310", "pub_year": "2025", "author_list": "Janda, Felix and Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/90s0t-khx62", "eprint_status": "archive", "datestamp": "2025-12-11 21:17:19", "lastmod": "2026-03-09 21:41:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fernandes-Francesca", "name": { "family": "Fernandes", "given": "Francesca" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Formal languages, spin systems, and quasicrystals", "ispublished": "pub", "full_text_status": "public", "keywords": "Multiple context free grammars; Rational transductions; Spin systems; Zamolodchikov symplex equation; Ammann quasilattice; Icosahedral quasicrystal", "note": "

© 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

\n\n

The first author is supported by the Carl F. Braun Residuary Trust and the Caltech WAVE program for undergraduate research. The second author is supported by NSF grant DMS-2104330.

", "abstract": "We present a categorical formalism for context-free languages with morphisms given by correspondences obtained from rational transductions. We show that D0L-systems are a special case of the correspondences that define morphisms in this category. We construct a functorial mapping to aperiodic spin chains. We then generalize this construction to a class of mildly context sensitive grammars, the multiple-context-free grammars (MCFG), with a similar functorial mapping to spin systems in higher dimensions, with Boltzmann weights describing interacting spins on vertices of hypercubes. We show that a particular motivating example for this general construction is provided by the Korepin completely integrable model on the icosahedral quasicrystal, which we construct as the spin system associated to a multiple-context-free grammar describing the geometry of the Ammann planes quasilattice. We review the main properties of this spin system, including solvability, bulk free energy, and criticality, based on results of Baxter and the known relation to the Zamolodchikov tetrahedron equation, and we show that the latter has a generalization for the Boltzmann weights on hypercubes of the spin systems associated to more general MCFGs in terms of two dual cubulations of the n-simplex. We formulate analogous questions about bulk free energy and criticality for our construction of spin systems.", "date": "2025-10", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "216", "publisher": "Elsevier", "pagerange": "105568", "issn": "0393-0440", "official_url": "https://authors.library.caltech.edu/records/90s0t-khx62", "funders": { "items": [ {}, { "grant_number": "DMS-2104330" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2025.105568", "pub_year": "2025", "author_list": "Fernandes, Francesca and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/3m800-6jm64", "eprint_status": "archive", "datestamp": "2026-01-13 22:17:51", "lastmod": "2026-03-08 17:37:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Lim-Jeck", "name": { "family": "Lim", "given": "Jeck" } } ] }, "title": "Sums of linear transformations", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025 American Mathematical Society.

\n\n

The research of the first author was supported by NSF Awards DMS-2054452 and DMS2348859. The research of the second author was partially supported by an NUS Overseas Graduate Scholarship.

", "abstract": "

We show that if $\\mathcal{L}_1$ and $\\mathcal{L}_2$ are linear transformations from $\\mathbb{Z}^d$ to $\\mathbb{Z}^d$ satisfying certain mild conditions, then, for any finite subset $A$ of $\\mathbb{Z}^d$,

\n

$$\\begin{equation*} |\\mathcal{L}_1 A+\\mathcal{L}_2 A|\\geq \\left( |\\det (\\mathcal{L}_1)|^{1/d}+|\\det (\\mathcal{L}_2)|^{1/d} \\right)^d|A|- o(|A|). \\end{equation*}$$

\n

This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for certain choices of $\\mathcal{L}_1$ and $\\mathcal{L}_2$. As an application, we prove a lower bound for $|A + \\lambda \\cdot A|$ when $A$ is a finite set of real numbers and $\\lambda$ is an algebraic number. In particular, when $\\lambda$ is of the form $(p/q)^{1/d}$ for some $p, q, d \\in \\mathbb{N}$, each taken as small as possible for such a representation, we show that

\n

$$\\begin{equation*} |A + \\lambda \\cdot A| \\geq (p^{1/d} + q^{1/d})^d |A| - o(|A|). \\end{equation*}$$

\n

This is again best possible up to the lower-order term and extends a recent result of Krachun and Petrov which treated the case $\\lambda = \\sqrt {2}$.

", "date": "2025-10", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "378", "number": "10", "publisher": "American Mathematical Society (AMS)", "pagerange": "7009-7032", "issn": "1088-6850", "official_url": "https://authors.library.caltech.edu/records/3m800-6jm64", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/9433", "pub_year": "2025", "author_list": "Conlon, David and Lim, Jeck" }, { "id": "https://authors.library.caltech.edu/records/z0pdg-nhd11", "eprint_status": "archive", "datestamp": "2025-09-20 22:56:21", "lastmod": "2026-03-09 02:35:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Berestycki", "given": "Nathana\u00ebl" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "name": { "family": "Jego", "given": "Antoine" } } ] }, "title": "Thick points of 4D critical branching Brownian motion", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

\n\n

The authors thank Amine Asselah, Diederik van Engelenburg, Robin Khanfir, Bruno Schapira and Yilin Wang for stimulating discussions related to this work. This paper was initiated during a Spring 2022 programme at the Mathematical Sciences Research Institute in Berkeley, California, that was supported by NSF grant DMS-1928930; N.B. and A.J. attended the full programme and began work on the project, while T.H. attended one of the associated workshops. The hospitality and stimulating atmosphere of the institute is gratefully acknowledged. Part of the work also took place during visits by A.J. and N.B. to Caltech and by A.J. to the University of Vienna; we also acknowledge the hospitality of both institutions.

\n\n

N.B. is supported by FWF Grant 10.55776/P33083 on ‘Scaling limits in random conformal geometry’, T.H. is supported by NSF grant DMS-2246494 and A.J. was supported by Eccellenza grant 194648 of the Swiss National Science Foundation and was a member of NCCR SwissMAP.

", "abstract": "

We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension . We determine the exponent governing the probability to hit a small ball with an exceptionally high number of pioneers, showing that this has a second-order transition between an exponential phase and a stretched exponential phase at an explicit value () of the thickness parameter . We apply the outputs of this analysis to prove that the associated set of thick points T(a) has dimension (4 - a)\u208a, so that there is a change in behaviour at a = 4 but not at a = 2 in this case. Along the way, we obtain related results for the non-positive solutions of a boundary value problem associated to the semi-linear partial differential equation (PDE) Δv = v² and develop a strong coupling between tree-indexed random walk and tree-indexed Brownian motion that allows us to deduce analogues of some of our results in the discrete case. We also obtain in each dimension d \u2a7e 1 an infinite-order asymptotic expansion for the probability that critical branching Brownian motion hits a distant unit ball, finding that this expansion is convergent when d ≠ 4 and divergent when d = 4. This reveals a novel, dimension-dependent critical exponent governing the higher order terms of the expansion, which we compute in every dimension.

", "date": "2025-09", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "131", "number": "3", "publisher": "Wiley", "pagerange": "e70086", "issn": "0024-6115", "official_url": "https://authors.library.caltech.edu/records/z0pdg-nhd11", "funders": { "items": [ { "grant_number": "DMS-1928930" }, { "grant_number": "10.55776/P33083" }, { "grant_number": "DMS\u20102246494" }, { "grant_number": "194648" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.70086", "pub_year": "2025", "author_list": "Berestycki, Nathana\u00ebl; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/mbmh8-6jw41", "eprint_status": "archive", "datestamp": "2026-06-03 16:51:00", "lastmod": "2026-06-03 16:51:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Katzarkov", "given": "Ludmil" } }, { "name": { "family": "Svoboda", "given": "Josef" } } ] }, "title": "\u1e90 and Splice Diagrams", "ispublished": "pub", "full_text_status": "public", "keywords": "3-manifold topology; quantum invariant; surface singularity; splice diagram", "note": "

© 2025 SIGMA.

\n\n

We would like to thank Denis Auroux, Martin Cech, Shimal Harichurn, Mrunmay Jagadale, Maxim Kontsevich, Slava Krushkal, Andr´as N´emethi, Sunghyuk Park, Pavel Putrov and Nikolai Saveliev for helpful conversations and Zuzana Urbanov´a for the help with computer experiments. We thank the anonymous referees for valuable suggestions and comments.

\n\n

S. Gukov was partially supported by NSF grant DMS-1664227, DOE grant DE-SC0011632. S. Gukov and J. Svoboda were partially suported by the Simons Grant New structures in low-dimensional topology. L. Katzarkov was supported by NSF Grant theory of Atoms, Simons investigators grant HMF Simons Foundation, grant SFI-MPS-T-Institutes-00007697, and the Ministry of Education and Science of the Republic of Bulgaria, grant DO1-239/10.12.2024.

", "abstract": "

We study quantum $q$-series invariants of 3-manifolds $\\widehat{Z}_\\sigma$ of Gukov-Pei-Putrov-Vafa, using techniques from the theory of normal surface singularities such as splice diagrams. We show that the (suitably normalized) sum of all $\\widehat{Z}_\\sigma$ depends only on the splice diagram, and in particular, it agrees for manifolds with the same universal abelian cover. We use these ideas to find simple formulas for $\\widehat{Z}_\\sigma$ invariants of Seifert manifolds. Applications include a better understanding of the vanishing of the $q$-series $\\widehat{Z}_\\sigma$. Additionally, we study moduli spaces of flat $\\operatorname{SL}_2(\\mathbb{C})$ connections on Seifert manifolds and their relation to spectra of surface singularities, extending a result of Boden and Curtis for Brieskorn spheres to Seifert rational homology spheres with 3 singular fibers and to Seifert homology spheres with any number of fibers.

", "date": "2025-08-26", "date_type": "published", "publication": "Symmetry, Integrability and Geometry: Methods and Applications", "volume": "21", "publisher": "SIGMA (Symmetry, Integrability and Geometry: Methods and Application)", "pagerange": "073", "issn": "1815-0659", "official_url": "https://authors.library.caltech.edu/records/mbmh8-6jw41", "funders": { "items": [ { "grant_number": "DMS-1664227" }, { "grant_number": "DE-SC0011632" }, { "grant_number": "SFI-MPS-T-Institutes-00007697" }, { "grant_number": "DO1-239/10.12.2024" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.3842/sigma.2025.073", "pub_year": "2025", "author_list": "Gukov, Sergei; Katzarkov, Ludmil; et al." }, { "id": "https://authors.library.caltech.edu/records/kkz0e-yzf53", "eprint_status": "archive", "datestamp": "2025-08-05 22:16:01", "lastmod": "2026-03-10 03:55:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Kusuki", "given": "Yuya" }, "orcid": "0000-0002-9784-0975" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Pal-Sridip", "name": { "family": "Pal", "given": "Sridip" }, "orcid": "0000-0002-3813-9513" } ] }, "title": "Universality of R\u00e9nyi Entropy in Conformal Field Theory", "ispublished": "pub", "full_text_status": "public", "note": "

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

\n\n

The authors thank David Simmons-Duffin for helpful discussions and comments on the draft. This research was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics at Caltech. H. O. is also supported in part by the Simons Investigator grant (MP-SIP-00005259) and by JSPS Grants-in-Aid for Scientific Research 23K03379. His work was performed in part at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, which is supported by the World Premier International Research Center Initiative, MEXT, Japan, at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara, which is supported by grant NSF PHY-2309135, and at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611. Y. K. is also supported by the INAMORI Frontier Program at Kyushu University and JSPS KAKENHI Grant No. 23K20046. The authors thank Kyushu University Institute for Advanced Study and RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program. Discussions during the “Kyushu IAS-iTHEMS workshop: Nonperturbative methods in QFT” were useful in completing this work.

", "abstract": "We use the thermal effective theory to prove that, for the vacuum state in any conformal field theory in d dimensions, the nth R\u00e9nyi entropy SA(n) behaves as SA(n)=[f/(2\u03c0n)d\u22121][Area(\u2202A)/(d\u22122)\u03b5d\u22122](1+O(n)) in the n\u21920 limit when the boundary of the entanglement domain A is spherical with the UV cutoff \u03b5. The theory dependence is encapsulated in the cosmological constant f in the thermal effective action. Using this result, we estimate the density of states for large eigenvalues of the modular Hamiltonian for the domain A. In two dimensions, we can use the hot spot idea, which describes the effective action in the high-temperature limit when the temperature is position-dependent, to derive more powerful formulas valid for arbitrary positive n. We discuss the difference between two and higher dimensions and clarify the applicability of the hot spot idea. We also use the thermal effective theory to derive an analog of the Cardy formula for boundary operators in higher dimensions.", "date": "2025-08-08", "date_type": "published", "publication": "Physical Review Letters", "volume": "135", "number": "6", "publisher": "American Physical Society", "pagerange": "061603", "issn": "0031-9007", "official_url": "https://authors.library.caltech.edu/records/kkz0e-yzf53", "funders": { "items": [ {}, {}, { "grant_number": "DE-SC0011632" }, { "grant_number": "-" }, { "grant_number": "MP-SIP-00005259" }, { "grant_number": "23K03379" }, { "grant_number": "23K20046" }, {}, {}, { "grant_number": "PHY-2309135" }, { "grant_number": "PHY-1607611" }, {}, { "agency": "World Premier International Research Center Initiative" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/fsg7-bs7q", "primary_object": { "basename": "fsg7-bs7q.pdf", "url": "https://authors.library.caltech.edu/records/kkz0e-yzf53/files/fsg7-bs7q.pdf" }, "pub_year": "2025", "author_list": "Kusuki, Yuya; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/trdg9-74g06", "eprint_status": "archive", "datestamp": "2025-08-12 23:04:45", "lastmod": "2026-03-09 02:14:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Larson", "given": "Simon" }, "orcid": "0000-0002-0057-8211" } ] }, "title": "Riesz means asymptotics for Dirichlet and Neumann Laplacians on Lipschitz domains", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025, The Author(s). Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

\n\n

The authors are grateful for the anonymous referee’s careful reading and helpful suggestions. We would like to thank Jean Lagacé for stimulating discussions on asymptotics for polygons and Nikolay Filonov for making us aware of a number of inaccuracies in an earlier version of this paper.

\n\n

Open Access funding enabled and organized by Projekt DEAL. Partial support through US National Science Foundation grant DMS-1954995 (R.L.F.), as well as through German Research Foundation grants EXC-2111-390814868 and TRR 352-Project-ID 470903074 (R.L.F.), the Knut and Alice Wallenberg foundation grant KAW 2017.0295 (S.L.), as well as the Swedish Research Council grant no. 2023-03985 (S.L.) is acknowledged.

", "abstract": "

We consider the eigenvalues of the Dirichlet and Neumann Laplacians on a bounded domain with Lipschitz boundary and prove two-term asymptotics for their Riesz means of arbitrary positive order. Moreover, when the underlying domain is convex, we obtain universal, non-asymptotic bounds that correctly reproduce the two leading terms in the asymptotics and depend on the domain only through simple geometric characteristics. Important ingredients in our proof are non-asymptotic versions of various Tauberian theorems.

", "date": "2025-08-07", "date_type": "published", "publication": "Inventiones mathematicae", "publisher": "Springer Science and Business Media LLC", "issn": "0020-9910", "official_url": "https://authors.library.caltech.edu/records/trdg9-74g06", "funders": { "items": [ { "agency": "Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-025-01352-x", "primary_object": { "basename": "s00222-025-01352-x.pdf", "url": "https://authors.library.caltech.edu/records/trdg9-74g06/files/s00222-025-01352-x.pdf" }, "pub_year": "2025", "author_list": "Frank, Rupert L. and Larson, Simon" }, { "id": "https://authors.library.caltech.edu/records/j2c0f-g7e10", "eprint_status": "archive", "datestamp": "2025-08-21 17:20:14", "lastmod": "2026-03-10 03:30:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Adams", "given": "Griffen" }, "orcid": "0009-0009-0535-4469" }, { "name": { "family": "Costin", "given": "Ovidiu" }, "orcid": "0000-0001-7105-7379" }, { "name": { "family": "Dunne", "given": "Gerald V." }, "orcid": "0000-0003-1338-339X" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "\u00d6ner", "given": "O\u011fuz" }, "orcid": "0009-0002-3620-6783" } ] }, "title": "Orientation reversal and the Chern-Simons natural boundary", "ispublished": "pub", "full_text_status": "public", "keywords": "Chern-Simons Theories; Nonperturbative Effects; Topological Field Theories", "note": "

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP³.

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\n
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Thanks to John Chae, Miranda C. N. Cheng, Daniele Dorigoni, Jean Écalle, Angus Gruen, Mrunmay Jagadale, Albrecht Klemm, and Don Zagier for discussions, ideas, help, advice, support and inspiration that have greatly benefited this project. The work of OC is supported in part by the U.S. National Science Foundation, Division of Mathematical Sciences, Award NSF DMS-2206241. The work of GD and GA is supported in part by the U.S. Department of Energy, Office of High Energy Physics, Award DE-SC0010339. The work of SG was supported in part by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology, by the NSF grant DMS-2245099, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The authors OC, GD and SG thank the Galileo Galilei Institute for Theoretical Physics for hospitality, and the INFN for partial support, during the workshop “Resurgence and Modularity in QFT and String Theory”, Spring 2024. GD thanks the Max Planck Institute for Mathematics, Bonn, for support during the program “Combinatorics, Resurgence and Algebraic Geometry in Quantum Field Theory”, August 2024. GA and OÖ thank L’École de Physique des Houches for support during the Les Houches School “Quantum Geometry”, Summer 2024.

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", "abstract": "

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart q~, and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and q~ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

", "date": "2025-08", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2025", "number": "8", "publisher": "Springer Science and Business Media LLC", "pagerange": "154", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/j2c0f-g7e10", "funders": { "items": [ { "grant_number": "DMS-2206241" }, { "grant_number": "DE-SC0010339" }, {}, { "grant_number": "DMS-2245099" }, { "grant_number": "DE-SC0011632" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep08(2025)154", "primary_object": { "basename": "JHEP08(2025)154.pdf", "url": "https://authors.library.caltech.edu/records/j2c0f-g7e10/files/JHEP08(2025)154.pdf" }, "pub_year": "2025", "author_list": "Adams, Griffen; Costin, Ovidiu; et al." }, { "id": "https://authors.library.caltech.edu/records/dea92-cpt57", "eprint_status": "archive", "datestamp": "2025-11-30 01:56:09", "lastmod": "2026-03-09 22:48:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "P. Albion", "given": "Seamus" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "name": { "family": "Warnaar", "given": "S. Ole" } } ] }, "title": "Elliptic A_n Selberg Integrals", "ispublished": "pub", "full_text_status": "public", "keywords": "A_n Selberg integrals; Elliptic interpolation kernel; Elliptic interpolation functions; Elliptic beta integrals", "note": "

© The Author(s) 2025. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Open access funding provided by University of Vienna.

", "abstract": "

We use the elliptic interpolation kernel due to the second author to prove an A_n extension of the elliptic Selberg integral. More generally, we obtain elliptic analogues of the A_n Kadell, Hua–Kadell and Alba–Fateev–Litvinov–Tarnopolsky (or AFLT) integrals.

", "date": "2025-08", "date_type": "published", "publication": "Constructive Approximation", "volume": "62", "number": "1", "publisher": "Springer Science and Business Media LLC", "pagerange": "151-184", "issn": "0176-4276", "official_url": "https://authors.library.caltech.edu/records/dea92-cpt57", "funders": { "items": [ { "agency": "University of Vienna" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00365-025-09705-8", "primary_object": { "basename": "s00365-025-09705-8.pdf", "url": "https://authors.library.caltech.edu/records/dea92-cpt57/files/s00365-025-09705-8.pdf" }, "pub_year": "2025", "author_list": "P. Albion, Seamus; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/1vrqc-68655", "eprint_status": "archive", "datestamp": "2026-01-22 19:42:06", "lastmod": "2026-03-10 00:00:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Sandomirskiy", "given": "Fedor" }, "orcid": "0000-0001-9886-3688" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "On the origin of the Boltzmann distribution", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.

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We thank Tim Austin, Alexander Guterman, Ramon van Handel, Tom Hutchcroft, Daniel Litt, Gil Refael, Barry Simon, and Stanislav Smirnov for illuminating conversations and helpful suggestions.

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Omer Tamuz was supported by a BSF award (#2018397) and a National Science Foundation CAREER award (DMS-1944153).

", "abstract": "

Boltzmann distributions are used in statistical mechanics to describe how the states of a system are distributed at a given temperature. We give a novel characterization of this family as the unique one satisfying independence for uncoupled systems. The theorem boils down to a statement about endomorphisms of the convolution semi-group of finitely supported probability measures on the natural numbers, or, alternatively, about endomorphisms of the multiplicative semi-group of polynomials with non-negative coefficients.

", "date": "2025-08", "date_type": "published", "publication": "Mathematische Annalen", "volume": "392", "number": "4", "publisher": "Springer Science and Business Media LLC", "pagerange": "5617-5638", "issn": "0025-5831", "official_url": "https://authors.library.caltech.edu/records/1vrqc-68655", "funders": { "items": [ { "grant_number": "2018397" }, { "grant_number": "DMS-1944153" } ] }, "local_group": { "items": [ { "id": "Division-of-the-Humanities-and-Social-Sciences" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-025-03263-x", "pub_year": "2025", "author_list": "Sandomirskiy, Fedor and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/3vb4a-bkd39", "eprint_status": "archive", "datestamp": "2025-07-11 19:21:45", "lastmod": "2026-03-10 03:55:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Karch", "given": "Andreas" }, "orcid": "0000-0002-5725-2124" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "name": { "family": "Wang", "given": "Mianqi" }, "orcid": "0009-0005-9804-4849" } ] }, "title": "Nonrenormalization theorem for N = (4, 4) interface entropy", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence; Conformal Field Models in String Theory; Extended Supersymmetry", "note": "

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Article funded by SCOAP3.

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We thank Paul Aspinwall, Sergio Cecotti, Michael Gutperle, and Ling-Yan Hung for discussion. We also thank Costas Bachas, Ilka Brunner, and Michael Gutperle for their comments on the draft of this paper. AK and MW are supported in part by the U.S. Department of Energy, Office of High Energy Physics, under Grant No. DE-SC0022021 and a grant from the Simons Foundation (Grant 651678, AK). HO is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, the Simons Investigator Award (MP-SIP-00005259), and JSPS Grants-in-Aid for Scientific Research 23K03379. His work was performed in part at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, which is supported by the World Premier International Research Center Initiative, MEXT, Japan, and at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611.

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", "abstract": "

We derive a formula for the half-BPS interface entropy between any pair of  N = (4, 4) theories on the same conformal manifold. This generalizes the diastasis formula derived in [1] for  = (2, 2) theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of  = (2, 2) supersymmetry. To derive the  N = (4, 4) formula, we use the fact that the conformal manifold of  N = (4, 4) theories is symmetric and quaternionic-Kähler and that its isotropy group contains the SU(2) ⊗ SU(2) external automorphism of the  N = (4, 4) superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in [2] that the interface entropy for half-BPS Janus solutions in type IIB supergravity on AdS3 × S3 × T4 coincides with the corresponding quantity in their free conformal field limits.

", "date": "2025-07", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2025", "number": "7", "publisher": "Springer Science and Business Media LLC", "pagerange": "109", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/3vb4a-bkd39", "funders": { "items": [ { "grant_number": "DE-SC0022021" }, { "grant_number": "651678" }, { "grant_number": "DE-SC0011632" }, { "grant_number": "MP-SIP-00005259" }, { "grant_number": "23K03379" }, {}, { "grant_number": "PHY-1607611" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep07(2025)109", "primary_object": { "basename": "JHEP07(2025)109.pdf", "url": "https://authors.library.caltech.edu/records/3vb4a-bkd39/files/JHEP07(2025)109.pdf" }, "pub_year": "2025", "author_list": "Karch, Andreas; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/w8rb6-zw356", "eprint_status": "archive", "datestamp": "2025-06-27 12:33:13", "lastmod": "2026-03-09 23:57:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" }, "orcid": "0000-0001-8285-6627" } ] }, "title": "Entropy and Stability of Hyperbolic Manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Volume entropy; Hyperbolic manifolds; Metric currents; Plateau problem", "note": "

© The Author(s) 2025.

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This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.

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I am grateful to Gérard Besson, Gilles Courtois, Juan Souto, John Lott, Ursula Hamenstädt, Ben Lowe and Demetre Kazaras for insightful discussions during the writing of this article. I would especially like to thank Cosmin Manea, Hyun Chul Jang, Xingzhe Li and Dongming (Merrick) Hua for their careful reading, suggestions and for several corrections.

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A.S. was partially supported by NSF grant DMS-2104254. This research was conducted during the period A.S. served as a Clay Research Fellow.

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", "abstract": "

Let (M,g0) be a closed oriented hyperbolic manifold of dimension at least 3. By the volume entropy inequality of G. Besson, G. Courtois and S. Gallot, for any Riemannian metric g on M with same volume as g0, its volume entropy h(g) satisfies h(g)≥n−1 with equality only when g is isometric to g0. We show that the hyperbolic metric g0 is stable in the following sense: if gi is a sequence of Riemaniann metrics on M of same volume as g0 and if h(gi) converges to n−1, then there are smooth subsets Zi⊂M such that both Vol(Zi,gi) and Area(∂Zi,gi) tend to 0, and (M\u2216Zi,gi) converges to (M,g0) in the measured Gromov-Hausdorff topology. The proof relies on showing that any spherical Plateau solution for M is intrinsically isomorphic to (M,(n−1)²/4n g\u2080).

", "date": "2025-06", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "35", "number": "6", "publisher": "Springer Science and Business Media LLC", "pagerange": "877-914", "issn": "1016-443X", "official_url": "https://authors.library.caltech.edu/records/w8rb6-zw356", "funders": { "items": [ { "grant_number": "DMS-2104254" }, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-025-00711-3", "primary_object": { "basename": "s00039-025-00711-3.pdf", "url": "https://authors.library.caltech.edu/records/w8rb6-zw356/files/s00039-025-00711-3.pdf" }, "pub_year": "2025", "author_list": "Song, Antoine" }, { "id": "https://authors.library.caltech.edu/records/65hmq-ms383", "eprint_status": "archive", "datestamp": "2025-05-29 16:41:36", "lastmod": "2026-03-08 17:40:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "Gunby", "given": "Benjamin" } }, { "name": { "family": "He", "given": "Xiaoyu" } }, { "name": { "family": "Mubayi", "given": "Dhruv" } }, { "name": { "family": "Suk", "given": "Andrew" } }, { "name": { "family": "Verstra\u00ebte", "given": "Jacques" } } ] }, "title": "On Off-Diagonal Hypergraph Ramsey Numbers", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) 2025. Published by Oxford University Press. All rights reserved.

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This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/pages/standard-publication-reuse-rights)

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This research was initiated during a visit to the American Institute of Mathematics under their SQuaREs program.

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Communicated by Benny Sudakov.

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D.C. was supported by NSF Awards DMS-2054452 and DMS-2348859.

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J.F. was supported by NSF Award DMS-2154129.

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X.H. was supported by NSF Award DMS-2103154.

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D.M. was partially supported by NSF Awards DMS-1763317, DMS-1952767, and DMS-2153576, by a Humboldt Research Award, and by a Simons Fellowship.

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A.S. was supported by an NSF CAREER Award and by NSF Awards DMS-1952786 and DMS-2246847.

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J.V. was supported by NSF Award DMS-1800332.

", "abstract": "

A fundamental problem in Ramsey theory is to determine the growth rate in terms of n of the Ramsey number r(H,Kn(3)) of a fixed 3-uniform hypergraph H versus the complete 3-uniform hypergraph with n vertices. We study this problem, proving two main results. First, we show that for a broad class of H\u2060, including links of odd cycles and tight cycles of length not divisible by three, r(H,Kn(3))≥2ΩH(n log\u2061n)\u2060. This significantly generalizes and simplifies an earlier construction of Fox and He which handled the case of links of odd cycles and is sharp both in this case and for all but finitely many tight cycles of length not divisible by three. Second, disproving a folklore conjecture in the area, we show that there exists a linear hypergraph H for which r(H,Kn(3)) is superpolynomial in n\u2060. This provides the first example of a separation between r(H,Kn(3)) and r(H,Kn,n,n(3))\u2060, since the latter is known to be polynomial in n when H is linear.

", "date": "2025-06", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2025", "number": "11", "publisher": "Oxford University Press (OUP)", "pagerange": "rnaf122", "issn": "1073-7928", "official_url": "https://authors.library.caltech.edu/records/65hmq-ms383", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "grant_number": "DMS-2348859" }, { "grant_number": "DMS-2154129" }, { "grant_number": "DMS-2103154" }, { "grant_number": "DMS-1763317" }, { "grant_number": "DMS-1952767" }, { "grant_number": "DMS-2153576" }, {}, {}, { "grant_number": "DMS-1952786" }, { "grant_number": "DMS-2246847" }, { "grant_number": "DMS-1800332" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnaf122", "pub_year": "2025", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/rys3t-0gj61", "eprint_status": "archive", "datestamp": "2025-06-24 22:53:12", "lastmod": "2026-03-10 03:30:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Halverson", "given": "James" }, "orcid": "0000-0003-0535-2622" }, { "name": { "family": "Manolescu", "given": "Ciprian" }, "orcid": "0000-0003-0600-8751" }, { "name": { "family": "Ruehle", "given": "Fabian" }, "orcid": "0000-0002-8409-9823" } ] }, "title": "Searching for ribbons with machine learning", "ispublished": "pub", "full_text_status": "public", "keywords": "reinforcement learning; Bayesian optimization; knot theory; low-dimensional topology", "note": "

© 2025 The Author(s). Published by IOP Publishing Ltd.

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Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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We would like to thank Nathan Dunfield, Sherry Gong, Mark Hughes, and Lisa Piccirillo for helpful discussions during the preparation of this work. The code for attaching a band using the dual graph of the knot is based on previous work by Gong [Gon].

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SG and CM are supported by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology. CM is also supported by a Simons Investigator Award, and the NSF Grant DMS-2003488. SG is also partially supported by the NSF Grant DMS-1664227. JH and FR are supported by the National Science Foundation under Cooperative Agreement PHY-2019786 (The NSF AI Institute for Artificial Intelligence and Fundamental Interactions). JH is also supported by NSF CAREER Grant PHY-1848089. FR is also supported by NSF Grant PHY-2210333 and startup funding from Northeastern University.

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The data cannot be made publicly available upon publication because the cost of preparing, depositing and hosting the data would be prohibitive within the terms of this research project. The data that support the findings of this study are available upon reasonable request from the authors. https://github.com/ruehlef/ribbon.

", "abstract": "

We apply Bayesian optimization and reinforcement learning to a problem in topology: the question of when a knot bounds a ribbon disk. This question is relevant in an approach to disproving the four-dimensional smooth Poincaré conjecture; using our programs, we rule out many potential counterexamples to the conjecture. We also show that the programs are successful in detecting many ribbon knots in the range of up to 70 crossings.

", "date": "2025-06", "date_type": "published", "publication": "Machine Learning: Science and Technology", "volume": "6", "number": "2", "publisher": "IOP Publishing", "pagerange": "025065", "issn": "2632-2153", "official_url": "https://authors.library.caltech.edu/records/rys3t-0gj61", "funders": { "items": [ {}, { "grant_number": "DMS-1664227" }, { "grant_number": "PHY-2019786" }, { "grant_number": "PHY-1848089" }, { "grant_number": "PHY-2210333" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1088/2632-2153/ade362", "primary_object": { "basename": "Gukov_2025_Mach._Learn.__Sci._Technol._6_025065.pdf", "url": "https://authors.library.caltech.edu/records/rys3t-0gj61/files/Gukov_2025_Mach._Learn.__Sci._Technol._6_025065.pdf" }, "pub_year": "2025", "author_list": "Gukov, Sergei; Halverson, James; et al." }, { "id": "https://authors.library.caltech.edu/records/mmvj8-7gt83", "eprint_status": "archive", "datestamp": "2026-01-05 21:20:59", "lastmod": "2026-03-09 21:43:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Aluffi", "given": "Paolo" }, "orcid": "0000-0002-8249-685X" }, { "name": { "family": "Chen", "given": "Stephanie" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Log concavity of the Grothendieck class of M\u2080,n", "ispublished": "pub", "full_text_status": "public", "keywords": "Log concavity; Betti numbers; Moduli space of curves; Grothendieck class", "note": "

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

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The authors are grateful to J. Huh for pointing out reference [6] and to Luis Ferroni, Matt Larson, and Sam Payne for helpful comments. P.A. was supported in part by the Simons Foundation, collaboration grant #625561, and by an FSU ‘COFRS’ award. He thanks Caltech for hospitality. S.C. was supported by a Summer Undergraduate Research Fellowship at Caltech. M.M. was supported by NSF grant DMS-2104330.

", "abstract": "

Using a known recursive formula for the Grothendieck classes of the moduli spaces M\u2080,n, we prove that they satisfy an asymptotic form of ultra-log-concavity as polynomials in the Lefschetz class. We also observe that these polynomials are γ-positive. Both properties, along with numerical evidence, support the conjecture that these polynomials only have real zeros. This conjecture may be viewed as a particular case of a possible extension of a conjecture of Ferroni-Schröter and Huh on Hilbert series of Chow rings of matroids. We prove asymptotic ultra-log-concavity by studying differential equations obtained from the recursion, whose solutions are the generating functions of the individual Betti numbers of M\u2080,n. We obtain a rather complete description of these generating functions, determining their asymptotic behavior; their dominant term is controlled by the coefficients of the Lambert W function. The γ-positivity property follows directly from the recursion, extending the argument of Ferroni et al. proving γ-positivity for the Hilbert series of the Chow ring of matroids.

", "date": "2025-06", "date_type": "published", "publication": "Journal of Algebraic Combinatorics", "volume": "61", "number": "4", "publisher": "Springer Science and Business Media LLC", "pagerange": "47", "issn": "0925-9899", "official_url": "https://authors.library.caltech.edu/records/mmvj8-7gt83", "funders": { "items": [ { "grant_number": "625561" }, {}, {}, { "grant_number": "DMS-2104330" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10801-025-01428-0", "pub_year": "2025", "author_list": "Aluffi, Paolo; Chen, Stephanie; et al." }, { "id": "https://authors.library.caltech.edu/records/8j74t-1r107", "eprint_status": "archive", "datestamp": "2026-01-15 00:34:17", "lastmod": "2026-03-09 22:10:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Nenadov", "given": "Rajko" }, "orcid": "0009-0003-3777-021X" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "Short proof of the hypergraph container theorem", "ispublished": "pub", "full_text_status": "public", "abstract": "

We present a short and simple proof of the celebrated hypergraph container theorem of Balogh–Morris–Samotij and Saxton–Thomason. On a high level, our argument utilises the idea of iteratively taking vertices of largest degree from an independent set and constructing a hypergraph of lower uniformity which preserves independent sets and inherits edge distribution. The original algorithms for constructing containers also remove in each step vertices of high degree, which are not in the independent set. Our modified algorithm postpones this until the end, which surprisingly results in a significantly simplified analysis.

", "date": "2025-05-16", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "34", "number": "5", "publisher": "Cambridge University Press (CUP)", "pagerange": "621-624", "issn": "0963-5483", "official_url": "https://authors.library.caltech.edu/records/8j74t-1r107", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548325000112", "pub_year": "2025", "author_list": "Nenadov, Rajko and Pham, Huy Tuan" }, { "id": "https://authors.library.caltech.edu/records/bd9z9-tnv25", "eprint_status": "archive", "datestamp": "2025-09-25 18:11:14", "lastmod": "2026-03-09 02:15:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Minimizing Schr\u00f6dinger eigenvalues for confining potentials", "ispublished": "pub", "full_text_status": "public", "keywords": "functional inequality; stability; log-Sobolev inequality; relative entropy; eigenvalue; Schr\u00f6dinger operator", "note": "

Open Access. ©2025 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. © 2025 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes.

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Partial support through US National Science Foundation (DMS-1954995), as well as through the German Research Foundation (EXC-2111-390814868 and TRR 352-470903074) is acknowledged.

", "abstract": "

We consider the problem of minimizing the lowest eigenvalue of the Schrödinger operator −Δ + V in L²(Rd) when the integral ∫e−tV \u202fdx is given for some t > 0. We show that the eigenvalue is minimal for the harmonic oscillator and derive a quantitative version of the corresponding inequality.

", "date": "2025-05-05", "date_type": "published", "publication": "Advanced Nonlinear Studies", "publisher": "Walter de Gruyter GmbH", "pagerange": "ans-2023-0169", "issn": "1536-1365", "official_url": "https://authors.library.caltech.edu/records/bd9z9-tnv25", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "TRR 352-470903074" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1515/ans-2023-0169", "primary_object": { "basename": "10.1515_ans-2023-0169.pdf", "url": "https://authors.library.caltech.edu/records/bd9z9-tnv25/files/10.1515_ans-2023-0169.pdf" }, "pub_year": "2025", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/y8eh7-0na55", "eprint_status": "archive", "datestamp": "2026-01-23 21:49:10", "lastmod": "2026-03-07 04:15:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Intrinsic components in involution centralizers of fusion systems", "ispublished": "pub", "full_text_status": "public", "keywords": "fusion systems; finite simple groups", "note": "

© 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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This work was partially supported by DMS NSF-1601063.

", "abstract": "

This paper lays the foundation for the study of the saturated 2-fusion systems in which the centralizer of some fully centralized involution has a component whose center is nontrivial.

", "date": "2025-05", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "336", "number": "1-2", "publisher": "Mathematical Sciences Publishers", "pagerange": "7-27", "issn": "1945-5844", "official_url": "https://authors.library.caltech.edu/records/y8eh7-0na55", "funders": { "items": [ { "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.2140/pjm.2025.336.7", "primary_object": { "basename": "pjm-v336-n1-p02-s.pdf", "url": "https://authors.library.caltech.edu/records/y8eh7-0na55/files/pjm-v336-n1-p02-s.pdf" }, "pub_year": "2025", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/ahwd7-z3537", "eprint_status": "archive", "datestamp": "2026-06-03 14:37:28", "lastmod": "2026-06-03 14:37:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Haghighat", "given": "Babak" }, "orcid": "0000-0002-6688-7076" }, { "name": { "family": "Reshetikhin", "given": "Nicolai" }, "orcid": "0000-0002-5352-2676" } ] }, "title": "Foams and KZ-equations in Rozansky-Witten theories", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025 Published by Elsevier B.V. Funded by SCOAP³. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/)

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It is our pleasure to thank Alexander Braverman, Will Donovan, Boris Feigin, Daniel Huybrechts, Hiraku Nakajima, Justin Sawaon, Yan Soibelman, Johannes Walcher and Maxim Zabzine for helpful discussions and suggestions. The work of S.G. is supported by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology, by the NSF grant DMS-2245099, and by the U.S. Department of Energy Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of B.H. is supported by NSFC grant 12250610187. B.H. would also like to thank the Max-Planck institute of Mathematics in Bonn, where part of this work was completed, for hospitality and financial support. The work of N.R. was supported by the Simons Collaboration “Categorical symmetries”, by the grant BMSTC and ACZSP (Grant no. Z221100002722017) and by the Changjiang fund.

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The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Babak Haghighat reports financial support and travel were provided by Max-Planck-Institute for Mathematics. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
", "abstract": "

In this paper, we present a geometric description of foams, which are prevalent in topological quantum field theories (TQFTs) based on quantum algebra, and reciprocally explore the geometry of Rozansky-Witten (RW) theory from an algebraic perspective. This approach illuminates various aspects of decorated TQFTs via geometry of the target space X of RW theory. Through the formulation of the Knizhnik-Zamolodchikov (KZ) equation within this geometric framework, we derive the corresponding braiding and associator morphisms. We discuss applications where the target space of RW theory emerges as the Coulomb branch of a compactified 6d SCFT or Little String Theory, with the latter being particularly intriguing as it results in a compact X.

", "date": "2025-05", "date_type": "published", "publication": "Nuclear Physics B", "volume": "1014", "publisher": "Elsevier", "pagerange": "116856", "issn": "0550-3213", "official_url": "https://authors.library.caltech.edu/records/ahwd7-z3537", "funders": { "items": [ {}, { "grant_number": "DMS-2245099" }, {}, { "grant_number": "DE-SC0011632" }, { "grant_number": "12250610187" }, { "grant_number": "Z221100002722017" }, {} ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1016/j.nuclphysb.2025.116856", "primary_object": { "basename": "1-s2.0-S0550321325000653-main.pdf", "url": "https://authors.library.caltech.edu/records/ahwd7-z3537/files/1-s2.0-S0550321325000653-main.pdf" }, "pub_year": "2025", "author_list": "Gukov, Sergei; Haghighat, Babak; et al." }, { "id": "https://authors.library.caltech.edu/records/db58r-k4q96", "eprint_status": "archive", "datestamp": "2025-07-20 16:32:57", "lastmod": "2026-03-09 02:13:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Matzke", "given": "Ryan W." } } ] }, "title": "Minimizers for an Aggregation Model with Attractive\u2013Repulsive Interaction", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) (2025). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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The authors are grateful to D. Bilyk, J. A. Carrillo, D. Chafaï, C. Davies, T. Lim, J. Mateu, R. McCann, E. B. Saff, J. Verdera, M. Vu, and R. Womersley for several discussions, correspondences, and help with references during the process of working on this problem.

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R.L.F. is partially supported through US National Science Foundation grant DMS-1954995, as well as through the Deutsche Forschungsgemeinschaft Excellence Strategy EXC-2111-390814868 and TRR 352 (Project-ID 470903074). R.W.M. is supported by US National Science Foundation Postdoctoral Research Fellowship Grant 2202877.

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Open Access funding enabled and organized by Projekt DEAL.

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", "abstract": "

We solve explicitly a certain minimization problem for probability measures involving an interaction energy that is repulsive at short distances and attractive at large distances. We complement earlier works by showing that in an optimal part of the remaining parameter regime all minimizers are uniform distributions on a surface of a sphere, thus showing concentration on a lower dimensional set. Our method of proof uses convexity estimates on hypergeometric functions.

", "date": "2025-04", "date_type": "published", "publication": "Archive for Rational Mechanics and Analysis", "volume": "249", "number": "2", "publisher": "Springer Science and Business Media LLC", "pagerange": "15", "issn": "0003-9527", "official_url": "https://authors.library.caltech.edu/records/db58r-k4q96", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "TRR 352 (Project-ID 470903074)" }, { "grant_number": "DMS-2202877" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00205-025-02084-1", "primary_object": { "basename": "s00205-025-02084-1.pdf", "url": "https://authors.library.caltech.edu/records/db58r-k4q96/files/s00205-025-02084-1.pdf" }, "pub_year": "2025", "author_list": "Frank, Rupert L. and Matzke, Ryan W." }, { "id": "https://authors.library.caltech.edu/records/e7d32-zgc98", "eprint_status": "archive", "datestamp": "2025-03-25 19:45:45", "lastmod": "2026-03-09 02:13:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Jin", "given": "Tianling" }, "orcid": "0000-0002-6739-1101" }, { "name": { "family": "Wang", "given": "Wei" } } ] }, "title": "On the sharp constants in the regional fractional Sobolev inequalities", "ispublished": "pub", "full_text_status": "public", "keywords": "Primary 26D15; Secondary 26D33; 31C25; 46E35", "note": "

© The Author(s) 2025. 

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This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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R. L. F. was partially supported by the US National Science Foundation grant DMS-1954995 and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany’s Excellence Strategy EXC-2111-390814868. T. J. was partially supported by NSFC 12122120 and Hong Kong RGC grant GRF 16302519.

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Open access funding provided by Hong Kong University of Science and Technology.

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Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

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This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

", "abstract": "

In this paper, we study the sharp constants in fractional Sobolev inequalities associated with the regional fractional Laplacian in domains.

", "date": "2025-03-20", "date_type": "published", "publication": "Partial Differential Equations and Applications", "volume": "6", "number": "2", "publisher": "Springer Science and Business Media LLC", "pagerange": "15", "issn": "2662-2963", "official_url": "https://authors.library.caltech.edu/records/e7d32-zgc98", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "12122120" }, { "grant_number": "16302519" }, {} ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s42985-025-00317-2", "primary_object": { "basename": "s42985-025-00317-2.pdf", "url": "https://authors.library.caltech.edu/records/e7d32-zgc98/files/s42985-025-00317-2.pdf" }, "pub_year": "2025", "author_list": "Frank, Rupert L.; Jin, Tianling; et al." }, { "id": "https://authors.library.caltech.edu/records/wak0c-vbx30", "eprint_status": "archive", "datestamp": "2025-04-30 22:06:46", "lastmod": "2026-03-10 00:02:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Martin", "given": "James B." } }, { "name": { "family": "Sly", "given": "Allan" } }, { "id": "Zhang-Lingfu", "name": { "family": "Zhang", "given": "Lingfu" }, "orcid": "0000-0002-4794-7678" } ] }, "title": "Convergence of the environment seen from geodesics in exponential last-passage percolation", "ispublished": "pub", "full_text_status": "public", "keywords": "last passage percolation; KPZ universality class; exclusion process; empirical measure; competition interface; geodesic", "note": "

© European Mathematical Society. CC-BY-4.0

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We thank Timo Seppäläinen and Pablo Ferrari for valuable conversations. We
thank the organizers of the workshop on integrable probability at the Open Online Probability School in June 2020 for hosting a talk by LZ on joint work with AS, which led to this collaboration. We would also like to thank anonymous referees for carefully reading this paper and providing many valuable comments that helped improve the exposition.

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AS was supported by NSF grants DMS-1352013 and DMS-1855527, Simons Investigator grant and a MacArthur Fellowship. LZ was supported by NSF grant DMS-2505625.

", "abstract": "A well-known question in planar first-passage percolation concerns the convergence of the empirical distribution of weights as seen along geodesics. We demonstrate this convergence for an explicit model, directed last-passage percolation on \n \n \\mathbb{Z}^{2}\n \n with i.i.d. exponential weights, and provide explicit formulae for the limiting distributions, which depend on the asymptotic direction. For example, for geodesics in the direction of the diagonal, the limiting weight distribution has density \n \n (1/4+x/2+x^{2}/8)e^{-x}\n \n , and so is a mixture of Gamma(\n \n 1,1\n \n ), Gamma(\n \n 2,1\n \n ), and Gamma(\n \n 3,1\n \n ) distributions with weights \n \n 1/4\n \n , \n \n 1/2\n \n , and \n \n 1/4\n \n respectively. More generally, we study the local environment as seen from vertices along geodesics (including information about the shape of the path and about the weights on and off the path in a local neighborhood). We consider finite geodesics from \n \n (0,0)\n \n to \n \n n\\boldsymbol{\\rho}\n \n for some vector \n \n \\boldsymbol{\\rho}\n \n in the first quadrant, in the limit as \n \n n\\to\\infty\n \n , as well as semi-infinite geodesics in direction \n \n \\boldsymbol{\\rho}\n \n . We show almost sure convergence of the empirical distributions of the environments along these geodesics, as well as convergence of the distributions of the environment around a typical point in these geodesics, to the same limiting distribution, for which we give an explicit description.We make extensive use of a correspondence with TASEP as seen from an isolated second-class particle for which we prove new results concerning ergodicity and convergence to equilibrium. Our analysis relies on geometric arguments involving estimates for last-passage times, available from the integrable probability literature.", "date": "2025-03-06", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "27", "number": "3", "publisher": "European Mathematical Society - EMS - Publishing House GmbH", "pagerange": "877\u2013970", "issn": "1435-9855", "official_url": "https://authors.library.caltech.edu/records/wak0c-vbx30", "funders": { "items": [ { "grant_number": "DMS-1352013" }, { "grant_number": "DMS-1855527" }, { "grant_number": "DMS-2505625" }, { "grant_number": "-" }, { "grant_number": "-" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4171/jems/1594", "primary_object": { "basename": "10.4171-jems-1594.pdf", "url": "https://authors.library.caltech.edu/records/wak0c-vbx30/files/10.4171-jems-1594.pdf" }, "pub_year": "2025", "author_list": "Martin, James B.; Sly, Allan; et al." }, { "id": "https://authors.library.caltech.edu/records/yvmkn-8m670", "eprint_status": "archive", "datestamp": "2025-03-10 22:24:31", "lastmod": "2026-03-09 02:35:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Critical cluster volumes in hierarchical percolation", "ispublished": "pub", "full_text_status": "public", "keywords": "JEL: 60K35, 82B27, 82B43 (Primary), 82B28 (Secondary)", "note": "

© 2025 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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We thank Gordon Slade for helpful comments on an earlier version of the manuscript, and thank Roland Bauerschmidt and David Brydges for sharing their insights both on the possible reasons for the discrepancy between our results and the predictions of Essam, Gaunt, and Guttmann and the relations between this work and the physics literature more broadly. We also thank Nicolas Broutin for useful discussions on inhomogeneous random graphs and the multiplicative coalescent and Lily Reeves for double-checking the calculations in Section 6.

", "abstract": "

We consider long-range Bernoulli bond percolation on the d-dimensional hierarchical lattice in which each pair of points x and y are connected by an edge with probability 1−exp\u2061(−β\u2062\u2225x−y\u2225−d−α), where 0<α<d is fixed and β\u2a7e0 is a parameter. We study the volume of clusters in this model at its critical point β=βc, proving precise estimates on the moments of all orders of the volume of the cluster of the origin inside a box. We apply these estimates to prove up-to-constants estimates on the tail of the volume of the cluster of the origin, denoted as K, at criticality, namely,

\n
Pβc\u2062(|K|\u2a7en)\u224d{n−(d−α)/(d+α)d<3\u2062αn−1/2\u2062(log\u2061n)1/4d=3\u2062αn−1/2d>3\u2062α.
\n

In particular, we compute the critical exponent δ to be (d+α)/(d−α) when d is below the upper-critical dimension dc=3\u2062α and establish the precise order of polylogarithmic corrections to scaling at the upper-critical dimension itself. Our work also lays the foundations for the study of the scaling limit of the model: In the high-dimensional case d\u2a7e3\u2062α, we prove that the sized-biased distribution of the volume of the cluster of the origin inside a box converges under suitable normalization to a chi-squared random variable, while in the low-dimensional case d<3\u2062α, we prove that the suitably normalized decreasing list of cluster sizes in a box is tight in \u2113p\u2216{0} if and only if p>2\u2062d/(d+α).

", "date": "2025-01", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "130", "number": "1", "publisher": "Wiley", "pagerange": "e70023", "issn": "0024-6115", "official_url": "https://authors.library.caltech.edu/records/yvmkn-8m670", "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.70023", "primary_object": { "basename": "Proceedings of London Math Soc - 2025 - Hutchcroft - Critical cluster volumes in hierarchical percolation.pdf", "url": "https://authors.library.caltech.edu/records/yvmkn-8m670/files/Proceedings of London Math Soc - 2025 - Hutchcroft - Critical cluster volumes in hierarchical percolation.pdf" }, "pub_year": "2025", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/evq8c-2a349", "eprint_status": "archive", "datestamp": "2025-02-21 00:02:09", "lastmod": "2026-03-09 23:57:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Dong", "given": "Conghan" }, "orcid": "0009-0008-5284-1174" }, { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" }, "orcid": "0000-0001-8285-6627" } ] }, "title": "Stability of Euclidean 3-space for the positive mass theorem", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

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We would like to thank Gerhard Huisken for suggesting an application of the main theorem to the Bartnik capacity, and Marcus Khuri, Hubert Bray, Christos Mantoulidis and Hyun Chul Jang for helpful discussions. The writing of this paper was substantially improved thanks to suggestions of the referees.

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C.D. would like to thank his advisor Xiuxiong Chen for his encouragements. Part of the revised version was supported by the NSF grant DMS-1928930, while C.D. was in residence at the Simons Laufer Mathematical Sciences Institute (formerly MSRI) in Berkeley, California, during the Fall 2024 semester. A.S. was partially supported by the NSF grant DMS-2104254. This research was conducted during the period A.S. served as a Clay Research Fellow.

", "abstract": "

We show that the Euclidean 3-space R3 is stable for the Positive Mass Theorem in the following sense. Let (Mi,gi) be a sequence of complete asymptotically flat 3-manifolds with nonnegative scalar curvature and suppose that the ADM mass m(gi) of one end of Mi converges to 0. Then for all i, there is a subset Zi in Mi such that Mi\u2216Zi contains the given end, the area of the boundary ∂Zi converges to zero, and (Mi\u2216Zi,gi) converges to R3 in the pointed measured Gromov-Hausdorff topology for any choice of basepoints. This confirms a conjecture of G. Huisken and T. Ilmanen. Additionally, we find an almost quadratic upper bound for the area of ∂Zi in terms of m(gi). As an application of the main result, we also prove R. Bartnik’s strict positivity conjecture.

", "date": "2025-01", "date_type": "published", "publication": "Inventiones mathematicae", "volume": "239", "publisher": "Springer Science and Business Media LLC", "pagerange": "287\u2013319", "issn": "0020-9910", "official_url": "https://authors.library.caltech.edu/records/evq8c-2a349", "funders": { "items": [ { "grant_number": "DMS-1928930" }, { "grant_number": "DMS-2104254" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-024-01302-z", "primary_object": { "basename": "s00222-024-01302-z.pdf", "url": "https://authors.library.caltech.edu/records/evq8c-2a349/files/s00222-024-01302-z.pdf" }, "related_objects": [ { "basename": "2302.07414v3.pdf", "url": "https://authors.library.caltech.edu/records/evq8c-2a349/files/2302.07414v3.pdf" } ], "pub_year": "2025", "author_list": "Dong, Conghan and Song, Antoine" }, { "id": "https://authors.library.caltech.edu/records/zdm4m-js302", "eprint_status": "archive", "datestamp": "2025-06-24 01:42:44", "lastmod": "2026-03-10 03:55:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "name": { "family": "Wang", "given": "Yifan" }, "orcid": "0000-0001-9965-9777" } ] }, "title": "Universal bounds on CFT Distance Conjecture", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence; Conformal Field Models in String Theory; Scale and Conformal Symmetries", "note": "

© 2025 The Authors.

\n

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

\n

Article funded by SCOAP3.

\n\n

We thank Ofer Aharony, Bruno Balthazar, Nathan Benjamin, José Calderón-Infante, Sergio Cecotti, Thomas Hartman, Zohar Komargodski, Ying-Hsuan Lin, Juan Maldacena, Sridip Pal, Julio Parra-Martinez, Eric Perlmutter, Massimo Porrati, Daniel Roggenkamp, Thomas Rudelius, Shu-Heng Shao, Eva Silverstein, David Simmons-Duffin, Yan Soibelman, Cumrun Vafa, Irene Valenzuela, Katrin Wendland, Edward Witten, and Xi Yin for discussions. The work of HO is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, JSPS Grants-in-Aid for Scientific Research 23K03379, the Bershadsky Fellowship, the Guggenheim Fellowship, and the Simons Investigator Award (MPS-SIP-00005259). The work of YW is supported in part by the NSF grant PHY-2210420 and by the Simons Junior Faculty Fellows program. HO thanks the hospitalities of the Center for Cosmology and Particle Physics at New York University, where this work was initiated, and of the Center for the Fundamental Laws of Nature at Harvard University, where this work was completed. His work was also performed in part at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, which is supported by the World Premier International Research Center Initiative, MEXT, Japan, and at the Kavli Institute for Theoretical Physics (KITP) at the University of California, Santa Barbara, which is supported by NSF grant PHY-2309135.

", "abstract": "

For any unitary conformal field theory in two dimensions with the central charge c, we prove that, if there is a nontrivial primary operator whose conformal dimension \u2206 vanishes in some limit on the conformal manifold, the Zamolodchikov distance t to the limit is infinite, the approach to this limit is exponential \u2206 = exp(−αt + O(1)), and the decay rate obeys the universal bounds c−1/2 ≤ α ≤ 1. In the limit, we also find that an infinite tower of primary operators emerges without a gap above the vacuum and that the conformal field theory becomes locally a tensor product of a sigma-model in the large radius limit and a compact theory. As a corollary, we establish a part of the Distance Conjecture about gravitational theories in three-dimensional anti-de Sitter space. In particular, our bounds on α indicate that the emergence of exponentially light states is inevitable as the moduli field corresponding to t rolls beyond the Planck scale along the steepest path and that this phenomenon can begin already at the curvature scale of the bulk geometry. We also comment on implications of our bounds for gravity in asymptotically flat spacetime by taking the flat space limit and compare with the Sharpened Distance Conjecture.

", "date": "2024-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2024", "number": "12", "publisher": "Springer Science and Business Media LLC", "pagerange": "154", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/zdm4m-js302", "funders": { "items": [ { "grant_number": "DE-SC0011632" }, { "grant_number": "23K03379" }, {}, { "grant_number": "MPS-SIP-00005259" }, { "grant_number": "PHY-2210420" }, { "grant_number": "PHY-2309135" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep12(2024)154", "primary_object": { "basename": "JHEP12(2024)154.pdf", "url": "https://authors.library.caltech.edu/records/zdm4m-js302/files/JHEP12(2024)154.pdf" }, "pub_year": "2024", "author_list": "Ooguri, Hirosi and Wang, Yifan" }, { "id": "https://authors.library.caltech.edu/records/kp6nw-4h735", "eprint_status": "archive", "datestamp": "2026-06-02 20:58:19", "lastmod": "2026-06-02 20:58:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei G." }, "orcid": "0000-0002-9486-1762" }, { "id": "Jagadale-Mrunmay", "name": { "family": "Jagadale", "given": "Mrunmay" }, "orcid": "0000-0002-7950-4636" } ] }, "title": "c_(eff) for 3D \ud835\udca9=2 theories", "ispublished": "pub", "full_text_status": "public", "keywords": "RG flows; 3d \ud835\udca9=2 theories; c-effective", "note": "

© 2024 World Scientific Publishing Company.

\n\n

We would like to thank Miranda C. N. Cheng, Boris Feigin, Kathrin Bringmann, John Cardy, Angus Gruen, Antun Milas, Piotr Kucharski, Sunghyuk Park, Du Pei, Silviu Pufu and Nicolai Reshetikhin for helpful discussions.

\n\n

This work is supported by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology, by the NSF grant DMS-2245099, and by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632.

", "abstract": "

Based on the observed behavior of the superconformal index in three-dimensional \ud835\udca9=2 theories, we propose a quantity that can be considered as an analogue of the \"effective central charge.\" We discuss the general properties of this quantity and ways of computing it in a variety of different theories, including simple Lagrangian theories as well as more interesting strongly coupled examples that come from 3d-3d correspondence.

", "date": "2024-11-30", "date_type": "published", "publication": "International Journal of Modern Physics A", "volume": "39", "number": "33", "publisher": "World Scientific Pub Co Pte Ltd", "pagerange": "2446012", "issn": "0217-751X", "official_url": "https://authors.library.caltech.edu/records/kp6nw-4h735", "funders": { "items": [ {}, { "grant_number": "DMS-2245099" }, { "grant_number": "DE-SC0011632" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Engineering-and-Applied-Science" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1142/s0217751x24460126", "pub_year": "2024", "author_list": "Gukov, Sergei G. and Jagadale, Mrunmay" }, { "id": "https://authors.library.caltech.edu/records/6vyny-emz02", "eprint_status": "archive", "datestamp": "2024-11-19 16:01:11", "lastmod": "2026-03-09 21:51:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Baldwin", "given": "John A." } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" }, "orcid": "0000-0002-5287-4258" }, { "name": { "family": "Sivek", "given": "Steven" } } ] }, "title": "Floer homology and right-veering monodromy", "ispublished": "pub", "full_text_status": "public", "note": "

© 2024 Walter de Gruyter GmbH, Berlin/Boston.

\n\n

We thank Andy Cotton-Clay, Nathan Dunfield, Matt Hedden, Ying Hu, Siddhi Krishna, Tye Lidman, Rachel Roberts, and Shea Vela-Vick for helpful correspondence. We particularly thank Siddhi for pointing out Corollary 1.9, and for first introducing us to the question posed in [15, Question 8.2]. We are also grateful to the referee for their helpful feedback on the initial version of this paper.

\n\n

 J. A. Baldwin was supported by NSF FRG Grant DMS-1952707, Y. Ni was supported by NSF Grant DMS-181190.

", "abstract": "

We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic characterization of tight contact structures, by the work of Honda–Kazez–Mati\u0107. Our proof makes use of the relationship between the Heegaard Floer homology of mapping tori and the symplectic Floer homology of area-preserving surface diffeomorphisms. We describe applications of this work to Dehn surgeries and taut foliations.

", "date": "2024-10-31", "date_type": "published", "publication": "Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)", "volume": "2025", "number": "818", "publisher": "Walter de Gruyter GmbH", "pagerange": "263-290", "issn": "0075-4102", "official_url": "https://authors.library.caltech.edu/records/6vyny-emz02", "funders": { "items": [ { "grant_number": "DMS-1952707" }, { "grant_number": "DMS-181190" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2024-0079", "pub_year": "2024", "author_list": "Baldwin, John A.; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/0y8b5-wha71", "eprint_status": "archive", "datestamp": "2024-10-03 18:06:59", "lastmod": "2026-03-10 03:35:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Soluble Model of a Nonequilibrium Steady State: The Van Kampen Objection and Other Lessons", "ispublished": "pub", "full_text_status": "public", "keywords": "Classical transport; Dissipative dynamics; Electrical conductivity", "note": "

© 2024 American Physical Society.

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The author would like to thank Gregory Falkovich and Boris Spivak for numerous illuminating discussions and to the Weizmann Institute of Science for hospitality. This work was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632 and by the Simons Investigator Award.

\n\n

The supplemental material contains a derivation of the Fokker-Planck equation. The derivation is a slight generalization of an existing one in the literature (Ref. 13) to account for a weak dissipation.

\n

Supplement

\n

 

", "abstract": "

A simple model of charge transport is provided by a classical particle in a random potential and a dissipative coupling to the environment. The corresponding nonequilibrium steady state (NESS) can be determined analytically when both the disorder and dissipation are weak. We use it to illuminate some foundational issues in nonequilibrium statistical mechanics. We show that at nonlinear level dissipative response sensitively depends on the system-environment coupling, and the range of validity of the linear response theory is set by this coupling. This validates the Van Kampen objection. We also show that the principle of minimum entropy production does not determine the NESS beyond linear order in the electric field, while entropy maximization fails to produce the correct NESS already at linear order.

", "date": "2024-10-02", "date_type": "published", "publication": "Physical Review Letters", "volume": "133", "number": "14", "publisher": "American Physical Society", "pagerange": "147101", "issn": "0031-9007", "official_url": "https://authors.library.caltech.edu/records/0y8b5-wha71", "funders": { "items": [ { "grant_number": "DE-SC0011632" }, { "agency": "Simons Investigator Award" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/physrevlett.133.147101", "primary_object": { "basename": "PhysRevLett.133.147101.pdf", "url": "https://authors.library.caltech.edu/records/0y8b5-wha71/files/PhysRevLett.133.147101.pdf" }, "related_objects": [ { "basename": "supplemental.pdf", "url": "https://authors.library.caltech.edu/records/0y8b5-wha71/files/supplemental.pdf" } ], "pub_year": "2024", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/evnx5-paj70", "eprint_status": "archive", "datestamp": "2024-10-25 21:35:07", "lastmod": "2026-03-09 00:47:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Duong", "given": "Giao Ky" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Le", "given": "Thi Minh Thao" } }, { "name": { "family": "Nam", "given": "Phan Th\u00e0nh" } }, { "name": { "family": "Nguyen", "given": "Phuoc-Tai" } } ] }, "title": "Cwikel\u2013Lieb\u2013Rozenblum type inequalities for Hardy\u2013Schr\u00f6dinger operator", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator; Semiclassical estimates; Cwikel\u2013Lieb\u2013Rozenblum inequality; Singular potentials", "note": "

© 2024 The Author(s). Published by Elsevier Masson SAS. This is an open access
article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

\n\n

We thank the referees for helpful suggestions. Partial support through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Germany's Excellence Strategy EXC - 2111 - 390814868 and through TRR 352 – Project-ID 470903074 (G.K. Duong, R.L. Frank, P.T. Nam), through the U.S. National Science Foundation grant DMS-1954995 (R.L. Frank), and through the Czech Science Foundation Project GA22-17403S (T.M.T. Le, P.T. Nam, P.T. Nguyen) is acknowledged.

", "abstract": "
\n
\n
We prove a Cwikel–Lieb–Rozenblum type inequality for the number of negative eigenvalues of the Hardy–Schrödinger operator −Δ−(d−2)2/(4|x|2)−W(x) on L2(Rd). The bound is given in terms of a weighted Ld/2-norm of W which is sharp in both large and small coupling regimes. We also obtain a similar bound for the fractional Laplacian.
\n
\n
", "date": "2024-10", "date_type": "published", "publication": "Journal de Math\u00e9matiques Pures et Appliqu\u00e9es", "volume": "190", "publisher": "Elsevier", "pagerange": "103598", "issn": "0021-7824", "official_url": "https://authors.library.caltech.edu/records/evnx5-paj70", "funders": { "items": [ { "grant_number": "EXC - 2111 - 390814868" }, { "grant_number": "TRR 352 \u2013 Project-ID 470903074" }, { "grant_number": "DMS-1954995" }, { "grant_number": "GA22-17403S" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.matpur.2024.103598", "primary_object": { "basename": "1-s2.0-S0021782424000965-main.pdf", "url": "https://authors.library.caltech.edu/records/evnx5-paj70/files/1-s2.0-S0021782424000965-main.pdf" }, "pub_year": "2024", "author_list": "Duong, Giao Ky; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/fjd86-gk764", "eprint_status": "archive", "datestamp": "2025-09-25 18:39:36", "lastmod": "2026-03-09 21:43:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Yuri-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Homotopy Theoretic and Categorical Models of Neural Information Networks", "ispublished": "pub", "full_text_status": "public", "note": "

© 2024. 

\n

arXiv.org - Non-exclusive license to distribute

\n\n

Partially supported by NSF grants DMS-1707882 and DMS-2104330, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by FQXi grants FQXi-RFP-1 804 and FQXi-RFP-CPW-2014, SVCF grant 2020-2240.

", "abstract": "

In this paper we develop a novel mathematical formalism for the modeling of neural information networks endowed with additional structure in the form of assignments of resources, either computational or metabolic or informational. The starting point for this construction is the notion of summing functors and of Segal's Gamma-spaces in homotopy theory. The main results in this paper include functorial assignments of concurrent/distributed computing architectures and associated binary codes to networks and their subsystems, a categorical form of the Hopfield network dynamics, which recovers the usual Hopfield equations when applied to a suitable category of weighted codes, a functorial assignment to networks of corresponding information structures and information cohomology, and a cohomological version of integrated information.

", "date": "2024-09-06", "date_type": "published", "publication": "Compositionality", "volume": "6", "number": "4", "publisher": "Centre pour la Communication Scientifique Directe (CCSD)", "pagerange": "14135", "issn": "2631-4444", "official_url": "https://authors.library.caltech.edu/records/fjd86-gk764", "funders": { "items": [ { "grant_number": "DMS-1707882" }, { "grant_number": "DMS-2104330" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "grant_number": "FQXi-RFP-1 804" }, { "grant_number": "FQXi-RFP-CPW-2014" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.46298/compositionality-6-4", "primary_object": { "basename": "2006.15136.pdf", "url": "https://authors.library.caltech.edu/records/fjd86-gk764/files/2006.15136.pdf" }, "pub_year": "2024", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/nts23-99e09", "eprint_status": "archive", "datestamp": "2024-09-09 19:35:57", "lastmod": "2026-03-10 03:55:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Karch-Andreas", "name": { "family": "Karch", "given": "Andreas" }, "orcid": "0000-0002-5725-2124" }, { "id": "Kusuki-Yuya", "name": { "family": "Kusuki", "given": "Yuya" }, "orcid": "0000-0002-9784-0975" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Sun-Hao-Yu", "name": { "family": "Sun", "given": "Hao-Yu" } }, { "id": "Wang-Mianqi", "name": { "family": "Wang", "given": "Mianqi" }, "orcid": "0009-0005-9804-4849" } ] }, "title": "Universal Bound on Effective Central Charge and Its Saturation", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal field theory; Entanglement entropy; Entanglement in field theory; Gauge-gravity dualities", "note": "

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. 

\n\n

We would like to thank Costas Bachas, Ilka Brunner, Shinsei Ryu, and Yifan Wang for careful reading and valuable comments on a draft of this Letter. 

\n\n

A. K., H. S., and M. W. are supported in part by the U.S. Department of Energy under Grant No. DE-SC0022021 and a grant from the Simons Foundation (Grant No. 651440, A. K.). H. O. and Y. K. are supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. In addition, Y. K. is supported by the Brinson Prize Fellowship at Caltech and the INAMORI Frontier Program at Kyushu University. H. O. is supported in part by the Simons Investigator Award (No. MP-SIP-00005259), the Guggenheim Fellowship, the World Premier International Research Center Initiative, MEXT, Japan, and JSPS Grants-in-Aid for Scientific Research 23K03379. This work was performed in part at the Aspen Center for Physics, which is supported by NSF Grant No. PHY-1607611, and at the Kavli Institute for Theoretical Physics (KITP), which is supported by NSF Grant No. PHY-2309135.

\n\n

The supplemental material presents a detail of the construction of an example on the CFT side that saturates the upper bound. This is just for readers who are interested in the explicit construction.

", "abstract": "

The effective central charge (denoted by c_(eff)) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient c_(LR) of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this Letter, we propose the inequalities, 0≤c_(LR)≤c_(eff)≤min(c_L,c_R). They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.

", "date": "2024-08-30", "date_type": "published", "publication": "Physical Review Letters", "volume": "133", "number": "9", "publisher": "American Physical Society", "pagerange": "091604", "issn": "0031-9007", "official_url": "https://authors.library.caltech.edu/records/nts23-99e09", "funders": { "items": [ { "grant_number": "DE-SC0022021" }, { "grant_number": "651440" }, { "grant_number": "DE-SC0011632" }, {}, {}, { "grant_number": "MP-SIP-00005259" }, {}, { "grant_number": "23K03379" }, { "grant_number": "PHY-1607611" }, { "grant_number": "PHY-2309135" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/physrevlett.133.091604", "primary_object": { "basename": "PhysRevLett.133.091604.pdf", "url": "https://authors.library.caltech.edu/records/nts23-99e09/files/PhysRevLett.133.091604.pdf" }, "related_objects": [ { "basename": "supp_mat.pdf", "url": "https://authors.library.caltech.edu/records/nts23-99e09/files/supp_mat.pdf" } ], "pub_year": "2024", "author_list": "Karch, Andreas; Kusuki, Yuya; et al." }, { "id": "https://authors.library.caltech.edu/records/7fph3-97388", "eprint_status": "archive", "datestamp": "2024-08-21 23:38:17", "lastmod": "2026-03-10 03:30:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Seong", "given": "Rak-Kyeong" }, "orcid": "0000-0003-3247-6540" } ] }, "title": "Machine learning BPS spectra and the gap conjecture", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric field theories; Particles & Fields; Interdisciplinary Physics", "note": "

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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The authors would like to thank Miranda Cheng, Hee-Joong Chung, Shimal Harichurn, Arnav S. Kabra, Davide Passaro, Fabian Ruehle, and Josef Svoboda for discussions and comments. The work of S. G. is supported in part by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology, by the NSF Grant No. DMS-2245099, and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. R.-K. S. is supported by a Basic Research Grant of the National Research Foundation of Korea (NRF-2022R1F1A1073128). He is also supported by a Start-up Research Grant for new faculty at UNIST (1.210139.01) and a UNIST AI Incubator Grant (1.240022.01). He is also partly supported by the BK21 Program (“Next Generation Education Program for Mathematical Sciences,” 4299990414089) funded by the Ministry of Education in Korea and the National Research Foundation of Korea (NRF).

", "abstract": "We explore statistical properties of Bogomol'nyi-Prasad-Sommerfield q-series for 3d N=2 strongly coupled supersymmetric theories that correspond to a particular family of three-manifolds Y. We discover that gaps between exponents in the q-series are statistically more significant at the beginning of the q-series compared to gaps that appear in higher powers of q. Our observations are obtained by calculating saliencies of q-series features used as input data for principal component analysis, which is a standard example of an explainable machine learning technique that allows for a direct calculation and a better analysis of feature saliencies.\n \n \n \n \n Published by the American Physical Society\n 2024", "date": "2024-08-16", "date_type": "published", "publication": "Physical Review D", "volume": "110", "number": "4", "publisher": "American Physical Society", "pagerange": "046016", "issn": "2470-0010", "official_url": "https://authors.library.caltech.edu/records/7fph3-97388", "funders": { "items": [ { "grant_number": "DMS-2245099" }, {}, {}, { "grant_number": "DE-SC0011632" }, { "grant_number": "NRF-2022R1F1A1073128" }, { "grant_number": "1.210139.01" }, { "grant_number": "1.240022.01" }, { "agency": "Institute of BioMed-IT, Energy-IT and Smart-IT Technology (Best), Yonsei University", "grant_number": "4299990414089" }, {}, { "agency": "Simons Collaboration" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/physrevd.110.046016", "primary_object": { "basename": "PhysRevD.110.046016.pdf", "url": "https://authors.library.caltech.edu/records/7fph3-97388/files/PhysRevD.110.046016.pdf" }, "pub_year": "2024", "author_list": "Gukov, Sergei and Seong, Rak-Kyeong" }, { "id": "https://authors.library.caltech.edu/records/7sz4q-0za84", "eprint_status": "archive", "datestamp": "2024-06-26 20:29:31", "lastmod": "2026-03-08 20:41:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Sukochev-Fedor", "name": { "family": "Sukochev", "given": "Fedor" }, "orcid": "0000-0002-6063-3163" }, { "id": "Zanin-Dmitriy", "name": { "family": "Zanin", "given": "Dmitriy" } } ] }, "title": "Endpoint Schatten class properties of commutators", "ispublished": "pub", "full_text_status": "public", "note": "

© 2024 The Author(s). Published by Elsevier Under a Creative Commons license.

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Partial support through US National Science Foundation grant DMS-1954995 (RLF), the Deutsche Forschungsgemeinschaft (German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868 (RLF), and through Australian Research Council, Laureate Fellowship FL170100052 (FS) and DP230100434 (DZ) is acknowledged.

", "abstract": "

We study the trace ideal properties of the commutators [(−Δ)^(\ud835\udf16/2),\ud835\udc40\u0562] of a power of the Laplacian with the multiplication operator by a function f on \ud835\udc45^\ud835\udc51. For a certain range of \ud835\udf16∈\ud835\udc45, we show that this commutator belongs to the weak Schatten class \ud835\udc3f_(\ud835\udc51_(1−\ud835\udf16,∞)) if and only if the distributional gradient of f belongs to \ud835\udc3f_(\ud835\udc51_(1−\ud835\udf16)). Moreover, in this case we determine the asymptotics of the singular values. Our proofs use, among other things, the tool of Double Operator Integrals.

", "date": "2024-07", "date_type": "published", "publication": "Advances in Mathematics", "volume": "450", "publisher": "Elsevier", "pagerange": "109738", "issn": "0001-8708", "official_url": "https://authors.library.caltech.edu/records/7sz4q-0za84", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "agency": "Australian Research Council", "grant_number": "FL170100052" }, { "agency": "Australian Research Council", "grant_number": "DP230100434" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2024.109738", "primary_object": { "basename": "1-s2.0-S0001870824002536-main.pdf", "url": "https://authors.library.caltech.edu/records/7sz4q-0za84/files/1-s2.0-S0001870824002536-main.pdf" }, "pub_year": "2024", "author_list": "Frank, Rupert L.; Sukochev, Fedor; et al." }, { "id": "https://authors.library.caltech.edu/records/cvhrx-tay03", "eprint_status": "archive", "datestamp": "2024-10-17 23:52:54", "lastmod": "2026-03-09 02:11:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "name": { "family": "Hoffmann-Ostenhof", "given": "Thomas" } }, { "name": { "family": "Laptev", "given": "Ari" }, "orcid": "0000-0002-1286-8670" }, { "name": { "family": "Solovej", "given": "Jan\u00a0Philip" }, "orcid": "0000-0002-0244-1497" } ] }, "title": "Hardy inequalities for large fermionic systems", "ispublished": "pub", "full_text_status": "public", "keywords": "Hardy inequalities; fermions; semi-classical limit; electrostatic inequalities", "note": "

CC-BY 4.0 European Mathematical Society. This article is published open access under our Subscribe to Open model.

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RLF was partially supported by the US National Science Foundation Grant number DMS-1954995 and the DFG grants EXC-2111-390814868 and TRR 352-Project-ID 470903074. The support of the villum Centre of Excellence for the Mathematics of Quantum Theory (QMATH) Grant number 10059 to JPS is acknowledged.

", "abstract": "

Given 0<s<2d with s≤1, we are interested in the large N-behavior of the optimal constant κN in the Hardy inequality ∑n=1N(−Δn)s≥κN∑n<m\u2223Xn−Xm\u2223−2s, when restricted to antisymmetric functions. We show that N1−d2sκN has a positive, finite limit given by a certain variational problem, thereby generalizing a result of Lieb and Yau related to the Chandrasekhar theory of gravitational collapse.

", "date": "2024-06-13", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "14", "number": "2", "publisher": "European Mathematical Society - EMS - Publishing House GmbH", "pagerange": "805-835", "issn": "1664-039X", "official_url": "https://authors.library.caltech.edu/records/cvhrx-tay03", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-3908148" }, { "grant_number": "TRR 352-Project-ID 4709030" }, { "grant_number": "10059" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/jst/511", "primary_object": { "basename": "10.4171-jst-511.pdf", "url": "https://authors.library.caltech.edu/records/cvhrx-tay03/files/10.4171-jst-511.pdf" }, "pub_year": "2024", "author_list": "Frank, Rupert L.; Hoffmann-Ostenhof, Thomas; et al." }, { "id": "https://authors.library.caltech.edu/records/atth2-7h963", "eprint_status": "archive", "datestamp": "2024-06-03 18:06:29", "lastmod": "2026-03-10 14:34:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Banks-Jess", "name": { "family": "Banks", "given": "Jess" }, "orcid": "0000-0003-3803-1702" }, { "id": "Breuer-Jonathan", "name": { "family": "Breuer", "given": "Jonathan" }, "orcid": "0000-0002-2765-910X" }, { "id": "Garza-Vargas-Jorge", "name": { "family": "Garza-Vargas", "given": "Jorge" }, "orcid": "0000-0001-6258-0600" }, { "id": "Seelig-Eyal", "name": { "family": "Seelig", "given": "Eyal" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A useful formula for periodic Jacobi matrices on trees", "ispublished": "pub", "full_text_status": "public", "note": "

© 2024 the Author(s). Published by PNAS. This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).

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Research of J. Breuer, J.G.-V., E.S., and B.S. supported in part by Israeli Binational Science Foundation (BSF) Grant No. 2020027. Research of J. Breuer and E.S. supported in part by Israel Science Foundation Grant No. 1378/20. Research of J.G.-V. supported in part by NSF Focused Research Group (FRG) Award 1952777 and Caltech Carver Mead New Adventures Fund under the aegis of Joel Tropp’s award, and Caltech Center for the Mathematics of Information (CMI) Postdoctoral Fellowship. We would like to thank Misha Sodin for pointing out to us that one could view Ψ as generalization of the Marchenko–Ostrovskii theory from cyclic graphs to general finite graphs.
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J. Banks, J. Breuer, J.G.-V., E.S., and B.S. performed research; and wrote the paper.

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There are no data underlying this work.
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The authors declare no competing interest.

", "abstract": "
We introduce a function of the density of states for periodic Jacobi matrices on trees and prove a useful formula for it in terms of entries of the resolvent of the matrix and its “half-tree” restrictions. This formula is closely related to the one-dimensional Thouless formula and associates a natural phase with points in the bands. This allows streamlined proofs of the gap labeling and Aomoto index theorems. We give a complete proof of gap labeling and sketch the proof of the Aomoto index theorem. We also prove a version of this formula for the Anderson model on trees.
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", "date": "2024-06-04", "date_type": "published", "publication": "Proceedings of the National Academy of Sciences", "volume": "121", "number": "23", "publisher": "National Academy of Sciences", "pagerange": "e2315218121", "issn": "0027-8424", "official_url": "https://authors.library.caltech.edu/records/atth2-7h963", "funders": { "items": [ { "grant_number": "2020027" }, { "grant_number": "1378/20" }, { "grant_number": "DMS-1952777" }, { "grant_number": "Carver Mead New Adventure Fund" }, { "grant_number": "Center for the Mathematics of Information" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1073/pnas.2315218121", "primary_object": { "basename": "banks-et-al-2024-a-useful-formula-for-periodic-jacobi-matrices-on-trees.pdf", "url": "https://authors.library.caltech.edu/records/atth2-7h963/files/banks-et-al-2024-a-useful-formula-for-periodic-jacobi-matrices-on-trees.pdf" }, "pub_year": "2024", "author_list": "Banks, Jess; Breuer, Jonathan; et al." }, { "id": "https://authors.library.caltech.edu/records/eebg4-rbt63", "eprint_status": "archive", "datestamp": "2026-01-13 16:39:29", "lastmod": "2026-03-08 17:37:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "Fox", "given": "Jacob" }, "orcid": "0000-0002-0664-497X" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Zhao", "given": "Yufei" }, "orcid": "0000-0002-1995-3755" } ] }, "title": "Set-Coloring Ramsey Numbers and Error-Correcting Codes Near the Zero-Rate Threshold", "ispublished": "pub", "full_text_status": "public", "keywords": "Error-correcting codes; Ramsey numbers; zero-rate threshold; linear programming bound", "note": "

© 2023 IEEE.

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The authors would like to thank Xiaoyu He, Dhruv Mubayi, Andrew Suk, and Jacques Verstraëte for helpful conversations. They would also like to thank Maria Axenovich for bringing the work of Yen Hoang Le to their attention.

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The work of David Conlon was supported by the NSF under Award DMS-2054452. The work of Jacob Fox was
supported in part by a Packard Fellowship and in part by the NSF under Awards DMS-1953990 and DMS-2154129. The work of Huy Tuan Pham was supported in part by a Clay Fellowship and in part by a Two Sigma
Fellowship. The work of Yufei Zhao was supported by the NSF under Career Award DMS-2044606, in part by a Sloan Research Fellowship, and in part by an MIT Solomon Buchsbaum Fund.

", "abstract": "

For positive integers n,r,s with r > s , the set-coloring Ramsey number R(n;r,s) is the minimum N such that if every edge of the complete graph KN receives a set of s colors from a palette of r colors, then there is a subset of n vertices where all of the edges between them receive a common color. If n is fixed and sr is less than and bounded away from 1−1n−1 , then R(n;r,s) is known to grow exponentially in r , while if sr is greater than and bounded away from 1−1n−1 , then R(n;r,s) is bounded. Here we prove bounds for R(n;r,s) in the intermediate range where sr is close to 1−1n−1 by establishing a connection to the maximum size of error-correcting codes near the zero-rate threshold.

", "date": "2024-06", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "70", "number": "6", "publisher": "IEEE", "pagerange": "4074-4078", "issn": "0018-9448", "official_url": "https://authors.library.caltech.edu/records/eebg4-rbt63", "funders": { "items": [ { "grant_number": "DMS-2054452" }, { "agency": "Packard Fellowship" }, { "grant_number": "DMS-1953990" }, { "grant_number": "DMS-2154129" }, { "agency": "Clay Fellowship" }, { "agency": "Two Sigma Fellowship" }, { "grant_number": "DMS-2044606" }, { "agency": "Sloan Research Fellowship" }, { "agency": "MIT Solomon Buchsbaum Fund" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1109/tit.2023.3327846", "pub_year": "2024", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/sc4y5-c1068", "eprint_status": "archive", "datestamp": "2026-01-15 00:34:29", "lastmod": "2026-03-09 22:09:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Park", "given": "Jinyoung" }, "orcid": "0000-0003-3962-5668" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "On a conjecture of Talagrand on selector processes and a consequence on positive empirical processes", "ispublished": "pub", "full_text_status": "public", "abstract": "

For appropriate Gaussian processes, as a corollary of the majorizing measure theorem, Michel Talagrand (1987) proved that the event that the supremum is significantly larger than its expectation can be covered by a set of half-spaces whose sum of measures is small. We prove a conjecture of Talagrand that is the analog of this result in the Bernoulli-p setting, and answer a question of Talagrand on the analogous result for general positive empirical processes.

", "date": "2024-05-01", "date_type": "published", "publication": "Annals of Mathematics", "volume": "199", "number": "3", "publisher": "Annals of Mathematics", "issn": "0003-486X", "official_url": "https://authors.library.caltech.edu/records/sc4y5-c1068", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2024.199.3.6", "pub_year": "2024", "author_list": "Park, Jinyoung and Pham, Huy Tuan" }, { "id": "https://authors.library.caltech.edu/records/w1ek3-w2755", "eprint_status": "archive", "datestamp": "2024-04-10 23:35:56", "lastmod": "2026-06-01 21:55:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Halverson", "given": "James" }, "orcid": "0000-0003-0535-2622" }, { "name": { "family": "Ruehle", "given": "Fabian" }, "orcid": "0000-0002-8409-9823" } ] }, "title": "Rigor with machine learning from field theory to the Poincar\u00e9 conjecture", "ispublished": "pub", "full_text_status": "public", "keywords": "General Physics and Astronomy", "note": "

© Springer Nature Limited 2024.

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S.G. is supported in part by a Simons Collaboration Grant on New Structures in Low-Dimensional Topology and by the Department of Energy grant DE-SC0011632. J.H. is supported by National Science Foundation CAREER grant PHY-1848089. F.R. is supported by the National Science Foundation grants PHY-2210333 and startup funding from Northeastern University. The work of J.H. and F.R. is also supported by the National Science Foundation under Cooperative Agreement PHY-2019786 (The NSF AI Institute for Artificial Intelligence and Fundamental Interactions).

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The authors contributed equally to all aspects of the article.

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The authors declare no competing interests.

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", "abstract": "
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Despite their successes, machine learning techniques are often stochastic, error-prone and blackbox. How could they then be used in fields such as theoretical physics and pure mathematics for which error-free results and deep understanding are a must? In this Perspective, we discuss techniques for obtaining zero-error results with machine learning, with a focus on theoretical physics and pure mathematics. Non-rigorous methods can enable rigorous results via conjecture generation or verification by reinforcement learning. We survey applications of these techniques-for-rigor ranging from string theory to the smooth 4D Poincaré conjecture in low-dimensional topology. We also discuss connections between machine learning theory and mathematics or theoretical physics such as a new approach to field theory motivated by neural network theory, and a theory of Riemannian metric flows induced by neural network gradient descent, which encompasses Perelman’s formulation of the Ricci flow that was used to solve the 3D Poincaré conjecture.

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", "date": "2024-05", "date_type": "published", "publication": "Nature Reviews Physics", "volume": "6", "number": "5", "publisher": "Nature Publishing Group", "pagerange": "310-319", "issn": "2522-5820", "official_url": "https://authors.library.caltech.edu/records/w1ek3-w2755", "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/s42254-024-00709-0", "pub_year": "2024", "author_list": "Gukov, Sergei; Halverson, James; et al." }, { "id": "https://authors.library.caltech.edu/records/zaber-9mz98", "eprint_status": "archive", "datestamp": "2026-01-15 00:34:52", "lastmod": "2026-03-09 22:10:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Cook", "given": "Nicholas A." }, "orcid": "0000-0002-1148-1642" }, { "name": { "family": "Dembo", "given": "Amir" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "Regularity method and large deviation principles for the Erd\u0151s\u2013R\u00e9nyi hypergraph", "ispublished": "pub", "full_text_status": "public", "abstract": "

We develop a quantitative large deviations theory for random hypergraphs, which rests on tensor decomposition and counting lemmas under a novel family of cut-type norms. As our main application, we obtain sharp asymptotics for joint upper and lower tails of homomorphism counts in the r-uniform Erd\u0151s–Rényi hypergraph for any fixed r≥2, generalizing and improving on previous results for the Erd\u0151s–Rényi graph (r=2). The theory is sufficiently quantitative to allow the density of the hypergraph to vanish at a polynomial rate, and additionally yields tail asymptotics for other nonlinear functionals, such as induced homomorphism counts.

", "date": "2024-04-01", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "173", "number": "5", "publisher": "Duke University Press", "issn": "0012-7094", "official_url": "https://authors.library.caltech.edu/records/zaber-9mz98", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/00127094-2023-0029", "pub_year": "2024", "author_list": "Cook, Nicholas A.; Dembo, Amir; et al." }, { "id": "https://authors.library.caltech.edu/records/gqw1x-yeh18", "eprint_status": "archive", "datestamp": "2024-05-03 21:54:24", "lastmod": "2026-03-09 21:50:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Panangaden-Jane", "name": { "family": "Panangaden", "given": "Jane" }, "orcid": "0000-0002-6214-2130" } ] }, "title": "Quantum statistical mechanics and the boundary of modular curves", "ispublished": "pub", "full_text_status": "public", "note": "
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© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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M.M. was partially supported by NSF Grant Nos. DMS-1707882 and DMS-2104330, by NSERC Discovery Grant No. RGPIN-2018-04937 and Accelerator Supplement Grant No. RGPAS-2018-522593.

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Matilde Marcolli: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal). Jane Panangaden: Conceptualization (equal); Formal analysis (equal); Writing – original draft (equal); Writing – review & editing (equal).

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Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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The authors have no conflicts to disclose.

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", "abstract": "
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The theory of limiting modular symbols provides a noncommutative geometric model of the boundary of modular curves that includes irrational points in addition to cusps. A noncommutative space associated to this boundary is constructed, as part of a family of noncommutative spaces associated to different continued fractions algorithms, endowed with the structure of a quantum statistical mechanical system. Two special cases of this family of quantum systems can be interpreted as a boundary of the system associated to the Shimura variety of GL2 and an analog for SL2. The structure of equilibrium states for this family of systems is discussed. In the geometric cases, the ground states evaluated on boundary arithmetic elements are given by pairings of cusp forms and limiting modular symbols.

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", "date": "2024-04", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "65", "number": "4", "publisher": "American Institute of Physics", "pagerange": "042104", "issn": "0022-2488", "official_url": "https://authors.library.caltech.edu/records/gqw1x-yeh18", "funders": { "items": [ { "grant_number": "DMS-1707882" }, { "grant_number": "DMS-2104330" }, { "grant_number": "RGPIN-2018-04937" }, { "grant_number": "RGPAS-2018-522593" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/5.0179805", "primary_object": { "basename": "042104_1_5.0179805.pdf", "url": "https://authors.library.caltech.edu/records/gqw1x-yeh18/files/042104_1_5.0179805.pdf" }, "pub_year": "2024", "author_list": "Marcolli, Matilde and Panangaden, Jane" }, { "id": "https://authors.library.caltech.edu/records/r60tw-te731", "eprint_status": "archive", "datestamp": "2025-03-20 15:10:24", "lastmod": "2026-03-10 03:55:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benjamin-Nathan", "name": { "family": "Benjamin", "given": "Nathan" }, "orcid": "0000-0003-3661-6563" }, { "id": "Lee-Jaeha", "name": { "family": "Lee", "given": "Jaeha" }, "orcid": "0000-0001-9124-450X" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Simmons-Duffin-D", "name": { "family": "Simmons-Duffin", "given": "David" }, "orcid": "0000-0002-2937-9515" } ] }, "title": "Universal asymptotics for high energy CFT data", "ispublished": "pub", "full_text_status": "public", "keywords": "Effective Field Theories; Field Theory Hydrodynamics; Scale and Conformal Symmetries; Thermal Field Theory", "note": "

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Article funded by SCOAP3.

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We thank Alex Belin, Alejandra Castro, Stuart Dowker, Liam Fitzpatrick, Tom Hartman, Zohar Komargodski, Petr Kravchuk, Alex Maloney, Henry Maxfield, Dalimil Mazá\u010d, Jake McNamara, Shiraz Minwalla, Sridip Pal, Julio Parra-Martinez, Mukund Rangamani, Edgar Shaghoulian, Douglas Stanford, Herman Verlinde, Pedro Vieira, Yifan Wang, and Sasha Zhiboedov for helpful discussions. We thank Zohar Komargodski, Edgar Shaghoulian, and Yifan Wang for comments on the draft. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, NB is supported in part by the Sherman Fairchild Foundation. HO is supported in part by the World Premier International Research Center Initiative, MEXT, Japan, and by JSPS Grants-in-Aid for Scientific Research 20K03965 and 23K03379. DSD is supported in part by Simons Foundation grant 488657 (Simons Collaboration on the Nonperturbative Bootstrap) and a DOE Early Career Award under grant No. DE-SC0019085.

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", "abstract": "

Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields — a \"thermal effective action\". This effective action determines the asymptotic density of states of a CFT as a detailed function of dimension and spin. We discuss subleading perturbative and nonperturbative corrections to the density, comparing with free and holographic examples. We furthermore show how to use the thermal effective action on more complicated geometries at special locations called \"hot spots\". The hot spot idea makes a prediction for a CFT partition function on a higher-dimensional version of a genus-2 Riemann surface, in a particular high temperature limit. By decomposing the partition function into a novel higher-dimensional version of genus-2 conformal blocks (which we compute at large scaling dimension), we extract the asymptotic density of heavy-heavy-heavy OPE coefficients in a higher-dimensional CFT. We also compute asymptotics of thermal 1-point functions using the same techniques.

", "date": "2024-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2024", "number": "3", "publisher": "Springer Science and Business Media LLC", "pagerange": "115", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/r60tw-te731", "funders": { "items": [ { "grant_number": "DE-SC0011632" }, {}, {}, { "grant_number": "20K03965" }, { "grant_number": "23K03379" }, { "grant_number": "488657" }, { "grant_number": "DE-SC0019085" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep03(2024)115", "primary_object": { "basename": "JHEP03(2024)115.pdf", "url": "https://authors.library.caltech.edu/records/r60tw-te731/files/JHEP03(2024)115.pdf" }, "pub_year": "2024", "author_list": "Benjamin, Nathan; Lee, Jaeha; et al." }, { "id": "https://authors.library.caltech.edu/records/bd6ph-62c84", "eprint_status": "archive", "datestamp": "2026-02-24 22:48:17", "lastmod": "2026-02-25 21:56:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gherman-Matthew-M", "name": { "family": "Gherman", "given": "M." }, "orcid": "0009-0007-2601-7862" }, { "name": { "family": "Merkurjev", "given": "A." }, "orcid": "0000-0002-4447-1838" } ] }, "title": "Krull dimension of the negligible quotient in mod p cohomology of a finite group", "ispublished": "pub", "full_text_status": "public", "keywords": "Negligible cohomology; Formally real fields; Galois cohomology", "note": "

© 2023 Elsevier B.V. All rights reserved.

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The work of the second author has been supported by the NSF grant DMS #1801530.

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The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Alexander Merkurjev reports financial support was provided by National Science Foundation.
", "abstract": "For a finite group G, a G-module M, and a field F, an element u \u2208 H d ( G , M ) is negligible over F if for each field extension L / F and every continuous group homomorphism from Gal ( L sep / L ) to G, u belongs to the kernel of the induced homomorphism H d ( G , M ) \u2192 H d ( L , M ) . For p a prime and a trivial G-action on the coefficients, the negligible elements in the cohomology ring H \u204e ( G , Z / p Z ) form an ideal. We compute the generators of the negligible ideal in the mod p cohomology of elementary abelian p-groups. We further show that when p is odd or p = 2 and either | G | is odd or F is not formally real, the Krull dimension of the quotient of mod p cohomology by the negligible ideal is 0. However, when p = 2 , | G | is even, and F is formally real, the Krull dimension of the quotient of mod 2 cohomology of a finite 2-group by the negligible ideal is 1.", "date": "2024-03", "date_type": "published", "publication": "Journal of Pure and Applied Algebra", "volume": "228", "number": "3", "publisher": "Elsevier", "pagerange": "107489", "issn": "0022-4049", "official_url": "https://authors.library.caltech.edu/records/bd6ph-62c84", "funders": { "items": [ { "grant_number": "DMS #1801530" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jpaa.2023.107489", "pub_year": "2024", "author_list": "Gherman, M. and Merkurjev, A." }, { "id": "https://authors.library.caltech.edu/records/4ttta-y1w22", "eprint_status": "archive", "datestamp": "2024-12-05 23:44:09", "lastmod": "2026-03-08 19:57:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert" }, "orcid": "0000-0001-7973-4688" }, { "id": "Laptev-Ari", "name": { "family": "Laptev", "given": "Ari" }, "orcid": "0000-0002-1286-8670" }, { "name": { "family": "Read", "given": "Larry" }, "orcid": "0000-0003-2744-5854" } ] }, "title": "Weighted CLR type bounds in two dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "MSC (2020): Primary 35P15; Secondary 81Q10", "note": "

© Copyright 2024 by the authors

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The first author was partially supported through US National Science Foundation grant DMS-1954995, as well as through the Excellence Strategy of the German Research Foundation grant EXC-2111-390814868 and through German Research Foundation project TRR 352 - Project-ID 470903074. The second author was supported by the Ministry of Science and Higher Education of the Russian Federation (Agreement 075-10-2021-093, Project MTH-RND-2124).The third author was partially supported through German Research Foundation project TRR 352 - Project-ID 470903074.

", "abstract": "

We derive weighted versions of the Cwikel\u2013Lieb\u2013Rozenblum inequality for the Schr\u00f6dinger operator in two dimensions with a nontrivial Aharonov\u2013Bohm magnetic field. Our bounds capture the optimal dependence on the flux and we identify a class of long-range potentials that saturate our bounds in the strong coupling limit. We also extend our analysis to the two-dimensional Schr\u00f6dinger operator acting on antisymmetric functions and obtain similar results.

", "date": "2024-02-26", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "377", "number": "5", "publisher": "American Mathematical Society (AMS)", "pagerange": "3357-3371", "issn": "0002-9947", "official_url": "https://authors.library.caltech.edu/records/4ttta-y1w22", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "TRR 352 - Project-ID 470903074" }, { "grant_number": "Project MTH-RND-2124" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/9124", "primary_object": { "basename": "S0002-9947-2024-09124-9.pdf", "url": "https://authors.library.caltech.edu/records/4ttta-y1w22/files/S0002-9947-2024-09124-9.pdf" }, "pub_year": "2024", "author_list": "Frank, Rupert; Laptev, Ari; et al." }, { "id": "https://authors.library.caltech.edu/records/amyc1-hkk39", "eprint_status": "archive", "datestamp": "2026-01-15 00:35:13", "lastmod": "2026-03-09 22:10:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "Luo", "given": "Sammy" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Zhou", "given": "Yunkun" } } ] }, "title": "Small subsets with large sumset: Beyond the Cauchy\u2013Davenport bound", "ispublished": "pub", "full_text_status": "public", "abstract": "AbstractFor a subset \n$A$\n of an abelian group \n$G$\n, given its size \n$|A|$\n, its doubling \n$\\kappa =|A+A|/|A|$\n, and a parameter \n$s$\n which is small compared to \n$|A|$\n, we study the size of the largest sumset \n$A+A'$\n that can be guaranteed for a subset \n$A'$\n of \n$A$\n of size at most \n$s$\n. We show that a subset \n$A'\\subseteq A$\n of size at most \n$s$\n can be found so that \n$|A+A'| = \\Omega (\\!\\min\\! (\\kappa ^{1/3},s)|A|)$\n. Thus, a sumset significantly larger than the Cauchy\u2013Davenport bound can be guaranteed by a bounded size subset assuming that the doubling \n$\\kappa$\n is large. Building up on the same ideas, we resolve a conjecture of Bollob\u00e1s, Leader and Tiba that for subsets \n$A,B$\n of \n$\\mathbb{F}_p$\n of size at most \n$\\alpha p$\n for an appropriate constant \n$\\alpha \\gt 0$\n, one only needs three elements \n$b_1,b_2,b_3\\in B$\n to guarantee \n$|A+\\{b_1,b_2,b_3\\}|\\ge |A|+|B|-1$\n. Allowing the use of larger subsets \n$A'$\n, we show that for sets \n$A$\n of bounded doubling, one only needs a subset \n$A'$\n with \n$o(|A|)$\n elements to guarantee that \n$A+A'=A+A$\n. We also address another conjecture and a question raised by Bollob\u00e1s, Leader and Tiba on high-dimensional analogues and sets whose sumset cannot be saturated by a bounded size subset.", "date": "2024-02-21", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "33", "number": "4", "publisher": "Cambridge University Press (CUP)", "pagerange": "411-431", "issn": "0963-5483", "official_url": "https://authors.library.caltech.edu/records/amyc1-hkk39", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548324000014", "pub_year": "2024", "author_list": "Fox, Jacob; Luo, Sammy; et al." }, { "id": "https://authors.library.caltech.edu/records/64s8h-p1a44", "eprint_status": "archive", "datestamp": "2026-06-02 19:57:28", "lastmod": "2026-06-02 19:57:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Cheng", "given": "Miranda C. N." }, "orcid": "0000-0002-4651-095X" }, { "name": { "family": "Chun", "given": "Sungbong" } }, { "name": { "family": "Feigin", "given": "Boris" } }, { "name": { "family": "Ferrari", "given": "Francesca" }, "orcid": "0000-0003-1169-4661" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei G." }, "orcid": "0000-0002-9486-1762" }, { "name": { "family": "Harrison", "given": "Sarah M." } }, { "name": { "family": "Passaro", "given": "Davide" }, "orcid": "0000-0001-5368-4635" } ] }, "title": "3-Manifolds and VOA Characters", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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We would like to thank Kathrin Bringmann, John Cardy, Thomas Creutzig, Tobias Ekholm, Pavel Etingof, Dennis Gaitsgory, Angus Gruen, Antun Milas, Piotr Kucharski, Sunghyuk Park, Du Pei, Nicolai Reshetikhin, Vyacheslav Rychkov, Marko Stosic, Piotr Sulkowski and Alexander Zamolodchikov for helpful discussions. The work of M.C. and D. P. is supported by an NWO vidi Grant (Number 016.Vidi.189.182). The work of S.C. is supported by the US Department of Energy under Grant DE-SC0010008. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The work of B.F. has been funded within the framework of the HSE University Basic Research Program. The work of S.M.H. is supported by the National Science and Engineering Council of Canada and the Canada Research Chairs program. This research was initiated at the American Institute of Mathematics (AIM) as part of the SQuaRE meeting.

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", "abstract": "

By studying the properties of q-series \u1e90-invariants, we develop a dictionary between 3-manifolds and vertex algebras. In particular, we generalize previously known entries in this dictionary to Lie groups of higher rank, to 3-manifolds with toral boundaries, and to BPS partition functions with line operators. This provides a new physical realization of logarithmic vertex algebras in the framework of the 3d-3d correspondence and opens new avenues for their future study. For example, we illustrate how invoking a knot-quiver correspondence for \u1e90-invariants leads to many infinite families of new fermionic formulae for VOA characters.

", "date": "2024-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "405", "number": "2", "publisher": "Springer Science and Business Media LLC", "pagerange": "44", "issn": "0010-3616", "official_url": "https://authors.library.caltech.edu/records/64s8h-p1a44", "funders": { "items": [ { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek", "grant_number": "016.Vidi.189.182" }, { "agency": "U.S. Department of Energy, Office of High Energy Physics", "grant_number": "DE-SC0010008" }, { "agency": "U.S. Department of Energy, Office of High Energy Physics", "grant_number": "DE-SC0011632" }, { "grant_number": "DMS-1664227" }, { "agency": "HSE University Basic Research Program" }, { "agency": "National Science and Engineering Council of Canada" }, {} ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.1007/s00220-023-04889-1", "primary_object": { "basename": "s00220-023-04889-1.pdf", "url": "https://authors.library.caltech.edu/records/64s8h-p1a44/files/s00220-023-04889-1.pdf" }, "pub_year": "2024", "author_list": "Cheng, Miranda C. N.; Chun, Sungbong; et al." }, { "id": "https://authors.library.caltech.edu/records/bxqj9-jy145", "eprint_status": "archive", "datestamp": "2024-02-06 17:27:54", "lastmod": "2026-03-09 02:34:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Easo", "given": "Philip" }, "orcid": "0000-0002-5606-3727" }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "name": { "family": "Kurrek", "given": "Jana" }, "orcid": "0009-0002-8449-8899" } ] }, "title": "Double-exponential susceptibility growth in Dyson's hierarchical model with |x\u00a0\u2212\u00a0y|\u207b\u00b2 interaction", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "
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© 2024 Author(s). Published under an exclusive license by AIP Publishing.
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This work was carried out as part of Caltech’s Summer Undergraduate Research Fellowship (SURF) program 2022, during which J.K. was mentored by P.E. and T.H. During the research, J.K. was also supported by an NSERC USRA. We thank Louigi Addario-Berry and Johannes Bäumler for helpful comments on a draft.

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Philip Easo: Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (supporting); Writing – original draft (equal); Writing – review & editing (supporting). Tom Hutchcroft: Conceptualization (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (lead); Writing – original draft (supporting); Writing – review & editing (lead). Jana Kurrek: Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (supporting).

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Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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The authors have no conflicts to disclose.

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", "abstract": "

We study long-range percolation on the d-dimensional hierarchical lattice, in which each possible edge {x, y} is included independently at random with inclusion probability 1 − exp(−β \u2016x − y\u2016−d−α), where α > 0 is fixed and β ≥ 0 is a parameter. This model is known to have a phase transition at some βc < ∞ if and only if α < d. We study the model in the regime α ≥ d, in which βc = ∞, and prove that the susceptibility χ(β) (i.e., the expected volume of the cluster at the origin) satisfies χ(β) = β(d/1−d)^(−o(1)) as β↑∞ if α > d and χ(β) = e^(e^e(Θ(β) as β↑∞ if α = d. This resolves a problem raised by Georgakopoulos and Haslegrave (2020), who showed that χ(β) grows between exponentially and double-exponentially when α = d. Our results imply that analogous results hold for a number of related models including Dyson’s hierarchical Ising model, for which the double-exponential susceptibility growth we establish appears to be a new phenomenon even at the heuristic level.

", "date": "2024-02", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "65", "number": "2", "publisher": "AIP Publishing", "pagerange": "023301", "issn": "0022-2488", "official_url": "https://authors.library.caltech.edu/records/bxqj9-jy145", "funders": { "items": [ { "grant_number": "Summer Undergraduate Research Fellowship" }, {} ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/5.0147340", "primary_object": { "basename": "023301_1_5.0147340.pdf", "url": "https://authors.library.caltech.edu/records/bxqj9-jy145/files/023301_1_5.0147340.pdf" }, "pub_year": "2024", "author_list": "Easo, Philip; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/hd7e7-7mb42", "eprint_status": "archive", "datestamp": "2026-01-15 00:34:35", "lastmod": "2026-03-26 20:52:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "Luo", "given": "Sammy" }, "orcid": "0000-0002-4618-5472" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Tuan Pham", "given": "Huy" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "On random irregular subgraphs", "ispublished": "pub", "full_text_status": "public", "abstract": "

Let G be a d\u2010regular graph on n vertices. Frieze, Gould, Karo\u0144ski, and Pfender began the study of the following random spanning subgraph model H = H(G). Assign independently to each vertex v of G a uniform random number x (v) ∈ [0.1], and an edge (u, v) of G is an edge of H if and only if x(U) + x(v) ≥ 1. Addressing a problem of Alon and Wei, we prove that if d = o(n/(log n)¹²), then with high probability, for each nonnegative integer k ≤ d, there are (1 + o(1))n/(d + 1) vertices of degree k in H.

", "date": "2023-11-28", "date_type": "published", "publication": "Random Structures & Algorithms", "volume": "64", "number": "4", "publisher": "Wiley", "pagerange": "899-917", "issn": "1042-9832", "official_url": "https://authors.library.caltech.edu/records/hd7e7-7mb42", "funders": { "items": [ { "grant_number": "DMS\u20101800053" }, { "grant_number": "DMS\u20102154169" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.21204", "pub_year": "2023", "author_list": "Fox, Jacob; Luo, Sammy; et al." }, { "id": "https://authors.library.caltech.edu/records/xb8cx-v1483", "eprint_status": "archive", "datestamp": "2025-06-24 17:40:26", "lastmod": "2026-03-27 23:21:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kusuki-Yuya", "name": { "family": "Kusuki", "given": "Yuya" }, "orcid": "0000-0002-9784-0975" }, { "id": "Murciano-Sara", "name": { "family": "Murciano", "given": "Sara" }, "orcid": "0000-0002-1638-5692" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Pal-Sridip", "name": { "family": "Pal", "given": "Sridip" }, "orcid": "0000-0002-3813-9513" } ] }, "title": "Symmetry-resolved entanglement entropy, spectra & boundary conformal field theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Field Theories in Lower Dimensions; Global Symmetries", "note": "

\u20dd© 2025 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Article funded by SCOAP3.

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We thank Filiberto Ares, Pasquale Calabrese, Giuseppe Di Giulio, Michele Fossati, Kantaro Ohmori, Brandon Rayhaun, Shu-Heng Shao, Yuji Tachikawa, and Yijian Zou for useful discussions and comments on the draft. The work by YK, HO, and SP is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, YK is supported by the Brinson Prize Fellowship at Caltech. HO is supported in part by the Simons Investigator Award (MP-SIP-00005259), the World Premier International Research Center Initiative, MEXT, Japan, and JSPS Grants-in-Aid for Scientific Research 20K03965 and 23K03379. SP is supported in part by the Sherman Fairchild Postdoctoral Fellowship at Caltech. SM thanks support from Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics at Caltech. This work was performed in part at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611.

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", "abstract": "

We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a 1 + 1D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie group, G. We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE and its first correction, which explicitly depends on the irreducible representation under consideration and breaks the equipartition of entanglement. We present two distinct schemes to carry out these computations. The first relies on the evaluation of the charged moments of the reduced density matrix. This involves studying the action of the defect-line, that generates the symmetry, on the boundary states of the theory. This perspective also paves the way for discussing the infeasibility of studying symmetry resolution when an anomalous symmetry is present. The second scheme draws a parallel between the SREE and the partition function of an orbifold CFT. This approach allows for the direct computation of the SREE without the need to use charged moments. From this standpoint, the infeasibility of defining the symmetry-resolved EE for an anomalous symmetry arises from the obstruction to gauging. Finally, we derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group. We revisit a similar problem for CFT with compact Lie group, explicitly deriving an improved formula for U(1) resolved entanglement spectra. Using the Tauberian formalism, we can estimate the aforementioned EE spectra rigorously by proving an optimal lower and upper bound on the same. In the abelian case, we perform numerical checks on the bound and find perfect agreement.

", "date": "2023-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2023", "number": "11", "publisher": "Springer Science and Business Media LLC", "pagerange": "216", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/xb8cx-v1483", "funders": { "items": [ { "grant_number": "DE-SC0011632" }, { "grant_number": "-" }, { "grant_number": "MP-SIP-00005259" }, {}, { "grant_number": "20K03965" }, { "grant_number": "23K03379" }, {}, { "grant_number": "PHY-1607611" }, {} ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/jhep11(2023)216", "primary_object": { "basename": "JHEP11(2023)216.pdf", "url": "https://authors.library.caltech.edu/records/xb8cx-v1483/files/JHEP11(2023)216.pdf" }, "pub_year": "2023", "author_list": "Kusuki, Yuya; Murciano, Sara; et al." }, { "id": "https://authors.library.caltech.edu/records/ctg25-jhh53", "eprint_status": "archive", "datestamp": "2025-11-12 17:32:49", "lastmod": "2026-03-09 22:01:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Karch", "given": "Andreas" }, "orcid": "0000-0002-5725-2124" }, { "id": "Kusuki-Yuya", "name": { "family": "Kusuki", "given": "Yuya" }, "orcid": "0000-0002-9784-0975" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "name": { "family": "Sun", "given": "Hao-Yu" }, "orcid": "0000-0002-7211-3704" }, { "name": { "family": "Wang", "given": "Mianqi" }, "orcid": "0009-0005-9804-4849" } ] }, "title": "Universality of effective central charge in interface CFTs", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence; Gauge-Gravity Correspondence", "note": "

©The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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We thank Constantin Bachas, Horacio Casini, and Gonzalo Torroba for useful discussions. AK, HS, and MW are supported in part by the U.S. Department of Energy under Grant No. DE-SC0022021 and a grant from the Simons Foundation (Grant 651440, AK). The work by YK and HO is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, YK is supported by the Brinson Prize Fellowship at Caltech. HO is supported in part by the Simons Investigator Award (MP-SIP-00005259), the World Premier International Research Center Initiative, MEXT, Japan, and JSPS Grants-in-Aid for Scientific Research 20K03965 and 23K03379. This work was performed in part at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611.

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", "abstract": "

When an interface connects two CFTs, the entanglement entropy between the two CFTs is determined by a quantity called the effective central charge. The effective central charge does not have a simple form in terms of the central charges of the two CFTs, but intricately depends on the transmissive properties of the interface. In this article, we examine universal properties of the effective central charge. We first clarify how the effective central charge appears when considering general subsystems of the interface CFT. Then using this result and ideas used in the proof of the c-theorem, we provide a universal upper bound on the effective central charge. In past studies, the effective central charge was defined only in two dimensions. We propose an analogue of the effective central charge in general dimensions possessing similar universal properties as in two dimensions.

", "date": "2023-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2023", "number": "11", "publisher": "Springer Science and Business Media LLC", "pagerange": "126", "issn": "1029-8479", "official_url": "https://authors.library.caltech.edu/records/ctg25-jhh53", "funders": { "items": [ { "grant_number": "DE-SC0022021" }, { "grant_number": "651440" }, { "grant_number": "DE-SC0011632" }, { "grant_number": "-" }, { "grant_number": "MP-SIP-00005259" }, {}, { "grant_number": "20K03965" }, { "grant_number": "23K03379" }, { "grant_number": "PHY-1607611" }, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/jhep11(2023)126", "primary_object": { "basename": "JHEP11(2023)126.pdf", "url": "https://authors.library.caltech.edu/records/ctg25-jhh53/files/JHEP11(2023)126.pdf" }, "pub_year": "2023", "author_list": "Karch, Andreas; Kusuki, Yuya; et al." }, { "id": "https://authors.library.caltech.edu/records/h14k6-y1m12", "eprint_status": "archive", "datestamp": "2026-06-05 21:21:54", "lastmod": "2026-06-05 21:21:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei G." }, "orcid": "0000-0002-9486-1762" }, { "id": "Sheshmani-Artan", "name": { "family": "Sheshmani", "given": "Artan" }, "orcid": "0000-0003-3241-0576" }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" } } ] }, "title": "3-manifolds and Vafa\u2013Witten theory", "ispublished": "pub", "full_text_status": "public", "note": "

© 2024 International Press of Boston, Inc. All Rights Reserved.

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S. G. was supported by the National Science Foundation under Grant No. NSF DMS 1664227 and by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632.

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The research of A. S. was partially supported by the NSF DMS-1607871, NSF DMS-1306313, the Simons 38558, and HSE University Basic Research Program. A.S. would like to further sincerely thank the Center for Mathematical Sciences and Applications at Harvard University, and Harvard University Physics department, IMSA University of Miami, as well as the Laboratory of Mirror Symmetry in Higher School of Economics, Russian federation, for the great help and support.

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The work of S.-T. Y. was partially supported by the Simons Foundation grant 38558.

", "abstract": "

We initiate explicit computations of Vafa–Witten invariants of 3-manifolds, analogous to Floer groups in the context of Donaldson theory. In particular, we explicitly compute the Vafa–Witten invariants of 3-manifolds in a family of concrete examples relevant to various surgery operations (the Gluck twist, knot surgeries, log-transforms). We also describe the structural properties that are expected to hold for general 3-manifolds, including the modular group action, relation to Floer homology, infinite-dimensionality for an arbitrary 3-manifold, and the absence of instantons.

", "date": "2023-10-12", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "27", "number": "2", "publisher": "International Press of Boston", "pagerange": "523-561", "issn": "1095-0761", "official_url": "https://authors.library.caltech.edu/records/h14k6-y1m12", "funders": { "items": [ { "grant_number": "DMS-1664227" }, { "grant_number": "DE-SC0011632" }, { "grant_number": "DMS-1607871" }, { "grant_number": "DMS-130631" }, { "grant_number": "38558" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.4310/atmp.2023.v27.n2.a3", "pub_year": "2023", "author_list": "Gukov, Sergei G.; Sheshmani, Artan; et al." }, { "id": "https://authors.library.caltech.edu/records/vkhej-47e23", "eprint_status": "archive", "datestamp": "2026-01-15 00:35:35", "lastmod": "2026-03-26 20:52:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Nguyen", "given": "Phan-Minh" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "A rigorous framework for the mean field limit of multilayer neural networks", "ispublished": "pub", "full_text_status": "public", "abstract": "We develop a mathematically rigorous framework for multilayer neural networks in the mean field regime. As the network's widths increase, the network's learning trajectory is shown to be well captured by a meaningful and dynamically nonlinear limit (the\n mean field\n limit), which is characterized by a system of ODEs. Our framework applies to a broad range of network architectures, learning dynamics and network initializations. Central to the framework is the new idea of a\n neuronal embedding\n , which comprises of a non-evolving probability space that allows to embed neural networks of arbitrary widths. Using our framework, we prove several properties of large-width multilayer neural networks. Firstly we show that independent and identically distributed initializations cause strong degeneracy effects on the network's learning trajectory when the network's depth is at least four. Secondly we obtain several global convergence guarantees for feedforward multilayer networks under a number of different setups. These include two-layer and three-layer networks with independent and identically distributed initializations, and multilayer networks of arbitrary depths with a special type of correlated initializations that is motivated by the new concept of\n bidirectional diversity\n . Unlike previous works that rely on convexity, our results admit non-convex losses and hinge on a certain universal approximation property, which is a distinctive feature of infinite-width neural networks and it is shown to hold throughout the training process. Aside from being the first known results for global convergence of multilayer networks in the mean field regime, they demonstrate flexibility of our framework and incorporate several new ideas and insights that depart from the conventional convex optimization wisdom.", "date": "2023-10-09", "date_type": "published", "publication": "Mathematical Statistics and Learning", "volume": "6", "number": "3", "publisher": "European Mathematical Society - EMS - Publishing House GmbH", "pagerange": "201-357", "issn": "2520-2316", "official_url": "https://authors.library.caltech.edu/records/vkhej-47e23", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/msl/42", "pub_year": "2023", "author_list": "Nguyen, Phan-Minh and Pham, Huy Tuan" }, { "id": "https://authors.library.caltech.edu/records/xqysk-d3b17", "eprint_status": "archive", "datestamp": "2024-11-08 21:31:33", "lastmod": "2026-03-27 18:26:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" } ] }, "title": "Regularity in time along the coarse scale flow for the incompressible Euler equations", "ispublished": "pub", "full_text_status": "public", "note": "

© 2023 American Mathematical Society.

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The author thanks P. Constantin, C. De Lellis and V. Vicol for conversations related to Theorem 1.2 and for discussions regarding an earlier draft of the paper. The author also thanks S.-J. Oh for discussions that motivated the proof of
the endpoint regularity for v, as well as an anonymous referee for suggestions for improved presentation.

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This material is based upon work supported by the NSF under Awards DGE-1148900, DMS-1402370 and DMS-2055019.

", "abstract": "

One of the most remarkable features of known nonstationary solutions to the incompressible Euler equations is the phenomenon known as the Taylor hypothesis, which predicts that fine scale features of the flow are advected by the mean velocity. In this work, we develop an extensive theory of time regularity for Euler weak solutions in any dimension based on quantitative realizations of this idea.

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Our work provides the key estimates for showing that the particle trajectories of any Euler flow that is C^α in the spatial variables uniformly in time are of class C^(1/(1−α)) when 1/(1−α) is not an integer, whether or not the trajectories or solutions are unique. In particular, we prove the smoothness of trajectories in borderline spaces such as v ∈ C¹ or bounded vorticity in any dimension. An essential point is the existence and improved regularity of advective derivatives of high order.

", "date": "2023-10", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "376", "number": "10", "publisher": "American Mathematical Society (AMS)", "pagerange": "6927-6987", "issn": "0002-9947", "official_url": "https://authors.library.caltech.edu/records/xqysk-d3b17", "funders": { "items": [ { "grant_number": "DGE-1148900" }, { "grant_number": "DMS-1402370" }, { "grant_number": "DMS-2055019" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/8899", "pub_year": "2023", "author_list": "Isett, Philip" }, { "id": "https://authors.library.caltech.edu/records/ynbpx-c4633", "eprint_id": 122369, "eprint_status": "archive", "datestamp": "2023-08-22 21:08:23", "lastmod": "2026-03-08 03:40:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Lim-Jeck", "name": { "family": "Lim", "given": "Jeck" } } ] }, "title": "Sums of transcendental dilates", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "\u00a9 2023 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.\n\nResearch supported by NSF Award DMS-2054452 and partially supported by an NUS Overseas Graduate Scholarship.", "abstract": "We show that there is an absolute constant c > 0 such that |A + \u03bb \u2022 A| \u2a7e e^(c\u221alog|A)| |A| for any finite subset A of \u211d and any transcendental number \u03bb \u2208 \u211d. By a construction of Konyagin and \u0141aba, this is best possible up to the constant c.", "date": "2023-08-18", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "publisher": "London Mathematical Society", "id_number": "CaltechAUTHORS:20230725-500420000.2", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230725-500420000.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS\u20102054452" }, { "agency": "National University of Singapore" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/blms.12870", "pub_year": "2023", "author_list": "Conlon, David and Lim, Jeck" }, { "id": "https://authors.library.caltech.edu/records/ne4cd-2a765", "eprint_id": 122406, "eprint_status": "archive", "datestamp": "2023-08-22 17:41:39", "lastmod": "2026-03-07 04:13:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Fusion systems with 2-small components", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; General Mathematics", "note": "\u00a9 2023 American Mathematical Society. \n\nThis work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.", "abstract": "We show that there are no odd simple 2-fusion systems F in which the centralizer of some fully centralized involution contains a component C that is the 2-fusion system of a simple group K such that C is J-maximal or maximal and subintrinsic in C(F), as appropriate, and such that K is of Lie type over the field of order 2, but not Sp\u2099(2) or F\u2084(2); or K is one of many sporadic groups; or K is P\u03a9\u207a\u2088(3).", "date": "2023-08-17", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "publisher": "American Mathematical Society", "id_number": "CaltechAUTHORS:20230725-746861000.32", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230725-746861000.32", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/8797", "pub_year": "2023", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/z589a-6dp27", "eprint_id": 122337, "eprint_status": "archive", "datestamp": "2023-08-22 21:15:09", "lastmod": "2026-03-27 19:32:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Nenadov-Rajko", "name": { "family": "Nenadov", "given": "Rajko" } }, { "id": "Truji\u0107-Milo\u0161", "name": { "family": "Truji\u0107", "given": "Milo\u0161" }, "orcid": "0000-0002-7592-3630" } ] }, "title": "On the size-Ramsey number of grids", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; Computational Theory and Mathematics; Statistics and Probability; Theoretical Computer Science", "note": "\u00a9 The Author(s), 2023. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. \n\nDavid Conlon: Research supported by NSF Award DMS-2054452.\nMilo\u0161 Truji\u0107: Research supported by grant no. 200020 197138 of the Swiss National Science Foundation.\n\n

In Press - on-the-size-ramsey-number-of-grids.pdf

", "abstract": "We show that the size-Ramsey number of the \u221an \u00d7 \u221an grid graph is O(n^(5/4)), improving a previous bound of n^(3/2 + o(1)) by Clemens, Miralaei, Reding, Schacht, and Taraz.", "date": "2023-08-16", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "publisher": "Cambridge University Press", "id_number": "CaltechAUTHORS:20230717-55915200.33", "issn": "0963-5483", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230717-55915200.33", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200020 197138" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548323000147", "primary_object": { "basename": "on-the-size-ramsey-number-of-grids.pdf", "url": "https://authors.library.caltech.edu/records/z589a-6dp27/files/on-the-size-ramsey-number-of-grids.pdf" }, "pub_year": "2023", "author_list": "Conlon, David; Nenadov, Rajko; et al." }, { "id": "https://authors.library.caltech.edu/records/2d31p-cjn16", "eprint_status": "archive", "datestamp": "2026-01-15 00:34:23", "lastmod": "2026-03-26 20:52:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Park", "given": "Jinyoung" }, "orcid": "0000-0003-3962-5668" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "A proof of the Kahn\u2013Kalai conjecture", "ispublished": "pub", "full_text_status": "public", "abstract": "

Proving the \"expectation-threshold\" conjecture of Kahn and Kalai [Combin. Probab. Comput. 16 (2007), pp.\u00a0495\u2013502], we show that for any increasing property \n\n \n \n F\n \n \\mathcal {F}\n \n\n on a finite set \n\n \n X\n X\n \n\n, \n\\[\n\n \n \n \n p\n c\n \n (\n \n F\n \n )\n =\n O\n (\n q\n (\n \n F\n \n )\n log\n \u2061\n \u2113\n (\n \n F\n \n )\n )\n ,\n \n p_c(\\mathcal {F})=O(q(\\mathcal {F})\\log \\ell (\\mathcal {F})),\n \n\n\\]\n where \n\n \n \n \n p\n c\n \n (\n \n F\n \n )\n \n p_c(\\mathcal {F})\n \n\n and \n\n \n \n q\n (\n \n F\n \n )\n \n q(\\mathcal {F})\n \n\n are the threshold and \"expectation threshold\" of \n\n \n \n F\n \n \\mathcal {F}\n \n\n, and \n\n \n \n \u2113\n (\n \n F\n \n )\n \n \\ell (\\mathcal {F})\n \n\n is the maximum of \n\n \n 2\n 2\n \n\n and the maximum size of a minimal member of \n\n \n \n F\n \n \\mathcal {F}\n \n\n.

", "date": "2023-08-07", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "37", "number": "1", "publisher": "American Mathematical Society (AMS)", "pagerange": "235-243", "issn": "0894-0347", "official_url": "https://authors.library.caltech.edu/records/2d31p-cjn16", "funders": { "items": [ { "grant_number": "DMS-2153844" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/jams/1028", "pub_year": "2023", "author_list": "Park, Jinyoung and Pham, Huy" }, { "id": "https://authors.library.caltech.edu/records/xfvsq-pqf42", "eprint_status": "archive", "datestamp": "2026-01-15 00:35:40", "lastmod": "2026-03-26 20:52:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Jain", "given": "Vishesh" }, "orcid": "0000-0002-7275-3218" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Vuong", "given": "Thuy-Duong" }, "orcid": "0000-0003-0271-9687" } ] }, "title": "Dimension reduction for maximum matchings and the Fastest Mixing Markov Chain", "ispublished": "pub", "full_text_status": "public", "abstract": "Let\n \n \n G\n =\n (\n V\n ,\n E\n )\n \n \n be an undirected graph with maximum degree\n \n \u0394\n \n and vertex conductance\n \n \n \n \u03a8\n *\n \n \n (\n G\n )\n \n \n \n . We show that there exists a symmetric, stochastic matrix\n \n P\n \n , with off-diagonal entries supported on\n \n E\n \n , whose spectral gap\n \n \n \n \u03b3\n *\n \n \n (\n P\n )\n \n \n \n satisfies\n \n \n \n \n \n \u03a8\n *\n \n \n \n (\n G\n )\n \n 2\n \n /\n log\n \u0394\n \u2272\n \n \u03b3\n *\n \n \n (\n P\n )\n \n \u2272\n \n \u03a8\n *\n \n \n (\n G\n )\n \n .\n \n \n \n \n Our bound is optimal under the Small Set Expansion Hypothesis, and answers a question of Olesker-Taylor and Zanetti, who obtained such a result with\n \n \n log\n \u0394\n \n \n replaced by\n \n \n log\n |\n V\n |\n \n \n .\n \n \n In order to obtain our result, we show how to embed a negative-type semi-metric\n \n d\n \n defined on\n \n V\n \n into a negative-type semi-metric\n \n \n d\n \u2032\n \n \n supported in\n \n \n \u211d\n \n O\n (\n log\n \u0394\n )\n \n \n \n , such that the (fractional) matching number of the weighted graph\n \n \n (\n V\n ,\n E\n ,\n d\n )\n \n \n is approximately equal to that of\n \n \n (\n V\n ,\n E\n ,\n \n d\n \u2032\n \n )\n \n \n .", "date": "2023-07-18", "date_type": "published", "publication": "Comptes Rendus. Math\u00e9matique", "volume": "361", "number": "G5", "publisher": "MathDoc/Centre Mersenne", "pagerange": "869-876", "issn": "1631-073X", "official_url": "https://authors.library.caltech.edu/records/xfvsq-pqf42", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.5802/crmath.447", "pub_year": "2023", "author_list": "Jain, Vishesh; Pham, Huy; et al." }, { "id": "https://authors.library.caltech.edu/records/r3t9j-wjw61", "eprint_status": "archive", "datestamp": "2023-08-22 18:59:13", "lastmod": "2026-06-01 21:59:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Collins-Tristan-C", "name": { "family": "Collins", "given": "Tristan C." }, "orcid": "0000-0002-1127-0458" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Picard-Sebastien", "name": { "family": "Picard", "given": "Sebastien" }, "orcid": "0000-0001-9015-8976" }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" }, "orcid": "0000-0003-3394-2187" } ] }, "title": "Special Lagrangian Cycles and Calabi-Yau Transitions", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. \n\nT.C.C is supported in part by NSF CAREER Grant DMS-194452 and an Alfred P. Sloan Fellowship. \n\nS.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227.", "abstract": "We construct special Lagrangian 3-spheres in non-K\u00e4hler compact threefolds equipped with the Fu\u2013Li\u2013Yau geometry. These non-K\u00e4hler geometries emerge from topological transitions of compact Calabi-Yau threefolds. From this point of view, a conifold transition exchanges holomorphic 2-cycles for special Lagrangian 3-cycles.", "date": "2023-07", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "401", "number": "1", "publisher": "Springer", "pagerange": "769-802", "issn": "0010-3616", "official_url": "https://authors.library.caltech.edu/records/r3t9j-wjw61", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-194452" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-023-04655-3", "pub_year": "2023", "author_list": "Collins, Tristan C.; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/gvjnv-zpg10", "eprint_id": 121259, "eprint_status": "archive", "datestamp": "2023-08-22 20:47:02", "lastmod": "2026-03-09 23:57:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" } } ] }, "title": "Existence of infinitely many minimal hypersurfaces in closed manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Statistics, Probability and Uncertainty; Mathematics (miscellaneous)", "note": "\u00a9 2022 Annals of Mathematics. \n\nThe author was partially supported by NSF-DMS-1509027. \n\nI am very grateful to my advisor Fernando Cod\u00e1 Marques for his constant support, his generosity and inspiring discussions during the course of this work. I also thank him for pointing out references [47] and [5]. I would like to thank Andr\u00e9 Neves for many valuable conversations.", "abstract": "Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds on the methods developed by F. C. Marques and A. Neves.", "date": "2023-05", "date_type": "published", "publication": "Annals of Mathematics", "volume": "197", "number": "3", "publisher": "Annals of Mathematics", "pagerange": "859-895", "id_number": "CaltechAUTHORS:20230502-19603700.3", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230502-19603700.3", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1509027" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2023.197.3.1", "pub_year": "2023", "author_list": "Song, Antoine" }, { "id": "https://authors.library.caltech.edu/records/rcj0j-a9h90", "eprint_status": "archive", "datestamp": "2026-01-23 15:50:29", "lastmod": "2026-03-27 18:30:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-Jacob-S", "name": { "family": "Christiansen", "given": "Jacob S." }, "orcid": "0000-0002-3417-8574" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-Maxim", "name": { "family": "Zinchenko", "given": "Maxim" }, "orcid": "0000-0002-9559-0650" } ] }, "title": "Asymptotics of Chebyshev polynomials, V. residual polynomials", "ispublished": "pub", "full_text_status": "public", "keywords": "Residual polynomials; Szeg\u0151\u2013Widom asymptotics; Totik\u2013Widom upper bound", "note": "

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.

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\n
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We would like to thank M. Ismail, D. Lubinsky, and K. Schiefermayr for useful comments.

\n
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\n\n

J. S. Christiansen: Research supported by VR Grant 2018-03500 from the Swedish Research Council.
B. Simon: Research supported by NSF Grant DMS-1665526.
M. Zinchenko: Research supported in part by Simons Foundation Grant CGM-581256.

", "abstract": "

We study residual polynomials, R^((e))_(x\u2080,n), e ⊂ \u211d, x\u2080 ∈ \u211d\u2216e, which are the degree at most n polynomials with R(x\u2080) = 1 that minimize the sup sup norm on e. New are upper bounds on their norms (that are optimal in some cases) and Szeg\u0151–Widom asymptotics under fairly general circumstances. We also discuss several illuminating examples and some results in the complex case such as root asymptotics, a universal lower bound, and a new characterization of sets saturating this lower bound.

", "date": "2023-05", "date_type": "published", "publication": "Ramanujan Journal", "volume": "61", "number": "1", "publisher": "Springer", "pagerange": "251-278", "issn": "1382-4090", "official_url": "https://authors.library.caltech.edu/records/rcj0j-a9h90", "funders": { "items": [ { "agency": "Swedish Research Council", "grant_number": "2018-03500" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Simons Foundation", "grant_number": "CGM-581256" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s11139-021-00500-0", "pub_year": "2023", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/63x2m-2mh86", "eprint_id": 121520, "eprint_status": "archive", "datestamp": "2023-08-22 20:46:15", "lastmod": "2026-03-09 02:14:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Sharp inequalities for coherent states and their optimizers", "ispublished": "pub", "full_text_status": "public", "keywords": "functional inequalities; coherent states; inequalities for analytic functions; representations of Lie groups; isoperimetric inequality; General Mathematics; Statistical and Nonlinear Physics", "note": "\u00a9 2023 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. \n\nPartial support through the US National Science Foundation grant DMS-1954995, as well as through the Deutsche Forschungsgemeinschaft (German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868, is acknowledged.\n\n

Published - 10.1515_ans-2022-0050.pdf

", "abstract": "We are interested in sharp functional inequalities for the coherent state transform related to the Wehrl conjecture and its generalizations. This conjecture was settled by Lieb in the case of the Heisenberg group, Lieb and Solovej for SU(2), and Kulikov for SU(1,\u00a01) and the affine group. In this article, we give alternative proofs and characterize, for the first time, the optimizers in the general case. We also extend the recent Faber-Krahn-type inequality for Heisenberg coherent states, due to Nicola and Tilli, to the SU(2) and SU(1,\u00a01) cases. Finally, we prove a family of reverse H\u00f6lder inequalities for polynomials, conjectured by Bodmann.", "date": "2023-04-29", "date_type": "published", "publication": "Advanced Nonlinear Studies", "volume": "23", "publisher": "Walter de Gruyter GmbH", "pagerange": "Art. No. 20220050", "id_number": "CaltechAUTHORS:20230525-771644200.5", "issn": "2169-0375", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230525-771644200.5", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/ans-2022-0050", "primary_object": { "basename": "10.1515_ans-2022-0050.pdf", "url": "https://authors.library.caltech.edu/records/63x2m-2mh86/files/10.1515_ans-2022-0050.pdf" }, "pub_year": "2023", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/y9141-cjk45", "eprint_id": 121093, "eprint_status": "archive", "datestamp": "2023-08-22 20:36:28", "lastmod": "2026-03-09 02:34:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Sousi-Perla", "name": { "family": "Sousi", "given": "Perla" } } ] }, "title": "Logarithmic Corrections to Scaling in the Four-dimensional Uniform Spanning Tree", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "\u00a9 2023 Springer Nature.\n\nThis work was carried out while TH was a Herchel Smith Postdoctoral Research Fellow at the University of Cambridge and a Junior Research Fellow at Trinity College Cambridge. PS's research was supported by the Engineering and Physical Sciences Research Council: EP/R022615/1.", "abstract": "We compute the precise logarithmic corrections to mean-field scaling for various quantities describing the uniform spanning tree of the four-dimensional hypercubic lattice Z\u2074. We are particularly interested in the distribution of the past of the origin, that is, the finite piece of the tree that is separated from infinity by the origin. We prove that the probability that the past contains a path of length n is of order (log n)^(1/3)n\u207b\u00b9, that the probability that the past containsat least n vertices is of order (log n)^(1/6)n^(\u22121/2), and that the probability that the past reaches the boundary of the box [\u2212n, n]\u2074 is of order (log n)^(2/3+o(1))n\u207b\u00b2. An important part of our proof is to prove concentration estimates for the capacity of the four-dimensional loop-erased random walk which may be of independent interest. Our results imply that the Abelian sandpile model also exhibits non-trivial polylogarithmic corrections to mean-field scaling in four dimensions, although it remains open to compute the precise order of these corrections.", "date": "2023-04-27", "date_type": "published", "publication": "Communications in Mathematical Physics", "publisher": "Springer", "id_number": "CaltechAUTHORS:20230420-614686900.16", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230420-614686900.16", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/R022615/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-023-04686-w", "pub_year": "2023", "author_list": "Hutchcroft, Tom and Sousi, Perla" }, { "id": "https://authors.library.caltech.edu/records/7wfn5-g5k36", "eprint_id": 121573, "eprint_status": "archive", "datestamp": "2023-08-22 20:36:08", "lastmod": "2026-03-09 21:41:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Combe-No\u00e9mie", "name": { "family": "Combe", "given": "No\u00e9mie" }, "orcid": "0000-0002-8038-3683" }, { "id": "Manin-Yuri-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Moufang patterns and geometry of information", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "\u00a9 2023 International Press of Boston, Inc. \n\nN. C. Combe acknowledges support from the Minerva Fast track grant from the Max Planck Institute for Mathematics in the Sciences, in Leipzig. \n\nY. I. Manin acknowledges the continuing strong support from the Max Planck Institute for Mathematics in Bonn. \n\nM. Marcolli acknowledges support from NSF grants DMS-1707882 and DMS-2104330.", "abstract": "Technology of data collection and information transmission is based on various mathematical models of encoding. The words \"Geometry of information\" refer to such models, whereas the words \"Moufang patterns\" refer to various sophisticated symmetries appearing naturally in such models.\n\nIn this paper, we show that the symmetries of spaces of probability distributions, endowed with their canonical Riemannian metric of information geometry, have the structure of a commutative Moufang loop. We also show that the F-manifold structure on the space of probability distribution can be described in terms of differential \n-webs and Malcev algebras. We then present a new construction of (non-commutative) Moufang loops associated to almost-symplectic structures over finite fields, and use them to construct a new class of code loops with associated quantum error-correcting codes and networks of perfect tensors.", "date": "2023-04-03", "date_type": "published", "publication": "Pure and Applied Mathematics Quarterly", "volume": "19", "number": "1", "publisher": "International Press of Boston", "pagerange": "149-189", "id_number": "CaltechAUTHORS:20230526-436673000.11", "issn": "1558-8599", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230526-436673000.11", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Max Planck Institute for Mathematics in the Sciences" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "DMS-2104330" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/pamq.2023.v19.n1.a7", "pub_year": "2023", "author_list": "Combe, No\u00e9mie; Manin, Yuri I.; et al." }, { "id": "https://authors.library.caltech.edu/records/y0way-hwz71", "eprint_id": 121570, "eprint_status": "archive", "datestamp": "2023-08-20 16:46:55", "lastmod": "2026-03-09 02:40:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Mrini-Luke", "name": { "family": "Mrini", "given": "Luke" }, "orcid": "0000-0002-4672-013X" } ] }, "title": "Universal time-dependent Ginzburg-Landau theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2023 American Physical Society. \n\nWe are grateful to H. Liu for sharing with us his unpublished notes on the hydrodynamics of superconductors and for comments on the draft. L.M. would like to thank Caltech's Summer Undergraduate Research Fellowship program for their hospitality. This work was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, as well as by the Simons Investigator Award.\n\n

Published - PhysRevB.107.144514.pdf

", "abstract": "We study the hydrodynamics of superconductors within the framework of Schwinger-Keldysh effective field theory (EFT). We show that in the vicinity of the superconducting phase transition the most general leading-order EFT satisfying the local Kubo-Martin-Schwinger condition is described by a version of the time-dependent Ginzburg-Landau (TDGL) equations augmented with stochastic terms. This version of TDGL is applicable in the gapless regime independent of any microscopic details. Within this approach, it is possible to include systematically the effects of nonuniform temperature and heat conductivity, as well as explicit or spontaneous breaking of time reversal. We also introduce a thermal version of the Josephson relation and use it to construct an exotic hydrodynamics describing a phase of matter where heat can flow without dissipation.", "date": "2023-04-01", "date_type": "published", "publication": "Physical Review B", "volume": "107", "number": "14", "publisher": "American Physical Society", "pagerange": "Art. No. 144514", "id_number": "CaltechAUTHORS:20230526-436610000.5", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230526-436610000.5", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/physrevb.107.144514", "primary_object": { "basename": "PhysRevB.107.144514.pdf", "url": "https://authors.library.caltech.edu/records/y0way-hwz71/files/PhysRevB.107.144514.pdf" }, "pub_year": "2023", "author_list": "Kapustin, Anton and Mrini, Luke" }, { "id": "https://authors.library.caltech.edu/records/w07zy-4g815", "eprint_id": 119907, "eprint_status": "archive", "datestamp": "2023-08-22 20:30:07", "lastmod": "2026-03-18 04:01:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Vigneaux-Juan-Pablo", "name": { "family": "Vigneaux", "given": "Juan Pablo" }, "orcid": "0000-0003-4696-4537" } ] }, "title": "A characterization of generalized multinomial coefficients related to the entropic chain rule", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; Discrete Mathematics and Combinatorics; General Mathematics", "note": "\u00a9 2023 Springer Nature.", "abstract": "There is an asymptotic correspondence between the multiplicative relations among multinomial coefficients and the (additive) recursive property of Shannon entropy known as the chain rule. We show that both types of identities are manifestations of a unique algebraic construction: a 1-cocycle condition in information cohomology, an algebraic invariant of presheaves of modules on certain categories of observables. Depending on the coefficients, the 1-cocycles can be information measures (Shannon entropy, Tsallis \u03b1-entropy) or generalized (Fonten\u00e9-Ward) multinomial coefficients. In each case the 1-cocycle condition encodes a system of functional equations. We obtain in particular a combinatorial analogue of the \"fundamental equation of information theory\": a simple functional equation that uniquely characterizes the generalized binomial coefficients. The asymptotic correspondence mentioned above extends to any \u03b1-entropy and certain multinomial coefficients with compatible asymptotic behavior, shedding new light on the meaning of the chain rule and its deformations.", "date": "2023-04", "date_type": "published", "publication": "Aequationes Mathematicae", "volume": "97", "number": "2", "publisher": "Springer", "pagerange": "231-255", "id_number": "CaltechAUTHORS:20230308-468102500.13", "issn": "0001-9054", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230308-468102500.13", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00010-022-00938-7", "pub_year": "2023", "author_list": "Vigneaux, Juan Pablo" }, { "id": "https://authors.library.caltech.edu/records/br2f4-g6b80", "eprint_id": 120730, "eprint_status": "archive", "datestamp": "2023-08-22 20:23:18", "lastmod": "2026-03-09 02:21:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Costantino-Francesco", "name": { "family": "Costantino", "given": "Francesco" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-Pavel", "name": { "family": "Putrov", "given": "Pavel" }, "orcid": "0000-0002-7207-4688" } ] }, "title": "Non-Semisimple TQFT's and BPS q-Series", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology; Mathematical Physics; Analysis", "note": "The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License. \n\nContribution to the Special Issue on Enumerative and Gauge-Theoretic Invariants in honor of Lothar G\u00f6ttsche on the occasion of his 60th birthday. The full collection is available at\nhttps://www.emis.de/journals/SIGMA/Gottsche.html \n\nWe would like to thank Francesco Benini, Christian Copetti, Boris Feigin, Azat Gainutdinov, Hiraku Nakajima, Sunghyuk Park, Du Pei, and Nicolai Reshetikhin for helpful discussions and the anonymous Referees for the valuable suggestions on the improvement of the paper. We also would like to thank the organizers of the 2019 conference \"New Developments in Quantum Topology\" at UC Berkeley, where the discussion on the relation between the two invariants was initiated. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award no. DE-SC0011632, and by the National Science Foundation under Grant no. NSF DMS 1664227. The work of F.C. was supported by the French Agence Nationale de la Recherche via the ANR Project QUANTACT and by the Labex CIMI ANR-11-LABX-0040.\n\n

Published - sigma23-010.pdf

", "abstract": "We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic q. Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows to study (and perhaps even to formulate) q-series invariants labeled by spin\u1d9c structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.", "date": "2023-03-15", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "19", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 10", "id_number": "CaltechAUTHORS:20230411-695015900.13", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230411-695015900.13", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "Agence Nationale de la Recherche (ANR)", "grant_number": "ANR-11-LABX-0040" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.3842/sigma.2023.010", "primary_object": { "basename": "sigma23-010.pdf", "url": "https://authors.library.caltech.edu/records/br2f4-g6b80/files/sigma23-010.pdf" }, "pub_year": "2023", "author_list": "Costantino, Francesco; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/em9gs-e7c18", "eprint_id": 120724, "eprint_status": "archive", "datestamp": "2023-08-22 20:15:30", "lastmod": "2026-03-09 02:35:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Michta-Emmanuel", "name": { "family": "Michta", "given": "Emmanuel" }, "orcid": "0000-0001-7222-0422" }, { "id": "Slade-Gordon", "name": { "family": "Slade", "given": "Gordon" }, "orcid": "0000-0001-9389-9497" } ] }, "title": "High-dimensional near-critical percolation and the torus plateau", "ispublished": "pub", "full_text_status": "public", "keywords": "Statistics, Probability and Uncertainty; Statistics and Probability", "note": "\u00a9 2023 Institute of Mathematical Statistics. \n\nThis work was carried out primarily while TH was a Senior Research Associate at the University of Cambridge, during which time he was supported by ERC starting grant 804166 (SPRS). \n\nThe work of EM and GS was supported in part by NSERC of Canada.", "abstract": "We consider percolation on Z\u1d48 and on the d-dimensional discrete torus, in dimensions d \u2265 11 for the nearest-neighbour model and in dimensions d > 6 for spread-out models. For Z\u1d48 we employ a wide range of techniques and previous results to prove that there exist positive constants c and C such that the slightly subcritical two-point function and one-arm probabilities satisfy \nP_(p_c \u2212 \u03b5)(0 \u2194 x) \u2264 C/(\u2225x\u2225\u1d48\u207b\u00b2)e^(\u2212c\u03b5^(1/2)\u2225x\u2225), \n(c/r\u00b2)e^(\u2212C\u03b5^((1/2)r)) \u2264 P_(pc\u2212\u03b5)(0 \u2194 \u2202[\u2212r,r]\u1d48) \u2264 C/(r\u00b2)e^(\u2212c\u03b5(1/2)r). \n\nUsing this, we prove that throughout the critical window the torus two-point function has a \"plateau,\" meaning that it decays for small x as \u2225x\u2225\u207b\u207d\u1d48\u207b\u00b2\u207e but for large x is essentially constant and of order V^(\u22122/3) where V is the volume of the torus. The plateau for the two-point function leads immediately to a proof of the torus triangle condition, which is known to have many implications for the critical behaviour on the torus, and also leads to a proof that the critical values on the torus and on Z\u1d48 are separated by a multiple of V^(\u22121/3). The torus triangle condition and the size of the separation of critical points have been proved previously, but our proofs are different and are direct consequences of the bound on the Z\u1d48 two-point function. In particular, we use results derived from the lace expansion on Z\u1d48, but in contrast to previous work on high-dimensional torus percolation, we do not need or use a separate torus lace expansion.", "date": "2023-03", "date_type": "published", "publication": "Annals of Probability", "volume": "51", "number": "2", "publisher": "Institute of Mathematical Statistics", "pagerange": "580-625", "id_number": "CaltechAUTHORS:20230411-695015900.4", "issn": "0091-1798", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230411-695015900.4", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "804166" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/22-aop1608", "pub_year": "2023", "author_list": "Hutchcroft, Tom; Michta, Emmanuel; et al." }, { "id": "https://authors.library.caltech.edu/records/q1z9c-5zw82", "eprint_id": 121474, "eprint_status": "archive", "datestamp": "2023-08-22 20:17:07", "lastmod": "2026-03-09 21:52:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" }, "orcid": "0000-0002-5287-4258" }, { "id": "Zhang-Xingru", "name": { "family": "Zhang", "given": "Xingru" } } ] }, "title": "Characterizing slopes for torus knots, II", "ispublished": "pub", "full_text_status": "public", "keywords": "Algebra and Number Theory", "note": "\u00a9 2023 World Scientific Publishing. \n\nThe first author was partially supported by NSF grant number DMS-1811900.", "abstract": "A slope p/q is called a characterizing slope for a given knot K\u2080 \u2282 S\u00b3 if whenever the p/q-surgery on a knot K \u2282 S\u00b3 is homeomorphic to the p/q-surgery on K\u2080 via an orientation preserving homeomorphism, then K = K\u2080. In a previous paper, we showed that, outside a certain finite set of slopes, only the negative integers could possibly be non-characterizing slopes for the torus knot T\u2085,\u2082. More explicitly besides all negative integer slopes there are 247 slopes which were unknown to be characterizing for T\u2085,\u2082, including 89 nontrivial L-space slopes. Applying recent work of Baldwin\u2013Hu\u2013Sivek, we improve our result by showing that a nontrivial slope p/q is a characterizing slope for T\u2085,\u2082 if p/q > \u22121 and p/q \u2209 {0, 1, \u00b11/2, \u00b11/3}. In particular every nontrivial L-space slope of T\u2085,\u2082 is characterizing for T\u2085,\u2082. More explicitly this work yields 121 new characterizing slopes for T\u2085,\u2082. Another interesting consequence of this work is that if a nontrivial p/q-surgery on a non-torus knot in S\u00b3 yields a manifold of finite fundamental group, then |p| > 9.", "date": "2023-03", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "32", "number": "3", "publisher": "World Scientific Publishing Co.", "pagerange": "Art. No. 2350023", "id_number": "CaltechAUTHORS:20230522-906181000.6", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230522-906181000.6", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1811900" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/s0218216523500232", "pub_year": "2023", "author_list": "Ni, Yi and Zhang, Xingru" }, { "id": "https://authors.library.caltech.edu/records/rs79n-nfc80", "eprint_id": 118915, "eprint_status": "archive", "datestamp": "2023-08-22 19:06:59", "lastmod": "2026-03-27 19:56:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert" }, "orcid": "0000-0001-7973-4688" }, { "id": "Sukochev-Fedor", "name": { "family": "Sukochev", "given": "Fedor" }, "orcid": "0000-0002-6063-3163" }, { "id": "Zanin-Dmitriy", "name": { "family": "Zanin", "given": "Dmitriy" } } ] }, "title": "Asymptotics of singular values for quantum derivatives", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; General Mathematics", "note": "This work was partially supported through U.S. National Science Foundation grant DMS-1954995 and through the German Research Foundation grant EXC-2111-390814868 (R.L.F.).", "abstract": "We obtain Weyl type asymptotics for the quantised derivative \\dj \u0192 of a function \u0192 from the homgeneous Sobolev space \u1e86^(1)_(d) on (\u211d\u1d48). The asymptotic coefficient ||\u2207\u0192||_[L_(d)(\u211d\u1d48)] is equivalent to the norm of \\dj \u0192 in the principal ideal L_(d,\u221e), thus, providing a non-asymptotic, uniform bound on the spectrum of \\dj \u0192. Our methods are based on the C*-algebraic notion of the principal symbol mapping on \u211d\u1d48, as developed recently by the last two authors and collaborators.", "date": "2023-03", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "376", "number": "3", "publisher": "American Mathematical Society", "pagerange": "2047-2088", "id_number": "CaltechAUTHORS:20230124-11595100.7", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230124-11595100.7", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/8827", "pub_year": "2023", "author_list": "Frank, Rupert; Sukochev, Fedor; et al." }, { "id": "https://authors.library.caltech.edu/records/0vgg5-qww26", "eprint_status": "archive", "datestamp": "2025-09-08 15:39:14", "lastmod": "2026-03-08 18:14:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "name": { "family": "Fox", "given": "Jacob" } }, { "name": { "family": "Wigderson", "given": "Yuval" }, "orcid": "0000-0001-5909-9250" } ] }, "title": "Off-diagonal book Ramsey numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey theory; book graphs; Ramsey goodness", "note": "

© The Author(s), 2023. Published by Cambridge University Press. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

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We are grateful to the anonymous referee for helpful comments which improved the presentation of this paper.

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Research supported by NSF Award DMS-2054452.
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Research supported by a Packard Fellowship and by NSF Awards DMS-1800053 and DMS-2154169.
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Research supported by NSF GRFP Grant DGE-1656518, NSF-BSF Grant 20196, and by ERC Consolidator Grants 863438 and 101044123.
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", "abstract": "

The book graph B(k)_n consists of n copies of K_(k+1) joined along a common K_k. In the prequel to this paper, we studied the diagonal Ramsey number r(B(k)_n, B(k)_n. Here we consider the natural off-diagonal variant r(B(k)_cn, B(k)_n for fixed c ∈ (0,1]. In this more general setting, we show that an interesting dichotomy emerges: for very small c, a simple k-partite construction dictates the Ramsey function and all nearly-extremal colourings are close to being k-partite, while, for c bounded away from 0, random colourings of an appropriate density are asymptotically optimal and all nearly-extremal colourings are quasirandom. Our investigations also open up a range of questions about what happens for intermediate values of c.

", "date": "2023-03", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "32", "number": "3", "publisher": "Cambridge University Press (CUP)", "pagerange": "516-545", "issn": "0963-5483", "official_url": "https://authors.library.caltech.edu/records/0vgg5-qww26", "funders": { "items": [ { "grant_number": "DMS-2054452" }, {}, { "grant_number": "DMS-1800053" }, { "grant_number": "DMS-2154169" }, { "grant_number": "DGE-1656518" }, { "grant_number": "20196" }, { "grant_number": "863438" }, { "grant_number": "101044123" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548322000360", "primary_object": { "basename": "off-diagonal-book-ramsey-numbers.pdf", "url": "https://authors.library.caltech.edu/records/0vgg5-qww26/files/off-diagonal-book-ramsey-numbers.pdf" }, "pub_year": "2023", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/6s3f4-hd670", "eprint_id": 122497, "eprint_status": "archive", "datestamp": "2023-08-22 19:04:53", "lastmod": "2026-04-16 01:40:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Acharya-Rajeev", "name": { "family": "Acharya", "given": "Rajeev" } }, { "name": { "family": "Aleiner", "given": "Igor" }, "orcid": "0000-0002-9096-254X" }, { "name": { "family": "Allen", "given": "Richard M." } }, { "name": { "family": "Andersen", "given": "Trond I." } }, { "name": { "family": "Ansmann", "given": "Markus" }, "orcid": "0000-0001-8765-5621" }, { "name": { "family": "Arute", "given": "Frank" } }, { "name": { "family": "Arya", "given": "Kunal" }, "orcid": "0000-0002-6486-7100" }, { "name": { "family": "Asfaw", "given": "Abraham" } }, { "name": { "family": "Atalaya", "given": "Juan" }, "orcid": "0000-0003-3055-2730" }, { "name": { "family": "Babbush", "given": "Ryan" }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Bacon", "given": "Dave" } }, { "name": { "family": "Bardin", "given": "Joseph C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Basso", "given": "Joao" }, "orcid": "0000-0001-5547-691X" }, { "name": { "family": "Bengtsson", "given": "Andreas" }, "orcid": "0000-0001-5264-4025" }, { "name": { "family": "Boixo", "given": "Sergio" }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Bortoli", "given": "Gina" } }, { "name": { "family": "Bourassa", "given": "Alexandre" }, "orcid": "0000-0002-8517-7475" }, { "name": { "family": "Bovaird", "given": "Jenna" } }, { "name": { "family": "Brill", "given": "Leon" } }, { "name": { "family": "Broughton", "given": "Michael" } }, { "name": { "family": "Buckley", "given": "Bob B." }, "orcid": "0000-0001-5139-7931" }, { "name": { "family": "Buell", "given": "David A." } }, { "name": { "family": "Burger", "given": "Tim" } }, { "name": { "family": "Burkett", "given": "Brian" }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Bushnell", "given": "Nicholas" }, "orcid": "0000-0001-7445-1654" }, { "name": { "family": "Chen", "given": "Yu" } }, { "name": { "family": "Chen", "given": "Zijun" } }, { "name": { "family": "Chiaro", "given": "Benjamin" }, "orcid": "0000-0002-2913-2790" }, { "name": { "family": "Cogan", "given": "Josh" } }, { "name": { "family": "Collins", "given": "Roberto" }, "orcid": "0000-0002-6164-0007" }, { "name": { "family": "Conner", "given": "Paul" } }, { "name": { "family": "Courtney", "given": "William" } }, { "name": { "family": "Crook", "given": "Alexander L." } }, { "name": { "family": "Curtin", "given": "Ben" } }, { "name": { "family": "Debroy", "given": "Dripto M." } }, { "name": { "family": "Del Toro Barba", "given": "Alexander" }, "orcid": "0000-0003-0869-5110" }, { "name": { "family": "Demura", "given": "Sean" }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Dunsworth", "given": "Andrew" } }, { "name": { "family": "Eppens", "given": "Daniel" }, "orcid": "0000-0001-7134-5733" }, { "name": { "family": "Erickson", "given": "Catherine" } }, { "name": { "family": "Faoro", "given": "Lara" } }, { "name": { "family": "Farhi", "given": "Edward" } }, { "name": { "family": "Fatemi", "given": "Reza" }, "orcid": "0000-0001-9081-2608" }, { "name": { "family": "Flores Burgos", "given": "Leslie" } }, { "name": { "family": "Forati", "given": "Ebrahim" } }, { "name": { "family": "Fowler", "given": "Austin G." }, "orcid": "0000-0002-9048-2896" }, { "name": { "family": "Foxen", "given": "Brooks" }, "orcid": "0000-0002-3732-168X" }, { "name": { "family": "Giang", "given": "William" } }, { "name": { "family": "Gidney", "given": "Craig" } }, { "name": { "family": "Gilboa", "given": "Dar" } }, { "name": { "family": "Giustina", "given": "Marissa" } }, { "name": { "family": "Grajales Dau", "given": "Alejandro" } }, { "name": { "family": "Gross", "given": "Jonathan A." }, "orcid": "0000-0001-7049-6206" }, { "name": { "family": "Habegger", "given": "Steve" }, "orcid": "0000-0001-9867-2371" }, { "name": { "family": "Hamilton", "given": "Michael C." } }, { "name": { "family": "Harrigan", "given": "Matthew P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "Sean D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Higgott", "given": "Oscar" } }, { "name": { "family": "Hilton", "given": "Jeremy" } }, { "name": { "family": "Hoffmann", "given": "Markus" }, "orcid": "0000-0002-7051-5558" }, { "name": { "family": "Hong", "given": "Sabrina" } }, { "name": { "family": "Huang", "given": "Trent" } }, { "name": { "family": "Huff", "given": "Ashley" } }, { "name": { "family": "Huggins", "given": "William J." }, "orcid": "0000-0003-2735-1380" }, { "name": { "family": "Ioffe", "given": "Lev B." } }, { "name": { "family": "Isakov", "given": "Sergei V." } }, { "name": { "family": "Iveland", "given": "Justin" } }, { "name": { "family": "Jeffrey", "given": "Evan" } }, { "name": { "family": "Jiang", "given": "Zhang" }, "orcid": "0000-0003-0435-655X" }, { "name": { "family": "Jones", "given": "Cody" } }, { "name": { "family": "Juhas", "given": "Pavol" }, "orcid": "0000-0001-8751-4458" }, { "name": { "family": "Kafri", "given": "Dvir" }, "orcid": "0000-0001-9160-5176" }, { "name": { "family": "Kechedzhi", "given": "Kostyantyn" }, "orcid": "0000-0002-0136-1428" }, { "name": { "family": "Kelly", "given": "Julian" }, "orcid": "0000-0002-2596-2121" }, { "name": { "family": "Khattar", "given": "Tanuj" } }, { "name": { "family": "Khezri", "given": "Mostafa" }, "orcid": "0000-0002-3638-6967" }, { "name": { "family": "Kieferov\u00e1", "given": "M\u00e1ria" }, "orcid": "0000-0002-0749-8126" }, { "name": { "family": "Kim", "given": "Seon" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Klimov", "given": "Paul V." }, "orcid": "0000-0002-9481-4456" }, { "name": { "family": "Klots", "given": "Andrey R." } }, { "name": { "family": "Korotkov", "given": "Alexander N." } }, { "name": { "family": "Kostritsa", "given": "Fedor" } }, { "name": { "family": "Kreikebaum", "given": "John Mark" }, "orcid": "0000-0002-0253-4183" }, { "name": { "family": "Landhuis", "given": "David" }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "Pavel" }, "orcid": "0000-0002-5305-3312" }, { "name": { "family": "Lau", "given": "Kim-Ming" } }, { "name": { "family": "Laws", "given": "Lily" } }, { "name": { "family": "Lee", "given": "Joonho" } }, { "name": { "family": "Lee", "given": "Kenny" } }, { "name": { "family": "Lester", "given": "Brian J." }, "orcid": "0000-0002-4297-2508" }, { "name": { "family": "Lill", "given": "Alexander" } }, { "name": { "family": "Liu", "given": "Wayne" } }, { "name": { "family": "Locharla", "given": "Aditya" }, "orcid": "0009-0004-5055-9504" }, { "name": { "family": "Lucero", "given": "Erik" }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Malone", "given": "Fionn D." }, "orcid": "0000-0001-9239-0162" }, { "name": { "family": "Marshall", "given": "Jeffrey" }, "orcid": "0000-0002-5011-1281" }, { "name": { "family": "Martin", "given": "Orion" }, "orcid": "0000-0002-9576-573X" }, { "name": { "family": "McClean", "given": "Jarrod R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McCourt", "given": "Trevor" }, "orcid": "0000-0002-5807-2600" }, { "name": { "family": "McEwen", "given": "Matt" }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Megrant", "given": "Anthony" }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Meurer Costa", "given": "Bernardo" } }, { "name": { "family": "Mi", "given": "Xiao" }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Miao", "given": "Kevin C." }, "orcid": "0000-0001-9151-3028" }, { "name": { "family": "Mohseni", "given": "Masoud" }, "orcid": "0000-0003-4065-9400" }, { "name": { "family": "Montazeri", "given": "Shirin" }, "orcid": "0000-0002-7124-4585" }, { "name": { "family": "Morvan", "given": "Alexis" }, "orcid": "0000-0002-9515-6184" }, { "name": { "family": "Mount", "given": "Emily" } }, { "name": { "family": "Mruczkiewicz", "given": "Wojciech" }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Naaman", "given": "Ofer" }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "Matthew" }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Neill", "given": "Charles" }, "orcid": "0000-0001-8509-9836" }, { "name": { "family": "Nersisyan", "given": "Ani" } }, { "name": { "family": "Neven", "given": "Hartmut" }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Newman", "given": "Michael" } }, { "name": { "family": "Ng", "given": "Jiun How" }, "orcid": "0000-0002-7246-6761" }, { "name": { "family": "Nguyen", "given": "Anthony" }, "orcid": "0000-0001-8076-1501" }, { "name": { "family": "Nguyen", "given": "Murray" } }, { "name": { "family": "Niu", "given": "Murphy Yuezhen" } }, { "name": { "family": "O'Brien", "given": "Thomas E." }, "orcid": "0000-0002-8406-6626" }, { "name": { "family": "Opremcak", "given": "Alex" } }, { "name": { "family": "Platt", "given": "John" }, "orcid": "0000-0002-5652-5303" }, { "name": { "family": "Petukhov", "given": "Andre" } }, { "name": { "family": "Potter", "given": "Rebecca" } }, { "name": { "family": "Pryadko", "given": "Leonid P." }, "orcid": "0000-0002-4990-0259" }, { "name": { "family": "Quintana", "given": "Chris" }, "orcid": "0000-0003-4408-8318" }, { "name": { "family": "Roushan", "given": "Pedram" }, "orcid": "0000-0003-1917-3879" }, { "name": { "family": "Rubin", "given": "Nicholas C." }, "orcid": "0000-0003-3963-1830" }, { "name": { "family": "Saei", "given": "Negar" } }, { "name": { "family": "Sank", "given": "Daniel" }, "orcid": "0000-0001-8188-364X" }, { "name": { "family": "Sankaragomathi", "given": "Kannan" }, "orcid": "0000-0001-8930-7081" }, { "name": { "family": "Satzinger", "given": "Kevin J." }, "orcid": "0000-0001-5865-0813" }, { "name": { "family": "Schurkus", "given": "Henry F." }, "orcid": "0000-0002-3210-5929" }, { "name": { "family": "Schuster", "given": "Christopher" } }, { "name": { "family": "Shearn", "given": "Michael J." } }, { "name": { "family": "Shorter", "given": "Aaron" } }, { "name": { "family": "Shvarts", "given": "Vladimir" } }, { "name": { "family": "Skruzny", "given": "Jindra" } }, { "name": { "family": "Smelyanskiy", "given": "Vadim" }, "orcid": "0000-0002-3000-6732" }, { "name": { "family": "Smith", "given": "W. Clarke" } }, { "name": { "family": "Sterling", "given": "George" }, "orcid": "0000-0003-4751-3244" }, { "name": { "family": "Strain", "given": "Doug" } }, { "name": { "family": "Szalay", "given": "Marco" }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Torres", "given": "Alfredo" } }, { "name": { "family": "Vidal", "given": "Guifre" } }, { "name": { "family": "Villalonga", "given": "Benjamin" }, "orcid": "0000-0002-3299-7226" }, { "name": { "family": "Vollgraff Heidweiller", "given": "Catherine" }, "orcid": "0000-0002-6513-9885" }, { "name": { "family": "White", "given": "Theodore" } }, { "name": { "family": "Xing", "given": "Cheng" } }, { "name": { "family": "Yao", "given": "Z. Jamie" } }, { "name": { "family": "Yeh", "given": "Ping" }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "Juhwan" } }, { "name": { "family": "Young", "given": "Grayson" } }, { "name": { "family": "Zalcman", "given": "Adam" }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Zhang", "given": "Yaxing" } }, { "name": { "family": "Zhu", "given": "Ningfeng" }, "orcid": "0000-0002-3037-2003" } ] }, "title": "Suppressing quantum errors by scaling a surface code logical qubit", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \n\nWe are grateful to S.\u2009Brin, S.\u2009Pichai, R.\u2009Porat, J.\u2009Dean, E.\u2009Collins and J.\u2009Yagnik for their executive sponsorship of the Google Quantum AI team, and for their continued engagement and support. A portion of this work was performed in the University of California, Santa Barbara Nanofabrication Facility, an open access laboratory. J.M. acknowledges support from the National Aeronautics and Space Administration (NASA) Ames Research Center (NASA-Google SAA 403512), NASA Advanced Supercomputing Division for access to NASA high-performance computing systems, and NASA Academic Mission Services (NNA16BD14C). D.B. is a CIFAR Associate Fellow in the Quantum Information Science Program. \n\nData availability: The data that support the findings of this study are available at https://doi.org/10.5281/zenodo.6804040. \n\nContributions: The Google Quantum AI team conceived and designed the experiment. The theory and experimental teams at Google Quantum AI developed the data analysis, modelling and metrological tools that enabled the experiment, built the system, performed the calibrations and collected the data. The modelling was carried out jointly with collaborators outside Google Quantum AI. All authors wrote and revised the manuscript and the Supplementary Information. \n\nThe authors declare no competing interests.\n\n

Published - s41586-022-05434-1.pdf

Supplemental Material - 41586_2022_5434_MOESM1_ESM.pdf

", "abstract": "Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914\u2009\u00b1\u20090.016)% compared to (3.028\u2009\u00b1\u20090.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7\u2009\u00d7\u200910\u207b\u2076 logical error per cycle floor set by a single high-energy event (1.6\u2009\u00d7\u200910\u207b\u2077 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.", "date": "2023-02-23", "date_type": "published", "publication": "Nature", "volume": "614", "number": "7949", "publisher": "Nature Publishing Group", "pagerange": "676-681", "id_number": "CaltechAUTHORS:20230725-857426000.73", "issn": "0028-0836", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230725-857426000.73", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NASA-Google", "grant_number": "SAA 403512" }, { "agency": "NASA", "grant_number": "NNA16BD14C" }, { "agency": "Canadian Institute for Advanced Research (CIFAR)" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "corp_creators": { "items": [ "Google Quantum AI" ] }, "doi": "10.1038/s41586-022-05434-1", "pmcid": "PMC9946823", "primary_object": { "basename": "41586_2022_5434_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/6s3f4-hd670/files/41586_2022_5434_MOESM1_ESM.pdf" }, "related_objects": [ { "basename": "s41586-022-05434-1.pdf", "url": "https://authors.library.caltech.edu/records/6s3f4-hd670/files/s41586-022-05434-1.pdf" } ], "pub_year": "2023", "author_list": "Acharya, Rajeev; Aleiner, Igor; et al." }, { "id": "https://authors.library.caltech.edu/records/a7hr1-srd50", "eprint_id": 118647, "eprint_status": "archive", "datestamp": "2023-08-22 18:28:48", "lastmod": "2026-03-27 18:07:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Kent-Alexander", "name": { "family": "Kent", "given": "Alexander" } }, { "id": "Nizi\u0107-Nikolac-Petar", "name": { "family": "Nizi\u0107-Nikolac", "given": "Petar" } } ] }, "title": "The bunkbed conjecture holds in the p \u2191 1 limit", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; Computational Theory and Mathematics; Statistics and Probability; Theoretical Computer Science", "note": "This paper is the result of an undergraduate summer research project at the University of Cambridge in the summer of 2020, where PNN and AK were mentored by TH. PNN was supported jointly by a Trinity College Summer Studentship (F. J. Woods Fund) and a CMS Summer Studentship, AK was supported by a CMS Summer Research in Mathematics bursary, and TH was supported in part by ERC starting grant 804166 (SPRS). We thank Piet Lammers for helpful comments on a draft.", "abstract": "Let G = (V, E) be a countable graph. The Bunkbed graph of G is the product graph G x K\u2082, which has vertex set V x {0,1} with \"horizontal\" edges inherited from G and additional \"vertical\" edges connecting (w,0) and (w,1) for each w \u03f5 V. Kasteleyn's Bunkbed conjecture states that for each u, v \u03f5 V and p \u03f5 [0,1], the vertex (u,0) is at least as likely to be connected to (v,0) as to (v,1) under Bernoulli-p bond percolation on the bunkbed graph. We prove that the conjecture holds in the p \u2191 1 limit in the sense that for each finite graph G there exists \u03b5(G) > 0 such that the bunkbed conjecture holds for p \u2a7e 1 - \u03b5(G).", "date": "2023-02-07", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "publisher": "Cambridge University Press", "pagerange": "1-7", "id_number": "CaltechAUTHORS:20230103-818063100.57", "issn": "0963-5483", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230103-818063100.57", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Trinity College" }, { "agency": "European Research Council (ERC)", "grant_number": "804166" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s096354832200027x", "pub_year": "2023", "author_list": "Hutchcroft, Tom; Kent, Alexander; et al." }, { "id": "https://authors.library.caltech.edu/records/95j8r-pwq77", "eprint_id": 122379, "eprint_status": "archive", "datestamp": "2023-08-22 18:47:31", "lastmod": "2026-03-09 02:34:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Transience and anchored isoperimetric dimension of supercritical percolation clusters", "ispublished": "pub", "full_text_status": "public", "keywords": "Statistics, Probability and Uncertainty; Statistics and Probability", "note": "\u00a9 2023 Institute of Mathematical Statistics. Rights: Creative Commons Attribution 4.0 International License. \n\nWe thank Russ Lyons his careful reading and helpful comments on an earlier version of this manuscript and thank Philip Easo for catching several typos.\n\n

Published - 23-EJP905.pdf

", "abstract": "We establish several equivalent characterisations of the anchored isoperimetric dimension of supercritical clusters in Bernoulli bond percolation on transitive graphs. We deduce from these characterisations together with a theorem of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin (Duke Math. J. 2020) that if G is a transient transitive graph then the infinite clusters of Bernoulli percolation on G are transient for p sufficiently close to 1. It remains open to extend this result down to the critical probability. Along the way we establish two new cluster repulsion inequalities that are of independent interest.", "date": "2023-01-20", "date_type": "published", "publication": "Electronic Journal of Probability", "volume": "28", "publisher": "Institute of Mathematical Statistics", "pagerange": "1-15", "id_number": "CaltechAUTHORS:20230725-745306000.2", "issn": "1083-6489", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230725-745306000.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/23-ejp905", "primary_object": { "basename": "23-EJP905.pdf", "url": "https://authors.library.caltech.edu/records/95j8r-pwq77/files/23-EJP905.pdf" }, "pub_year": "2023", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/jv318-5fg33", "eprint_id": 119359, "eprint_status": "archive", "datestamp": "2023-08-22 18:46:30", "lastmod": "2026-03-27 20:00:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" }, "orcid": "0000-0002-5287-4258" } ] }, "title": "The next-to-top term in knot Floer homology", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology; Mathematical Physics", "note": "This article is published open access under our Subscribe to Open model. CC-BY-4.0 \n\nThe author is indebted to Robert Lipshitz for many fruitful discussions and critical comments which shaped this work. The author also wishes to thank an anonymous referee for suggestions which improved this paper. \n\nThe author was partially supported by NSF grant number DMS-1811900.\n\n

Published - 9127416-10.4171-qt-174-print.pdf

", "abstract": "Let K be a null-homologous knot in a generalized L-space Z with b\u2081(Z) \u2264 1. Let F be a Seifert surface of K with genus g. We show that if HFK(Z,K,[F],g) is supported in a single \u2124/2\u2124-grading, then rank HFK(Z,K,[F],g-1) \u2265 rank HFK(Z,K,[F],g).", "date": "2023-01-20", "date_type": "published", "publication": "Quantum Topology", "volume": "13", "number": "3", "publisher": "European Mathematical Society", "pagerange": "579-591", "id_number": "CaltechAUTHORS:20230221-18374200.9", "issn": "1663-487X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230221-18374200.9", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1811900" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/qt/174", "primary_object": { "basename": "9127416-10.4171-qt-174-print.pdf", "url": "https://authors.library.caltech.edu/records/jv318-5fg33/files/9127416-10.4171-qt-174-print.pdf" }, "pub_year": "2023", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/r5v2z-p6s17", "eprint_id": 119188, "eprint_status": "archive", "datestamp": "2023-08-22 18:45:52", "lastmod": "2026-03-09 02:12:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Merz-Konstantin", "name": { "family": "Merz", "given": "Konstantin" }, "orcid": "0000-0003-4841-8556" }, { "id": "Siedentop-Heinz", "name": { "family": "Siedentop", "given": "Heinz" }, "orcid": "0000-0003-1422-7882" } ] }, "title": "The Scott conjecture for large Coulomb systems: a review", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nPartial support through U.S. National Science Foundation grant DMS-1954995 (R.L.F.), by the Deutsche Forschungsgemeinschaft through Germany's Excellence Strategy, grant EXC-2111-390814868 (R.L.F.& H.S.), and by the PRIME programme of the German Academic Exchange Service (DAAD) with funds from the German Federal Ministry of Education and Research (BMBF) (K.M.) is acknowledged.\n\nOpen Access funding enabled and organized by Projekt DEAL.\n\n

Published - s11005-023-01631-9.pdf

", "abstract": "We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the limit of a large number of particles. Particular emphasis is put on models that take relativistic kinematics into account. While non-relativistic models are typically rather well understood, this is generally not the case for relativistic ones and leads to a variety of open questions.", "date": "2023-01-19", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "113", "publisher": "Springer", "pagerange": "Art. No. 11", "id_number": "CaltechAUTHORS:20230209-988069100.27", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230209-988069100.27", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" }, { "agency": "Bundesministerium f\u00fcr Bildung und Forschung (BMBF)" }, { "agency": "Projekt DEAL" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-023-01631-9", "primary_object": { "basename": "s11005-023-01631-9.pdf", "url": "https://authors.library.caltech.edu/records/r5v2z-p6s17/files/s11005-023-01631-9.pdf" }, "pub_year": "2023", "author_list": "Frank, Rupert L.; Merz, Konstantin; et al." }, { "id": "https://authors.library.caltech.edu/records/skrax-s4s40", "eprint_status": "archive", "datestamp": "2024-07-09 00:03:52", "lastmod": "2026-03-09 22:02:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Kang", "given": "Monica Jinwoo" }, "orcid": "0000-0002-0454-2064" }, { "name": { "family": "Lee", "given": "Jaeha" }, "orcid": "0000-0001-9124-450X" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Universal formula for the density of states with continuous symmetry", "ispublished": "pub", "full_text_status": "public", "note": "

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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Funded by SCOAP3.

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We thank J. Bhattacharya, D. Harlow, G. Horowitz, T. Melia, S. Minwalla, S. Pal, D. Simmons-Dufffin, Z. Sun, T. Takayanagi, and Z. Zhang for discussion. This work is supported in part by the US Department of Energy under the Award No. DE-SC0011632. M. J. K. is supported in part by the Sherman Fairchild Postdoctoral Fellowship. H. O. is supported in part by the World Premier International Research Center Initiative, MEXT, Japan, and by JSPS Grant-in-Aid for Scientific Research 20K03965. This work was performed in part at the Aspen Center for Physics, which is supported by NSF Grant No. PHY-1607611.

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", "abstract": "

We consider a \ud835\udc51-dimensional unitary conformal field theory with a compact Lie group global symmetry \ud835\udc3a and show that, at high temperature \ud835\udc47 and on a compact Cauchy surface, the probability of a randomly chosen state being in an irreducible unitary representation \ud835\udc45 of \ud835\udc3a is proportional to (dim \u2062\ud835\udc45)2²exp\u2061[−\ud835\udc50\u2082\u2061(\ud835\udc45)/(\ud835\udc4f\u2062\ud835\udc47^(\ud835\udc51−1))]. We use the spurion analysis to derive this formula and relate the constant \ud835\udc4f to a domain wall tension. We also verify it for free field theories and holographic conformal field theories and compute \ud835\udc4f in these cases. This generalizes the result in 2109.03838 that the probability is proportional to (dim\u2061\ud835\udc45)² when \ud835\udc3a is a finite group. As a byproduct of this analysis, we clarify thermodynamical properties of black holes with non-Abelian hair in anti–de Sitter space.

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", "date": "2023-01-15", "date_type": "published", "publication": "Physical Review D", "volume": "107", "number": "2", "publisher": "American Physical Society", "pagerange": "026021", "issn": "2470-0010", "official_url": "https://authors.library.caltech.edu/records/skrax-s4s40", "funders": { "items": [ { "grant_number": "DE-SC0011632" }, {}, { "grant_number": "20K03965" }, { "grant_number": "PHY-1607611" }, {}, {} ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/physrevd.107.026021", "primary_object": { "basename": "PhysRevD.107.026021.pdf", "url": "https://authors.library.caltech.edu/records/skrax-s4s40/files/PhysRevD.107.026021.pdf" }, "pub_year": "2023", "author_list": "Kang, Monica Jinwoo; Lee, Jaeha; et al." }, { "id": "https://authors.library.caltech.edu/records/1a03j-3p565", "eprint_id": 119319, "eprint_status": "archive", "datestamp": "2023-08-20 08:58:52", "lastmod": "2026-03-27 18:37:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Lee-Vincent-S-H", "name": { "family": "Lee", "given": "Vincent S.\u2009H." }, "orcid": "0000-0002-3481-3590" }, { "id": "Zurek-K-M", "name": { "family": "Zurek", "given": "Kathryn M." }, "orcid": "0000-0002-2629-337X" } ] }, "title": "Near-horizon quantum dynamics of 4D Einstein gravity from 2D Jackiw-Teitelboim gravity", "ispublished": "pub", "full_text_status": "public", "note": "Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3.\n\nWe thank Tom Banks, Temple He, Cynthia Keeler, Juan Maldacena, Allic Sivaramakrishnan, and Erik Verlinde for discussion on these directions. K.\u2009Z. and V.\u2009L. are supported by the Heising-Simons Foundation \"Observational Signatures of Quantum Gravity\" collaboration Grant No. 2021-2817, and by a Simons Investigator award. The work of S.\u2009G. and K.\u2009Z. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632.\n\n

Published - PhysRevD.107.016004.pdf

", "abstract": "We study quantum fluctuations in the light-cone metric of the 4D Einstein-Hilbert action via dimensional reduction to Jackiw-Teitelboim (JT) gravity. In particular, we show that, in Einstein gravity, the causal development of a region in flat Minkowski spacetime, near a horizon defined by light sheets, can be described by an effective two-dimensional dilaton theory. This enables us to make use of known solutions of the JT action, where the spacetime position of a horizon has quantum uncertainty due to metric fluctuations. This quantum uncertainty can be then directly related to the original 4D light-cone coordinates, allowing us to compute the uncertainty in the time of a photon to travel from tip-to-tip of a causal diamond in flat 4D Minkowski space. We find that both Planck and infrared scales (with the latter set by the size of the causal diamond) enter the uncertainty in photon travel time, such that the quantum fluctuation in the arrival time may be observably large.", "date": "2023-01-01", "date_type": "published", "publication": "Physical Review D", "volume": "107", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 016004", "id_number": "CaltechAUTHORS:20230217-513857800.4", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230217-513857800.4", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Heising-Simons Foundation", "grant_number": "2021-2817" }, { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/physrevd.107.016004", "primary_object": { "basename": "PhysRevD.107.016004.pdf", "url": "https://authors.library.caltech.edu/records/1a03j-3p565/files/PhysRevD.107.016004.pdf" }, "pub_year": "2023", "author_list": "Gukov, Sergei; Lee, Vincent S.\u2009H.; et al." }, { "id": "https://authors.library.caltech.edu/records/hjwhg-sd610", "eprint_id": 117650, "eprint_status": "archive", "datestamp": "2023-08-22 18:33:33", "lastmod": "2026-03-08 04:08:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Gishboliner-Lior", "name": { "family": "Gishboliner", "given": "Lior" }, "orcid": "0000-0003-0688-8111" }, { "id": "Levanzov-Yevgeny", "name": { "family": "Levanzov", "given": "Yevgeny" } }, { "id": "Shapira-Asaf", "name": { "family": "Shapira", "given": "Asaf" } } ] }, "title": "A new bound for the Brown-Erd\u0151s-S\u00f3s problem", "ispublished": "pub", "full_text_status": "public", "keywords": "Brown-Erd\u0151s-S\u00f3s conjecture; Hypergraph removal lemma; Computational Theory and Mathematics; Discrete Mathematics and Combinatorics; Theoretical Computer Science", "note": "[Conlon] supported in part by NSF Award DMS-2054452. \n[Gishboliner] supported in part by SNSF grant 200021_196965. \n[Shapira] supported in part by ISF Grant 1028/16, ERC Consolidator Grant 863438 and NSF-BSF Grant 20196.\n\n

Published - 1-s2.0-S0095895622000818-main.pdf

", "abstract": "Let f(n, v, e) denote the maximum number of edges in a 3-uniform hypergraph not containing e edges spanned by at most v vertices. One of the most influential open problems in extremal combinatorics then asks, for a given number of edges e \u2265 3, what is the smallest integer d = d(e) such that f(n, e+d, e) = o(n\u00b2)? This question has its origins in work of Brown, Erd\u0151s and S\u00f3s from the early 70's and the standard conjecture is that d(e) = 3 for every e \u2265 3. The state of the art result regarding this problem was obtained in 2004 by S\u00e1rk\u00f6zy and Selkow, who showed that f(n, e+2+[log\u2082e], e) = o(n\u00b2). The only improvement over this result was a recent breakthrough of Solymosi and Solymosi, who improved the bound for d(10) from 5 to 4. We obtain the first asymptotic improvement over the S\u00e1rk\u00f6zy\u2013Selkow bound, showing that f(n, e+O(log e / log log e), e) = o(n\u00b2).", "date": "2023-01", "date_type": "published", "publication": "Journal of Combinatorial Theory. Series B", "volume": "158", "number": "2", "publisher": "Elsevier", "pagerange": "1-35", "id_number": "CaltechAUTHORS:20221031-575177800.7", "issn": "0095-8956", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221031-575177800.7", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021_196965" }, { "agency": "Israel Science Foundation", "grant_number": "1028/16" }, { "agency": "European Research Council (ERC)", "grant_number": "863438" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "20196" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jctb.2022.08.005", "primary_object": { "basename": "1-s2.0-S0095895622000818-main.pdf", "url": "https://authors.library.caltech.edu/records/hjwhg-sd610/files/1-s2.0-S0095895622000818-main.pdf" }, "pub_year": "2023", "author_list": "Conlon, David; Gishboliner, Lior; et al." }, { "id": "https://authors.library.caltech.edu/records/v1t30-85j35", "eprint_id": 117353, "eprint_status": "archive", "datestamp": "2023-08-22 18:33:17", "lastmod": "2026-03-07 16:33:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-Jacob", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-Benny", "name": { "family": "Sudakov", "given": "Benny" } }, { "id": "Wei-Fan", "name": { "family": "Wei", "given": "Fan" } } ] }, "title": "Threshold Ramsey multiplicity for paths and even cycles", "ispublished": "pub", "full_text_status": "public", "keywords": "Discrete Mathematics and Combinatorics", "note": "Research supported by National Science Foundation Award DMS-2054452.\n\nResearch supported by a Packard Fellowship and by National Science Foundation Award DMS-1855635.\n\nResearch supported by SNSF Grant 200021_196965.\n\nResearch supported by National Science Foundation Award DMS-1953958.", "abstract": "The Ramsey number r(H) of a graph H is the minimum integer such that any two-coloring of the edges of the complete graph K\u2099 contains a monochromatic copy of H. While this definition only asks for a single monochromatic copy of H, it is often the case that every two-edge-coloring of the complete graph on r(H) vertices contains many monochromatic copies of H. The minimum number of such copies over all two-colorings of K_(r(H)) will be referred to as the threshold Ramsey multiplicity of H. Addressing a problem of Harary and Prins, who were the first to systematically study this quantity, we show that there is a positive constant c such that the threshold Ramsey multiplicity of a path or an even cycle on k vertices is at least (ck)\u1d4f. This bound is tight up to the constant c. We prove a similar result for odd cycles in a companion paper.", "date": "2023-01", "date_type": "published", "publication": "European Journal of Combinatorics", "volume": "107", "publisher": "Elsevier", "pagerange": "Art. No. 103612", "id_number": "CaltechAUTHORS:20221011-128968500.8", "issn": "0195-6698", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221011-128968500.8", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1855635" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021_196965" }, { "agency": "NSF", "grant_number": "DMS-1953958" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.ejc.2022.103612", "pub_year": "2023", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/e2ckf-gct87", "eprint_id": 118790, "eprint_status": "archive", "datestamp": "2023-08-20 08:53:25", "lastmod": "2026-03-09 02:38:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Spodyneiko-Lev", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "Hohenberg-Mermin-Wagner-type theorems and dipole symmetry", "ispublished": "pub", "full_text_status": "public", "note": "We thank Xiaoyang Huang, Ethan Lake, Leo Radzihovsky, and Senthil Todadri for discussions. A.K. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award. L.S. was supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant (Grant No. 651446) from the Simons Foundation.", "abstract": "We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For d-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for d \u2264 4, while dipole symmetry cannot be spontaneously broken for d \u2264 2. For T = 0, we show that charge symmetry cannot be spontaneously broken for d \u2264 2 if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.", "date": "2022-12-15", "date_type": "published", "publication": "Physical Review B", "volume": "106", "number": "24", "publisher": "American Physical Society", "pagerange": "Art. No. 245125", "id_number": "CaltechAUTHORS:20230112-143000300.1", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230112-143000300.1", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation", "grant_number": "651446" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/physrevb.106.245125", "pub_year": "2022", "author_list": "Kapustin, Anton and Spodyneiko, Lev" }, { "id": "https://authors.library.caltech.edu/records/1xqr6-fsg75", "eprint_id": 120011, "eprint_status": "archive", "datestamp": "2023-08-22 18:26:19", "lastmod": "2026-04-16 01:39:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Morvan-Alexis", "name": { "family": "Morvan", "given": "A." }, "orcid": "0000-0002-9515-6184" }, { "name": { "family": "Andersen", "given": "T. I." } }, { "name": { "family": "Mi", "given": "X." }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Neill", "given": "C." }, "orcid": "0000-0001-8509-9836" }, { "name": { "family": "Petukhov", "given": "A." } }, { "name": { "family": "Kechedzhi", "given": "K." } }, { "name": { "family": "Abanin", "given": "D. A." } }, { "name": { "family": "Michailidis", "given": "A." }, "orcid": "0000-0002-8443-1064" }, { "name": { "family": "Acharya", "given": "R." } }, { "name": { "family": "Arute", "given": "F." } }, { "name": { "family": "Arya", "given": "K." } }, { "name": { "family": "Asfaw", "given": "A." } }, { "name": { "family": "Atalaya", "given": "J." } }, { "name": { "family": "Bardin", "given": "J. C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Basso", "given": "J." }, "orcid": "0000-0001-5547-691X" }, { "name": { "family": "Bengtsson", "given": "A." } }, { "name": { "family": "Bortoli", "given": "G." } }, { "name": { "family": "Bourassa", "given": "A." }, "orcid": "0000-0002-8517-7475" }, { "name": { "family": "Bovaird", "given": "J." } }, { "name": { "family": "Brill", "given": "L." } }, { "name": { "family": "Broughton", "given": "M." } }, { "name": { "family": "Buckley", "given": "B. B." } }, { "name": { "family": "Buell", "given": "D. A." } }, { "name": { "family": "Burger", "given": "T." } }, { "name": { "family": "Burkett", "given": "B." }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Bushnell", "given": "N." } }, { "name": { "family": "Chen", "given": "Z." } }, { "name": { "family": "Chiaro", "given": "B." } }, { "name": { "family": "Collins", "given": "R." } }, { "name": { "family": "Conner", "given": "P." } }, { "name": { "family": "Courtney", "given": "W." } }, { "name": { "family": "Crook", "given": "A. L." } }, { "name": { "family": "Curtin", "given": "B." } }, { "name": { "family": "Debroy", "given": "D. M." } }, { "name": { "family": "Del Toro Barba", "given": "A." }, "orcid": "0000-0003-0869-5110" }, { "name": { "family": "Demura", "given": "S." }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Dunsworth", "given": "A." } }, { "name": { "family": "Eppens", "given": "D." }, "orcid": "0000-0001-7134-5733" }, { "name": { "family": "Erickson", "given": "C." } }, { "name": { "family": "Faoro", "given": "L." } }, { "name": { "family": "Farhi", "given": "E." } }, { "name": { "family": "Fatemi", "given": "R." } }, { "name": { "family": "Flores Burgos", "given": "L." } }, { "name": { "family": "Forati", "given": "E." } }, { "name": { "family": "Fowler", "given": "A. 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B." } }, { "name": { "family": "Roushan", "given": "P." }, "orcid": "0000-0003-1917-3879" } ] }, "title": "Formation of robust bound states of interacting microwave photons", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \n\nContributions. A. Morvan, C.N., I.A., L.B.I. and P.R. designed the experiment. A. Morvan and T.I.A. performed the experiment and analysed the data and wrote the supplement. K.K., D.A.A., I.A. and L.B.I. provided theoretical support and analysis. A. Morvan, T.A., X.M., C.N. and A.P. developed the calibration of the fSim gate. D.A.A. and A. Michailidis performed numerical simulation in the supplements. A. Morvan, T.A., I.A., L.B. and P.R. wrote the manuscript. All authors contributed to revising the manuscript and the Supplementary Information. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. \n\nData availability. The datasets generated and analysed for this study are available at https://doi.org/10.5281/zenodo.6981407. \n\nThe authors declare no competing interests.\n\n

Published - s41586-022-05348-y.pdf

Supplemental Material - 41586_2022_5348_MOESM1_ESM.pdf

", "abstract": "Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-\u00bd XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.", "date": "2022-12-08", "date_type": "published", "publication": "Nature", "volume": "612", "number": "7939", "publisher": "Nature Publishing Group", "pagerange": "240-245", "id_number": "CaltechAUTHORS:20230314-845402300.28", "issn": "0028-0836", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230314-845402300.28", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/s41586-022-05348-y", "pmcid": "PMC9729104", "primary_object": { "basename": "41586_2022_5348_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/1xqr6-fsg75/files/41586_2022_5348_MOESM1_ESM.pdf" }, "related_objects": [ { "basename": "s41586-022-05348-y.pdf", "url": "https://authors.library.caltech.edu/records/1xqr6-fsg75/files/s41586-022-05348-y.pdf" } ], "pub_year": "2022", "author_list": "Morvan, A.; Andersen, T. I.; et al." }, { "id": "https://authors.library.caltech.edu/records/h4vaa-m1r93", "eprint_status": "archive", "datestamp": "2026-02-24 22:43:16", "lastmod": "2026-03-28 03:48:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gherman-Matthew-M", "name": { "family": "Gherman", "given": "Matthew" }, "orcid": "0009-0007-2601-7862" }, { "name": { "family": "Merkurjev", "given": "Alexander" }, "orcid": "0000-0002-4447-1838" } ] }, "title": "Negligible degree two cohomology of finite groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Group cohomology; Negligible cycles; Galois cohomology", "note": "

© 2022 Elsevier Inc. All rights reserved.

\n\n

The second author has been supported by the NSF grant DMS #1801530

", "abstract": "

For a finite group G, a G-module M and a field F, an element u ∈ H d ( G , M ) is negligible over F if for each field extension L / F and every group homomorphism Gal ( L sep / L ) → G , u belongs to the kernel of the induced homomorphism H d ( G , M ) → H d ( L , M ) . We determine the group of negligible elements in H 2 ( G , M ) for every abelian group M with trivial G-action.

", "date": "2022-12-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "611", "publisher": "Elsevier", "pagerange": "82-93", "issn": "0021-8693", "official_url": "https://authors.library.caltech.edu/records/h4vaa-m1r93", "funders": { "items": [ { "grant_number": "DMS #1801530" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2022.07.039", "pub_year": "2022", "author_list": "Gherman, Matthew and Merkurjev, Alexander" }, { "id": "https://authors.library.caltech.edu/records/25tmg-55397", "eprint_id": 118926, "eprint_status": "archive", "datestamp": "2023-08-22 18:20:36", "lastmod": "2026-03-09 20:31:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frisch-Joshua-R", "name": { "family": "Frisch", "given": "Joshua R." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Shinko-Forte", "name": { "family": "Shinko", "given": "Forte" }, "orcid": "0000-0001-8142-1509" } ] }, "title": "Lifts of Borel actions on quotient spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "abstract": "Given a countable Borel equivalence relation E and a countable group G, we study the problem of when a Borel action of G on X/E can be lifted to a Borel action of G on X.", "date": "2022-12", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "251", "number": "2", "publisher": "Springer", "pagerange": "379-421", "id_number": "CaltechAUTHORS:20230125-514112400.2", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230125-514112400.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-022-2434-z", "pub_year": "2022", "author_list": "Frisch, Joshua R.; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/gdd4d-j1c06", "eprint_id": 122401, "eprint_status": "archive", "datestamp": "2023-08-22 18:12:53", "lastmod": "2026-04-16 01:39:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mi-Xiao", "name": { "family": "Mi", "given": "X." }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Sonner", "given": "M." }, "orcid": "0000-0002-9003-5914" }, { "name": { "family": "Niu", "given": "M. 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E." }, "orcid": "0000-0002-8406-6626" }, { "name": { "family": "Opremcak", "given": "A." } }, { "name": { "family": "Petukhov", "given": "A." } }, { "name": { "family": "Potter", "given": "R." } }, { "name": { "family": "Quintana", "given": "C." } }, { "name": { "family": "Rubin", "given": "N. C." }, "orcid": "0000-0003-3963-1830" }, { "name": { "family": "Saei", "given": "N." } }, { "name": { "family": "Sank", "given": "D." }, "orcid": "0000-0001-8188-364X" }, { "name": { "family": "Sankaragomathi", "given": "K." } }, { "name": { "family": "Satzinger", "given": "K. J." }, "orcid": "0000-0001-5865-0813" }, { "name": { "family": "Schuster", "given": "C." }, "orcid": "0000-0002-9611-7275" }, { "name": { "family": "Shearn", "given": "M. J." } }, { "name": { "family": "Shvarts", "given": "V." } }, { "name": { "family": "Strain", "given": "D." } }, { "name": { "family": "Su", "given": "Y." } }, { "name": { "family": "Szalay", "given": "M." }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Vidal", "given": "G." } }, { "name": { "family": "Villalonga", "given": "B." } }, { "name": { "family": "Vollgraff-Heidweiller", "given": "C." }, "orcid": "0000-0002-6513-9885" }, { "name": { "family": "White", "given": "T." }, "orcid": "0000-0002-9803-7471" }, { "name": { "family": "Yao", "given": "Z." }, "orcid": "0000-0003-1806-5454" }, { "name": { "family": "Yeh", "given": "P." }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "J." } }, { "name": { "family": "Zalcman", "given": "A." }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Zhang", "given": "Y." } }, { "name": { "family": "Zhu", "given": "N." }, "orcid": "0000-0002-3037-2003" }, { "name": { "family": "Neven", "given": "H." }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Bacon", "given": "D." }, "orcid": "0000-0001-6266-9269" }, { "name": { "family": "Hilton", "given": "J." } }, { "name": { "family": "Lucero", "given": "E." }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Babbush", "given": "R." }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Boixo", "given": "S." }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Megrant", "given": "A." }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Chen", "given": "Y." }, "orcid": "0000-0002-7473-6745" }, { "name": { "family": "Kelly", "given": "J." }, "orcid": "0000-0002-2596-2121" }, { "name": { "family": "Smelyanskiy", "given": "V." }, "orcid": "0000-0002-3000-6732" }, { "name": { "family": "Abanin", "given": "D. A." }, "orcid": "0000-0002-2461-0271" }, { "name": { "family": "Roushan", "given": "P." }, "orcid": "0000-0003-1917-3879" } ] }, "title": "Noise-resilient edge modes on a chain of superconducting qubits", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 2022 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. \n\nWe have benefited from discussions with M. H. Devoret, L. G. Dias, I. K. Drozdov, P. Ghaemi, and A. Rahmani. \n\nD.B. is a CIFAR Associate Fellow in the Quantum Information Science Program. \n\nAuthor contributions: D.A.A. and V.Sm. conceived of the project. X.M., D.A.A., and V.Sm. designed the experiment. X.M. executed the experiment. P.R., X.M., D.A.A., M.So., and M.Y.N. performed analysis of the experimental results. K.W.L. and B.F. contributed to measurements in the supplementary materials. X.M., P.R., and D.A.A. wrote the manuscript. V.Sm. and P.R. led and coordinated the project. Infrastructure support was provided by Google Quantum AI. All authors contributed to revising the manuscript and the supplementary materials. \n\nData and materials availability: Experimental data shown in the main text and supplementary materials, as well as simulation software code, are available in Zenodo (46). \n\nThe authors declare no competing interests.", "abstract": "Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with \u2124\u2082 parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.", "date": "2022-11-18", "date_type": "published", "publication": "Science", "volume": "378", "number": "6621", "publisher": "American Association for the Advancement of Science", "pagerange": "785-790", "id_number": "CaltechAUTHORS:20230725-746101000.26", "issn": "0036-8075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230725-746101000.26", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Canadian Institute for Advanced Research (CIFAR)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1126/science.abq5769", "pub_year": "2022", "author_list": "Mi, X.; Sonner, M.; et al." }, { "id": "https://authors.library.caltech.edu/records/ctnf1-pzc81", "eprint_status": "archive", "datestamp": "2023-08-22 17:20:43", "lastmod": "2026-06-01 22:14:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-Tobias", "name": { "family": "Ekholm", "given": "Tobias" }, "orcid": "0000-0003-2060-8462" }, { "id": "Gruen-Angus", "name": { "family": "Gruen", "given": "Angus" }, "orcid": "0000-0003-0284-009X" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kucharski-Piotr", "name": { "family": "Kucharski", "given": "Piotr" }, "orcid": "0000-0002-9599-5658" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "\u1e90 at Large N: From Curve Counts to Quantum Modularity", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "

© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Received: 7 June 2020 / Accepted: 29 June 2022. We would like to thank Sibasish Banerjee, Miranda Cheng, Luis Diogo, Boris Feigin, Francesca Ferrari, Sarah Harrison, Jakub Jankowski, Pietro Longhi, Ciprian Manolescu, Marko Stosic, Cumrun Vafa, and Don Zagier for insightful discussions and comments on the draft. The work of T.E. is supported by the Knut and Alice Wallenberg Foundation KAW2020.0307 and by the Swedish Research Council VR2020-04535. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of P.K. is supported by the Polish Ministry of Science and Higher Education through its programme Mobility Plus (decision no. 1667/MOB/V/2017/0). The research of S.P. is supported by Kwanjeong Educational Foundation. The work of P.S. is supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00).

\n\n

Submitted - 2005.13349.pdf

", "abstract": "

Reducing a 6d fivebrane theory on a 3-manifold Y gives a q-series 3-manifold invariant \u1e90(Y). We analyse the large-N behaviour of F_K = \u1e90(M_K), where M_K is the complement of a knot K in the 3-sphere, and explore the relationship between an a-deformed (a = q\u1d3a) version of F_K and HOMFLY-PT polynomials. On the one hand, in combination with counts of holomorphic annuli on knot complements, this gives an enumerative interpretation of F_K in terms of counts of open holomorphic curves. On the other, it leads to closed form expressions for a-deformed F_K for (2,2p+1) torus knots and an order-by-order construction for other cases. They both suggest a further t-deformation based on superpolynomials, which can be used to obtain a t-deformation of ADO polynomials, expected to be related to categorification. Moreover, studying how F_K transforms under natural geometric operations on K indicates relations to quantum modularity in a new setting.

", "date": "2022-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "396", "number": "1", "publisher": "Springer", "pagerange": "143-186", "issn": "0010-3616", "official_url": "https://authors.library.caltech.edu/records/ctnf1-pzc81", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW2020.0307" }, { "agency": "Swedish Research Council", "grant_number": "VR2020-04535" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Ministry of Science and Higher Education (Poland)", "grant_number": "1667/MOB/V/2017/0" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Foundation for Polish Science" }, { "agency": "European Regional Development Fund", "grant_number": "POIR.04.04.00-00-5C55/17-00" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-022-04469-9", "primary_object": { "basename": "2005.13349.pdf", "url": "https://authors.library.caltech.edu/records/ctnf1-pzc81/files/2005.13349.pdf" }, "pub_year": "2022", "author_list": "Ekholm, Tobias; Gruen, Angus; et al." }, { "id": "https://authors.library.caltech.edu/records/c1dgm-xs860", "eprint_id": 118141, "eprint_status": "archive", "datestamp": "2023-08-22 18:05:27", "lastmod": "2026-03-09 02:34:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Sharp hierarchical upper bounds on the critical two-point function for long-range percolation on \u2124\u1d48", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "We thank Philip Easo, Emmanuel Michta, Gordon Slade, and the anonymous referee for helpful comments on earlier versions of the manuscript.", "abstract": "Consider long-range Bernoulli percolation on \u2124\u1d48 in which we connect each pair of distinct points x and y by an edge with probability 1 \u2212 exp(\u2212\u03b2\u2016x \u2212 y\u2016^(\u2212d\u2212\u03b1)), where \u03b1 > 0 is fixed and \u03b2 \u2a7e 0 is a parameter. We prove that if 0 < \u03b1 < d, then the critical two-point function satisfies (1/|\u039b_r|)\u2211_(x\u03f5\u039b_(r))P_(\u03b2_(c))(0 \u2194 x) \u2264 r^(\u2212d+a) for every r \u2a7e 1, where \u039b_r = [\u2212r,r]\u1d48 \u2229 \u2124\u1d48. In other words, the critical two-point function on \u2124\u1d48 is always bounded above on average by the critical two-point function on the hierarchical lattice. This upper bound is believed to be sharp for values of \u03b1 strictly below the crossover value \u03b1_(c)(d), where the values of several critical exponents for long-range percolation on \u2124\u1d48 and the hierarchical lattice are believed to be equal.", "date": "2022-11", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "63", "number": "11", "publisher": "American Institute of Physics", "pagerange": "Art. No. 113301", "id_number": "CaltechAUTHORS:20221129-370786800.2", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221129-370786800.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/5.0088450", "pub_year": "2022", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/arcvz-53p88", "eprint_id": 117498, "eprint_status": "archive", "datestamp": "2023-08-22 17:56:05", "lastmod": "2026-03-09 02:15:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Larson-Simon", "name": { "family": "Larson", "given": "Simon" }, "orcid": "0000-0002-0057-8211" } ] }, "title": "An inequality for the normal derivative of the Lane-Emden ground state", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; Analysis", "note": "Funding statement: Partial support through U.S. National Science Foundation grant DMS-1954995 (R.\u2009L. Frank), through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868 (R.\u2009L. Frank), and through Knut and Alice Wallenberg Foundation grant KAW 2021.0193 (S. Larson) is acknowledged.\n\nThe authors would like to thank the anonymous referee for helpful suggestions.", "abstract": "We consider Lane\u2013Emden ground states with polytropic index 0 \u2264 q \u2212 1 \u2264 1, that is, minimizers of the Dirichlet integral among L^q-normalized functions. Our main result is a sharp lower bound on the L\u00b2-norm of the normal derivative in terms of the energy, which implies a corresponding isoperimetric inequality. Our bound holds for arbitrary bounded open Lipschitz sets \u03a9 \u2282 \u211d\u1d48, without assuming convexity.", "date": "2022-10-27", "date_type": "published", "publication": "Advances in Calculus of Variations", "publisher": "Walter de Gruyter GmbH", "id_number": "CaltechAUTHORS:20221019-344256700.16", "issn": "1864-8258", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221019-344256700.16", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" }, { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW 2021.0193" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/acv-2022-0005", "pub_year": "2022", "author_list": "Frank, Rupert L. and Larson, Simon" }, { "id": "https://authors.library.caltech.edu/records/z9sv6-y8604", "eprint_id": 117229, "eprint_status": "archive", "datestamp": "2023-08-22 16:54:49", "lastmod": "2026-03-09 21:51:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" }, "orcid": "0000-0002-5287-4258" } ] }, "title": "A Note on Knot Floer Homology and Fixed Points of Monodromy", "ispublished": "pub", "full_text_status": "public", "keywords": "General Engineering", "note": "The author was partially supported by NSF Grant Number DMS-1811900. The author wishes to thank John Baldwin for many helpful discussions and comments on a draft of this paper.", "abstract": "Using an argument of Baldwin\u2013Hu\u2013Sivek, we prove that if K is a hyperbolic fibered knot with fiber F in a closed, oriented 3-manifold Y, and HFK\u02c6(Y,K,[F],g(F)\u22121) has rank 1, then the monodromy of K is freely isotopic to a pseudo-Anosov map with no fixed points. In particular, this shows that the monodromy of a hyperbolic L-space knot is freely isotopic to a map with no fixed points.", "date": "2022-10-12", "date_type": "published", "publication": "Peking Mathematical Journal", "publisher": "Springer", "id_number": "CaltechAUTHORS:20221004-861294200.2", "issn": "2096-6075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221004-861294200.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1811900" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s42543-022-00051-3", "pub_year": "2022", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/vtna3-xc530", "eprint_id": 109463, "eprint_status": "archive", "datestamp": "2023-08-22 17:52:58", "lastmod": "2026-03-07 04:13:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Fusion systems with U\u2083(3) J-components", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Fusion systems; Finite simple groups", "note": "\u00a9 2021 Elsevier Inc. \n\nReceived 27 September 2020, Available online 9 June 2021. \n\nThis work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.", "abstract": "We determine the 2-fusion systems of J-component type in which the centralizer of some fully centralized involution has a maximal J-component that is the 2-fusion system of U\u2083(3).", "date": "2022-10-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "607", "publisher": "Elsevier", "pagerange": "34-63", "id_number": "CaltechAUTHORS:20210610-093254072", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210610-093254072", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2021.06.006", "pub_year": "2022", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/tnfj2-hdz88", "eprint_id": 116712, "eprint_status": "archive", "datestamp": "2023-08-22 17:49:13", "lastmod": "2026-03-09 21:52:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ballinger-William", "name": { "family": "Ballinger", "given": "William" }, "orcid": "0000-0001-8584-5835" }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" }, "orcid": "0000-0002-5287-4258" }, { "id": "Ochse-Tynan", "name": { "family": "Ochse", "given": "Tynan" } }, { "id": "Vafaee-Faramarz", "name": { "family": "Vafaee", "given": "Faramarz" } } ] }, "title": "The prism manifold realization problem III", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "This project started during Caltech's Summer Undergraduate Research Fellowships (SURF) program in the summer of 2017. Y.N. was partially supported by NSF grant numbers DMS-1252992 and DMS-1811900. F.V. was partially supported by an AMS-Simons Travel Grant. We thank the referee for many helpful suggestions.", "abstract": "Every prism manifold can be parametrized by a pair of relatively prime integers p > 1 and q. In our earlier papers, we determined a complete list of prism manifolds P(p,q) that can be realized by positive integral surgeries on knots in S\u00b3 when q < 0 or q > p; in the present work, we solve the case when 0 < q < p. This completes the solution of the realization problem for prism manifolds.", "date": "2022-10", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "125", "number": "4", "publisher": "London Mathematical Society", "pagerange": "841-878", "id_number": "CaltechAUTHORS:20220906-252468000", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220906-252468000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "NSF", "grant_number": "DMS-1811900" }, { "agency": "American Mathematical Society" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.12472", "pub_year": "2022", "author_list": "Ballinger, William; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/zwvhy-s1238", "eprint_id": 116429, "eprint_status": "archive", "datestamp": "2023-08-22 17:49:10", "lastmod": "2026-03-09 02:35:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "On the Derivation of Mean-Field Percolation Critical Exponents from the Triangle Condition", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "This work was carried out while the author was a Senior Research Associate at the University of Cambridge, and was supported in part by ERC starting Grant 804166 (SPRS). We thank Vivek Dewan, Emmanuel Michta, Stephen Muirhead, and Gordon Slade for helpful comments on a previous version of the manuscript.", "abstract": "We give a new derivation of mean-field percolation critical behaviour from the triangle condition that is quantitatively much better than previous proofs when the triangle diagram \u2207pc is large. In contrast to earlier methods, our approach continues to yield bounds of reasonable order when the triangle diagram \u2207p is unbounded but diverges slowly as p\u2191pc, as is expected to occur in percolation on Zd at the upper-critical dimension d=6. Indeed, we show in particular that if the triangle diagram diverges polylogarithmically as p\u2191pc then mean-field critical behaviour holds to within a polylogarithmic factor. We apply the methods we develop to deduce that for long-range percolation on the hierarchical lattice, mean-field critical behaviour holds to within polylogarithmic factors at the upper-critical dimension. As part of the proof, we introduce a new method for comparing diagrammatic sums on general transitive graphs that may be of independent interest.", "date": "2022-10", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "189", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 6", "id_number": "CaltechAUTHORS:20220823-628154700.756", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220823-628154700.756", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "804166" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10955-022-02967-7", "pub_year": "2022", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/3bzbc-xj302", "eprint_id": 117445, "eprint_status": "archive", "datestamp": "2023-08-22 17:50:36", "lastmod": "2026-03-08 03:39:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-Jacob", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "The upper logarithmic density of monochromatic subset sums", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "Research supported by NSF Award DMS-2054452. [Conlon] \n\nResearch supported by a Packard Fellowship and by NSF Awards DMS-1855635 and DMS-2154169. [Fox] \n\nResearch supported by a Two Sigma Fellowship. [Pham]", "abstract": "We show that in any two-coloring of the positive integers there is a color for which the set of positive integers that can be represented as a sum of distinct elements with this color has upper logarithmic density at least (2 + \u221a3)/4 and this is best possible. This answers a 40-year-old question of Erd\u0151s.", "date": "2022-10", "date_type": "published", "publication": "Mathematika", "volume": "68", "number": "4", "publisher": "University College London", "pagerange": "1292-1301", "id_number": "CaltechAUTHORS:20221017-10817000.4", "issn": "0025-5793", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221017-10817000.4", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1855635" }, { "agency": "NSF", "grant_number": "DMS-2154169" }, { "agency": "Two Sigma Investments, LP" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/mtk.12167", "pub_year": "2022", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/0pmve-wtk48", "eprint_id": 116736, "eprint_status": "archive", "datestamp": "2023-08-22 17:49:17", "lastmod": "2026-03-09 02:35:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Slightly supercritical percolation on non-amenable graphs I: The distribution of finite clusters", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "We thank Jonathan Hermon and Asaf Nachmias for many helpful discussions, and thank Remco van der Hofstad for helpful comments on an earlier version of this manuscript. We also thank Antoine Godin for sharing his simplified proof of Proposition 3.1 with us.", "abstract": "We study the distribution of finite clusters in slightly supercritical (p\u2193pc) Bernoulli bond percolation on transitive nonamenable graphs, proving in particular that if G is a transitive nonamenable graph satisfying the L2 boundedness condition (pc0 such that Pp(n\u2264|K|<\u221e)\u224dn\u22121/2exp[\u2212\u0398(|p\u2212pc|2n)] and Pp(r\u2264Rad(K)<\u221e)\u224dr\u22121exp[\u2212\u0398(|p\u2212pc|r)] for every p\u2208(pc\u2212\u03b4,pc+\u03b4) and n,r\u22651, where all implicit constants depend only on G. We deduce in particular that the critical exponents \u03b3\u2032 and \u0394\u2032 describing the rate of growth of the moments of a finite cluster as p\u2193pc take their mean-field values of 1 and 2 respectively. These results apply in particular to Cayley graphs of nonelementary hyperbolic groups, to products with trees, and to transitive graphs of spectral radius \u03c1<1/2. In particular, every finitely generated nonamenable group has a Cayley graph to which these results apply. They are new for graphs that are not trees. The corresponding facts are yet to be understood on \u2124d even for d very large. In a second paper in this series, we will apply these results to study the geometric and spectral properties of infinite slightly supercritical clusters in the same setting.", "date": "2022-10", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "125", "number": "4", "publisher": "London Mathematical Society", "pagerange": "968-1013", "id_number": "CaltechAUTHORS:20220907-386218000", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220907-386218000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.12474", "pub_year": "2022", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/b80br-qcv76", "eprint_status": "archive", "datestamp": "2026-01-15 00:35:58", "lastmod": "2026-03-28 03:48:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Zhao", "given": "Yufei" }, "orcid": "0000-0002-1995-3755" } ] }, "title": "Tower-type bounds for Roth's theorem with popular differences", "ispublished": "pub", "full_text_status": "public", "abstract": "Green developed an arithmetic regularity lemma to prove a strengthening of Roth's theorem on arithmetic progressions in dense sets. It states that for every\n \n \\epsilon > 0\n \n there is some\n \n N_0(\\epsilon)\n \n such that for every\n \n N \\ge N_0(\\epsilon)\n \n and\n \n A \\subset [N]\n \n with\n \n |A| = \\alpha N\n \n , there is some nonzero\n \n d\n \n such that\n \n A\n \n contains at least\n \n (\\alpha^3 - \\epsilon) N\n \n three-term arithmetic progressions with common difference\n \n d\n \n .\n \n \n We prove that the minimum\n \n N_0(\\epsilon)\n \n in Green's theorem is an exponential tower of twos of height on the order of\n \n \\log(1/\\epsilon)\n \n . Both the lower and upper bounds are new. This shows that the tower-type bounds that arise from the use of a regularity lemma in this application are quantitatively necessary.", "date": "2022-09-27", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "25", "number": "10", "publisher": "European Mathematical Society - EMS - Publishing House GmbH", "pagerange": "3795-3831", "issn": "1435-9855", "official_url": "https://authors.library.caltech.edu/records/b80br-qcv76", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/jems/1271", "pub_year": "2022", "author_list": "Fox, Jacob; Pham, Huy Tuan; et al." }, { "id": "https://authors.library.caltech.edu/records/6mxzy-0kt75", "eprint_id": 117068, "eprint_status": "archive", "datestamp": "2023-08-22 17:40:39", "lastmod": "2026-03-09 22:12:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feng-Tony", "name": { "family": "Feng", "given": "Tony" } }, { "id": "Landesman-Aaron", "name": { "family": "Landesman", "given": "Aaron" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "The geometric distribution of Selmer groups of elliptic curves over function fields", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nIt is our pleasure to thank Ravi Vakil for organizing the \"What's on My Mind\" seminar, which led to the genesis of this paper. We thank Johan de Jong, Chao Li, Bjorn Poonen, Arul Shankar, Doug Ulmer, and Melanie Matchett Wood for helpful discussions. We thank Lisa Sauermann for help translating [24]. We also thank David Zureick-Brown and Jackson Morrow for help with writing and running MAGMA code. The first author was supported by a Stanford ARCS Fellowship and an NSF Postdoctoral Fellowship under Grant No. 1902927, and the second author was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1656518.\n\nOpen Access funding provided by the MIT Libraries.\n\n

In Press - s00208-022-02429-1.pdf

", "abstract": "Fix a positive integer n and a finite field F_q. We study the joint distribution of the rank rk (E), the n-Selmer group Sel_n (E), and the n-torsion in the Tate\u2013Shafarevich group III(E)[n] as E varies over elliptic curves of fixed height d \u2265 2 over F_q (T). We compute this joint distribution in the large q limit. We also show that the \"large q, then large height\" limit of this distribution agrees with the one predicted by Bhargava\u2013Kane\u2013Lenstra\u2013Poonen\u2013Rains.", "date": "2022-09-24", "date_type": "published", "publication": "Mathematische Annalen", "publisher": "Springer", "id_number": "CaltechAUTHORS:20220919-81452600", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220919-81452600", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Stanford University" }, { "agency": "NSF", "grant_number": "DMS-1902927" }, { "agency": "NSF", "grant_number": "DGE-1656518" }, { "agency": "Massachusetts Institute of Technology (MIT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-022-02429-1", "primary_object": { "basename": "s00208-022-02429-1.pdf", "url": "https://authors.library.caltech.edu/records/6mxzy-0kt75/files/s00208-022-02429-1.pdf" }, "pub_year": "2022", "author_list": "Feng, Tony; Landesman, Aaron; et al." }, { "id": "https://authors.library.caltech.edu/records/wf08c-mwx40", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:05", "lastmod": "2026-03-28 03:48:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "He", "given": "Jimmy" }, "orcid": "0000-0003-4345-6537" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Tuan Pham", "given": "Huy" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Wenqiang Xu", "given": "Max" } } ] }, "title": "Universality for Low-Degree Factors of Random Polynomials over Finite Fields", "ispublished": "pub", "full_text_status": "public", "abstract": "Abstract\n We show that the counts of low-degree irreducible factors of a random polynomial $f$ over $\\mathbb {F}_q$ with independent but nonuniform coefficients behave like that of a uniform random polynomial, exhibiting a form of universality for random polynomials over finite fields. Our strongest results require various assumptions on the parameters, but we are able to obtain results requiring only $q=p$ a prime with $p\\leq \\exp ({n^{1/13}})$ where $n$ is the degree of the polynomial. Our proofs use Fourier analysis and rely on tools recently applied by Breuillard and Varj\u00fa to study the $ax+b$ process, which show equidistribution for $f(\\alpha )$ at a single point. We extend this to handle multiple roots and the Hasse derivatives of $f$, which allow us to study the irreducible factors with multiplicity.", "date": "2022-09-02", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2023", "number": "17", "publisher": "Oxford University Press (OUP)", "pagerange": "14752-14794", "issn": "1073-7928", "official_url": "https://authors.library.caltech.edu/records/wf08c-mwx40", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnac239", "pub_year": "2022", "author_list": "He, Jimmy; Tuan Pham, Huy; et al." }, { "id": "https://authors.library.caltech.edu/records/v5fwz-bfy91", "eprint_id": 117394, "eprint_status": "archive", "datestamp": "2023-08-22 17:33:55", "lastmod": "2026-03-09 02:37:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Sopenko-Nikita", "name": { "family": "Sopenko", "given": "Nikita" }, "orcid": "0000-0002-8479-1924" } ] }, "title": "Local Noether theorem for quantum lattice systems and topological invariants of gapped states", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "This paper is part of the Special Topic on Mathematical Aspects of Topological Phases.\n\nWe would like to thank Karl-Hermann Neeb and Bruno Nachtergaele for reading a preliminary draft of the paper and Bowen Yang for discussions. We are especially grateful to Bruno Nachtergaele for pointing out to us the relevance of the improved Lieb\u2013Robinson bounds from Refs. 25 and 29 and for informing us about his forthcoming work.30 This research was supported, in part, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award.", "abstract": "We study generalizations of the Berry phase for quantum lattice systems in arbitrary dimensions. For a smooth family of gapped ground states in d dimensions, we define a closed d + 2-form on the parameter space, which generalizes the curvature of the Berry connection. Its cohomology class is a topological invariant of the family. When the family is equivariant under the action of a compact Lie group G, topological invariants take values in the equivariant cohomology of the parameter space. These invariants unify and generalize the Hall conductance and the Thouless pump. A key role in these constructions is played by a certain differential graded Fr\u00e9chet\u2013Lie algebra attached to any quantum lattice system. As a by-product, we describe ambiguities in charge densities and conserved currents for arbitrary lattice systems with rapidly decaying interactions.", "date": "2022-09", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "63", "number": "9", "publisher": "American Institute of Physics", "pagerange": "Art. No. 091903", "id_number": "CaltechAUTHORS:20221013-48351800.2", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221013-48351800.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/5.0085964", "pub_year": "2022", "author_list": "Kapustin, Anton and Sopenko, Nikita" }, { "id": "https://authors.library.caltech.edu/records/fk795-afh19", "eprint_id": 115315, "eprint_status": "archive", "datestamp": "2023-08-22 17:24:25", "lastmod": "2026-03-09 21:42:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guicardi-Pedro", "name": { "family": "Guicardi", "given": "Pedro" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Fractality in cosmic topology models with spectral action gravity", "ispublished": "pub", "full_text_status": "public", "keywords": "Physics and Astronomy (miscellaneous)", "note": "\u00a9 2022 IOP Publishing Ltd. As the Version of Record of this article is going to be/has been published on a subscription basis, this Accepted Manuscript will be available for reuse under a CC BY-NC-ND 3.0 licence after a 12 month embargo period. \n\nReceived 30 October 2021. Revised 10 February 2022. Accepted 30 June 2022. Accepted Manuscript online 30 June 2022. \n\nThis work was supported by NSF grants DMS-1707882 and DMS-2104330. The first author acknowledges support from the Caltech WAVE program for undergraduate research. We thank the referees for their careful reading of the manuscript and for helpful comments.\n\n

Accepted Version - Guicardi+et+al_2022_Class._Quantum_Grav._10.1088_1361-6382_ac7d8c.pdf

Submitted - 2110.08878.pdf

", "abstract": "We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of spacetime. We show that the topology constrains the possible fractal structures, and in turn the correction terms to the spectral action due to fractality distinguish the various cosmic topology candidates, with effects detectable in a slow-roll inflation scenario, through the power spectra of the scalar and tensor fluctuations. We also discuss explicit effects of the presence of fractal structures on the gravitational waves equations.", "date": "2022-08-18", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "39", "number": "16", "publisher": "IOP", "pagerange": "Art. No. 165007", "id_number": "CaltechAUTHORS:20220705-671988000", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220705-671988000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "DMS-2104330" }, { "agency": "Caltech WAVE Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1361-6382/ac7d8c", "primary_object": { "basename": "2110.08878.pdf", "url": "https://authors.library.caltech.edu/records/fk795-afh19/files/2110.08878.pdf" }, "related_objects": [ { "basename": "Guicardi+et+al_2022_Class._Quantum_Grav._10.1088_1361-6382_ac7d8c.pdf", "url": "https://authors.library.caltech.edu/records/fk795-afh19/files/Guicardi+et+al_2022_Class._Quantum_Grav._10.1088_1361-6382_ac7d8c.pdf" } ], "pub_year": "2022", "author_list": "Guicardi, Pedro and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/kd92j-5zw50", "eprint_id": 117741, "eprint_status": "archive", "datestamp": "2023-08-22 17:11:08", "lastmod": "2026-03-07 23:29:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-Jacob", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-Benny", "name": { "family": "Sudakov", "given": "Benny" } }, { "id": "Wei-Fan", "name": { "family": "Wei", "given": "Fan" } } ] }, "title": "Threshold Ramsey multiplicity for odd cycles", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "The first author [Conlon] is supported by NSF Award DMS-2054452.\n\nThe second author [Fox] is supported by a Packard Fellowship and by NSF Award DMS-1855635.\n\nThe third author [Sudakov] is supported by SNSF grant 200021_196965.\n\nThe last author [Wei] is supported by NSF Award DMS-1953958.", "abstract": "The Ramsey number r(H) of a graph H is the minimum n such that any two-coloring of the edges of the complete graph K\u2099 contains a monochromatic copy of H. The threshold Ramsey multiplicity m(H) is then the minimum number of monochromatic copies of H taken over all two-edge-colorings of K_(r(H)). The study of this concept was first proposed by Harary and Prins almost fifty years ago. In a companion paper, the authors have shown that there is a positive constant c such that the threshold Ramsey multiplicity for a path or even cycle with k vertices is at least (ck)\u1d4f, which is tight up to the value of c. Here, using different methods, we show that the same result also holds for odd cycles with k vertices.", "date": "2022-08", "date_type": "published", "publication": "Revista de la Uni\u00f3n Matem\u00e1tica Argentina", "volume": "64", "number": "1", "publisher": "Union Matematica Argentina", "pagerange": "49-68", "id_number": "CaltechAUTHORS:20221107-997760900.3", "issn": "1669-9637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221107-997760900.3", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "NSF", "grant_number": "DMS-1855635" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021_196965" }, { "agency": "NSF", "grant_number": "DMS-1953958" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.33044/revuma.2874", "pub_year": "2022", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/2wcx5-6zd15", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:31", "lastmod": "2026-03-28 03:48:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Jain", "given": "Vishesh" }, "orcid": "0000-0002-7275-3218" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Vuong", "given": "Thuy-Duong" }, "orcid": "0000-0003-0271-9687" } ] }, "title": "Spectral independence, coupling, and the spectral gap of the Glauber dynamics", "ispublished": "pub", "full_text_status": "public", "abstract": "We present a new lower bound on the spectral gap of the Glauber dynamics for the Gibbs distribution of a spectrally independent q-spin system on a graph G = ( V , E ) with maximum degree \u0394. Our bound improves upon all previous bounds on the spectral gap obtained in this generality. Notably, for several interesting examples, we are able to handle the entire regime of \u0394 excluded by coupling arguments. As concrete applications, by combining our new lower bound with known spectral independence computations and known coupling arguments: (1) we show that for a triangle-free graph G = ( V , E ) with maximum degree \u0394 \u2265 3 , the Glauber dynamics for the uniform distribution on proper k-colorings with k \u2265 ( 1.763 \u2026 + \u03b4 ) \u0394 colors has spectral gap \u03a9 \u02dc \u03b4 ( | V | \u2212 1 ) . Previously, such a result was known either if the girth of G is at least 5 (Dyer et al. (2004) [12]), or under restrictions on \u0394 (Chen et al. (2021) [7]; Hayes and Vigoda (2003) [18]). (2) We show for the binomial random graph G ( n , d / n ) with d = O ( 1 ) , with high probability, an approximately uniformly random matching may be sampled in time O d ( n 2 + o ( 1 ) ) . This improves the corresponding running time of O \u02dc d ( n 3 ) due to Jerrum and Sinclair (1989) [22]; Jerrum (2003) [21].", "date": "2022-08", "date_type": "published", "publication": "Information Processing Letters", "volume": "177", "publisher": "Elsevier", "pagerange": "106268", "issn": "0020-0190", "official_url": "https://authors.library.caltech.edu/records/2wcx5-6zd15", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.ipl.2022.106268", "pub_year": "2022", "author_list": "Jain, Vishesh; Pham, Huy Tuan; et al." }, { "id": "https://authors.library.caltech.edu/records/63bb7-54c82", "eprint_id": 115854, "eprint_status": "archive", "datestamp": "2023-08-22 16:57:44", "lastmod": "2026-03-08 03:40:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Tyomkyn-Mykhaylo", "name": { "family": "Tyomkyn", "given": "Mykhaylo" } } ] }, "title": "Ramsey numbers of trails and circuits", "ispublished": "pub", "full_text_status": "public", "keywords": "Eulerian graphs; monochromatic components; Ramsey theory; Geometry and Topology; Discrete Mathematics and Combinatorics", "note": "\u00a9 2022 Wiley Periodicals LLC. \n\nVersion of Record online: 22 July 2022. Manuscript accepted: 27 June 2022. Manuscript revised: 19 April 2022. Manuscript received: 08 September 2021. \n\nConlon was supported by NSF Award DMS-2054452 and Tyomkyn by ERC Synergy Grant DYNASNET 810115, the H2020-MSCA-RISE Project CoSP-GA No. 823748 and GACR Grant 19-04113Y.\n\n

Accepted Version - 2109.02633.pdf

", "abstract": "We show that every two-colouring of the edges of the complete graph K\u2099 contains a monochromatic trail or circuit of length at least 2n\u00b2/9+o(n\u00b2), which is asymptotically best possible.", "date": "2022-07-27", "date_type": "published", "publication": "Journal of Graph Theory", "publisher": "Wiley", "id_number": "CaltechAUTHORS:20220726-997455000", "issn": "0364-9024", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220726-997455000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "European Research Council (ERC)", "grant_number": "810115" }, { "agency": "European Research Council (ERC)", "grant_number": "823748" }, { "agency": "Grant Agency of the Czech Republic", "grant_number": "19-04113Y" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/jgt.22865", "primary_object": { "basename": "2109.02633.pdf", "url": "https://authors.library.caltech.edu/records/63bb7-54c82/files/2109.02633.pdf" }, "pub_year": "2022", "author_list": "Conlon, David and Tyomkyn, Mykhaylo" }, { "id": "https://authors.library.caltech.edu/records/fe9rn-efx48", "eprint_id": 115850, "eprint_status": "archive", "datestamp": "2023-08-22 16:58:32", "lastmod": "2026-03-09 23:05:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-Pavel", "name": { "family": "Etingof", "given": "P." } }, { "id": "Kalinov-Daniil", "name": { "family": "Kalinov", "given": "D." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "New realizations of deformed double current algebras and Deligne categories", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology; Algebra and Number Theory", "note": "\u00a9 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived May 29, 2020. Accepted June 23, 2021. \n\nTo the memory of Ernest Borisovich Vinberg. \n\nThis paper owes its existence to Victor Ginzburg, who proposed to study deformed double current algebras in the spring of 2001 and suggested, around the same time, some of the important ideas explored below. We are very grateful to Victor for sharing these ideas and initiating this research. We are also grateful to N. Guay, V. Ostrik, and T. Schedler for useful discussions. The work of P. E. and D. K. was partially supported by the NSF grant DMS-1502244. The computer calculations for this paper were done using MAGMA ([BCP97]). \n\nOpen Access funding provided by the MIT Libraries.\n\n

Submitted - 2005.13604.pdf

In Press - ETINGOF2022_Article_NEWREALIZATIONSOFDEFORMEDDOUBL.pdf

", "abstract": "In this paper, we propose an alternative construction of a certain class of Deformed Double Current Algebras. We construct them as spherical subalgebras of symplectic reection algebras in the Deligne category. They can also be thought of as ultraproducts of the corresponding spherical subalgebras in finite rank. We also provide new presentations of DDCA of types A and B by generators and relations.", "date": "2022-07-27", "date_type": "published", "publication": "Transformation Groups", "publisher": "Springer", "id_number": "CaltechAUTHORS:20220726-997340000", "issn": "1083-4362", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220726-997340000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1502244" }, { "agency": "MIT Libraries" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00031-022-09717-9", "primary_object": { "basename": "2005.13604.pdf", "url": "https://authors.library.caltech.edu/records/fe9rn-efx48/files/2005.13604.pdf" }, "related_objects": [ { "basename": "ETINGOF2022_Article_NEWREALIZATIONSOFDEFORMEDDOUBL.pdf", "url": "https://authors.library.caltech.edu/records/fe9rn-efx48/files/ETINGOF2022_Article_NEWREALIZATIONSOFDEFORMEDDOUBL.pdf" } ], "pub_year": "2022", "author_list": "Etingof, P.; Kalinov, D.; et al." }, { "id": "https://authors.library.caltech.edu/records/tg42p-xc421", "eprint_id": 115674, "eprint_status": "archive", "datestamp": "2023-08-22 15:44:58", "lastmod": "2026-03-08 17:36:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Nenadov-Rajko", "name": { "family": "Nenadov", "given": "Rajko" } }, { "id": "Truji\u0107-Milo\u0161", "name": { "family": "Truji\u0107", "given": "Milo\u0161" } } ] }, "title": "The size\u2010Ramsey number of cubic graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "\u00a9 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. \n\nVersion of Record online: 26 May 2022; Manuscript accepted: 22 March 2022; Manuscript revised: 02 March 2022; Manuscript received: 06 October 2021. \n\nThis research has been supported by NSF Award DMS-2054452 and by the Swiss National Science Foundation under Grant Number: 200020_197138.\n\n

Submitted - 2110.01897.pdf

", "abstract": "We show that the size-Ramsey number of any cubic graph with n vertices is O(n^(8/5)), improving a bound of n^(5/3+o(1)) due to Kohayakawa, R\u00f6dl, Schacht, and Szemer\u00e9di. The heart of the argument is to show that there is a constant C such that a random graph with Cn vertices where every edge is chosen independently with probability p\u2a7eC_n^(\u22122/5) is with high probability Ramsey for any cubic graph with n vertices. This latter result is best possible up to the constant.", "date": "2022-07-20", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "publisher": "London Mathematical Society", "id_number": "CaltechAUTHORS:20220718-901273500", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220718-901273500", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200020_197138" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/blms.12682", "primary_object": { "basename": "2110.01897.pdf", "url": "https://authors.library.caltech.edu/records/tg42p-xc421/files/2110.01897.pdf" }, "pub_year": "2022", "author_list": "Conlon, David; Nenadov, Rajko; et al." }, { "id": "https://authors.library.caltech.edu/records/wqc14-p7h63", "eprint_id": 110986, "eprint_status": "archive", "datestamp": "2023-08-20 08:09:51", "lastmod": "2026-03-09 21:56:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harlow-Daniel", "name": { "family": "Harlow", "given": "Daniel" }, "orcid": "0000-0002-1005-4745" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "A universal formula for the density of states in theories with finite-group symmetry", "ispublished": "pub", "full_text_status": "public", "keywords": "black hole entropy, quantum field theory, symmetry", "note": "\u00a9 2022 IOP Publishing Ltd. \n\nReceived 3 December 2021; Revised 13 February 2022; Accepted 14 March 2022; Published 13 June 2022. \n\nWe thank Luca Iliesiu, Juan Maldacena, Subir Sachdev, and Joaquin Turiaci for pointing out an error in a discussion of the weak gravity conjecture which appeared in the first version of this paper, and we particularly thank Luca and Joaquin for many useful explanations. We also thank Chris Akers, Ben Heidenreich, Gary Horowitz, Henry Lin, Hong Liu, Juan Maldacena, Don Marolf, Sridip Pal, Matt Reece, Tom Rudelius, Ashoke Sen, and Cumrun Vafa for useful comments and discussion. DH is supported by the Simons Foundation as a member of the 'It from Qubit' collaboration, the Sloan Foundation as a Sloan Fellow, the Packard Foundation as a Packard Fellow, the Air Force Office of Scientific Research under the award number FA9550-19-1-0360, and the US Department of Energy under the task C Grant DE-SC0012567. The work of HO is supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under the award number DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, and by JSPS Grant-in-Aid for Scientific Research 20K03965. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. \n\nData availability statement: No new data were created or analysed in this study.\n\n

Submitted - 2109.03838.pdf

", "abstract": "In this paper we use Euclidean gravity to derive a simple formula for the density of black hole microstates which transform in each irreducible representation of any finite gauge group. Since each representation appears with nonzero density, this gives a new proof of the completeness hypothesis for finite gauge fields. Inspired by the generality of the argument we further propose that the formula applies at high energy in any quantum field theory with a finite-group global symmetry, and give some evidence for this conjecture.", "date": "2022-07-07", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "39", "number": "13", "publisher": "IOP Publishing", "pagerange": "Art. No. 134003", "id_number": "CaltechAUTHORS:20210922-181613283", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-181613283", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-19-1-0360" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0012567" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20K03965" }, { "agency": "NSF", "grant_number": "PHY-1607611" } ] }, "other_numbering_system": { "items": [ { "id": "2021-032", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1361-6382/ac5db2", "primary_object": { "basename": "2109.03838.pdf", "url": "https://authors.library.caltech.edu/records/wqc14-p7h63/files/2109.03838.pdf" }, "pub_year": "2022", "author_list": "Harlow, Daniel and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/cymfh-sq376", "eprint_id": 114255, "eprint_status": "archive", "datestamp": "2023-08-22 16:27:19", "lastmod": "2026-03-09 02:16:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-Tobias", "name": { "family": "Ekholm", "given": "Tobias" }, "orcid": "0000-0003-2060-8462" }, { "id": "Gruen-Angus", "name": { "family": "Gruen", "given": "Angus" }, "orcid": "0000-0003-0284-009X" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kucharski-Piotr", "name": { "family": "Kucharski", "given": "Piotr" }, "orcid": "0000-0002-9599-5658" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Sto\u0161i\u0107-Marko", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" }, "orcid": "0000-0002-4464-396X" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Branches, quivers, and ideals for knot complements", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Quantum invariants; A polynomial; Open curve counts; Geometry and Topology; General Physics and Astronomy; Mathematical Physics", "note": "\u00a9 2022 Elsevier. \n\nReceived 21 December 2021, Accepted 25 March 2022, Available online 1 April 2022, Version of Record 12 April 2022. \n\nP.K. was supported by the Polish Ministry of Education and Science through its programme Mobility Plus (decision number 1667/MOB/V/2017/0) and by NWO vidi grant (number 016.Vidi.189.182). S.P. was partially supported by junior fellowship at Institut Mittag-Leffler and by Kwanjeong Educational Foundation. The work of M.S. was supported by the Portuguese Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT) through the grant 'Higher Structures and Applications', no. PTDC/MAT-PUR/31089/2017, and FCT Exploratory Grant IF/0998/2015, and by the Ministry of Education, Science and Technological Development of the Republic of Serbia through Mathematical Institute SANU. In the final stages, his work was supported by the Science Fund of the Republic of Serbia, Grant No. 7749891, Graphical Languages \u2013 GWORDS. The work of P.S. was supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00). T.E. is supported by the Knut and Alice Wallenberg Foundation as a Wallenberg scholar KAW2020.0307 and by the Swedish Research Council VR2020-04535. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227.", "abstract": "We generalize the F_K invariant, i.e. \u1e90 for the complement of a knot K in the 3-sphere, the knots-quivers correspondence, and A-polynomials of knots, and find several interconnections between them. We associate an F_K invariant to any branch of the A-polynomial of K and we work out explicit expressions for several simple knots. We show that these F_K invariants can be written in the form of a quiver generating series, in analogy with the knots-quivers correspondence. We discuss various methods to obtain such quiver representations, among others using R-matrices. We generalize the quantum a-deformed A-polynomial to an ideal that contains the recursion relation in the group rank, i.e. in the parameter a, and describe its classical limit in terms of the Coulomb branch of a 3d-5d theory. We also provide t-deformed versions. Furthermore, we study how the quiver formulation for closed 3-manifolds obtained by surgery leads to the superpotential of 3d N = 2 theory T[M\u2083] and to the data of the associated modular tensor category MTC[M\u2083].", "date": "2022-07", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "177", "publisher": "Elsevier", "pagerange": "Art. No. 104520", "id_number": "CaltechAUTHORS:20220412-15486000", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220412-15486000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education and Science (Poland)", "grant_number": "1667/MOB/V/2017/0" }, { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)", "grant_number": "016.Vidi.189.182" }, { "agency": "Institut Mittag-Leffler" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT-PUR/31089/2017" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "IF/0998/2015" }, { "agency": "Ministry of Education, Science and Technological Development (Serbia)" }, { "agency": "Science Fund (Serbia)", "grant_number": "7749891" }, { "agency": "Foundation for Polish Science" }, { "agency": "European Regional Development Fund", "grant_number": "POIR.04.04.00-00-5C55/17-00" }, { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW2020.0307" }, { "agency": "Swedish Research Council", "grant_number": "VR2020-04535" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2022.104520", "pub_year": "2022", "author_list": "Ekholm, Tobias; Gruen, Angus; et al." }, { "id": "https://authors.library.caltech.edu/records/cq695-mc662", "eprint_id": 105368, "eprint_status": "archive", "datestamp": "2023-08-20 08:06:37", "lastmod": "2026-03-08 04:08:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Some remarks on the Zarankiewicz problem", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society. \n\nReceived 27 July 2020; revised 12 April 2021; accepted 14 April 2021. Published online by Cambridge University Press: 15 June 2021. \n\nI would like to thank Cosmin Pohoata for helpful discussions. I am also grateful to Dhruv Mubayi for drawing my attention to his work with Alon, Mellinger and Verstra\u00ebte [1].\n\n

Submitted - 2007.12816.pdf

", "abstract": "The Zarankiewicz problem asks for an estimate on z(m, n; s, t), the largest number of 1's in an m \u00d7 n matrix with all entries 0 or 1 containing no s \u00d7 t submatrix consisting entirely of 1's. We show that a classical upper bound for z(m, n; s, t) due to K\u0151v\u00e1ri, S\u00f3s and Tur\u00e1n is tight up to the constant for a broad range of parameters. The proof relies on a new quantitative variant of the random algebraic method.", "date": "2022-07", "date_type": "published", "publication": "Mathematical Proceedings of the Cambridge Philosophical Society", "volume": "173", "number": "1", "publisher": "Cambridge University Press", "pagerange": "155-161", "id_number": "CaltechAUTHORS:20200914-085046091", "issn": "0305-0041", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200914-085046091", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/S0305004121000475", "primary_object": { "basename": "2007.12816.pdf", "url": "https://authors.library.caltech.edu/records/cq695-mc662/files/2007.12816.pdf" }, "pub_year": "2022", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/1r9j1-d2d52", "eprint_id": 119537, "eprint_status": "archive", "datestamp": "2023-08-22 16:12:18", "lastmod": "2026-03-09 02:12:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Degenerate stability of some Sobolev inequalities", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Analysis; Applied Mathematics", "note": "\u00a9 2023 Association Publications de l'Institut Henri Poincar\u00e9 Paris. This article is published open access under our Subscribe to Open model. CC-BY-4.0\n\nThe author wishes to thank R. Neumayer for several discussions on the topic of this paper and her seminar talk in January 2021 at Caltech which motivated this work. J. Dolbeault's help with references is much appreciated.\n\nPartial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 and through the German Research Foundation grant EXC-2111-390814868 is acknowledged.\n\n

Published - 10.4171-aihpc-35.pdf

", "abstract": "We show that on S\u00b9(1/\u221a(d-2))x S\u1d48\u207b\u00b9(1) the conformally invariant Sobolev inequality holds with a remainder term that is the fourth power of the distance to the optimizers. The fourth power is best possible. This is in contrast to the more usual vanishing to second order and is motivated by work of Engelstein, Neumayer and Spolaor. A similar phenomenon arises for subcritical Sobolev inequalities on S\u1d48. Our proof proceeds by an iterated Bianchi\u2013Egnell strategy.", "date": "2022-06-02", "date_type": "published", "publication": "Analyse Nonlineaire, Annales Institute H. Poincar\u00e9", "volume": "39", "number": "6", "publisher": "Gauthier-Villars", "pagerange": "1459-1484", "id_number": "CaltechAUTHORS:20230227-87934600.14", "issn": "0294-1449", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230227-87934600.14", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/aihpc/35", "primary_object": { "basename": "10.4171-aihpc-35.pdf", "url": "https://authors.library.caltech.edu/records/1r9j1-d2d52/files/10.4171-aihpc-35.pdf" }, "pub_year": "2022", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/adpdw-y0d17", "eprint_id": 115248, "eprint_status": "archive", "datestamp": "2023-08-22 15:27:09", "lastmod": "2026-03-09 21:28:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Li-Wanlin", "name": { "family": "Li", "given": "Wanlin" } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } }, { "id": "Pries-Rachel", "name": { "family": "Pries", "given": "Rachel" }, "orcid": "0000-0001-5987-0324" }, { "id": "Tang-Yunqing", "name": { "family": "Tang", "given": "Yunqing" } } ] }, "title": "Newton Polygon Stratification of the Torelli Locus in Unitary Shimura Varieties", "ispublished": "pub", "full_text_status": "restricted", "keywords": "General Mathematics", "note": "\u00a9 The Author(s) 2020. Published by Oxford University Press. \nThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). \n\nReceived: 22 August 2019; Revision received: 31 July 2020; Accepted: 06 October 2020; Published: 09 December 2020. \n\nWe thank the Banff International Research Station for hosting Women in Numbers 4, the American Institute of Mathematics for supporting our square proposal, and anonymous referees for valuable suggestions. \n\nThis work was partially supported by the National Science Foundation [grants DMS-15-02227 and DMS-19-01819 to R.P.; grant DMS-18-01237 to Y.T.].", "abstract": "We study the intersection of the Torelli locus with the Newton polygon stratification of the modulo p reduction of certain Shimura varieties. We develop a clutching method to show that the intersection of the open Torelli locus with some Newton polygon strata is non-empty. This allows us to give a positive answer, under some compatibility conditions, to a question of Oort about smooth curves in characteristic p whose Newton polygons are an amalgamate sum. As an application, we produce infinitely many new examples of Newton polygons that occur for smooth curves that are cyclic covers of the projective line. Most of these arise in inductive systems that demonstrate unlikely intersections of the open Torelli locus with the Newton polygon stratification in Siegel modular varieties. In addition, for the 20 special Shimura varieties found in Moonen's work, we prove that all Newton polygon strata intersect the open Torelli locus (if p>>0 in the supersingular cases).", "date": "2022-05", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2022", "number": "9", "publisher": "Oxford University Press", "pagerange": "6464-6511", "id_number": "CaltechAUTHORS:20220623-483313800", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220623-483313800", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-15-02227" }, { "agency": "NSF", "grant_number": "DMS-19-01819" }, { "agency": "NSF", "grant_number": "DMS-18-01237" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnaa306", "pub_year": "2022", "author_list": "Li, Wanlin; Mantovan, Elena; et al." }, { "id": "https://authors.library.caltech.edu/records/514fv-v2k51", "eprint_id": 111200, "eprint_status": "archive", "datestamp": "2023-08-20 07:34:03", "lastmod": "2026-03-09 02:12:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Loss-Michael", "name": { "family": "Loss", "given": "Michael" }, "orcid": "0000-0001-5008-3340" } ] }, "title": "Which magnetic fields support a zero mode?", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2022 Walter de Gruyter GmbH, Berlin/Boston. \n\nReceived: 2021-01-29; Revised: 2021-11-29; Published Online: 2022-04-28. \n\nThe authors would like to thank H. Kovarik and M. Lewin for helpful remarks. \n\nPartial support through U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (Rupert L. Frank) and DMS-1856645 (Michael Loss) and through the Deutsche Forschungsgemeinschaft (German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868 (Rupert L. Frank) is acknowledged.\n\n

Submitted - 2012.13646.pdf

", "abstract": "This paper presents some results concerning the size of magnetic fields that support zero modes for the three-dimensional Dirac equation and related problems for spinor equations. It is a well-known fact that for the Schr\u00f6dinger equation in three dimensions to have a negative energy bound state, the 3/2 norm of the potential has to be greater than the Sobolev constant. We prove an analogous result for the existence of zero modes, namely that the 3/2 norm of the magnetic field has to greater than twice the Sobolev constant. The novel point here is that the spinorial nature of the wave function is crucial. It leads to an improved diamagnetic inequality from which the bound is derived. While the results are probably not sharp, other equations are analyzed where the results are indeed optimal.", "date": "2022-04-28", "date_type": "published", "publication": "Journal f\u00fcr die reine und angewandte Mathematik", "publisher": "de Gruyter", "id_number": "CaltechAUTHORS:20211004-222705713", "issn": "1435-5345", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211004-222705713", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "NSF", "grant_number": "DMS-1856645" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2022-0015", "primary_object": { "basename": "2012.13646.pdf", "url": "https://authors.library.caltech.edu/records/514fv-v2k51/files/2012.13646.pdf" }, "pub_year": "2022", "author_list": "Frank, Rupert L. and Loss, Michael" }, { "id": "https://authors.library.caltech.edu/records/14nww-5h270", "eprint_id": 115085, "eprint_status": "archive", "datestamp": "2023-08-20 07:27:24", "lastmod": "2026-03-09 02:40:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Radzihovsky-Leo", "name": { "family": "Radzihovsky", "given": "Leo" }, "orcid": "0000-0002-2281-0835" } ] }, "title": "Piezosuperconductivity: Novel effects in noncentrosymmetric superconductors", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2022 American Physical Society. \n\n(Received 8 February 2022; accepted 8 April 2022; published 20 April 2022)\n\nWe acknowledge financial support through the Simons Investigator Awards by the James Simons Foundation. A.K. was also supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. L.R. thanks D. Agterberg and L. Fu for discussions.\n\n

Published - PhysRevB.105.134514.pdf

", "abstract": "We study effects in noncentrosymmetric superconductors arising from their unique coupling of Cooper-pair condensate and elasticity. We show that although the much discussed Lifshitz coupling is not observable in a uniform bulk state, it strikingly endows dislocations with a fractional magnetic flux. We also predict a generation of voltage-free strain by a DC current in a P- and T-breaking Josephson junction. Viewing superconductors through the lens of higher-form symmetries we identify the Lifshitz coupling as a chemical potential for the approximately conserved winding number, drawing an analogy with pyroelectric insulators.", "date": "2022-04-01", "date_type": "published", "publication": "Physical Review B", "volume": "105", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 134514", "id_number": "CaltechAUTHORS:20220608-849426000", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220608-849426000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/physrevb.105.134514", "primary_object": { "basename": "PhysRevB.105.134514.pdf", "url": "https://authors.library.caltech.edu/records/14nww-5h270/files/PhysRevB.105.134514.pdf" }, "pub_year": "2022", "author_list": "Kapustin, Anton and Radzihovsky, Leo" }, { "id": "https://authors.library.caltech.edu/records/z91bd-r4c21", "eprint_id": 111199, "eprint_status": "archive", "datestamp": "2023-08-22 14:45:09", "lastmod": "2026-03-09 02:14:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carrillo-Jos\u00e9-Antonio", "name": { "family": "Carrillo", "given": "J. A." }, "orcid": "0000-0001-8819-4660" }, { "id": "Delgadino-Mat\u00edas-G", "name": { "family": "Delgadino", "given": "M. G." }, "orcid": "0000-0002-6897-1060" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "R. L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lewin-Mathieu", "name": { "family": "Lewin", "given": "M." }, "orcid": "0000-0002-1755-0207" } ] }, "title": "Fast Diffusion leads to partial mass concentration in Keller\u2013Segel type stationary solutions", "ispublished": "pub", "full_text_status": "public", "keywords": "Keller\u2013Segel; aggregation\u2013diffusion; mass concentration", "note": "\u00a9 2022 The Author(s). This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited. \n\nReceived 23 March 2021; Accepted 18 December 2021; Published: 10 March 2022. \n\nThe authors would like to thank Jean Dolbeault, David Gomez-Castro, Juan Luis Vazquez and an anonymous referee for pointing out references and fruitful comments. \n\nThis project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Advanced Grant Nonlocal-CPD 883363 of J.A.C. and Consolidator Grant MDFT 725528 of M.L.). M.G.D. was partially supported by CNPq-Brazil (#308800/2019-2) and Instituto Serrapilheira. R.L.F. was partially supported by the U.S. National Science Foundation through grants DMS-1363432 and DMS-1954995 and through Germany's Excellence Strategy EXC-2111-390814868.\n\n

Published - s021820252250018x.pdf

Submitted - 2012.08586.pdf

", "abstract": "We show that partial mass concentration can happen for stationary solutions of aggregation\u2013diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction potential, we find the exact range of the diffusion exponent where concentration occurs in space dimensions N\u22656. We then provide numerical computations which suggest the occurrence of mass concentration in all dimensions N\u22653, for homogeneous interaction potentials with higher power.", "date": "2022-04", "date_type": "published", "publication": "Mathematical Models and Methods in Applied Sciences", "volume": "32", "number": "4", "publisher": "World Scientific Publishing", "pagerange": "831-850", "id_number": "CaltechAUTHORS:20211004-222702303", "issn": "0218-2025", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211004-222702303", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "883363" }, { "agency": "European Research Council (ERC)", "grant_number": "725528" }, { "agency": "Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)", "grant_number": "308800/2019-2" }, { "agency": "Instituto Serrapilheira" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S021820252250018X", "primary_object": { "basename": "2012.08586.pdf", "url": "https://authors.library.caltech.edu/records/z91bd-r4c21/files/2012.08586.pdf" }, "related_objects": [ { "basename": "s021820252250018x.pdf", "url": "https://authors.library.caltech.edu/records/z91bd-r4c21/files/s021820252250018x.pdf" } ], "pub_year": "2022", "author_list": "Carrillo, J. A.; Delgadino, M. G.; et al." }, { "id": "https://authors.library.caltech.edu/records/979vv-4rp38", "eprint_id": 110557, "eprint_status": "archive", "datestamp": "2023-08-22 14:40:15", "lastmod": "2026-03-09 21:43:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Combe-No\u00e9mie", "name": { "family": "Combe", "given": "No\u00e9mie" } }, { "id": "Manin-Yuri-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Geometry of information: Classical and quantum aspects", "ispublished": "pub", "full_text_status": "public", "keywords": "F-manifolds; Motivic information geometry; Classical and quantum probability distributions; Convex cones of probability distributions on finite sets", "note": "\u00a9 2021 Published by Elsevier B.V. \n\nReceived 27 April 2021, Revised 17 August 2021, Accepted 19 October 2021, Available online 27 October 2021. \n\nN. C. Combe acknowledges support from the Minerva Fast track grant from the Max Planck Institute for Mathematics in the Sciences, in Leipzig. M. Marcolli acknowledges support from NSF grants DMS-1707882 and DMS-2104330. The authors of this paper thank the reviewer for suggesting interesting questions related to this work. \n\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n

Submitted - 2107.08006.pdf

", "abstract": "In this article, we describe various aspects of categorification of the structures, appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F\u2013manifolds, and motivic enrichments.", "date": "2022-03-24", "date_type": "published", "publication": "Theoretical Computer Science", "volume": "908", "publisher": "Elsevier", "pagerange": "2-27", "id_number": "CaltechAUTHORS:20210825-184625013", "issn": "0304-3975", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210825-184625013", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Max Planck Institute for Mathematics in the Sciences" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "DMS-2104330" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.tcs.2021.10.020", "primary_object": { "basename": "2107.08006.pdf", "url": "https://authors.library.caltech.edu/records/979vv-4rp38/files/2107.08006.pdf" }, "pub_year": "2022", "author_list": "Combe, No\u00e9mie; Manin, Yuri I.; et al." }, { "id": "https://authors.library.caltech.edu/records/rdzzb-z5f98", "eprint_id": 92302, "eprint_status": "archive", "datestamp": "2023-08-20 07:20:12", "lastmod": "2026-03-09 21:41:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Heydeman-Matthew", "name": { "family": "Heydeman", "given": "Matthew" }, "orcid": "0000-0001-7033-9075" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Parikh-Sarthak", "name": { "family": "Parikh", "given": "Sarthak" }, "orcid": "0000-0002-5831-3873" }, { "id": "Saberi-Ingmar-A", "name": { "family": "Saberi", "given": "Ingmar" } } ] }, "title": "Nonarchimedean holographic entropy from networks of perfect tensors", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2022 International Press of Boston, Inc. \n\nPublished 21 March 2022. \n\nI.A.S. thanks D. Aasen, J. Keating, and J. Walcher for conversations, and the Kavli Institute for Theoretical Physics in Santa Barbara for hospitality as this manuscript was being completed; he also gratefully acknowledges partial support by the Deutsche Forschungsgemeinschaft, within the framework of the Exzellenzinitiative an der Universit\u00e4t Heidelberg. M.H. and S.P. thank Perimeter Institute for their kind hospitality while this work was in its early stages. The work of M.H. and S.P. was supported in part by Perimeter Institute for Theoretical Physics. M.H. would like to thank S.S. Gubser and Princeton University for their hospitality while this work was being completed, and work done at Princeton was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671, and by the Simons Foundation, Grant 511167 (SSG). M.H. is also partially supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. M.M. is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science. Research at the Kavli Institute is supported in part by the National Science Foundation under Grant No. PHY-1748958.\n\n

Published - ATMP-2021-0025-0003-a002.pdf

Submitted - 1812.04057.pdf

", "abstract": "We consider a class of holographic quantum error-correcting codes, built from perfect tensors in network configurations dual to Bruhat\u2013Tits trees and their quotients by Schottky groups corresponding to BTZ black holes. The resulting holographic states can be constructed in the limit of infinite network size. We obtain a p\u2011adic version of entropy which obeys a Ryu\u2013Takayanagi like formula for bipartite entanglement of connected or disconnected regions, in both genus-zero and genus-one p\u2011adic backgrounds, along with a Bekenstein\u2013Hawking-type formula for black hole entropy.We prove entropy inequalities obeyed by such tensor networks, such as subadditivity, strong subadditivity, and monogamy of mutual information (which is always saturated). In addition, we construct infinite classes of perfect tensors directly from semiclassical states in phase spaces over finite fields, generalizing the CRSS algorithm, and give Hamiltonians exhibiting these as vacua.", "date": "2022-03-21", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "25", "number": "3", "publisher": "International Press", "pagerange": "591-721", "id_number": "CaltechAUTHORS:20190115-160601117", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190115-160601117", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-91ER40671" }, { "agency": "Simons Foundation", "grant_number": "511167" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Department of Innovation, Science and Economic Development (Canada)" }, { "agency": "Province of Ontario Ministry of Research, Innovation and Science" }, { "agency": "NSF", "grant_number": "PHY-1748958" } ] }, "other_numbering_system": { "items": [ { "id": "2018-053", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2021.v25.n3.a2", "primary_object": { "basename": "1812.04057.pdf", "url": "https://authors.library.caltech.edu/records/rdzzb-z5f98/files/1812.04057.pdf" }, "related_objects": [ { "basename": "ATMP-2021-0025-0003-a002.pdf", "url": "https://authors.library.caltech.edu/records/rdzzb-z5f98/files/ATMP-2021-0025-0003-a002.pdf" } ], "pub_year": "2022", "author_list": "Heydeman, Matthew; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/pqpqt-9ba35", "eprint_id": 105381, "eprint_status": "archive", "datestamp": "2023-08-20 07:15:45", "lastmod": "2026-03-08 03:31:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-Jacob", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Wigderson-Yuval", "name": { "family": "Wigderson", "given": "Yuval" }, "orcid": "0000-0001-5909-9250" } ] }, "title": "Ramsey Numbers of Books and Quasirandomness", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2022 Springer. \n\nReceived 04 January 2020; Revised 11 November 2020; Published 10 March 2022. \n\nWe would like to thank Freddie Illingworth for pointing out an error in an earlier draft of this paper. We would also like to thank the anonymous referees for their careful reviews and helpful suggestions. \n\nResearch supported by ERC Starting Grant 676632 and NSF Award DMS-2054452. \n\nResearch supported by a Packard Fellowship and by NSF Career Award DMS-1352121. \n\nResearch supported by NSF GRFP Grant DGE-1656518.\n\n

Submitted - 2001.00407.pdf

", "abstract": "The book graph B^((k))_n consists of n copies of K_(k+1) joined along a common K_k. The Ramsey numbers of B^((k))_n are known to have strong connections to the classical Ramsey numbers of cliques. Recently, the first author determined the asymptotic order of these Ramsey numbers for fixed k, thus answering an old question of Erd\u0151s, Faudree, Rousseau, and Schelp. In this paper, we first provide a simpler proof of this theorem. Next, answering a question of the first author, we present a different proof that avoids the use of Szemer\u00e9di's regularity lemma, thus providing much tighter control on the error term. Finally, we prove a conjecture of Nikiforov, Rousseau, and Schelp by showing that all extremal colorings for this Ramsey problem are quasirandom.", "date": "2022-03-10", "date_type": "published", "publication": "Combinatorica", "publisher": "Springer", "id_number": "CaltechAUTHORS:20200914-140122041", "issn": "0209-9683", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200914-140122041", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-1656518" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-021-4409-9", "primary_object": { "basename": "2001.00407.pdf", "url": "https://authors.library.caltech.edu/records/pqpqt-9ba35/files/2001.00407.pdf" }, "pub_year": "2022", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/fss3j-6y378", "eprint_id": 112175, "eprint_status": "archive", "datestamp": "2023-08-22 14:30:59", "lastmod": "2026-03-09 02:16:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borichev-Alexander", "name": { "family": "Borichev", "given": "Alexander" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Volberg-Alexander", "name": { "family": "Volberg", "given": "Alexander" } } ] }, "title": "Counting eigenvalues of Schr\u00f6dinger operators with fast decaying complex potentials", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Nonselfadjoint operator; Schr\u00f6dinger operators; Eigenvalues; Quasianalyticity; Zeros of analytic functions; General Mathematics", "note": "\u00a9 2021 Elsevier. \n\nReceived 14 August 2020, Revised 14 September 2021, Accepted 3 October 2021, Available online 25 November 2021. \n\nThe second and third author acknowledge partial support by the U.S. National Science Foundation through grants DMS-1363432, DMS-1954995 (R.L.F.) and DMS-1600065 (A.V.). This paper is based upon work supported by the National Science Foundation under Grant No. DMS-1440140 while the second and the third author were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the Spring 2017 semester. The first and the third authors were partially supported by the grant 346300 for IMPAN from the Simons Foundation and the matching 2015-2019 Polish MNiSW fund.", "abstract": "We give a sharp estimate of the number of zeros of analytic functions in the unit disc belonging to analytic quasianalytic Carleman\u2013Gevrey classes. As an application, we estimate the number of the eigenvalues for discrete Schr\u00f6dinger operators with rapidly decreasing complex-valued potentials, and, more generally, for non-symmetric Jacobi matrices.", "date": "2022-03-05", "date_type": "published", "publication": "Advances in Mathematics", "volume": "397", "publisher": "Elsevier", "pagerange": "Art. No. 108115", "id_number": "CaltechAUTHORS:20211202-191328270", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211202-191328270", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "NSF", "grant_number": "DMS-1600065" }, { "agency": "NSF", "grant_number": "DMS-1440140" }, { "agency": "Simons Foundation", "grant_number": "346300" }, { "agency": "Ministerstwo Nauki i Szkolnictwa Wy\u017cszego (MNiSW)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2021.108115", "pub_year": "2022", "author_list": "Borichev, Alexander; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/yevya-b5221", "eprint_id": 116819, "eprint_status": "archive", "datestamp": "2023-08-22 14:26:28", "lastmod": "2026-03-09 21:42:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Port-Alexander", "name": { "family": "Port", "given": "Alexander" }, "orcid": "0000-0002-2862-6895" }, { "id": "Karidi-Taelin", "name": { "family": "Karidi", "given": "Taelin" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Topological Analysis of Syntactic Structures", "ispublished": "pub", "full_text_status": "public", "keywords": "Applied Mathematics; Computational Theory and Mathematics; Computational Mathematics", "note": "The third author was supported by NSF grants DMS-1707882 and DMS-2104330 and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593.", "abstract": "We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality, of hierarchical clustering structures, and of non-trivial loops. We show there are relations that hold across language families and additional relations that are family-specific. We then analyze the trees describing the merging structure of persistent connected components for languages in different language families and we show that they partly correlate to historical phylogenetic trees but with significant differences. We also show the existence of interesting non-trivial persistent first homology groups in various language families. We give examples where explicit generators for the persistent first homology can be identified, some of which appear to correspond to homoplasy phenomena, while others may have an explanation in terms of historical linguistics, corresponding to known cases of syntactic borrowing across different language subfamilies.", "date": "2022-03", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "16", "number": "1", "publisher": "Springer Verlag", "pagerange": "Art. No. 2", "id_number": "CaltechAUTHORS:20220909-227096000", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220909-227096000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "DMS-2104330" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-021-00520-5", "pub_year": "2022", "author_list": "Port, Alexander; Karidi, Taelin; et al." }, { "id": "https://authors.library.caltech.edu/records/080n4-p0z46", "eprint_id": 112277, "eprint_status": "archive", "datestamp": "2023-08-22 14:15:02", "lastmod": "2026-03-09 02:12:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Minimizers for a one-dimensional interaction energy", "ispublished": "pub", "full_text_status": "public", "keywords": "Minimization problem; Interaction energy; Explicit solution; Applied Mathematics; Analysis", "note": "\u00a9 2021 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived 18 September 2021, Accepted 4 November 2021, Available online 3 December 2021. \n\nPartial support through U.S. National Science Foundation grant DMS-1954995 and through the Deutsche Forschungsgemeinschaft (German Research Foundation) through Germany's Excellence Strategy EXC-2111-390814868 is acknowledged.\n\n

Published - 1-s2.0-S0362546X21002716-main.pdf

Accepted Version - 2109.08929.pdf

", "abstract": "We solve explicitly a certain minimization problem for probability measures in one dimension involving an interaction energy that arises in the modeling of aggregation phenomena. We show that in a certain regime minimizers are absolutely continuous with an unbounded density, thereby settling a question that was left open in previous works.", "date": "2022-03", "date_type": "published", "publication": "Nonlinear Analysis", "volume": "216", "publisher": "Elsevier", "pagerange": "Art. No. 112691", "id_number": "CaltechAUTHORS:20211208-559893000", "issn": "0362-546X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211208-559893000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.na.2021.112691", "primary_object": { "basename": "1-s2.0-S0362546X21002716-main.pdf", "url": "https://authors.library.caltech.edu/records/080n4-p0z46/files/1-s2.0-S0362546X21002716-main.pdf" }, "related_objects": [ { "basename": "2109.08929.pdf", "url": "https://authors.library.caltech.edu/records/080n4-p0z46/files/2109.08929.pdf" } ], "pub_year": "2022", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/dv0h8-wnc25", "eprint_id": 111042, "eprint_status": "archive", "datestamp": "2023-08-20 07:06:54", "lastmod": "2026-03-09 02:36:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Halberstam-Noah", "name": { "family": "Halberstam", "given": "Noah" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "What are the limits of universality?", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2022 The Author(s). Published by the Royal Society. \n\nManuscript received 28/11/2021; Manuscript accepted 22/02/2022; Published online 30/03/2022; Published in print 30/03/2022. \n\nWe thank Romain Tessera for very helpful correspondence on the quasi-isometric classification of nilpotent groups, and thank Tyler Helmuth for enjoyable discussions on models of large upper-critical dimension. We thank Aleks Reinhardt for helpful advice on stylistic matters. The Cambridge Faculty of Mathematics HPC system, fawcett, was used for all Monte Carlo simulations. \n\nThe work of T.H. was carried out while he was a Senior Research Associate at the University of Cambridge and was supported by ERC starting grant no. 804166 (SPRS). N.H. was supported by the doctoral training centre, Cambridge Mathematics of Information (CMI). \n\nWe declare we have no competing interests.\n\n

Submitted - 2106.13218.pdf

Supplemental Material - 19367092.zip

", "abstract": "It is a central prediction of renormalization group theory that the critical behaviours of many statistical mechanics models on Euclidean lattices depend only on the dimension and not on the specific choice of lattice. We investigate the extent to which this universality continues to hold beyond the Euclidean setting, taking as case studies Bernoulli bond percolation and lattice trees. We present strong numerical evidence that the critical exponents governing these models on transitive graphs of polynomial volume growth depend only on the volume-growth dimension of the graph and not on any other large-scale features of the geometry. For example, our results strongly suggest that percolation, which has upper-critical dimension 6, has the same critical exponents on Z\u2074 and the Heisenberg group despite the distinct large-scale geometries of these two lattices preventing the relevant percolation models from sharing a common scaling limit. On the other hand, we also show that no such universality should be expected to hold on fractals, even if one allows the exponents to depend on a large number of standard fractal dimensions. Indeed, we give natural examples of two fractals which share Hausdorff, spectral, topological and topological Hausdorff dimensions but exhibit distinct numerical values of the percolation Fisher exponent \u03c4. This gives strong evidence against a conjecture of Balankin et al. (2018 Phys. Lett. A382, 12\u201319 (doi:10.1016/j.physleta.2017.10.035)).", "date": "2022-03", "date_type": "published", "publication": "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences", "volume": "478", "number": "2259", "publisher": "Royal Society", "pagerange": "Art. No. 20210857", "id_number": "CaltechAUTHORS:20210924-203748960", "issn": "1364-5021", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-203748960", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "804166" }, { "agency": "University of Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1098/rspa.2021.0857", "primary_object": { "basename": "2106.13218.pdf", "url": "https://authors.library.caltech.edu/records/dv0h8-wnc25/files/2106.13218.pdf" }, "related_objects": [ { "basename": "19367092.zip", "url": "https://authors.library.caltech.edu/records/dv0h8-wnc25/files/19367092.zip" } ], "pub_year": "2022", "author_list": "Halberstam, Noah and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/7ak9d-96772", "eprint_id": 113676, "eprint_status": "archive", "datestamp": "2023-10-09 20:57:34", "lastmod": "2026-03-18 00:02:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The strong Gauss\u2013Lucas theorem and analyticity of correlation functions via the Lee\u2013Yang theorem", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "\u00a9 2022 Author(s). Published under an exclusive license by AIP Publishing. \n\nSubmitted: 31 October 2021 \u2022 Accepted: 27 January 2022 \u2022 Published Online: 1 March 2022. \n\nThis research was supported, in part, by Israeli BSF (Grant No. 2020027). \n\nDedicated to the memory of Freeman Dyson. \n\nDATA AVAILABILITY. Data sharing is not applicable to this article as no new data were created or analyzed in this study. \n\nThe author has no conflicts of interest to disclose.\n\n

Published - 033302_1_online.pdf

Submitted - 2111-00650.pdf

", "abstract": "We provide a simple mechanism for going from Lee\u2013Yang type theorems to analyticity of correlation functions by exploiting under-appreciated inequalities of Newman. We also describe a Lee\u2013Yang approach that recovers the consequences of a low density cluster expansion for spin S models without any combinatorics.", "date": "2022-03", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "63", "number": "3", "publisher": "American Institute of Physics", "pagerange": "Art. No. 033302", "id_number": "CaltechAUTHORS:20220301-900160000", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220301-900160000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2020027" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/5.0077229", "primary_object": { "basename": "2111-00650.pdf", "url": "https://authors.library.caltech.edu/records/7ak9d-96772/files/2111-00650.pdf" }, "related_objects": [ { "basename": "033302_1_online.pdf", "url": "https://authors.library.caltech.edu/records/7ak9d-96772/files/033302_1_online.pdf" } ], "pub_year": "2022", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/dzqj3-58221", "eprint_id": 114017, "eprint_status": "archive", "datestamp": "2023-08-22 14:21:58", "lastmod": "2026-04-16 01:39:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Zhang-Pengfei-PHYSICS", "name": { "family": "Zhang", "given": "Pengfei" }, "orcid": "0000-0002-7408-0918" } ] }, "title": "A two-way approach to out-of-time-order correlators", "ispublished": "pub", "full_text_status": "public", "keywords": "1/N Expansion; Field Theories in Lower Dimensions; AdS-CFT Correspondence; Nuclear and High Energy Physics", "note": "\u00a9 2022 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived 01 December 2021. Accepted 01 March 2022. Published 21 March 2022. \n\nWe thank Douglas Stanford and Juan Maldacena for useful comments. Yingfei Gu and Pengfei Zhang also thank Shunyu Yao for explaining the paper [22] to them. Yingfei Gu is supported by the Simons Foundation through the \"It from Qubit\" program. Alexei Kitaev is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. Pengfei Zhang acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.\n\n

Published - Gu2022_Article_ATwo-wayApproachToOut-of-time-.pdf

Accepted Version - 2111.12007.pdf

", "abstract": "Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-N systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour. We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time. These dynamical perturbations, or scrambling modes, are considered on the thermofield double background and decomposed into a coherent and an incoherent part. For the large-q SYK, we obtain the OTOC in a closed form. We also prove a previously conjectured relation between the Lyapunov exponent and high-frequency behavior of the spectral function.", "date": "2022-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2022", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 133", "id_number": "CaltechAUTHORS:20220323-545297000", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220323-545297000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep03(2022)133", "primary_object": { "basename": "Gu2022_Article_ATwo-wayApproachToOut-of-time-.pdf", "url": "https://authors.library.caltech.edu/records/dzqj3-58221/files/Gu2022_Article_ATwo-wayApproachToOut-of-time-.pdf" }, "related_objects": [ { "basename": "2111.12007.pdf", "url": "https://authors.library.caltech.edu/records/dzqj3-58221/files/2111.12007.pdf" } ], "pub_year": "2022", "author_list": "Gu, Yingfei; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/avt12-hxn63", "eprint_id": 111208, "eprint_status": "archive", "datestamp": "2023-08-22 14:00:13", "lastmod": "2026-03-09 02:12:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00f6nig-Tobias", "name": { "family": "K\u00f6nig", "given": "Tobias" }, "orcid": "0000-0002-8808-897X" }, { "id": "Tang-Hanli", "name": { "family": "Tang", "given": "Hanli" }, "orcid": "0000-0001-8060-9884" } ] }, "title": "Reverse conformally invariant Sobolev inequalities on the sphere", "ispublished": "pub", "full_text_status": "public", "keywords": "Sharp constants; Sobolev inequality; Conformal invariance", "note": "\u00a9 2021 Elsevier Inc. \n\nReceived 11 May 2021, Accepted 11 November 2021, Available online 30 November 2021. \n\nPartial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 and Deutsche Forschungsgemeinschaft grant EXC-2111-390814868 (R.L.F.), Studienstiftung des Deutschen Volkes and ANR BLADE-JC ANR-18-CE40-002 (T.K.) and National Natural Science Foundation of China (Grant No. 11701032) and National Key Research and Development Program of China (Grant No. 2020YFA0712900) (H.T.) is acknowledged.\n\n

Submitted - 2105.05141.pdf

", "abstract": "We consider the optimization problem corresponding to the sharp constant in a conformally invariant Sobolev inequality on the n-sphere involving an operator of order 2s > n. In this case the Sobolev exponent is negative. Our results extend existing ones to noninteger values of s and settle the question of validity of a corresponding inequality in all dimensions n \u2265 2.", "date": "2022-02-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "282", "number": "4", "publisher": "Elsevier", "pagerange": "Art. No. 109339", "id_number": "CaltechAUTHORS:20211004-232831449", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211004-232831449", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" }, { "agency": "Studienstiftung des deutschen Volkes" }, { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-18-CE40-002" }, { "agency": "National Natural Science Foundation of China", "grant_number": "11701032" }, { "agency": "National Key Research and Development Program of China", "grant_number": "2020YFA0712900" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2021.109339", "primary_object": { "basename": "2105.05141.pdf", "url": "https://authors.library.caltech.edu/records/avt12-hxn63/files/2105.05141.pdf" }, "pub_year": "2022", "author_list": "Frank, Rupert L.; K\u00f6nig, Tobias; et al." }, { "id": "https://authors.library.caltech.edu/records/qwtt1-50b88", "eprint_id": 113523, "eprint_status": "archive", "datestamp": "2023-08-22 13:44:36", "lastmod": "2026-03-17 23:59:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Twelve tales in mathematical physics: An expanded Heineman prize lecture", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Mathematical Physics; Statistical and Nonlinear Physics", "note": "\u00a9 2022 Author(s). Published under an exclusive license by AIP Publishing. \n\nSubmitted: 05 May 2021 \u2022 Accepted: 31 October 2021 \u2022 Published Online: 22 February 2022. \n\nThis research was supported, in part, by the NSF (Grant Nos. DMS-1265592 and DMS-1665526) and Israeli BSF (Grant No. 2014337). \n\nDATA AVAILABILITY. Data sharing is not applicable to this article as no new data were created or analyzed in this study. \n\nThe author has no conflicts of interest to disclose.", "abstract": "This is an extended version of my 2018 Heineman prize lecture describing the work for which I got the prize. The citation is very broad, so this describes virtually all my work prior to 1995 and some afterward. It discusses work in non-relativistic quantum mechanics, constructive quantum field theory, and statistical mechanics.", "date": "2022-02", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "63", "number": "2", "publisher": "American Institute of Physics", "pagerange": "Art. No. 021101", "id_number": "CaltechAUTHORS:20220222-706506000", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220222-706506000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/5.0056008", "pub_year": "2022", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/gqnzf-xkk05", "eprint_id": 108659, "eprint_status": "archive", "datestamp": "2023-08-20 06:53:30", "lastmod": "2026-03-09 22:01:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benjamin-Nathan", "name": { "family": "Benjamin", "given": "Nathan" }, "orcid": "0000-0003-3661-6563" }, { "id": "Keller-Christoph-A", "name": { "family": "Keller", "given": "Christoph A." }, "orcid": "0000-0003-2592-2012" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Zadeh-Ida-G", "name": { "family": "Zadeh", "given": "Ida G." }, "orcid": "0000-0002-8803-0823" } ] }, "title": "Narain to Narnia", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. \n\nReceived 22 April 2021; Accepted 25 August 2021; Published 13 September 2021. \n\nWe thank A. Adams, K. Bringmann, S. Collier, S. Kachru, T. Kohno, A. Maloney, J. Manschot, G. Moore, K. Motegi, K. Ono, B. Rayhaun, L. Rolen, M. Sakuma, and A. Yasuhara for very helpful discussions. We thank S. Collier, T. Hartman, and A. Maloney for very helpful comments on a draft. The work of N.B. is supported in part by the Simons Foundation Grant No. 488653. The work of C.A.K. is supported in part by the Simons Foundation Grant No. 629215. The work of H.O. is supported in part by U.S. Department of Energy grant DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research 17K05407 and 20K03965, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. H.O. thanks the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant PHY-1607611, where part of this work was done.\n\n

Submitted - 2103.15826.pdf

", "abstract": "We generalize the holographic correspondence between topological gravity coupled to an abelian Chern\u2013Simons theory in three dimensions and an ensemble average of Narain's family of massless free bosons in two dimensions, discovered by Afkhami-Jeddi et al. and by Maloney and Witten. We find that the correspondence also works for toroidal orbifolds but not for K3 or Calabi\u2013Yau sigma-models and not always for the minimal models. We conjecture that the correspondence requires that the central charge is equal to the critical central charge defined by the asymptotic density of states of the chiral algebra. For toroidal orbifolds, we extend the holographic correspondence to correlation functions of twist operators by using topological properties of rational tangles in the three-dimensional ball, which represent configurations of vortices associated to a discrete gauge symmetry.", "date": "2022-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "390", "number": "1", "publisher": "Springer", "pagerange": "425-470", "id_number": "CaltechAUTHORS:20210408-122435918", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210408-122435918", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "488653" }, { "agency": "Simons Foundation", "grant_number": "629215" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "17K05407" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20K03965" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1607611" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-021-04211-x", "primary_object": { "basename": "2103.15826.pdf", "url": "https://authors.library.caltech.edu/records/gqnzf-xkk05/files/2103.15826.pdf" }, "pub_year": "2022", "author_list": "Benjamin, Nathan; Keller, Christoph A.; et al." }, { "id": "https://authors.library.caltech.edu/records/39xfc-ekz38", "eprint_id": 111035, "eprint_status": "archive", "datestamp": "2023-09-15 07:06:56", "lastmod": "2026-03-09 02:35:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Halberstam-Noah", "name": { "family": "Halberstam", "given": "Noah" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Collisions of random walks in dynamic random environments", "ispublished": "pub", "full_text_status": "public", "keywords": "Collisions, dynamic random environments, Dynamical percolation, Random walks", "note": "\u00a9 2022 Institute of Mathematical Statistics. Creative Commons Attribution 4.0 International License. \n\nSubmitted to EJP on January 4, 2021, final version accepted on December 30, 2021. First available in Project Euclid: 17 January 2022. \n\nWe thank Sebastian Andres and Jonathan Hermon for helpful\ncomments on a draft of the paper.\n\n

Published - 21-EJP738.pdf

Submitted - 2009.13951.pdf

", "abstract": "We study dynamic random conductance models on \u2124\u00b2 in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally independent random walks in the same environment collide infinitely often almost surely. These results apply in particular to random walks on dynamical percolation.", "date": "2022-01-17", "date_type": "published", "publication": "Electronic Journal of Probability", "volume": "27", "publisher": "Institute of Mathematical Statistics", "pagerange": "Art. No. 8", "id_number": "CaltechAUTHORS:20210924-202129801", "issn": "1083-6489", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-202129801", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/21-EJP738", "primary_object": { "basename": "2009.13951.pdf", "url": "https://authors.library.caltech.edu/records/39xfc-ekz38/files/2009.13951.pdf" }, "related_objects": [ { "basename": "21-EJP738.pdf", "url": "https://authors.library.caltech.edu/records/39xfc-ekz38/files/21-EJP738.pdf" } ], "pub_year": "2022", "author_list": "Halberstam, Noah and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/etx50-81w86", "eprint_id": 85188, "eprint_status": "archive", "datestamp": "2023-09-22 22:45:52", "lastmod": "2026-03-09 21:53:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ballinger-William", "name": { "family": "Ballinger", "given": "William" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" }, "orcid": "0000-0002-5287-4258" }, { "id": "Ochse-Tynan", "name": { "family": "Ochse", "given": "Tynan" } }, { "id": "Vafaee-Faramarz", "name": { "family": "Vafaee", "given": "Faramarz" } } ] }, "title": "The prism manifold realization problem II", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2022 by International Press. \n\nReceived 4 May 2018; Accepted 17 December 2018; Published 11 January 2022. \n\nThe heart of this project was done during the Caltech's Summer Undergraduate Research Fellowships (SURF) program in the summer of 2017. Y. N. was partially supported by NSF grant number DMS-1252992 and an Alfred P. Sloan Research Fellowship. F. V. was partially supported by an AMS-Simons Travel Grant. W. B. would like to thank William H. and Helen Lang, as well as Samuel P. and Frances Krown, for their generous support through the SURF program. T. O. would like to thank Joanna Wall Muir and Mr. James Muir for their generous support through the SURF program. We thank the referees for the thoughtful comments.\n\n

Submitted - 1710.00089.pdf

", "abstract": "We continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers p > 1 and q. We determine a complete list of prism manifolds P(p,q) that can be realized by positive integral surgeries on knots in S\u00b3 when q > p. The methodology undertaken to obtain the classification is similar to that of the case q < 0 in an earlier paper.", "date": "2022-01-11", "date_type": "published", "publication": "Communications in Analysis and Geometry", "volume": "29", "number": "6", "publisher": "International Press", "pagerange": "1279-1334", "id_number": "CaltechAUTHORS:20180308-070652999", "issn": "1019-8385", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180308-070652999", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "American Mathematical Society" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CAG.2021.v29.n6.a1", "primary_object": { "basename": "1710.00089.pdf", "url": "https://authors.library.caltech.edu/records/etx50-81w86/files/1710.00089.pdf" }, "pub_year": "2022", "author_list": "Ballinger, William; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/mr2ph-2s557", "eprint_id": 111515, "eprint_status": "archive", "datestamp": "2023-08-22 13:20:41", "lastmod": "2026-03-09 00:46:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dolbeault-Jean", "name": { "family": "Dolbeault", "given": "Jean" }, "orcid": "0000-0003-4234-2298" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Jeanjean-Louis", "name": { "family": "Jeanjean", "given": "Louis" }, "orcid": "0000-0002-7864-0900" } ] }, "title": "Logarithmic estimates for mean-field models in dimension two and the Schr\u00f6dinger\u2013Poisson system", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger-Poisson system; nonlinear Schr\u00f6dinger equation; mean-field coupling; Poisson equation; Newton equation; interpolation; logarithmic Hardy-Littlewood-Sobolev inequality; logarithmic Sobolev inequality", "note": "\u00a9 Acad\u00e9mie des sciences, Paris and the authors, 2021. This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/. \n\nReceived on: 2021-07-01; Accept it : 2021-09-17; Published on : 2022-01-04. \n\nPartial support through the French National Research Agency grant EFI ANR-17-CE40-0030 (J.D.), the US National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and the German Research Foundation DFG grant EXC-2111 - 390814868 (R.L.F.) is acknowledged. \n\nJ.D. and L.J. address some special thanks to the organizers of the conference Nonlinear days in Alghero, (September 16-20, 2019) where key results of this paper have been established.\n\n

Published - CRMATH_2021__359_10_1279_0.pdf

Submitted - 2107.00610.pdf

", "abstract": "In dimension two, we investigate a free energy and the ground state energy of the Schr\u00f6dinger\u2013Poisson system coupled with a logarithmic nonlinearity in terms of underlying functional inequalities which take into account the scaling invariances of the problem. Such a system can be considered as a nonlinear Schr\u00f6dinger equation with a cubic but nonlocal Poisson nonlinearity, and a local logarithmic nonlinearity. Both cases of repulsive and attractive forces are considered. We also assume that there is an external potential with minimal growth at infinity, which turns out to have a logarithmic growth. Our estimates rely on new logarithmic interpolation inequalities which combine logarithmic Hardy\u2013Littlewood\u2013Sobolev and logarithmic Sobolev inequalities. The two-dimensional model appears as a limit case of more classical problems in higher dimensions.", "date": "2022-01-04", "date_type": "published", "publication": "Comptes Rendus Math\u00e9matique", "volume": "359", "number": "10", "publisher": "Acad\u00e9mie des Sciences", "pagerange": "1279-1293", "id_number": "CaltechAUTHORS:20211018-185208122", "issn": "1631-073X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211018-185208122", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-17-CE40-0030" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111 - 390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.5802/crmath.272", "primary_object": { "basename": "2107.00610.pdf", "url": "https://authors.library.caltech.edu/records/mr2ph-2s557/files/2107.00610.pdf" }, "related_objects": [ { "basename": "CRMATH_2021__359_10_1279_0.pdf", "url": "https://authors.library.caltech.edu/records/mr2ph-2s557/files/CRMATH_2021__359_10_1279_0.pdf" } ], "pub_year": "2022", "author_list": "Dolbeault, Jean; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/rqnfa-1pg82", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:24", "lastmod": "2026-03-28 03:49:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "He", "given": "Jimmy" }, "orcid": "0000-0003-4345-6537" }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Xu", "given": "Max Wenqiang" } } ] }, "title": "Mixing time of fractional random walk on finite fields", "ispublished": "pub", "full_text_status": "public", "abstract": "

We study a random walk on F_p defined by X_(n+1) = 1\u2215X_n + ε_(n+1) if X_n ≠ 0, and X_(n+1) = ε_(n+1) if X_n = 0, where ε_(n+1) are independent and identically distributed. This can be seen as a non-linear analogue of the Chung–Diaconis–Graham process. We show that the mixing time is of order log p, answering a question of Chatterjee and Diaconis.

", "date": "2022-01-01", "date_type": "published", "publication": "Electronic Journal of Probability", "volume": "27", "number": "none", "publisher": "Institute of Mathematical Statistics", "issn": "1083-6489", "official_url": "https://authors.library.caltech.edu/records/rqnfa-1pg82", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/22-ejp858", "pub_year": "2022", "author_list": "He, Jimmy; Pham, Huy Tuan; et al." }, { "id": "https://authors.library.caltech.edu/records/fstjd-qqb57", "eprint_id": 98033, "eprint_status": "archive", "datestamp": "2023-08-20 06:23:28", "lastmod": "2026-03-08 17:37:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Monochromatic combinatorial lines of length three", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 American Mathematical Society. \n\nReceived by the editors September 8, 2019. \n\nResearch was supported by ERC Starting Grant 676632 and by NSF Award DMS-2054452.\n\n

Submitted - 1810.09767.pdf

", "abstract": "We show that there is a positive constant c such that any colouring of the cube [3]^n in c log log n colours contains a monochromatic combinatorial line.", "date": "2022-01", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "150", "number": "1", "publisher": "American Mathematical Society", "pagerange": "1-4", "id_number": "CaltechAUTHORS:20190819-170936221", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-170936221", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "NSF", "grant_number": "DMS-2054452" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/proc/15739", "primary_object": { "basename": "1810.09767.pdf", "url": "https://authors.library.caltech.edu/records/fstjd-qqb57/files/1810.09767.pdf" }, "pub_year": "2022", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/yk4b8-2q134", "eprint_id": 112788, "eprint_status": "archive", "datestamp": "2023-08-22 13:05:46", "lastmod": "2026-03-09 20:36:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Malicki-Maciej", "name": { "family": "Malicki", "given": "Maciej" } }, { "id": "Panagiotopoulos-Aristotelis", "name": { "family": "Panagiotopoulos", "given": "Aristotelis" }, "orcid": "0000-0002-7695-4842" }, { "id": "Zielinski-Joseph", "name": { "family": "Zielinski", "given": "Joseph" } } ] }, "title": "On Polish groups admitting non-essentially countable actions", "ispublished": "pub", "full_text_status": "public", "keywords": "Borel reduction, essentially countable, locally compact group, nonarchimedean\nPolish groups, stormy action; Applied Mathematics; General Mathematics", "note": "\u00a9 The Author(s), 2020. Published by Cambridge\nUniversity Press. This is an Open Access article, distributed under the terms of the Creative Commons\nAttribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use,\ndistribution, and reproduction in any medium, provided the original work is properly cited.\n\nReceived 17 September 2019 and accepted in revised form 11 November 2020. Published online by Cambridge University Press: 29 December 2020.\n\nThe research of A.S. Kechris was partially supported by NSF Grants\nDMS-1464475 and DMS-1950475. We are grateful to Anush Tserunyan, Forte Shinko and\nTodor Tsankov for their active interest in this project and their helpful suggestions. We\nalso thank the anonymous referee for many valuable detailed comments and for providing\nalternative arguments for some results.\n\n

Published - on-polish-groups-admitting-non-essentially-countable-actions.pdf

Accepted Version - 1909.08110.pdf

", "abstract": "It is a long-standing open question whether every Polish group that is not locally compact admits a Borel action on a standard Borel space whose associated orbit equivalence relation is not essentially countable. We answer this question positively for the class of all Polish groups that embed in the isometry group of a locally compact metric space. This class contains all non-archimedean Polish groups, for which we provide an alternative proof based on a new criterion for non-essential countability. Finally, we provide the following variant of a theorem of Solecki: every infinite-dimensional Banach space has a continuous action whose orbit equivalence relation is Borel but not essentially countable.", "date": "2022-01", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "42", "number": "1", "publisher": "Cambridge University Press", "pagerange": "180-194", "id_number": "CaltechAUTHORS:20220107-488030400", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220107-488030400", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1464475" }, { "agency": "NSF", "grant_number": "DMS-1950475" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/etds.2020.133", "primary_object": { "basename": "on-polish-groups-admitting-non-essentially-countable-actions.pdf", "url": "https://authors.library.caltech.edu/records/yk4b8-2q134/files/on-polish-groups-admitting-non-essentially-countable-actions.pdf" }, "related_objects": [ { "basename": "1909.08110.pdf", "url": "https://authors.library.caltech.edu/records/yk4b8-2q134/files/1909.08110.pdf" } ], "pub_year": "2022", "author_list": "Kechris, Alexander S.; Malicki, Maciej; et al." }, { "id": "https://authors.library.caltech.edu/records/srsrf-x1974", "eprint_id": 113804, "eprint_status": "archive", "datestamp": "2023-08-22 13:16:29", "lastmod": "2026-03-09 20:29:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chipeniuk-Karsten-O", "name": { "family": "Chipeniuk", "given": "Karsten O." } }, { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" }, { "id": "Walker-Todd-B", "name": { "family": "Walker", "given": "Todd B." } } ] }, "title": "Households, auctioneers, and aggregation", "ispublished": "pub", "full_text_status": "public", "keywords": "Aggregation; Heterogeneous agents; Incomplete markets; Economics and Econometrics; Finance", "note": "\u00a9 2021 The Authors. Published by Elsevier. This is an open access article under the CC BY-NC-ND license. \n\nReceived 12 April 2021, Revised 25 October 2021, Accepted 13 November 2021, Available online 11 December 2021, Version of Record 15 December 2021. \n\nKatz acknowledges support from National Science Foundation, United States grant DMS 1266104. We would like to thank participants at the NBER Summer Institute, the Federal Reserve Banks of Chicago, Cleveland, Dallas and Richmond, Reserve Bank of New Zealand, Australian National University, University of Virginia, Bundesbank Spring Conference, Stanford Institute for Theoretical Economics, Konstanz Seminar on Monetary Theory and Policy, CEMLA Research Seminar and World Congress of the Econometric Society; and Tom Winberry, Kurt Mitman, Tony Smith, Sevin Yeltekin, and Eric Young for helpful comments. We thank the editor, Florin Bilbiie, for several excellent suggestions.\n\n

Published - 1-s2.0-S0014292121002713-main.pdf

Supplemental Material - 1-s2.0-S0014292121002713-mmc1.pdf

", "abstract": "We examine aggregation in the neoclassical growth model with aggregate shocks and uninsurable employment risk, as well as related environments. We introduce a Walrasian auctioneer whose job is to report to households all possible state-contingent future prices. Households take these as given when forming expectations and making optimal consumption/savings decisions, and the auctioneer adjusts her forecasts until markets clear. This natural dichotomy between the households and the auctioneer allows us to study each problem in isolation as well as to discuss the intersection. On the household side, we separate an explicit expression for the linear permanent income component of savings from a well-behaved nonlinear adjustment arising from precautionary behavior and incomplete markets. Equipped with this decomposition, we then study how economies aggregate in the presence of various auctioneer types that are popular in the literature. The steady-state auctioneer of Huggett (1997) and Aiyagari (1994) offers a paper-and-pencil analysis of aggregation that provides a bound on more complex environments. We provide an economic interpretation of the regression coefficients and explain the lack of time variation in the auctioneer of Krusell and Smith (1998). We also introduce a new numerical method which uses the empirical distribution of auctioneer forecasts to substantially improve solution accuracy in cases where the standard coefficient of determination and other well-known statistics prove to be misleading.", "date": "2022-01", "date_type": "published", "publication": "European Economic Review", "volume": "141", "publisher": "Elsevier", "pagerange": "Art. No. 103997", "id_number": "CaltechAUTHORS:20220308-454082000", "issn": "0014-2921", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220308-454082000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1266104" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.euroecorev.2021.103997", "primary_object": { "basename": "1-s2.0-S0014292121002713-mmc1.pdf", "url": "https://authors.library.caltech.edu/records/srsrf-x1974/files/1-s2.0-S0014292121002713-mmc1.pdf" }, "related_objects": [ { "basename": "1-s2.0-S0014292121002713-main.pdf", "url": "https://authors.library.caltech.edu/records/srsrf-x1974/files/1-s2.0-S0014292121002713-main.pdf" } ], "pub_year": "2022", "author_list": "Chipeniuk, Karsten O.; Katz, Nets Hawk; et al." }, { "id": "https://authors.library.caltech.edu/records/5bfv1-vtn47", "eprint_id": 121410, "eprint_status": "archive", "datestamp": "2023-08-22 12:57:22", "lastmod": "2026-03-08 17:37:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-Jacob", "name": { "family": "Fox", "given": "Jacob" }, "orcid": "0000-0002-0664-497X" }, { "id": "Sudakov-Benny", "name": { "family": "Sudakov", "given": "Benny" }, "orcid": "0000-0003-3307-9475" }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" }, "orcid": "0000-0002-1995-3755" } ] }, "title": "Which graphs can be counted in C\u2084-free graphs?", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "\u00a9 2022 International Press. \n\nSpecial issue in honor of Fan Chung. \n\nDavid Conlon was supported by NSF Award DMS-2054452. \n\nJacob Fox was supported by a Packard Fellowship and by NSF Award DMS-1855635. \n\nBenny Sudakov is supported in part by SNSF grant 200021_196965. \n\nYufei Zhao is supported by NSF Award DMS-1764176, the MIT Solomon Buchsbaum Fund, and a Sloan Research Fellowship.", "abstract": "For which graphs F is there a sparse F-counting lemma in C\u2084-free graphs? We are interested in identifying graphs F with the property that, roughly speaking, if G is an n-vertex C\u2084-free graph with on the order of n^(3/2) edges, then the density of F in G, after a suitable normalization, is approximately at least the density of F in an \u03b5-regular approximation of G. In recent work, motivated by applications in extremal and additive combinatorics, we showed that C\u2085 has this property. Here we construct a family of graphs with the property.", "date": "2022", "date_type": "published", "publication": "Pure and Applied Mathematics Quarterly", "volume": "18", "number": "6", "publisher": "International Press", "pagerange": "2413-2432", "id_number": "CaltechAUTHORS:20230515-296699000.2", "issn": "1558-8599", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20230515-296699000.2", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "NSF", "grant_number": "DMS-1855635" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021_196965" }, { "agency": "NSF", "grant_number": "DMS-1764176" }, { "agency": "Massachusetts Institute of Technology (MIT)" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/pamq.2022.v18.n6.a4", "pub_year": "2022", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/k0xg6-g5870", "eprint_id": 116703, "eprint_status": "archive", "datestamp": "2023-08-20 06:22:59", "lastmod": "2026-03-07 04:13:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Fusion systems with J-components over F-_(2^e) with e > 1", "ispublished": "pub", "full_text_status": "public", "note": "Funding source: National Science Foundation\n\nAward Identifier / Grant number: DMS NSF-1265587\n\nAward Identifier / Grant number: DMS NSF-1601063\n\nFunding statement: This work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.\n\nCommunicated by: Christopher W. Parker", "abstract": "Let \u03ba be a finite simple group of Lie type over a field of even order q > 2. If \u03ba is not \u00b2F\u2084(q), then we determine the fusion systems \u2131 of J-component type with a fully centralized involution j such that C_(\u2131)(j) has a component realized by \u03ba. The exceptional case is treated in a later paper.", "date": "2022", "date_type": "published", "publication": "Journal of Group Theory", "publisher": "De Gruyter", "id_number": "CaltechAUTHORS:20220901-221643366", "issn": "1433-5883", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220901-221643366", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/jgth-2020-0156", "pub_year": "2022", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/2sbj7-6dx61", "eprint_id": 111675, "eprint_status": "archive", "datestamp": "2023-08-20 06:19:48", "lastmod": "2026-04-16 01:40:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mi-Xiao", "name": { "family": "Mi", "given": "Xiao" }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Roushan", "given": "Pedram" }, "orcid": "0000-0003-1917-3879" }, { "name": { "family": "Quintana", "given": "Chris" }, "orcid": "0000-0003-4408-8318" }, { "name": { "family": "Mandr\u00e0", "given": "Salvatore" }, "orcid": "0000-0002-3908-2694" }, { "name": { "family": "Marshall", "given": "Jeffrey" }, "orcid": "0000-0002-5011-1281" }, { "name": { "family": "Neill", "given": "Charles" }, "orcid": "0000-0002-6563-3568" }, { "name": { "family": "Arute", "given": "Frank" } }, { "name": { "family": "Arya", "given": "Kunal" }, "orcid": "0000-0002-6486-7100" }, { "name": { "family": "Atalaya", "given": "Juan" }, "orcid": "0000-0003-3055-2730" }, { "name": { "family": "Babbush", "given": "Ryan" }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Bardin", "given": "Joseph C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Barends", "given": "Rami" } }, { "name": { "family": "Basso", "given": "Joao" }, "orcid": "0000-0001-5547-691X" }, { "name": { "family": "Bengtsson", "given": "Andreas" }, "orcid": "0000-0001-5264-4025" }, { "name": { "family": "Boixo", "given": "Sergio" }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Bourassa", "given": "Alexandre" }, "orcid": "0000-0002-8517-7475" }, { "name": { "family": "Broughton", "given": "Michael" } }, { "name": { "family": "Buckley", "given": "Bob B." }, "orcid": "0000-0001-5139-7931" }, { "name": { "family": "Buell", "given": "David A." } }, { "name": { "family": "Burkett", "given": "Brian" }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Bushnell", "given": "Nicholas" }, "orcid": "0000-0001-7445-1654" }, { "name": { "family": "Chen", "given": "Zijun" } }, { "name": { "family": "Chiaro", "given": "Benjamin" }, "orcid": "0000-0002-2913-2790" }, { "name": { "family": "Collins", "given": "Roberto" }, "orcid": "0000-0002-6164-0007" }, { "name": { "family": "Courtney", "given": "William" } }, { "name": { "family": "Demura", "given": "Sean" }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Derk", "given": "Alan R." } }, { "name": { "family": "Dunsworth", "given": "Andrew" } }, { "name": { "family": "Eppens", "given": "Daniel" }, "orcid": "0000-0001-7134-5733" }, { "name": { "family": "Erickson", "given": "Catherine" } }, { "name": { "family": "Farhi", "given": "Edward" } }, { "name": { "family": "Fowler", "given": "Austin G." }, "orcid": "0000-0002-9048-2896" }, { "name": { "family": "Foxen", "given": "Brooks" }, "orcid": "0000-0002-3732-168X" }, { "name": { "family": "Gidney", "given": "Craig" } }, { "name": { "family": "Giustina", "given": "Marissa" } }, { "name": { "family": "Gross", "given": "Jonathan A." }, "orcid": "0000-0001-7049-6206" }, { "name": { "family": "Harrigan", "given": "Matthew P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "Sean D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Hilton", "given": "Jeremy" } }, { "name": { "family": "Ho", "given": "Alan" } }, { "name": { "family": "Hong", "given": "Sabrina" } }, { "name": { "family": "Huang", "given": "Trent" } }, { "name": { "family": "Huggins", "given": "William J." }, "orcid": "0000-0003-2735-1380" }, { "name": { "family": "Ioffe", "given": "L. B." }, "orcid": "0000-0002-8777-6789" }, { "name": { "family": "Isakov", "given": "Sergei V." } }, { "name": { "family": "Jeffrey", "given": "Evan" } }, { "name": { "family": "Jiang", "given": "Zhang" }, "orcid": "0000-0003-0435-655X" }, { "name": { "family": "Jones", "given": "Cody" } }, { "name": { "family": "Kafri", "given": "Dvir" }, "orcid": "0000-0001-9160-5176" }, { "name": { "family": "Kelly", "given": "Julian" }, "orcid": "0000-0002-2596-2121" }, { "name": { "family": "Kim", "given": "Seon" }, "orcid": "0000-0003-3397-0444" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Klimov", "given": "Paul V." } }, { "name": { "family": "Korotkov", "given": "Alexander N." } }, { "name": { "family": "Kostritsa", "given": "Fedor" } }, { "name": { "family": "Landhuis", "given": "David" }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "Pavel" } }, { "name": { "family": "Lucero", "given": "Erik" }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Martin", "given": "Orion" }, "orcid": "0000-0002-9576-573X" }, { "name": { "family": "McClean", "given": "Jarrod R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McCourt", "given": "Trevor" } }, { "name": { "family": "McEwen", "given": "Matt" }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Megrant", "given": "Anthony" }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Miao", "given": "Kevin C." } }, { "name": { "family": "Mohseni", "given": "Masoud" } }, { "name": { "family": "Montazeri", "given": "Shirin" } }, { "name": { "family": "Mruczkiewicz", "given": "Wojciech" }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Mutus", "given": "Josh" } }, { "name": { "family": "Naaman", "given": "Ofer" }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "Matthew" }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Newman", "given": "Michael" } }, { "name": { "family": "Niu", "given": "Murphy Yuezhen" } }, { "name": { "family": "O'Brien", "given": "Thomas E." }, "orcid": "0000-0002-8406-6626" }, { "name": { "family": "Opremcak", "given": "Alex" } }, { "name": { "family": "Ostby", "given": "Eric" } }, { "name": { "family": "Pato", "given": "Balint" } }, { "name": { "family": "Petukhov", "given": "Andre" } }, { "name": { "family": "Redd", "given": "Nicholas" }, "orcid": "0000-0002-6549-5441" }, { "name": { "family": "Rubin", "given": "Nicholas C." }, "orcid": "0000-0003-3963-1830" }, { "name": { "family": "Sank", "given": "Daniel" }, "orcid": "0000-0001-8188-364X" }, { "name": { "family": "Satzinger", "given": "Kevin J." }, "orcid": "0000-0001-5865-0813" }, { "name": { "family": "Shvarts", "given": "Vladimir" } }, { "name": { "family": "Strain", "given": "Doug" } }, { "name": { "family": "Szalay", "given": "Marco" }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Trevithick", "given": "Matthew D." }, "orcid": "0000-0001-6700-3140" }, { "name": { "family": "Villalonga", "given": "Benjamin" } }, { "name": { "family": "White", "given": "Theodore" }, "orcid": "0000-0002-9803-7471" }, { "name": { "family": "Yao", "given": "Z. Jamie" }, "orcid": "0000-0003-1806-5454" }, { "name": { "family": "Yeh", "given": "Ping" }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Zalcman", "given": "Adam" }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Neven", "given": "Hartmut" }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Aleiner", "given": "Igor" } }, { "name": { "family": "Kechedzhi", "given": "Kostyantyn" }, "orcid": "0000-0002-0136-1428" }, { "name": { "family": "Smelyanskiy", "given": "Vadim" }, "orcid": "0000-0002-3000-6732" }, { "name": { "family": "Chen", "given": "Yu" }, "orcid": "0000-0002-7473-6745" } ] }, "title": "Information scrambling in quantum circuits", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 American Association for the Advancement of Science. \n\nReceived 9 January 2021; accepted 19 October 2021. Published online 28 October 2021. \n\nP.R. and X.M. acknowledge fruitful discussions with P. Zoller, B. Vermersch, A. Elben, and M. Knapp. \n\nS.Ma. and J.Ma. acknowledge support from the NASA Ames Research Center and support from the NASA Advanced Supercomputing Division for providing access to the NASA HPC systems, Pleiades and Merope. S.Ma. and J.Ma. also acknowledge support from the AFRL Information Directorate under grant no. F4HBKC4162G001. J.Ma. is partially supported by NAMS contract no. NNA16BD14C. S.Ma. is also supported by the Prime contract no. 80ARC020D0010 with the NASA Ames Research Center. \n\nAuthor contributions: V.Sm., K.K., X.M., and P.R. devised the experiment. X.M., C.Q., and P.R. executed the experiment on the Google quantum hardware. X.M., P.R., K.K., and Y.C. wrote the manuscript. X.M., S.Ma., J.Ma., and K.K. wrote the supplementary materials. V.Sm., I.A., X.M., K.K., S.Ma., and J.Ma. provided theoretical support, analysis techniques, and numerical computations. I.A. and K.K. developed the Markov process model. S.Ma. designed and performed the large-scale numerical simulation, including the algorithms and software development. J.Ma. performed the noisy numerical simulations. P.R., Y.C., V.Sm., and H.N. led and coordinated the project. Infrastructure support was provided by the Google Quantum AI hardware team. The NASA Advanced Supercomputing Division at NASA Ames provided the infrastructure to run high-performance computing (HPC) simulations. All authors contributed to revising the manuscript and the supplementary materials. \n\nThe authors declare no competing interest. \n\nData and materials availability: All experimental and numerical data in the main text and supplementary materials, along with the software code for generating quantum circuits, measurements, population dynamics simulation, and tensor contraction simulation are available at Zenodo (43).\n\n

Submitted - 2101.08870.pdf

Supplemental Material - science.abg5029_sm.pdf

", "abstract": "Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.", "date": "2021-12-17", "date_type": "published", "publication": "Science", "volume": "374", "number": "6574", "publisher": "American Association for the Advancement of Science", "pagerange": "1479-1483", "id_number": "CaltechAUTHORS:20211028-210102101", "issn": "0036-8075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211028-210102101", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Research Laboratory (AFRL)", "grant_number": "F4HBKC4162G001" }, { "agency": "NASA", "grant_number": "NNA16BD14C" }, { "agency": "NASA", "grant_number": "80ARC020D0010" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1126/science.abg5029", "primary_object": { "basename": "2101.08870.pdf", "url": "https://authors.library.caltech.edu/records/2sbj7-6dx61/files/2101.08870.pdf" }, "related_objects": [ { "basename": "science.abg5029_sm.pdf", "url": "https://authors.library.caltech.edu/records/2sbj7-6dx61/files/science.abg5029_sm.pdf" } ], "pub_year": "2021", "author_list": "Mi, Xiao; Roushan, Pedram; et al." }, { "id": "https://authors.library.caltech.edu/records/a1g0e-36b86", "eprint_id": 112190, "eprint_status": "archive", "datestamp": "2023-08-22 12:43:02", "lastmod": "2026-04-16 01:40:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Satzinger-Kevin-J", "name": { "family": "Satzinger", "given": "K. J." }, "orcid": "0000-0001-5865-0813" }, { "name": { "family": "Liu", "given": "Y.-J" }, "orcid": "0000-0002-7657-9464" }, { "name": { "family": "Smith", "given": "A." }, "orcid": "0000-0002-6744-4592" }, { "id": "Knapp-Christina", "name": { "family": "Knapp", "given": "C." }, "orcid": "0000-0002-5982-8107" }, { "name": { "family": "Newman", "given": "M." } }, { "name": { "family": "Jones", "given": "C." } }, { "name": { "family": "Chen", "given": "Z." } }, { "name": { "family": "Quintana", "given": "C." } }, { "name": { "family": "Mi", "given": "X." }, "orcid": "0000-0003-0507-0211" }, { "name": { "family": "Dunsworth", "given": "A." } }, { "name": { "family": "Gidney", "given": "C." } }, { "name": { "family": "Aleiner", "given": "I." } }, { "name": { "family": "Arute", "given": "F." } }, { "name": { "family": "Arya", "given": "K." }, "orcid": "0000-0002-6486-7100" }, { "name": { "family": "Atalaya", "given": "J." } }, { "name": { "family": "Babbush", "given": "R." }, "orcid": "0000-0001-6979-9533" }, { "name": { "family": "Bardin", "given": "J. C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Barends", "given": "R." } }, { "name": { "family": "Basso", "given": "J." }, "orcid": "0000-0001-5547-691X" }, { "name": { "family": "Bengtsson", "given": "A." }, "orcid": "0000-0001-5264-4025" }, { "name": { "family": "Bilmes", "given": "A." } }, { "name": { "family": "Broughton", "given": "M." } }, { "name": { "family": "Buckley", "given": "B. B." }, "orcid": "0000-0001-5139-7931" }, { "name": { "family": "Buell", "given": "D. A." } }, { "name": { "family": "Burkett", "given": "B." }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Bushnell", "given": "N." }, "orcid": "0000-0001-7445-1654" }, { "name": { "family": "Chiaro", "given": "B." } }, { "name": { "family": "Collins", "given": "R." }, "orcid": "0000-0002-6164-0007" }, { "name": { "family": "Courtney", "given": "W." } }, { "name": { "family": "Demura", "given": "S." }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Derk", "given": "A. R." } }, { "name": { "family": "Eppens", "given": "D." }, "orcid": "0000-0001-7134-5733" }, { "name": { "family": "Erickson", "given": "C." } }, { "name": { "family": "Faoro", "given": "L." } }, { "name": { "family": "Farhi", "given": "E." } }, { "name": { "family": "Fowler", "given": "A. G." }, "orcid": "0000-0002-9048-2896" }, { "name": { "family": "Foxen", "given": "B." }, "orcid": "0000-0002-3732-168X" }, { "name": { "family": "Giustina", "given": "M." } }, { "name": { "family": "Greene", "given": "A." }, "orcid": "0000-0002-4034-8744" }, { "name": { "family": "Gross", "given": "J. A." }, "orcid": "0000-0001-7049-6206" }, { "name": { "family": "Harrigan", "given": "M. P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "S. D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Hilton", "given": "J." } }, { "name": { "family": "Hong", "given": "S." } }, { "name": { "family": "Huang", "given": "T." } }, { "name": { "family": "Huggins", "given": "W. J." } }, { "name": { "family": "Ioffe", "given": "L. B." }, "orcid": "0000-0002-8777-6789" }, { "name": { "family": "Isakov", "given": "S. V." } }, { "name": { "family": "Jeffrey", "given": "E." } }, { "name": { "family": "Jiang", "given": "Z." }, "orcid": "0000-0003-0435-655X" }, { "name": { "family": "Kafri", "given": "D." }, "orcid": "0000-0001-9160-5176" }, { "name": { "family": "Kechedzhi", "given": "K." }, "orcid": "0000-0002-0136-1428" }, { "name": { "family": "Khattar", "given": "T." } }, { "name": { "family": "Kim", "given": "S." }, "orcid": "0000-0003-3397-0444" }, { "name": { "family": "Klimov", "given": "P. V." } }, { "name": { "family": "Korotkov", "given": "A. N." } }, { "name": { "family": "Kostritsa", "given": "F." } }, { "name": { "family": "Landhuis", "given": "D." }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "P." } }, { "name": { "family": "Locharla", "given": "A." } }, { "name": { "family": "Lucero", "given": "E." }, "orcid": "0000-0002-6449-2273" }, { "name": { "family": "Martin", "given": "O." }, "orcid": "0000-0002-9576-573X" }, { "name": { "family": "McClean", "given": "J. R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McEwen", "given": "M." }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Miao", "given": "K. C." } }, { "name": { "family": "Mohseni", "given": "M." } }, { "name": { "family": "Montazeri", "given": "S." } }, { "name": { "family": "Mruczkiewicz", "given": "W." }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Mutus", "given": "J." } }, { "name": { "family": "Naaman", "given": "O." }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "M." }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Neill", "given": "C." }, "orcid": "0000-0002-6563-3568" }, { "name": { "family": "Niu", "given": "M. Y." } }, { "name": { "family": "O'Brien", "given": "T. E." }, "orcid": "0000-0002-8406-6626" }, { "name": { "family": "Opremcak", "given": "A." } }, { "name": { "family": "Pat\u00f3", "given": "B." } }, { "name": { "family": "Petukhov", "given": "A." } }, { "name": { "family": "Rubin", "given": "N. C." }, "orcid": "0000-0003-3963-1830" }, { "name": { "family": "Sank", "given": "D." }, "orcid": "0000-0001-8188-364X" }, { "name": { "family": "Shvarts", "given": "V." } }, { "name": { "family": "Strain", "given": "D." } }, { "name": { "family": "Szalay", "given": "M." }, "orcid": "0000-0002-1310-9174" }, { "name": { "family": "Villalonga", "given": "B." } }, { "name": { "family": "White", "given": "T. C." }, "orcid": "0000-0002-9803-7471" }, { "name": { "family": "Yao", "given": "Z." }, "orcid": "0000-0003-1806-5454" }, { "name": { "family": "Yeh", "given": "P." }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "J." } }, { "name": { "family": "Zalcman", "given": "A." }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Neven", "given": "H." }, "orcid": "0000-0002-9681-6746" }, { "name": { "family": "Boixo", "given": "S." }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Megrant", "given": "A." }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Chen", "given": "Y." }, "orcid": "0000-0002-7473-6745" }, { "name": { "family": "Kelly", "given": "J." } }, { "name": { "family": "Smelyanskiy", "given": "V." }, "orcid": "0000-0002-3000-6732" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A." }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Knap", "given": "M." }, "orcid": "0000-0002-7093-9502" }, { "name": { "family": "Pollmann", "given": "F." }, "orcid": "0000-0003-0320-9304" }, { "name": { "family": "Roushan", "given": "P." }, "orcid": "0000-0003-1917-3879" } ] }, "title": "Realizing topologically ordered states on a quantum processor", "ispublished": "pub", "full_text_status": "public", "keywords": "Multidisciplinary", "note": "\u00a9 2021 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. https://www.sciencemag.org/about/science-licenses-journal-article-reuse This is an article distributed under the terms of the Science Journals Default License. \n\n2 April 2021; accepted 28 October 2021. \n\nWe thank B. Bauer, A. Elben, B. Vermersch, and G. Vidal for useful discussions. \n\nF.P., Y.-J.L., A.S., and M.K. acknowledge support from the Technical University of Munich\u2013Institute for Advanced Study, funded by the German Excellence Initiative and the European Union FP7 under grant agreement 291763; the Max Planck Gesellschaft (MPG) through the International Max Planck Research School for Quantum Science and Technology (IMPRS-QST); the Deutsche Forschungsgemeinschaft (DFG; German Research Foundation) under Germany's Excellence Strategy\u2013EXC\u20132111\u2013390814868, TRR80, and DFG grant KN1254/2-1; and from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreements 771537 and 851161). A.S. was supported by a Research Fellowship from the Royal Commission for the Exhibition of 1851. C.K. was supported by the Walter Burke Institute for Theoretical Physics at Caltech, and by the IQIM, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, the Packard Foundation, and the Simons Foundation. \n\nAuthor contributions: A.S., M.K., F.P., K.J.S., Y.-J.L., C.K., and P.R. designed the experiment. K.J.S. and P.R. performed the experiment. K.J.S. and Y.-J.L. analyzed the data and wrote the supplement. Y.-J.L., A.S., C.K., M.K., F.P., and K.J.S. provided theoretical support and analysis. C.K., K.JS., Y.-J.L., A.S., M.K., F.P., and P.R. wrote the manuscript. All authors contributed to revising the manuscript and supplement. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. \n\nThe authors declare no competing interests. \n\nData and materials availability: Data and code used for analysis and simulation are available at (44).\n\n

Submitted - 2104.01180.pdf

Supplemental Material - science.abi8378_sm.pdf

", "abstract": "The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error\u2013correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of \u2013ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.", "date": "2021-12-03", "date_type": "published", "publication": "Science", "volume": "374", "number": "6572", "publisher": "American Association for the Advancement of Science", "pagerange": "1237-1241", "id_number": "CaltechAUTHORS:20211203-174950058", "issn": "0036-8075", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211203-174950058", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Technical University of Munich" }, { "agency": "European Research Council (ERC)", "grant_number": "291763" }, { "agency": "International Max Planck Research School for Quantum Science and Technology" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "TRR80" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "KN1254/2-1" }, { "agency": "European Research Council (ERC)", "grant_number": "771537" }, { "agency": "European Research Council (ERC)", "grant_number": "851161" }, { "agency": "Royal Commission for the Exhibition of 1851" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "NSF" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1126/science.abi8378", "primary_object": { "basename": "2104.01180.pdf", "url": "https://authors.library.caltech.edu/records/a1g0e-36b86/files/2104.01180.pdf" }, "related_objects": [ { "basename": "science.abi8378_sm.pdf", "url": "https://authors.library.caltech.edu/records/a1g0e-36b86/files/science.abi8378_sm.pdf" } ], "pub_year": "2021", "author_list": "Satzinger, K. J.; Liu, Y.-J; et al." }, { "id": "https://authors.library.caltech.edu/records/4ygnq-sbn35", "eprint_id": 108743, "eprint_status": "archive", "datestamp": "2023-08-22 12:25:58", "lastmod": "2026-03-30 07:15:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Shu-Kevin", "name": { "family": "Shu", "given": "Kevin" } }, { "id": "Ortegaray-Andrew", "name": { "family": "Ortegaray", "given": "Andrew" } }, { "id": "Berwick-Robert-C", "name": { "family": "Berwick", "given": "Robert C." }, "orcid": "0000-0002-1061-1871" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Phylogenetics of Indo-European Language Families via an Algebro-Geometric Analysis of Their Syntactic Structures", "ispublished": "pub", "full_text_status": "public", "keywords": "Phylogenetic algebraic geometry; Syntactic parameters; Historical linguistics; Phylogenetic trees; Indo-European languages", "note": "\u00a9 The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021. \n\nReceived 30 April 2018; Revised 20 January 2019; Accepted 05 March 2021; Published 15 April 2021. \n\nThe first and second author were partially supported by a Summer Undergraduate Research Fellowship at Caltech. The last author is partially supported by NSF Grant DMS-1707882, NSERC Discovery Grant RGPIN-2018-04937, Accelerator Supplement Grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics. We are very grateful to the two anonymous referees for many very useful comments, corrections, and suggestions that greatly improved the paper.\n\n

Submitted - 1712.01719.pdf

", "abstract": "Using Phylogenetic Algebraic Geometry, we analyze computationally the phylogenetic tree of subfamilies of the Indo-European language family, using data of syntactic structures. The two main sources of syntactic data are the SSWL database and Longobardi's recent data of syntactic parameters. We compute phylogenetic invariants and estimates of the Euclidean distance functions for two sets of Germanic languages, a set of Romance languages, a set of Slavic languages and a set of early Indo-European languages, and we compare the results with what is known through historical linguistics.", "date": "2021-12", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "15", "number": "4", "publisher": "Springer", "pagerange": "803-857", "id_number": "CaltechAUTHORS:20210415-115930614", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210415-115930614", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-021-00507-2", "primary_object": { "basename": "1712.01719.pdf", "url": "https://authors.library.caltech.edu/records/4ygnq-sbn35/files/1712.01719.pdf" }, "pub_year": "2021", "author_list": "Shu, Kevin; Ortegaray, Andrew; et al." }, { "id": "https://authors.library.caltech.edu/records/137hj-tjx44", "eprint_id": 105369, "eprint_status": "archive", "datestamp": "2023-08-20 06:04:25", "lastmod": "2026-03-29 19:22:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-Jacob", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-Benny", "name": { "family": "Sudakov", "given": "Benny" } }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" } } ] }, "title": "The regularity method for graphs with few 4-cycles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. \n\nIssue Online: 21 December 2021; Version of Record online: 30 September 2021; Manuscript revised: 10 May 2021; Manuscript received: 10 December 2020. \n\nWe would like to thank Jacques Verstra\u00ebte and J\u00f3zsef Solymosi for helpful comments. \n\nConlon is supported by NSF Award DMS-2054452 and in part by ERC Starting Grant 676632. Fox is supported by a Packard Fellowship and by NSF Award DMS-1855635. Sudakov is supported in part by SNSF grant 200021_196965. Zhao is supported by NSF Award DMS-1764176, the MIT Solomon Buchsbaum Fund, and a Sloan Research Fellowship.\n\n

Submitted - 2004.10180.pdf

", "abstract": "We develop a sparse graph regularity method that applies to graphs with few 4-cycles, including new counting and removal lemmas for 5-cycles in such graphs. Some applications include: \n\nEvery n-vertex graph with no 5-cycle can be made triangle-free by deleting o(n^(3/2)) edges. \nFor r \u2a7e 3, every n-vertex r-graph with girth greater than 5 has o(n^(3/2)) edges. \nEvery subset of [n] without a nontrivial solution to the equation x\u2081 + x\u2082 + 2x\u2083 = x\u2084 + 3x\u2085 has size o(\u221an).", "date": "2021-12", "date_type": "published", "publication": "Journal of the London Mathematical Society", "volume": "104", "number": "5", "publisher": "Wiley", "pagerange": "2376-2401", "id_number": "CaltechAUTHORS:20200914-101307280", "issn": "0024-6107", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200914-101307280", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1855635" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021_196965" }, { "agency": "NSF", "grant_number": "DMS-1764176" }, { "agency": "Massachusetts Institute of Technology (MIT)" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/jlms.12500", "primary_object": { "basename": "2004.10180.pdf", "url": "https://authors.library.caltech.edu/records/137hj-tjx44/files/2004.10180.pdf" }, "pub_year": "2021", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/5p7hb-96a37", "eprint_id": 106024, "eprint_status": "archive", "datestamp": "2023-08-20 06:04:33", "lastmod": "2026-03-28 23:46:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Putrov-Pavel", "name": { "family": "Putrov", "given": "Pavel" }, "orcid": "0000-0002-7207-4688" } ] }, "title": "Cobordism Invariants from BPS q-Series", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 Springer Nature Switzerland AG. \n\nReceived 16 February 2021; Accepted 15 July 2021; Published 29 July 2021. \n\nWe are especially grateful to Francesca Ferrari, Ciprian Manolescu, and Yi Ni for their help and insightful comments. It is also a pleasure to thank Rob Kirby and Paul Melvin for stimulating discussions and inspiration at the triple-header birthday conference \"Topology in Dimensions 3, 3.5 and 4\" in Berkeley (June, 2018). We also thank Cumrun Vafa for encouragement and comments. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The research of S.P. is supported by Kwanjeong Educational Foundation.\n\n

Submitted - 2009.11874.pdf

", "abstract": "Many BPS partition functions depend on a choice of additional structure: fluxes, Spin or Spin^c structures, etc. In a context where the BPS-generating series depends on a choice of Spin^c structure, we show how different limits with respect to the expansion variable q and different ways of summing over Spin^c structures produce different invariants of homology cobordisms out of the BPS q-series.", "date": "2021-12", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "22", "number": "12", "publisher": "Springer", "pagerange": "4173-4203", "id_number": "CaltechAUTHORS:20201013-115124820", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201013-115124820", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "Kwanjeong Educational Foundation" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-021-01089-2", "primary_object": { "basename": "2009.11874.pdf", "url": "https://authors.library.caltech.edu/records/5p7hb-96a37/files/2009.11874.pdf" }, "pub_year": "2021", "author_list": "Gukov, Sergei; Park, Sunghyuk; et al." }, { "id": "https://authors.library.caltech.edu/records/by8sz-xt784", "eprint_id": 111359, "eprint_status": "archive", "datestamp": "2023-08-20 06:06:59", "lastmod": "2026-03-29 21:50:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Nam-Phan-Th\u00e0nh", "name": { "family": "Nam", "given": "Phan Th\u00e0nh" }, "orcid": "0000-0001-7599-9742" } ] }, "title": "Existence and nonexistence in the liquid drop model", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 06 January 2021; Accepted 26 July 2021; Published 16 September 2021. \n\nPartial support through U.S. National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and through the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Germany's Excellence Strategy EXC - 2111 - 390814868 (R.L.F., P.T.N.) is acknowledged. \n\nOpen Access funding enabled and organized by Projekt DEAL. \n\nThis paper may be reproduced, in its entirety, for non-commercial purposes. \n\nCommunicated by E. Lenzmann.\n\n

Published - Frank-Nam2021_Article_ExistenceAndNonexistenceInTheL.pdf

Submitted - 2101.02163.pdf

", "abstract": "We revisit the liquid drop model with a general Riesz potential. Our new result is the existence of minimizers for the conjectured optimal range of parameters. We also prove a conditional uniqueness of minimizers and a nonexistence result for heavy nuclei.", "date": "2021-12", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "60", "number": "6", "publisher": "Springer", "pagerange": "Art. No. 223", "id_number": "CaltechAUTHORS:20211011-213336774", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211011-213336774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111 - 390814868" }, { "agency": "Projekt DEAL" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-021-02072-9", "primary_object": { "basename": "Frank-Nam2021_Article_ExistenceAndNonexistenceInTheL.pdf", "url": "https://authors.library.caltech.edu/records/by8sz-xt784/files/Frank-Nam2021_Article_ExistenceAndNonexistenceInTheL.pdf" }, "related_objects": [ { "basename": "2101.02163.pdf", "url": "https://authors.library.caltech.edu/records/by8sz-xt784/files/2101.02163.pdf" } ], "pub_year": "2021", "author_list": "Frank, Rupert L. and Nam, Phan Th\u00e0nh" }, { "id": "https://authors.library.caltech.edu/records/q8cz8-mfn21", "eprint_id": 112851, "eprint_status": "archive", "datestamp": "2023-08-22 12:37:13", "lastmod": "2026-03-28 22:21:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "A Characterization of T_(2g+1,2) among Alternating Knots", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Alternating knots; Alexander polynomial; strongly quasipositive fibered knots; Applied Mathematics; General Mathematics", "note": "\u00a9 Springer-Verlag GmbH Germany & The Editorial Office of AMS 2021. \n\nReceived July 31, 2020, accepted May 31, 2021. \n\nSupported by NSF (Grant No. DMS-1811900).", "abstract": "Let K be a genus g alternating knot with Alexander polynomial \u0394_K(T) = \u2211^g_i = _(\u2212g)a_iT^. We show that if |a_g| = |a_(g\u22121)|, then K is the torus knot T_(2g+1,\u00b12). This is a special case of the Fox Trapezoidal Conjecture. The proof uses Ozsv\u00e1th and Szab\u00f3's work on alternating knots.", "date": "2021-12", "date_type": "published", "publication": "Acta Mathematica Sinica, English Series", "volume": "37", "number": "12", "publisher": "Springer", "pagerange": "1841-1846", "id_number": "CaltechAUTHORS:20220112-559780400", "issn": "1439-8516", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220112-559780400", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1811900" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10114-021-0408-4", "pub_year": "2021", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/yt07v-ykk89", "eprint_id": 111823, "eprint_status": "archive", "datestamp": "2023-08-20 06:07:20", "lastmod": "2026-03-29 21:25:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Albion-Seamus-P", "name": { "family": "Albion", "given": "Seamus P." }, "orcid": "0000-0002-8930-3109" }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Warnaar-Sven-Ole", "name": { "family": "Warnaar", "given": "S. Ole" }, "orcid": "0000-0002-9786-0175" } ] }, "title": "AFLT-type Selberg integrals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. \n\nReceived: 5 February 2020; Accepted: 27 June 2021. \n\nWork supported by the Australian Research Council Discovery Grant DP170102648.\n\n

Accepted Version - 2001.05637.pdf

", "abstract": "In their 2011 paper on the AGT conjecture, Alba, Fateev, Litvinov and Tarnopolsky (AFLT) obtained a closed-form evaluation for a Selberg integral over the product of two Jack polynomials, thereby unifying the well-known Kadell and Hua\u2013Kadell integrals. In this paper we use a variety of symmetric functions and symmetric function techniques to prove generalisations of the AFLT integral. These include (i) an A_n analogue of the AFLT integral, containing two Jack polynomials in the integrand; (ii) a generalisation of (i) for \u03b3 = 1 (the Schur or GUE case), containing a product of n+1 Schur functions; (iii) an elliptic generalisation of the AFLT integral in which the role of the Jack polynomials is played by a pair of elliptic interpolation functions; (iv) an AFLT integral for Macdonald polynomials.", "date": "2021-12", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "388", "number": "2", "publisher": "Springer", "pagerange": "735-791", "id_number": "CaltechAUTHORS:20211110-164135228", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211110-164135228", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council", "grant_number": "DP170102648" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-021-04157-0", "primary_object": { "basename": "2001.05637.pdf", "url": "https://authors.library.caltech.edu/records/yt07v-ykk89/files/2001.05637.pdf" }, "pub_year": "2021", "author_list": "Albion, Seamus P.; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/zjqcj-8vr56", "eprint_id": 110761, "eprint_status": "archive", "datestamp": "2023-08-22 11:44:40", "lastmod": "2026-03-28 21:11:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lima-Alicia", "name": { "family": "Lima", "given": "Alicia" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Functor of points and height functions for noncommutative Arakelov geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "Noncommutative arithmetic spaces; Functor of points; Arakelov height; Arithmetic curves", "note": "\u00a9 2021 Elsevier. \n\nReceived 1 March 2021, Revised 15 July 2021, Accepted 17 July 2021, Available online 22 July 2021. \n\nThe second author was partially supported by NSF grant DMS-1707882 and DMS-2104330, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593.\n\n

Accepted Version - 2012.15276.pdf

", "abstract": "We propose a notion of functor of points for noncommutative spaces, valued in categories of bimodules, and endowed with an action functional determined by a notion of hermitian structures and height functions, modeled on an interpretation of the classical functor of points as a physical sigma model. We discuss different choices of such height functions, based on different notions of volumes and traces, including one based on the Hattori-Stallings rank. We show that the height function determines a dynamical time evolution on an algebra of observables associated to our functor of points. We focus in particular the case of noncommutative arithmetic curves, where the relevant algebras are sums of matrix algebras over division algebras over number fields, and we discuss a more general notion of noncommutative arithmetic spaces in higher dimensions, where our approach suggests an interpretation of the Jones index as a height function.", "date": "2021-11", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "169", "publisher": "Elsevier", "pagerange": "Art. No. 104337", "id_number": "CaltechAUTHORS:20210908-171121986", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210908-171121986", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "DMS-2104330" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2021.104337", "primary_object": { "basename": "2012.15276.pdf", "url": "https://authors.library.caltech.edu/records/zjqcj-8vr56/files/2012.15276.pdf" }, "pub_year": "2021", "author_list": "Lima, Alicia and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/b2avf-5rb22", "eprint_id": 111029, "eprint_status": "archive", "datestamp": "2023-08-20 05:47:43", "lastmod": "2026-03-28 20:45:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hermon-Jonathan", "name": { "family": "Hermon", "given": "Jonathan" }, "orcid": "0000-0002-2935-3999" }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "No Percolation at Criticality on Certain Groups of Intermediate Growth", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2020. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). \n\nReceived: 01 October 2018; Revision received: 06 September 2019; Accepted: 10 September 2019; Published: 06 December 2019. \n\nWe thank Gidi Amir and Tianyi Zheng for sharing their expertise on groups of intermediate growth. \n\nThis work was supported by Engineering and Physical Sciences Research Council (EPSRC) (EP/L018896/1 to J.H.).\n\n

Accepted Version - 1809.11112.pdf

", "abstract": "We prove that critical percolation has no infinite clusters almost surely on any unimodular quasi-transitive graph satisfying a return probability upper bound of the form p_n(v,v) \u2264 exp[\u2212\u03a9(n^\u03b3)] for some \u03b3 > \u00bd\u2060. The result is new in the case that the graph is of intermediate volume growth.", "date": "2021-11", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2021", "number": "22", "publisher": "Oxford University Press", "pagerange": "17433-17455", "id_number": "CaltechAUTHORS:20210924-202109319", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-202109319", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/L018896/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnz265", "primary_object": { "basename": "1809.11112.pdf", "url": "https://authors.library.caltech.edu/records/b2avf-5rb22/files/1809.11112.pdf" }, "pub_year": "2021", "author_list": "Hermon, Jonathan and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/z0mra-apz46", "eprint_id": 108291, "eprint_status": "archive", "datestamp": "2023-08-20 05:37:56", "lastmod": "2026-03-29 21:06:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eischen-Ellen-E", "name": { "family": "Eischen", "given": "Ellen" } }, { "id": "Flander-Max", "name": { "family": "Flander", "given": "Max" } }, { "id": "Ghitza-Alexandru", "name": { "family": "Ghitza", "given": "Alexandru" } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } }, { "id": "McAndrew-Angus", "name": { "family": "McAndrew", "given": "Angus" } } ] }, "title": "Differential operators mod p: analytic continuation and consequences", "ispublished": "pub", "full_text_status": "public", "keywords": "theta operators, mod p differential operators, mod p automorphic forms, analytic continuation", "note": "\u00a9 2021 Mathematical Sciences Publishers. \n\nReceived: 5 November 2019; Revised: 5 December 2020; Accepted: 5 January 2021; Published: 16 October 2021. \n\nPartially supported by NSF Grants DMS-1559609 and DMS-1751281. \n\nSupported by an Australian Postgraduate Award. \n\nPartially supported by an Australian Postgraduate Award and the Albert Shimmins Writing Up Award.\n\n

Submitted - 1902.10911.pdf

", "abstract": "We study certain mod p differential operators that act on automorphic forms over Shimura varieties of type A or C. We show that, over the ordinary locus, these operators agree with the mod p reduction of the p-adic theta operators previously studied by some of the authors. In the characteristic 0, p-adic case, there is an obstruction that makes it impossible to extend the theta operators to the whole Shimura variety. On the other hand, our mod p operators extend (\"analytically continue\", in the language of de Shalit and Goren) to the whole Shimura variety. As a consequence, motivated by their use by Edixhoven and Jochnowitz in the case of modular forms for proving the weight part of Serre's conjecture, we discuss some effects of these operators on Galois representations. \n\nOur focus and techniques differ from those in the literature. Our intrinsic, coordinate-free approach removes difficulties that arise from working with q-expansions and works in settings where earlier techniques, which rely on explicit calculations, are not applicable. In contrast with previous constructions and analytic continuation results, these techniques work for any totally real base field, any weight, and all signatures and ranks of groups at once, recovering prior results on analytic continuation as special cases.", "date": "2021-10-16", "date_type": "published", "publication": "Algebra and Number Theory", "volume": "15", "number": "6", "publisher": "Mathematical Sciences Publishers", "pagerange": "1469-1504", "id_number": "CaltechAUTHORS:20210303-132200090", "issn": "1937-0652", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210303-132200090", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1559609" }, { "agency": "NSF", "grant_number": "DMS-1751281" }, { "agency": "Australian Postgraduate Award" }, { "agency": "Albert Shimmins Writing Up Award" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/ant.2021.15.1469", "primary_object": { "basename": "1902.10911.pdf", "url": "https://authors.library.caltech.edu/records/z0mra-apz46/files/1902.10911.pdf" }, "pub_year": "2021", "author_list": "Eischen, Ellen; Flander, Max; et al." }, { "id": "https://authors.library.caltech.edu/records/b8q0c-08f30", "eprint_id": 109624, "eprint_status": "archive", "datestamp": "2023-08-22 11:35:37", "lastmod": "2026-03-29 20:46:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Ivanisvili-Paata", "name": { "family": "Ivanisvili", "given": "Paata" } } ] }, "title": "Hypercontractivity of the semigroup of the fractional Laplacian on the n-sphere", "ispublished": "pub", "full_text_status": "public", "keywords": "hypercontractivity; Poisson semigroup; n-Sphere", "note": "\u00a9 2021 Elsevier. \n\nReceived 17 January 2021, Accepted 14 June 2021, Available online 18 June 2021. \n\nPartial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) as well as DMS-2052645, DMS-1856486, and CAREER-DMS-2052865, CAREER-DMS-1945102 (P.I.) is acknowledged.\n\n

Submitted - 2101.06209.pdf

", "abstract": "For 1 < p \u2264 q we show that the Poisson semigroup e^(-t\u221a-\u0394) on the n-sphere is hypercontractive from L^p to L^q in dimensions n \u2264 3 if and only if e^(-t\u221an) \u2264 \u221a((p - 1)/(q - 1)). We also show that the equivalence fails in large dimensions.", "date": "2021-10-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "281", "number": "8", "publisher": "Elsevier", "pagerange": "Art. No. 109145", "id_number": "CaltechAUTHORS:20210628-191053213", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053213", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "NSF", "grant_number": "DMS-2052645" }, { "agency": "NSF", "grant_number": "DMS-1856486" }, { "agency": "NSF", "grant_number": "DMS-2052865" }, { "agency": "NSF", "grant_number": "DMS-1945102" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2021.109145", "primary_object": { "basename": "2101.06209.pdf", "url": "https://authors.library.caltech.edu/records/b8q0c-08f30/files/2101.06209.pdf" }, "pub_year": "2021", "author_list": "Frank, Rupert L. and Ivanisvili, Paata" }, { "id": "https://authors.library.caltech.edu/records/gzavk-dpt69", "eprint_id": 100887, "eprint_status": "archive", "datestamp": "2023-08-20 05:15:49", "lastmod": "2026-03-28 23:09:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chase-Zachary", "name": { "family": "Chase", "given": "Zachary" }, "orcid": "0000-0001-7015-3537" }, { "id": "Hann-Caruthers-Wade", "name": { "family": "Hann-Caruthers", "given": "Wade" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Additive conjugacy and the Bohr compactification of orthogonal representations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. \n\nReceived 24 July 2019; Revised 09 January 2021; Accepted 21 April 2021; Published 27 April 2021. \n\nWe would like to thank Todor Tsankov for suggesting some improvements to our proofs, Yehuda Shalom for suggesting to us the classification of the additive conjugacy classes of the irreducible representations of Z, and Andreas Thom for pointing out an error in an earlier version, as well as suggesting a correct proof. We would also like to thank Joshua Frisch, Eli Glasner, Alexander Kechris, Jesse Peterson, Pooya Vahidi Ferdowsi, Benjamin Weiss, and Andy Zucker for helpful discussions. \n\nOmer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan research fellowship, a BSF award (#2018397), and an NSF CAREER award (DMS-1944153).\n\n

Submitted - 1905.11599.pdf

", "abstract": "We say that two unitary or orthogonal representations of a finitely generated group G are additive conjugates if they are intertwined by an additive map, which need not be continuous. We associate to each representation of G a topological action that is a complete additive conjugacy invariant: the action of G by group automorphisms on the Bohr compactification of the underlying Hilbert space. Using this construction we show that the property of having almost invariant vectors is an additive conjugacy invariant. As an application we show that G is amenable if and only if there is a nonzero homomorphism from L\u00b2(G) into R/Z that is invariant to the G-action.", "date": "2021-10", "date_type": "published", "publication": "Mathematische Annalen", "volume": "381", "number": "1-2", "publisher": "Springer Verlag", "pagerange": "319-333", "id_number": "CaltechAUTHORS:20200124-084913765", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-084913765", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2018397" }, { "agency": "NSF", "grant_number": "DMS-1944153" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-021-02191-w", "primary_object": { "basename": "1905.11599.pdf", "url": "https://authors.library.caltech.edu/records/gzavk-dpt69/files/1905.11599.pdf" }, "pub_year": "2021", "author_list": "Chase, Zachary; Hann-Caruthers, Wade; et al." }, { "id": "https://authors.library.caltech.edu/records/bek1j-4v298", "eprint_id": 109623, "eprint_status": "archive", "datestamp": "2023-08-22 11:21:06", "lastmod": "2026-03-30 15:45:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Hsin-Po-Shen", "name": { "family": "Hsin", "given": "Po-Shen" }, "orcid": "0000-0002-4764-1476" }, { "id": "Nakajima-Hiraku", "name": { "family": "Nakajima", "given": "Hiraku" }, "orcid": "0000-0002-6060-758X" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Sopenko-Nikita", "name": { "family": "Sopenko", "given": "Nikita" }, "orcid": "0000-0002-8479-1924" } ] }, "title": "Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants", "ispublished": "pub", "full_text_status": "public", "keywords": "Equivariant index formula; Verlinde formula; Rozansky-Witten theory; ADO invariants", "note": "\u00a9 2021 Elsevier. \n\nReceived 7 February 2021, Accepted 14 June 2021, Available online 18 June 2021. \n\nIt is pleasure to thank J\u00f8rgen Andersen, Francesco Costantino, Pavel Etingof, Boris Feigin, Igor Frenkel, Azat Gainutdinov, Amihay Hanany, Anna Lachowska, Ciprian Manolescu, Jun Murakami, Mark Penney, Lev Rozansky, and Shing-Tung Yau for illuminating discussions and comments. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of P.-S.H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of H.N. is supported in part by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and by JSPS Grant Number 16H06335, 19K21828. The work of S.P. is supported by Kwanjeong Educational Foundation. The work of D.P. is supported by the Center for Mathematical Sciences and Applications at Harvard University. N.S. gratefully acknowledges the support of the Dominic Orr Graduate Fellowship at Caltech.\n\n

Submitted - 2005.05347.pdf

", "abstract": "By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. This opens up several new avenues, which include a new formulation of q-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.", "date": "2021-10", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "168", "publisher": "Elsevier", "pagerange": "Art. No. 104311", "id_number": "CaltechAUTHORS:20210628-191053120", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210628-191053120", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "16H06335" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "19K21828" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Harvard University" }, { "agency": "Dominic Orr Graduate Fellowship" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2021.104311", "primary_object": { "basename": "2005.05347.pdf", "url": "https://authors.library.caltech.edu/records/bek1j-4v298/files/2005.05347.pdf" }, "pub_year": "2021", "author_list": "Gukov, Sergei; Hsin, Po-Shen; et al." }, { "id": "https://authors.library.caltech.edu/records/ypmvs-51734", "eprint_id": 105380, "eprint_status": "archive", "datestamp": "2023-08-20 05:13:51", "lastmod": "2026-03-30 14:04:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Tyomkyn-Mykhaylo", "name": { "family": "Tyomkyn", "given": "Mykhaylo" } } ] }, "title": "Repeated Patterns in Proper Colorings", "ispublished": "pub", "full_text_status": "public", "keywords": "graphs, coloring, extremal problems", "note": "\u00a9 2021 Society for Industrial and Applied Mathematics. \n\nReceived by the editors April 21, 2021; accepted for publication (in revised form) July 1, 2021; published electronically September 28, 2021. \n\nThe first author was supported by NSF award DMS-2054452. The second author was supported by ERC Synergy grant DYNASNET 810115, the H2020-MSCA-RISE project CoSP-GA 823748, and GACR grant 19-04113.\n\nWe are extremely grateful to Sean English and Bob Krueger for spotting an error in an earlier version of this paper and suggesting a fix.\n\n

Published - 21m1414103.pdf

Submitted - 2002.00921.pdf

", "abstract": "For a fixed graph H, what is the smallest number of colors C such that there is a proper edge-coloring of the complete graph K_n with C colors containing no two vertex-disjoint color-isomorphic copies, or repeats, of H? We study this function and its generalization to more than two copies using a variety of combinatorial, probabilistic, and algebraic techniques. For example, we show that for any tree T there exists a constant c such that any proper edge-coloring of K_n with at most c n^2 colors contains two repeats of T, while there are colorings with at most c' n^(3/2) colors for some absolute constant c' containing no three repeats of any tree with at least two edges. We also show that for any graph H containing a cycle there exist k and c such that there is a proper edge-coloring of K_n with at most c n colors containing no k repeats of H, while for a tree T with m edges, a coloring with o(n^((m+1)/m)) colors contains \u03c9(1) repeats of T.", "date": "2021-09-28", "date_type": "published", "publication": "SIAM Journal on Discrete Mathematics", "volume": "35", "number": "3", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "2249-2264", "id_number": "CaltechAUTHORS:20200914-134941914", "issn": "0895-4801", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200914-134941914", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "European Research Council (ERC)", "grant_number": "810115" }, { "agency": "European Research Council (ERC)", "grant_number": "823748" }, { "agency": "Charles University", "grant_number": "19-04113" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/21M1414103", "primary_object": { "basename": "2002.00921.pdf", "url": "https://authors.library.caltech.edu/records/ypmvs-51734/files/2002.00921.pdf" }, "related_objects": [ { "basename": "21m1414103.pdf", "url": "https://authors.library.caltech.edu/records/ypmvs-51734/files/21m1414103.pdf" } ], "pub_year": "2021", "author_list": "Conlon, David and Tyomkyn, Mykhaylo" }, { "id": "https://authors.library.caltech.edu/records/mzy87-2zv57", "eprint_id": 111772, "eprint_status": "archive", "datestamp": "2023-08-20 05:13:44", "lastmod": "2026-03-08 03:39:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Pohoata-Cosmin", "name": { "family": "Pohoata", "given": "Cosmin" }, "orcid": "0000-0002-3757-2526" }, { "id": "Zakharov-Dmitriy", "name": { "family": "Zakharov", "given": "Dmitriy" } } ] }, "title": "Random Multilinear Maps and the Erd\u0151s Box Problem", "ispublished": "pub", "full_text_status": "public", "keywords": "Erd\u0151s box problem, extremal numbers, Zarankiewicz problem, hypergraphs", "note": "\u00a9 2021 D. Conlon, C. Pohoata, and D. Zakharov. Licensed under a Creative Commons Attribution License (CC-BY). \n\nResearch supported by NSF Award DMS-2054452. \n\nResearch supported by a grant of the Russian Government N 075-15-2019-1926.\n\n

Published - 2011.09024.pdf

", "abstract": "By using random multilinear maps, we provide new lower bounds for the Erd\u0151s\nbox problem, the problem of estimating the extremal number of the complete d-partite duniform\nhypergraph with two vertices in each part, thereby improving on work of Gunderson,\nR\u00f6dl and Sidorenko.", "date": "2021-09-27", "date_type": "published", "publication": "Discrete Analysis", "volume": "2021", "publisher": "Scholastica", "pagerange": "Art. No. 17", "id_number": "CaltechAUTHORS:20211105-180659290", "issn": "2397-3129", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211105-180659290", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-2054452" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "075-15-2019-1926" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.19086/da.28336", "primary_object": { "basename": "2011.09024.pdf", "url": "https://authors.library.caltech.edu/records/mzy87-2zv57/files/2011.09024.pdf" }, "pub_year": "2021", "author_list": "Conlon, David; Pohoata, Cosmin; et al." }, { "id": "https://authors.library.caltech.edu/records/pkts0-4ms80", "eprint_id": 112128, "eprint_status": "archive", "datestamp": "2023-08-22 11:17:48", "lastmod": "2026-03-29 19:40:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-Elliott-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Proof of spherical flocking based on quantitative rearrangement inequalities", "ispublished": "pub", "full_text_status": "public", "keywords": "Mathematics (miscellaneous); Theoretical Computer Science", "note": "\u00a9 2021 Scuola Normale Superiore. \n\nReceived September 10, 2019; accepted in revised form May 05, 2020. Published online September 2021. \n\nPartial support through US National Science Foundation grant DMS-1363432 and through German Research Foundation grant EXC-2111 390814868 (R.L.F.) is acknowledged.\n\n

Submitted - 1909.04595.pdf

", "abstract": "Our recent work on the Burchard\u2013Choksi\u2013Topaloglu flocking problem showed that in the large mass regime the ground state density profile is the characteristic function of some set. Here we show that this set is, in fact, a round ball. The essential mathematical structure needed in our proof is a strict rearrangement inequality with a quantitative error estimate, which we deduce from recent deep results of M. Christ.", "date": "2021-09-27", "date_type": "published", "publication": "Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V", "volume": "22", "number": "3", "publisher": "Scuola Normale Superiore - Edizioni della Normale", "pagerange": "1241-1263", "id_number": "CaltechAUTHORS:20211201-160010515", "issn": "2036-2145", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211201-160010515", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111 390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2422/2036-2145.201909_007", "primary_object": { "basename": "1909.04595.pdf", "url": "https://authors.library.caltech.edu/records/pkts0-4ms80/files/1909.04595.pdf" }, "pub_year": "2021", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/xe7q7-39k14", "eprint_id": 112511, "eprint_status": "archive", "datestamp": "2023-08-22 11:14:21", "lastmod": "2026-03-29 19:39:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakamura-Akane", "name": { "family": "Nakamura", "given": "Akane" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Uniqueness of Polarization for the Autonomous 4-dimensional Painlev\u00e9-type Systems", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "\u00a9 The Author(s) 2020. Published by Oxford University Press. \nThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) \n\nReceived: 30 October 2019. Revision received: 30 October 2019. Accepted: 06 February 2020. Published: 24 February 2020. \n\nThe author would like to thank Professors Tadashi Ashikaga, Brian Conrad, Kazuki Hiroe, Yusuke Nakamura, Elena Mantovan, and Haruo Yoshida for valuable discussions and advices. \n\nThis work was partially supported by a grant from the National Science Foundation [DMS-1500806 to E.R.]; The first author is grateful for Professors Toshio Oshima (with JSPS grant-in-aid for scientific research B, No. 25287017) and Yoko Umeta (with Josai University President's Fund) for supporting part of her trips. The first author is grateful for the hospitality of Caltech while she stayed there.\n\n

Submitted - 1910.14168.pdf

", "abstract": "We prove that for any autonomous 4-dimensional integral system of Painlev\u00e9 type, the Jacobian of the generic spectral curve has a unique polarization, and thus by Torelli's theorem cannot be isomorphic as an unpolarized abelian surface to any other Jacobian. This enables us to identify the spectral curve and any irreducible genus 2 component of the boundary of an affine patch of the Liouville torus.", "date": "2021-09-15", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2021", "number": "18", "publisher": "Oxford University Press", "pagerange": "14204-14219", "id_number": "CaltechAUTHORS:20211217-98152000", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211217-98152000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1500806" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "25287017" }, { "agency": "Josai Universit" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnaa037", "primary_object": { "basename": "1910.14168.pdf", "url": "https://authors.library.caltech.edu/records/xe7q7-39k14/files/1910.14168.pdf" }, "pub_year": "2021", "author_list": "Nakamura, Akane and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/xww49-kn658", "eprint_id": 110032, "eprint_status": "archive", "datestamp": "2023-08-20 04:52:22", "lastmod": "2026-03-30 09:08:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Arieli-Itai", "name": { "family": "Arieli", "given": "Itai" }, "orcid": "0000-0001-8663-5776" }, { "id": "Babichenko-Yakov", "name": { "family": "Babichenko", "given": "Yakov" }, "orcid": "0000-0002-6970-1601" }, { "id": "Sandomirskiy-Fedor", "name": { "family": "Sandomirskiy", "given": "Fedor" }, "orcid": "0000-0001-9886-3688" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Feasible Joint Posterior Beliefs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 by The University of Chicago. \n\nElectronically published July 7, 2021. \n\nThis paper greatly benefited from multiple suggestions and comments of our colleagues. We are grateful to (in alphabetic order) Kim Border, Ben Brooks, Laura Doval, Piotr Dworczak, Nikita Gladkov, Sergiu Hart, Kevin He, Aviad Heifetz, Yuval Heller, Matthew Jackson, Eliott Lipnowski, Jeffrey Mensch, Benny Moldovanu, In\u00e9s Moreno de Barreda, Stephen Morris, Alexander Nesterov, Abraham Neyman, Michael Ostrovsky, Thomas Palfrey, Jim Pitman, Luciano Pomatto, Doron Ravid, Marco Scarsini, Eilon Solan, Theodore Zhu, Gabriel Ziegler, and seminar participants at Bar-Ilan University, Caltech, Hebrew University, the Higher School of Economics St. Petersburg, Technion, Tel Aviv University, Stanford, and the University of California San Diego. Arieli is supported by the Ministry of Science and Technology (2028255). Babichenko is supported by a BSF (United States\u2013Israel Binational Science Foundation) award (2018397). Sandomirskiy is supported by the Lady Davis Foundation, by grant 19-01-00762 of the Russian Foundation for Basic Research, by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (740435), and by the Basic Research Program of the National Research University Higher School of Economics. Tamuz is supported by a grant from the Simons Foundation (419427), by a BSF award (2018397), and by a Sloan Fellowship.\n\n

Published - 714993.pdf

Submitted - 2002.11362.pdf

", "abstract": "We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. For two agents, we introduce a quantitative version of Aumann's agreement theorem and show that it is equivalent to a characterization of feasible distributions from a 1995 work by Dawid and colleagues. For any number of agents, we characterize feasible distributions in terms of a \"no-trade\" condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.", "date": "2021-09", "date_type": "published", "publication": "Journal of Political Economy", "volume": "129", "number": "9", "publisher": "University of Chicago Press", "pagerange": "2546-2594", "id_number": "CaltechAUTHORS:20210727-175655408", "issn": "0022-3808", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210727-175655408", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Science and Technology (Israel)", "grant_number": "2028255" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2018397" }, { "agency": "Lady Davis Foundation" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "19-01-00762" }, { "agency": "European Research Council (ERC)", "grant_number": "740435" }, { "agency": "National Research University Higher School of Economics" }, { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1086/714993", "primary_object": { "basename": "2002.11362.pdf", "url": "https://authors.library.caltech.edu/records/xww49-kn658/files/2002.11362.pdf" }, "related_objects": [ { "basename": "714993.pdf", "url": "https://authors.library.caltech.edu/records/xww49-kn658/files/714993.pdf" } ], "pub_year": "2021", "author_list": "Arieli, Itai; Babichenko, Yakov; et al." }, { "id": "https://authors.library.caltech.edu/records/sqbep-vc039", "eprint_id": 98035, "eprint_status": "archive", "datestamp": "2023-08-20 04:22:46", "lastmod": "2026-03-30 13:41:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Janzer-Oliver", "name": { "family": "Janzer", "given": "Oliver" } }, { "id": "Lee-Joonkyung", "name": { "family": "Lee", "given": "Joonkyung" } } ] }, "title": "More on the extremal number of subdivisions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 J\u00e1nos Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg. \n\nReceived 16 April 2019; Revised 24 April 2020; Published 26 August 2021. \n\nWe would like to thank the anonymous referees for their careful reviews. \n\nResearch supported by ERC Starting Grant RanDM 676632. \n\nResearch supported by ERC Consolidator Grant PEPCo 724903.\n\n

Submitted - 1903.10631.pdf

", "abstract": "Given a graph H, the extremal number ex(n, H) is the largest number of edges in an H-free graph on n vertices. We make progress on a number of conjectures about the extremal number of bipartite graphs. First, writing K\u2032_(s,t) for the subdivision of the bipartite graph K_(s,t), we show that ex(n,K\u2032_(s,t)) = O(n^(3/2)\u22121/2s)). This proves a conjecture of Kang, Kim and Liu and is tight up to the implied constant for t sufficiently large in terms of s. Second, for any integers s,k \u2265 1, we show that ex(n,L) = \u0398(n^(1+s/sk+1)) for a particular graph L depending on s and k, answering another question of Kang, Kim and Liu. This result touches upon an old conjecture of Erd\u0151s and Simonovits, which asserts that every rational number r \u2208 (1, 2) is realisable in the sense that ex(n, H) = \u0398(n^r) for some appropriate graph H, giving infinitely many new realisable exponents and implying that 1 + 1/k is a limit point of realisable exponents for all k \u2265 1. Writing H^k for the k-subdivision of a graph H, this result also implies that for any bipartite graph H and any k, there exists \u03b4 > 0 such that ex(n, H^(k\u22121)) = O(^(n1+1/k\u2212\u03b4)), partially resolving a question of Conlon and Lee. Third, extending a recent result of Conlon and Lee, we show that any bipartite graph H with maximum degree r on one side which does not contain C\u2084 as a subgraph satisfies ex(n, H) = o(n^(2\u22121/r)).", "date": "2021-08", "date_type": "published", "publication": "Combinatorica", "volume": "41", "number": "4", "publisher": "Springer", "pagerange": "465-494", "id_number": "CaltechAUTHORS:20190819-170943053", "issn": "0209-9683", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-170943053", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "European Research Council (ERC)", "grant_number": "724903" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-020-4202-1", "primary_object": { "basename": "1903.10631.pdf", "url": "https://authors.library.caltech.edu/records/sqbep-vc039/files/1903.10631.pdf" }, "pub_year": "2021", "author_list": "Conlon, David; Janzer, Oliver; et al." }, { "id": "https://authors.library.caltech.edu/records/mjj31-veg11", "eprint_id": 117593, "eprint_status": "archive", "datestamp": "2023-08-22 10:46:06", "lastmod": "2026-03-29 14:01:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" } }, { "id": "Zhou-Xin", "name": { "family": "Zhou", "given": "Xin" } } ] }, "title": "Generic scarring for minimal hypersurfaces along stable hypersurfaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology; Analysis", "note": "This research was partially conducted during the period A.S. served as a Clay Research Fellow. X.Z. is partially supported by NSF Grants DMS-1811293, DMS-1945178, and an Alfred P. Sloan Research Fellowship. We would like to thank Peter Sarnak for discussions and for pointing out [BL67, Ral80].", "abstract": "Let M\u207f\u207a\u00b9 be a closed manifold of dimension 3 \u2264 n + 1 \u2264 7. We show that for a C\u221e-generic metric g on M, to any connected, closed, embedded, 2-sided, stable, minimal hypersurface S \u2282 (M,g) corresponds a sequence of closed, embedded, minimal hypersurfaces {\u03a3\u2096} scarring along S, in the sense that the area and Morse index of \u03a3\u2096 both diverge to infinity and, when properly renormalized, \u03a3\u2096 converges to S as varifolds. We also show that scarring of immersed minimal surfaces along stable surfaces occurs in most closed Riemannian 3-manifods.", "date": "2021-08", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "31", "number": "4", "publisher": "Springer", "pagerange": "948-980", "id_number": "CaltechAUTHORS:20221026-539124000.5", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221026-539124000.5", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "NSF", "grant_number": "DMS-1811293" }, { "agency": "NSF", "grant_number": "DMS-1945178" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-021-00571-7", "pub_year": "2021", "author_list": "Song, Antoine and Zhou, Xin" }, { "id": "https://authors.library.caltech.edu/records/bevf0-gey82", "eprint_id": 108260, "eprint_status": "archive", "datestamp": "2023-10-03 22:37:43", "lastmod": "2026-03-29 20:49:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Sopenko-Nikita", "name": { "family": "Sopenko", "given": "Nikita" }, "orcid": "0000-0002-8479-1924" }, { "id": "Yang-Bowen", "name": { "family": "Yang", "given": "Bowen" }, "orcid": "0000-0003-4778-831X" } ] }, "title": "A classification of invertible phases of bosonic quantum lattice systems in one dimension", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 Published under an exclusive license by AIP Publishing. \n\nSubmitted: 5 May 2021; Accepted: 25 July 2021; Published Online: 11 August 2021. \n\nWe would like to thank P. Etingof and B. Simon for advice. We are also grateful to Y. Ogata for drawing our attention to an error in Lemma 4.1 in the original version of this paper. This research was supported, in part, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award. B.Y. acknowledges the Caltech mathematics department for a graduate fellowship awarded in fall 2020.\n\n

Published - 081901_1_online.pdf

Submitted - 2012-15491a.pdf

Submitted - 2012-15491b.pdf

", "abstract": "We study invertible states of 1D bosonic quantum lattice systems. We show that every invertible 1D state is in a trivial phase: after tensoring with some unentangled ancillas, it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. If an invertible state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries, even after adding unentagled ancillas. We show that in the case of a finite unitary symmetry G, the only obstruction is an index valued in degree-2 cohomology of G. We show that two invertible G-invariant states are in the same phase if and only if their indices coincide.", "date": "2021-08", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "62", "number": "8", "publisher": "American Institute of Physics", "pagerange": "Art. No. 081901", "id_number": "CaltechAUTHORS:20210301-154744254", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210301-154744254", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "Caltech Division of Physics, Mathematics and Astronomy" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/5.0055996", "primary_object": { "basename": "081901_1_online.pdf", "url": "https://authors.library.caltech.edu/records/bevf0-gey82/files/081901_1_online.pdf" }, "related_objects": [ { "basename": "2012-15491a.pdf", "url": "https://authors.library.caltech.edu/records/bevf0-gey82/files/2012-15491a.pdf" }, { "basename": "2012-15491b.pdf", "url": "https://authors.library.caltech.edu/records/bevf0-gey82/files/2012-15491b.pdf" } ], "pub_year": "2021", "author_list": "Kapustin, Anton; Sopenko, Nikita; et al." }, { "id": "https://authors.library.caltech.edu/records/sn2vz-f5141", "eprint_id": 109786, "eprint_status": "archive", "datestamp": "2023-08-20 04:27:16", "lastmod": "2026-03-29 17:46:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "Dirk" }, "orcid": "0000-0002-0643-0138" }, { "id": "Jex-Michal", "name": { "family": "Jex", "given": "Michal" }, "orcid": "0000-0003-0910-0692" }, { "id": "Nam-Phan-Th\u00e0nh", "name": { "family": "Nam", "given": "Phan Th\u00e0nh" }, "orcid": "0000-0001-7599-9742" } ] }, "title": "The Lieb-Thirring inequality revisited", "ispublished": "pub", "full_text_status": "public", "keywords": "Lieb\u2013Thirring inequality, Schr\u00f6dinger operator, Sobolev inequality", "note": "\u00a9 2021 EMS Publishing House. \n\nPublished online: 2021-04-07. \n\nWe thank Sabine Boegli for helpful discussions. This work was partially supported by U.S. NSF grant DMS-1363432 (R.L.F.), the Alfried Krupp von Bohlen und Halbach Foundation, and the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173 (D.H.).\n\n

Submitted - 1808.09017.pdf

", "abstract": "We provide new estimates on the best constant of the Lieb\u2013Thirring inequality for the sum of the negative eigenvalues of Schr\u00f6dinger operators, which significantly improve the so far existing bounds.", "date": "2021-08", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "23", "number": "8", "publisher": "European Mathematical Society", "pagerange": "2583-2600", "id_number": "CaltechAUTHORS:20210713-164447574", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210713-164447574", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Alfried Krupp von Bohlen und Halbach Foundation" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "CRC 1173" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/jems/1062", "primary_object": { "basename": "1808.09017.pdf", "url": "https://authors.library.caltech.edu/records/sn2vz-f5141/files/1808.09017.pdf" }, "pub_year": "2021", "author_list": "Frank, Rupert L.; Hundertmark, Dirk; et al." }, { "id": "https://authors.library.caltech.edu/records/wpchd-rgq27", "eprint_id": 108279, "eprint_status": "archive", "datestamp": "2023-08-20 04:18:58", "lastmod": "2026-03-09 21:28:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eischen-Ellen", "name": { "family": "Eischen", "given": "E." } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "Entire Theta Operators at Unramified Primes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2021. Published by Oxford University Press. \n\nReceived August 14, 2020; Revised June 11, 2021; Accepted June 21, 2021. Communicated by Prof. Ana Caraiani. \n\nOur work on this project has benefitted from helpful conversations with Ehud de Shalit, Alex Ghitza, Eyal Goren, and Angus McAndrew, especially about their earlier papers on related topics. We completed key steps during our visit to the University of Lille, as well as the 2nd-named author's visits to the University of Oregon and the University of Padua, and we are grateful to these institutions for their hospitality. We are also grateful to the referee for helpful suggestions. \n\nThis work was supported by the National Science Foundation [DMS-1559609 and DMS-1751281].\n\n

Submitted - 2002.09450.pdf

", "abstract": "Starting with the work of Serre, Katz, and Swinnerton-Dyer, theta operators have played a key role in the study of p-adic and mod p modular forms and Galois representations. This paper achieves two main results for theta operators on automorphic forms on PEL-type Shimura varieties: (1) the analytic continuation at unramified primes p to the whole Shimura variety of the mod p reduction of p-adic Maass\u2013Shimura operators a priori defined only over the \u03bc-ordinary locus, and (2) the construction of new mod p theta operators that do not arise as the mod p reduction of Maass\u2013Shimura operators. While the main accomplishments of this paper concern the geometry of Shimura varieties and consequences for differential operators, we conclude with applications to Galois representations. Our approach involves a careful analysis of the behavior of Shimura varieties and enables us to obtain more general results than allowed by prior techniques, including for arbitrary signature, vector weights, and unramified primes in CM fields of arbitrary degree.", "date": "2021-07-23", "date_type": "published", "publication": "International Mathematics Research Notices", "publisher": "Oxford University Press", "id_number": "CaltechAUTHORS:20210302-154532505", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210302-154532505", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1559609" }, { "agency": "NSF", "grant_number": "DMS-1751281" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnab190", "primary_object": { "basename": "2002.09450.pdf", "url": "https://authors.library.caltech.edu/records/wpchd-rgq27/files/2002.09450.pdf" }, "pub_year": "2021", "author_list": "Eischen, E. and Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/akebf-7dn96", "eprint_id": 110054, "eprint_status": "archive", "datestamp": "2023-08-22 10:33:58", "lastmod": "2026-04-16 01:41:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Zijun", "name": { "family": "Chen", "given": "Zijun" } }, { "name": { "family": "Satzinger", "given": "Kevin J." } }, { "name": { "family": "Atalaya", "given": "Juan" } }, { "name": { "family": "Korotkov", "given": "Alexander N." } }, { "name": { "family": "Dunsworth", "given": "Andrew" } }, { "name": { "family": "Sank", "given": "Daniel" } }, { "name": { "family": "Quintana", "given": "Chris" } }, { "name": { "family": "McEwen", "given": "Matt" }, "orcid": "0000-0002-9544-141X" }, { "name": { "family": "Barends", "given": "Rami" } }, { "name": { "family": "Klimov", "given": "Paul V." } }, { "name": { "family": "Hong", "given": "Sabrina" } }, { "name": { "family": "Jones", "given": "Cody" } }, { "name": { "family": "Petukhov", "given": "Andre" } }, { "name": { "family": "Kafri", "given": "Dvir" } }, { "name": { "family": "Demura", "given": "Sean" }, "orcid": "0000-0003-3727-7380" }, { "name": { "family": "Burkett", "given": "Brian" }, "orcid": "0000-0001-8474-6317" }, { "name": { "family": "Gidney", "given": "Craig" } }, { "name": { "family": "Fowler", "given": "Austin G." } }, { "name": { "family": "Paler", "given": "Alexandru" }, "orcid": "0000-0002-1536-8858" }, { "id": "Putterman-Harald", "name": { "family": "Putterman", "given": "Harald" } }, { "name": { "family": "Aleiner", "given": "Igor" } }, { "name": { "family": "Arute", "given": "Frank" } }, { "name": { "family": "Arya", "given": "Kunal" } }, { "name": { "family": "Babbush", "given": "Ryan" } }, { "name": { "family": "Bardin", "given": "Joseph C." }, "orcid": "0000-0002-6523-6730" }, { "name": { "family": "Bengtsson", "given": "Andreas" } }, { "name": { "family": "Bourassa", "given": "Alexandre" } }, { "name": { "family": "Broughton", "given": "Michael" } }, { "name": { "family": "Buckley", "given": "Bob B." } }, { "name": { "family": "Buell", "given": "David A." } }, { "name": { "family": "Bushnell", "given": "Nicholas" } }, { "name": { "family": "Chiaro", "given": "Benjamin" } }, { "name": { "family": "Collins", "given": "Roberto" } }, { "name": { "family": "Courtney", "given": "William" } }, { "name": { "family": "Derk", "given": "Alan R." } }, { "name": { "family": "Eppens", "given": "Daniel" } }, { "name": { "family": "Erickson", "given": "Catherine" } }, { "name": { "family": "Farhi", "given": "Edward" } }, { "name": { "family": "Foxen", "given": "Brooks" } }, { "name": { "family": "Giustina", "given": "Marissa" } }, { "name": { "family": "Greene", "given": "Ami" } }, { "name": { "family": "Gross", "given": "Jonathan A." } }, { "name": { "family": "Harrigan", "given": "Matthew P." }, "orcid": "0000-0001-9412-0553" }, { "name": { "family": "Harrington", "given": "Sean D." }, "orcid": "0000-0003-0521-8378" }, { "name": { "family": "Hilton", "given": "Jeremy" } }, { "name": { "family": "Ho", "given": "Alan" } }, { "name": { "family": "Huang", "given": "Trent" } }, { "name": { "family": "Huggins", "given": "William J." }, "orcid": "0000-0003-2735-1380" }, { "name": { "family": "Ioffe", "given": "L. B." } }, { "name": { "family": "Isakov", "given": "Sergei V." } }, { "name": { "family": "Jeffrey", "given": "Evan" } }, { "name": { "family": "Jiang", "given": "Zhang" } }, { "name": { "family": "Kechedzhi", "given": "Kostyantyn" } }, { "name": { "family": "Kim", "given": "Seon" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "name": { "family": "Kostritsa", "given": "Fedor" } }, { "name": { "family": "Landhuis", "given": "David" }, "orcid": "0000-0001-9804-2185" }, { "name": { "family": "Laptev", "given": "Pavel" } }, { "name": { "family": "Lucero", "given": "Erik" } }, { "name": { "family": "Martin", "given": "Orion" } }, { "name": { "family": "McClean", "given": "Jarrod R." }, "orcid": "0000-0002-2809-0509" }, { "name": { "family": "McCourt", "given": "Trevor" } }, { "name": { "family": "Mi", "given": "Xiao" } }, { "name": { "family": "Miao", "given": "Kevin C." } }, { "name": { "family": "Mohseni", "given": "Masoud" } }, { "name": { "family": "Montazeri", "given": "Shirin" } }, { "name": { "family": "Mruczkiewicz", "given": "Wojciech" }, "orcid": "0000-0002-8497-6363" }, { "name": { "family": "Mutus", "given": "Josh" } }, { "name": { "family": "Naaman", "given": "Ofer" }, "orcid": "0000-0002-7760-9186" }, { "name": { "family": "Neeley", "given": "Matthew" }, "orcid": "0000-0002-5548-0051" }, { "name": { "family": "Neill", "given": "Charles" }, "orcid": "0000-0001-8509-9836" }, { "name": { "family": "Newman", "given": "Michael" } }, { "name": { "family": "Niu", "given": "Murphy Yuezhen" } }, { "name": { "family": "O'Brien", "given": "Thomas E." } }, { "name": { "family": "Opremcak", "given": "Alex" } }, { "name": { "family": "Ostby", "given": "Eric" } }, { "name": { "family": "Pat\u00f3", "given": "B\u00e1lint" } }, { "name": { "family": "Redd", "given": "Nicholas" }, "orcid": "0000-0002-6549-5441" }, { "name": { "family": "Roushan", "given": "Pedram" } }, { "name": { "family": "Rubin", "given": "Nicholas C." } }, { "name": { "family": "Shvarts", "given": "Vladimir" } }, { "name": { "family": "Strain", "given": "Doug" } }, { "name": { "family": "Szalay", "given": "Marco" } }, { "name": { "family": "Trevithick", "given": "Matthew D." } }, { "name": { "family": "Villalonga", "given": "Benjamin" } }, { "name": { "family": "White", "given": "Theodore" } }, { "name": { "family": "Yao", "given": "Z. Jamie" } }, { "name": { "family": "Yeh", "given": "Ping" }, "orcid": "0000-0003-0837-1028" }, { "name": { "family": "Yoo", "given": "Juhwan" } }, { "name": { "family": "Zalcman", "given": "Adam" }, "orcid": "0000-0002-2585-2424" }, { "name": { "family": "Neven", "given": "Hartmut" } }, { "name": { "family": "Boixo", "given": "Sergio" }, "orcid": "0000-0002-1090-7584" }, { "name": { "family": "Smelyanskiy", "given": "Vadim" } }, { "name": { "family": "Chen", "given": "Yu" } }, { "name": { "family": "Megrant", "given": "Anthony" }, "orcid": "0000-0002-6371-6140" }, { "name": { "family": "Kelly", "given": "Julian" }, "orcid": "0000-0002-2596-2121" } ] }, "title": "Exponential suppression of bit or phase errors with cyclic error correction", "ispublished": "pub", "full_text_status": "public", "keywords": "Quantum information; Qubits", "note": "\u00a9 The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 11 January 2021; Accepted 28 April 2021; Published 14 July 2021. \n\nWe thank J. Platt, J. Dean and J. Yagnik for their executive sponsorship of the Google Quantum AI team, and for their continued engagement and support. We thank S. Leichenauer and J. Platt for reviewing a draft of the manuscript and providing feedback. \n\nData availability: The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request. \n\nAuthor Contributions: Z.C., K.J.S., H.P., A.G.F., A.N.K. and J.K. designed the experiment. Z.C., K.J.S. and J.K. performed the experiment and analysed the data. C.Q., K.J.S., A. Petukhov and Y.C. developed the controlled-Z gate. M. McEwen, D.K., A. Petukhov and R. Barends developed the reset operation. M. McEwen and R. Barends performed experiments on leakage, reset and high-energy events in error correcting codes. D. Sank and Z.C. developed the readout operation. A.D., B.B., S.D. and A.M. led the design and fabrication of the processor. J.A. and A.N.K. developed and performed the pij analysis. C.J. developed the inverse \u039b model and performed the simulations. A.G.F. and C.G. wrote the decoder and interface software. S. H., K.J.S. and J.K. developed the dynamical decoupling protocols. P.V.K. developed error mitigation techniques based on system frequency optimization. Z.C., K.J.S., S.H., P.V.K. and J.K. developed error correction calibration techniques. Z.C., K.J.S. and J.K. wrote the manuscript. S.B., V. Smelyanskiy, Y.C., A.M. and J.K. coordinated the team-wide error correction effort. Work by H. Putterman was done prior to joining AWS. All authors contributed to revising the manuscript and writing the Supplementary Information. All authors contributed to the experimental and theoretical infrastructure to enable the experiment. \n\nThe authors declare no competing interests. \n\nPeer review information: Nature thanks Carmen Almudever, Benjamin Brown and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.\n\n

Published - s41586-021-03588-y.pdf

Supplemental Material - 41586_2021_3588_MOESM1_ESM.pdf

Supplemental Material - 41586_2021_3588_MOESM2_ESM.pdf

", "abstract": "Realizing the potential of quantum computing requires sufficiently low logical error rates(1). Many applications call for error rates as low as 10\u207b\u00b9\u2075 (refs. 2,3,4,5,6,7,8,9), but state-of-the-art quantum platforms typically have physical error rates near 10\u207b\u00b3 (refs. 10,11,12,13,14). Quantum error correction(15,16,17) promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device(18,19) and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.", "date": "2021-07-15", "date_type": "published", "publication": "Nature", "volume": "595", "number": "7867", "publisher": "Nature Publishing Group", "pagerange": "383-387", "id_number": "CaltechAUTHORS:20210728-191748877", "issn": "0028-0836", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210728-191748877", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "AWS-Center-for-Quantum-Computing" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "corp_creators": { "items": [ "Google Quantum AI" ] }, "doi": "10.1038/s41586-021-03588-y", "primary_object": { "basename": "41586_2021_3588_MOESM2_ESM.pdf", "url": "https://authors.library.caltech.edu/records/akebf-7dn96/files/41586_2021_3588_MOESM2_ESM.pdf" }, "related_objects": [ { "basename": "s41586-021-03588-y.pdf", "url": "https://authors.library.caltech.edu/records/akebf-7dn96/files/s41586-021-03588-y.pdf" }, { "basename": "41586_2021_3588_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/akebf-7dn96/files/41586_2021_3588_MOESM1_ESM.pdf" } ], "pub_year": "2021", "author_list": "Chen, Zijun; Satzinger, Kevin J.; et al." }, { "id": "https://authors.library.caltech.edu/records/cj1sv-yra98", "eprint_id": 109262, "eprint_status": "archive", "datestamp": "2023-08-20 04:15:11", "lastmod": "2026-03-29 19:44:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Spodyneiko-Lev", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "Microscopic formulas for thermoelectric transport coefficients in lattice systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 American Physical Society. \n\nReceived 16 May 2021; revised 6 July 2021; accepted 13 July 2021; published 26 July 2021. \n\nThe work was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award.\n\n

Published - PhysRevB.104.035150.pdf

Submitted - 2105.01626.pdf

", "abstract": "A macroscopic description of thermoelectric phenomena involves several tensorial transport coefficients. Textbook microscopic Kubo formulas for them are plagued with ambiguities in the definitions of the current operators and the magnetization. We derive a version of these formulas for lattice systems that is free from ambiguities but contains additional terms compared to the textbook results. For symmetric components of thermoelectric tensors, we identify a large class of lattice systems for which the additional terms vanish with a natural choice of the energy current. To eliminate ambiguities in the skew-symmetric components, one needs to interpret them as relative quantities: only their differences for pairs of materials are well-defined.", "date": "2021-07-15", "date_type": "published", "publication": "Physical Review B", "volume": "104", "number": "3", "publisher": "American Physical Society", "pagerange": "Art. No. 035150", "id_number": "CaltechAUTHORS:20210526-152353779", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210526-152353779", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.104.035150", "primary_object": { "basename": "2105.01626.pdf", "url": "https://authors.library.caltech.edu/records/cj1sv-yra98/files/2105.01626.pdf" }, "related_objects": [ { "basename": "PhysRevB.104.035150.pdf", "url": "https://authors.library.caltech.edu/records/cj1sv-yra98/files/PhysRevB.104.035150.pdf" } ], "pub_year": "2021", "author_list": "Kapustin, Anton and Spodyneiko, Lev" }, { "id": "https://authors.library.caltech.edu/records/44v61-x0t16", "eprint_id": 109429, "eprint_status": "archive", "datestamp": "2023-08-20 04:13:22", "lastmod": "2026-03-29 20:32:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Touraev-Marc", "name": { "family": "Touraev", "given": "Marc" } } ] }, "title": "Non-relativistic geometry and the equivalence principle", "ispublished": "pub", "full_text_status": "public", "keywords": "equivalence principle, Schr\u00f6dinger equation, Ehresmann connection", "note": "\u00a9 2021 IOP Publishing Ltd. \n\nReceived 23 January 2021; Revised 13 April 2021; Accepted 6 May 2021; Published 1 June 2021. \n\nMT is grateful to the Caltech SURF program for providing a research opportunity. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. AK was also supported by the Simons Investigator Award. \n\nData availability statement: No new data were created or analysed in this study.\n\n

Submitted - 2101.04153.pdf

", "abstract": "We describe a geometric and symmetry-based formulation of the equivalence principle in non-relativistic physics. It applies both on the classical and quantum levels and states that the Newtonian potential can be eliminated in favor of a curved and time-dependent spatial metric. It is this requirement that forces the gravitational mass to be equal to the inertial mass. We identify the symmetry responsible for the equivalence principle as the remnant of time-reparameterization symmetry of the relativistic theory. We also clarify the transformation properties of the Schr\u00f6dinger wave-function under arbitrary frame changes.", "date": "2021-07-12", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "38", "number": "13", "publisher": "IOP", "pagerange": "Art. No. 135003", "id_number": "CaltechAUTHORS:20210608-073034132", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210608-073034132", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1361-6382/abfea5", "primary_object": { "basename": "2101.04153.pdf", "url": "https://authors.library.caltech.edu/records/44v61-x0t16/files/2101.04153.pdf" }, "pub_year": "2021", "author_list": "Kapustin, Anton and Touraev, Marc" }, { "id": "https://authors.library.caltech.edu/records/7r4hq-qs353", "eprint_id": 113133, "eprint_status": "archive", "datestamp": "2023-08-22 10:25:09", "lastmod": "2026-03-28 20:44:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guth-Larry", "name": { "family": "Guth", "given": "Larry" } }, { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" }, { "id": "Zahl-Joshua", "name": { "family": "Zahl", "given": "Joshua" } } ] }, "title": "On the Discretized Sum-Product Problem", "ispublished": "pub", "full_text_status": "restricted", "keywords": "General Mathematics", "note": "\u00a9 The Author(s) 2020. Published by Oxford University Press. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). \n\nReceived: 24 April 2018; Revision received: 31 October 2019; Accepted: 28 November 2019; Published: 13 January 2020. \n\nThe authors would like to thank Brendan Murphy, Victor Lie, and Jianan Li for comments and corrections to a previous draft of this manuscript. The authors would also like to thank the anonymous referees for corrections and suggestions. \n\nThis work was supported by a Simons Investigator Award [to L.G.]; and a NSERC Discovery Grant [to J.Z.].", "abstract": "We give a new proof of the discretized ring theorem for sets of real numbers. As a special case, we show that if A \u2282 R is a (\u03b4,1/2)\u2081-set in the sense of Katz and Tao, then either A+A or A.A must have measure at least |A|1\u22121/68\u2060.", "date": "2021-07", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2021", "number": "13", "publisher": "Oxford University Press", "pagerange": "9769-9785", "id_number": "CaltechAUTHORS:20220127-965114100", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220127-965114100", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnz360", "pub_year": "2021", "author_list": "Guth, Larry; Katz, Nets Hawk; et al." }, { "id": "https://authors.library.caltech.edu/records/jjtjz-2za93", "eprint_id": 109392, "eprint_status": "archive", "datestamp": "2023-08-20 03:42:07", "lastmod": "2026-03-29 21:02:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Levin-Michael-A", "name": { "family": "Levin", "given": "Michael" }, "orcid": "0000-0002-5765-6591" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Spodyneiko-Lev", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "Nernst and Ettingshausen effects in gapped quantum materials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 American Physical Society. \n\n(Received 15 April 2021; accepted 14 May 2021; published 1 June 2021) \n\nA.K. would like to thank Assa Auerbach for a discussion of St\u0159eda formulas. The work of A.K. and L.S. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award. M.L. was supported in part by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440).\n\n

Published - PhysRevB.103.235101.pdf

Submitted - 2103.02628.pdf

", "abstract": "We investigate whether there could exist topological invariants of gapped two-dimensional materials related to dissipationless thermoelectric transport at low temperatures. We give both macroscopic and microscopic arguments showing that thermoelectric transport coefficients vanish in the limit of zero temperature, and thus topological invariants arise only from the electric Hall conductance and the thermal Hall conductance. Our arguments apply to systems with arbitrarily strong interactions. We also show that there is no analog of the Thouless pump for entropy.", "date": "2021-06-15", "date_type": "published", "publication": "Physical Review B", "volume": "103", "number": "23", "publisher": "American Physical Society", "pagerange": "Art. No. 235101", "id_number": "CaltechAUTHORS:20210604-140650926", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210604-140650926", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation", "grant_number": "651440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/physrevb.103.235101", "primary_object": { "basename": "2103.02628.pdf", "url": "https://authors.library.caltech.edu/records/jjtjz-2za93/files/2103.02628.pdf" }, "related_objects": [ { "basename": "PhysRevB.103.235101.pdf", "url": "https://authors.library.caltech.edu/records/jjtjz-2za93/files/PhysRevB.103.235101.pdf" } ], "pub_year": "2021", "author_list": "Levin, Michael; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/8gctx-1rp35", "eprint_id": 110305, "eprint_status": "archive", "datestamp": "2023-08-20 03:33:02", "lastmod": "2026-03-30 13:32:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Atiyah-Michael", "name": { "family": "Atiyah", "given": "Michael" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Anyon Networks from Geometric Models of Matter", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 The Author(s) 2021. Published by Oxford University Press.\nThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). \n\nReceived: 05 May 2020; Revision received: 16 December 2020; Accepted: 22 January 2021; Published: 08 February 2021. \n\nThis work was supported by National Science Foundation DMS-1707882 and Natural Sciences and Engineering Research Council of Canada RGPIN-2018-04937 and RGPAS-2018-522593.", "abstract": "This paper, completed in its present form by the second author after the first author passed away in 2019, describes an intended continuation of the previous joint work on anyons in geometric models of matter. This part outlines a construction of anyon tensor networks based on four-dimensional orbifold geometries and braid representations associated with surface-braids defined by multisections of the orbifold normal bundle of the surface of orbifold points.", "date": "2021-06", "date_type": "published", "publication": "Quarterly Journal of Mathematics", "volume": "72", "number": "1-2", "publisher": "Oxford University Press", "pagerange": "717-733", "id_number": "CaltechAUTHORS:20210818-171348862", "issn": "0033-5606", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210818-171348862", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/qmath/haab004", "pub_year": "2021", "author_list": "Atiyah, Michael and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/zgers-wd090", "eprint_id": 105038, "eprint_status": "archive", "datestamp": "2023-08-20 03:23:09", "lastmod": "2026-03-30 04:41:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Gontier-David", "name": { "family": "Gontier", "given": "David" }, "orcid": "0000-0001-8648-7910" }, { "id": "Lewin-Mathieu", "name": { "family": "Lewin", "given": "Mathieu" }, "orcid": "0000-0002-1755-0207" } ] }, "title": "The Nonlinear Schr\u00f6dinger Equation for Orthonormal Functions II: Application to Lieb\u2013Thirring Inequalities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 06 April 2020; Accepted 07 January 2021; Published 18 May 2021. \n\nThis project has received funding from the U.S. National Science Foundation (Grant Agreements DMS-1363432 and DMS-1954995 of R.L.F.) and from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement MDFT 725528 of M.L.). \n\nOpen Access funding enabled and organized by Projekt DEAL.\n\n

Published - Frank2021_Article_TheNonlinearSchr\u00f6dingerEquatio.pdf

Submitted - 2002.04964.pdf

", "abstract": "In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb\u2013Thirring constant when the eigenvalues of a Schr\u00f6dinger operator \u2212\u0394+V(x) are raised to the power \u03ba\u03ba is never given by the one-bound state case when \u03ba > max(0,2\u2212d/2) in space dimension d \u2265 1. When in addition \u03ba \u2265 1 we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result is to carefully compute the exponentially small interaction between two Gagliardo\u2013Nirenberg optimisers placed far away. For the second result, we study the dual version of the Lieb\u2013Thirring inequality, in the same spirit as in Part I of this work Gontier et al. (The nonlinear Schr\u00f6dinger equation for orthonormal functions I. Existence of ground states. Arch. Rat. Mech. Anal, 2021. https://doi.org/10.1007/s00205-021-01634-7). In a different but related direction, we also show that the cubic nonlinear Schr\u00f6dinger equation admits no orthonormal ground state in 1D, for more than one function.", "date": "2021-06", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "384", "number": "3", "publisher": "Springer", "pagerange": "1783-1828", "id_number": "CaltechAUTHORS:20200819-152827513", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200819-152827513", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "European Research Council (ERC)", "grant_number": "725528" }, { "agency": "Projekt DEAL" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-021-04039-5", "primary_object": { "basename": "2002.04964.pdf", "url": "https://authors.library.caltech.edu/records/zgers-wd090/files/2002.04964.pdf" }, "related_objects": [ { "basename": "Frank2021_Article_TheNonlinearSchr\u00f6dingerEquatio.pdf", "url": "https://authors.library.caltech.edu/records/zgers-wd090/files/Frank2021_Article_TheNonlinearSchr\u00f6dingerEquatio.pdf" } ], "pub_year": "2021", "author_list": "Frank, Rupert L.; Gontier, David; et al." }, { "id": "https://authors.library.caltech.edu/records/0nnh3-60036", "eprint_id": 106623, "eprint_status": "archive", "datestamp": "2023-08-20 03:23:45", "lastmod": "2026-03-30 05:33:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Halverson-James", "name": { "family": "Halverson", "given": "James" }, "orcid": "0000-0003-0535-2622" }, { "id": "Ruehle-Fabian", "name": { "family": "Ruehle", "given": "Fabian" }, "orcid": "0000-0002-8409-9823" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Learning to unknot", "ispublished": "pub", "full_text_status": "public", "keywords": "knot theory, string theory, machine learning, reinforcement learning", "note": "\u00a9 2021 The Author(s). Published by IOP Publishing Ltd.\nOriginal content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. \n\nReceived 9 November 2020; Accepted 23 February 2021; Published 21 April 2021. \n\nWe thank Peter Battaglia, Kyle Cranmer, Michael Freedman, Mark Hughes, Ciprian Manolescu, Alex Radovic, Danilo Rezende, and Adam Sikora for useful discussions. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. J.H. is supported by NSF CAREER grant PHY-1848089. The work of P.S. is supported by the TEAM programme of the Foundation for Polish Science co-financed by the European Union under the European Regional Development Fund (POIR.04.04.00-00-5C55/17-00). \n\nData availability statement: The data that support the findings of this study are available upon reasonable request from the authors.\n\n

Published - Gukov_2021_Mach._Learn.__Sci._Technol._2_025035.pdf

Submitted - 2010.16263.pdf

", "abstract": "We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an algorithm to randomly generate N-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem. We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform at \u227395% accuracy. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well, reducing \u227380% of the unknots with up to 96 crossings we tested to the empty braid word, and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves.", "date": "2021-06", "date_type": "published", "publication": "Machine Learning: Science and Technology", "volume": "2", "number": "2", "publisher": "IOP Publishing", "pagerange": "Art. No. 025035", "id_number": "CaltechAUTHORS:20201111-131628016", "issn": "2632-2153", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201111-131628016", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "NSF", "grant_number": "PHY-1848089" }, { "agency": "Foundation for Polish Science" }, { "agency": "European Regional Development Fund", "grant_number": "POIR.04.04.00-00-5C55/17-00" } ] }, "other_numbering_system": { "items": [ { "id": "2020-046", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1088/2632-2153/abe91f", "primary_object": { "basename": "2010.16263.pdf", "url": "https://authors.library.caltech.edu/records/0nnh3-60036/files/2010.16263.pdf" }, "related_objects": [ { "basename": "Gukov_2021_Mach._Learn.__Sci._Technol._2_025035.pdf", "url": "https://authors.library.caltech.edu/records/0nnh3-60036/files/Gukov_2021_Mach._Learn.__Sci._Technol._2_025035.pdf" } ], "pub_year": "2021", "author_list": "Gukov, Sergei; Halverson, James; et al." }, { "id": "https://authors.library.caltech.edu/records/a1a3t-zxy51", "eprint_id": 110306, "eprint_status": "archive", "datestamp": "2023-08-20 03:33:11", "lastmod": "2026-03-30 06:51:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Penrose-Roger", "name": { "family": "Penrose", "given": "Roger" } } ] }, "title": "Gluing Non-commutative Twistor Spaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2021. Published by Oxford University Press. \n\nThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). \n\nReceived: 04 December 2020; Revision received: 31 March 2021; Accepted: 07 April 2021; Published: 26 April 2021. \n\nMatilde Marcolli is partially supported by NSF grant DMS-1\u2009707\u2009882 and DMS-2104330 and by NSERC Discovery Grant RGPIN-2018-04\u2009937 and Accelerator Supplement grant RGPAS-2018-522\u2009593.\n\n

Submitted - 2012.02823.pdf

", "abstract": "We describe a general procedure, based on Gerstenhaber\u2013Schack complexes, for extending to quantized twistor spaces the Donaldson\u2013Friedman gluing of twistor spaces via deformation theory of singular spaces. We consider in particular various possible quantizations of twistor spaces that leave the underlying spacetime manifold classical, including the geometric quantization of twistor spaces originally constructed by the second author, as well as some variants based on non-commutative geometry. We discuss specific aspects of the gluing construction for these different quantization procedures.", "date": "2021-06", "date_type": "published", "publication": "Quarterly Journal of Mathematics", "volume": "72", "number": "1-2", "publisher": "Oxford University Press", "pagerange": "417-454", "id_number": "CaltechAUTHORS:20210818-171944955", "issn": "0033-5606", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210818-171944955", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "DMS-2104330" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/qmath/haab024", "primary_object": { "basename": "2012.02823.pdf", "url": "https://authors.library.caltech.edu/records/a1a3t-zxy51/files/2012.02823.pdf" }, "pub_year": "2021", "author_list": "Marcolli, Matilde and Penrose, Roger" }, { "id": "https://authors.library.caltech.edu/records/8w53p-t0j17", "eprint_id": 109345, "eprint_status": "archive", "datestamp": "2023-08-20 03:21:58", "lastmod": "2026-03-30 16:08:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Extremal Numbers of Cycles Revisited", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 The Mathematical Association of America. \n\nReceived 09 May 2020, Accepted 22 Nov 2020, Published online: 27 Apr 2021.\n\n

Submitted - 2011.11064.pdf

", "abstract": "We give a simple geometric interpretation of an algebraic construction of Wenger that gives n-vertex graphs with no cycle of length 4, 6, or 10 and close to the maximum number of edges.", "date": "2021-05-28", "date_type": "published", "publication": "American Mathematical Monthly", "volume": "128", "number": "5", "publisher": "Mathematical Association of America", "pagerange": "464-466", "id_number": "CaltechAUTHORS:20210602-132638631", "issn": "0002-9890", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210602-132638631", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1080/00029890.2021.1886845", "primary_object": { "basename": "2011.11064.pdf", "url": "https://authors.library.caltech.edu/records/8w53p-t0j17/files/2011.11064.pdf" }, "pub_year": "2021", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/1j2jy-xp413", "eprint_id": 110990, "eprint_status": "archive", "datestamp": "2023-08-20 03:05:37", "lastmod": "2026-03-29 16:34:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hermon-Jonathan", "name": { "family": "Hermon", "given": "Jonathan" }, "orcid": "0000-0002-2935-3999" }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived: 10 May 2019 / Accepted: 13 October 2020 / Published online: 22 October 2020. \n\nWe thank the anonymous referees for their close reading and helpful suggestions.\n\n

Published - Hermon-Hutchcroft2021_Article_SupercriticalPercolationOnNona.pdf

Accepted Version - 1904.10448.pdf

", "abstract": "Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and p > p_c(G) then there exists a positive constant c_p such that \n\nP_p(n \u2264 |K| < \u221e) \u2264 e^(\u2212c_p)n) \n\nfor every n \u2265 1, where K is the cluster of the origin. We deduce the following two corollaries: \n\n1. Every infinite cluster in supercritical percolation on a transitive nonamenable graph has anchored expansion almost surely. This answers positively a question of Benjamini, Lyons, and Schramm (1997). \n\n2. For transitive nonamenable graphs, various observables including the percolation probability, the truncated susceptibility, and the truncated two-point function are analytic functions of p throughout the supercritical phase.", "date": "2021-05", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "224", "number": "2", "publisher": "Springer", "pagerange": "445-486", "id_number": "CaltechAUTHORS:20210922-193306644", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193306644", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-020-01011-3", "primary_object": { "basename": "1904.10448.pdf", "url": "https://authors.library.caltech.edu/records/1j2jy-xp413/files/1904.10448.pdf" }, "related_objects": [ { "basename": "Hermon-Hutchcroft2021_Article_SupercriticalPercolationOnNona.pdf", "url": "https://authors.library.caltech.edu/records/1j2jy-xp413/files/Hermon-Hutchcroft2021_Article_SupercriticalPercolationOnNona.pdf" } ], "pub_year": "2021", "author_list": "Hermon, Jonathan and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/ypa0d-8xg06", "eprint_id": 108630, "eprint_status": "archive", "datestamp": "2023-08-20 02:57:53", "lastmod": "2026-03-29 21:23:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harlow-Daniel", "name": { "family": "Harlow", "given": "Daniel" }, "orcid": "0000-0002-1005-4745" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Symmetries in Quantum Field Theory and Quantum Gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021.\n\nReceived\n22 November 2019;\nAccepted\n12 February 2021;\nPublished\n05 April 2021.\n\nWe thank Tom Banks, Thomas Dumitrescu, Zohar Komargodski, Nati Seiberg, and Sasha Zhiboedov for many useful discussions on the issues in this paper. We also thank Nima Arkani-Hamed, Chris Beem, Mu-Chun Chen, Clay Cordova, Simeon Hellerman, Gary Horowitz, Ethan Lake, Hong Liu, Roberto Longo, Juan Maldacena, Greg Moore, Andy Strominger, Raman Sundrum, Wati Taylor, and Edward Witten for useful discussions. We thank the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1607611, the Harvard Center for the Fundamental Laws of Nature, the Institute for Advanced Study, the Kavli Institute for Theoretical Physics, the Okinawa Institute of Science and Technology Graduate School, the Perimeter Institute, the Simons Center for Geometry and Physics, the Yukawa Institute of Fundamental Physics, for their hospitality during various stages of this work. DH also thanks the Kavli Institute for Physics and Mathematics of the Universe and the Maryland Center for Fundamental Physics for hospitality, and Alexander Huabo Yu Harlow for creating a stimulating environment while this work was being completed. DH is supported by the US Department of Energy Grants DE-SC0018944 and DE-SC0019127, the Simons foundation as a member of the It from Qubit collaboration, and the MIT department of physics. HO is supported in part by U.S. Department of Energy Grant DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895.\n\n

Submitted - 1810.05338.pdf

", "abstract": "In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any \"long-range\" bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the \"convex hull condition\" of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and 't Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman\u2013Mandula theorem to discrete symmetries, and an improved explanation of the decay \u03c0\u2070\u2192\u03b3\u03b3 in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in d+1 dimensions with horizon topology T^p\u00d7S^(d\u2212p\u22121).", "date": "2021-05", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "383", "number": "3", "publisher": "Springer", "pagerange": "1669-1804", "id_number": "CaltechAUTHORS:20210406-085746056", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210406-085746056", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "Harvard University" }, { "agency": "Institute for Advanced Study" }, { "agency": "Kavli Institute for Theoretical Physics" }, { "agency": "Okinawa Institute of Science and Technology" }, { "agency": "Perimeter Institute" }, { "agency": "Simons Center for Geometry and Physics" }, { "agency": "Yukawa Institute of Fundamental Physics" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0018944" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0019127" }, { "agency": "Simons Foundation" }, { "agency": "Massachusetts Institute of Technology (MIT)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-021-04040-y", "primary_object": { "basename": "1810.05338.pdf", "url": "https://authors.library.caltech.edu/records/ypa0d-8xg06/files/1810.05338.pdf" }, "pub_year": "2021", "author_list": "Harlow, Daniel and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/tbg1f-ft873", "eprint_id": 99245, "eprint_status": "archive", "datestamp": "2023-08-20 02:52:31", "lastmod": "2026-03-28 20:44:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Putrov-Pavel", "name": { "family": "Putrov", "given": "Pavel" } }, { "id": "Vafa-Cumrun", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "4-manifolds and topological modular forms", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal Field Theory, Anomalies in Field and String Theories, Differential and Algebraic Geometry, Topological Field Theories", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: December 9, 2020; Accepted: April 5, 2021; Published: May 11, 2021. \n\nWe would like to thank Ali Daemi, Mike Freedman, Mike Hopkins, Anton Kapustin, Ciprian Manolescu, Kantaro Ohmori, Shlomo Razamat, Peter Teichner, Edward Witten, Ida Zadeh, Gabi Zafrir, and Michele del Zotto for fruitful discussions. We especially would like to thank Peter Teichner for extensive discusions on topological modular forms and Edward Witten for his suggestion to view the 4-manifold invariants we obtain from 6d (1, 0) theories as defining a class in TMF. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of D.P. is supported by the Walter Burke Institute for Theoretical Physics, the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and in part by the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95). P.P. gratefully acknowledges the support from Marvin L. Goldberger Fellowship and the DOE Grant 51 DE-SC0009988 during his affiliation with IAS. The work of C.V. is supported in part by NSF grant PHY-1067976. We would like to thank the hospitality of Simons Center for Geometry and Physics, Kavli Institute for Theoretical Physics, International Center for Theoretical Physics, and Max Planck Institute for Mathematics where parts of this work were done.\n\n

Published - Gukov2021_Article_4-manifoldsAndTopologicalModul.pdf

Submitted - 1811.07884.pdf

", "abstract": "We build a connection between topology of smooth 4-manifolds and the theory of topological modular forms by considering topologically twisted compactification of 6d (1, 0) theories on 4-manifolds with flavor symmetry backgrounds. The effective 2d theory has (0, 1) supersymmetry and, possibly, a residual flavor symmetry. The equivariant topological Witten genus of this 2d theory then produces a new invariant of the 4-manifold equipped with a principle bundle, valued in the ring of equivariant weakly holomorphic (topological) modular forms. We describe basic properties of this map and present a few simple examples. As a byproduct, we obtain some new results on 't Hooft anomalies of 6d (1, 0) theories and a better understanding of the relation between 2d (0, 1) theories and TMF spectra.", "date": "2021-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 84", "id_number": "CaltechAUTHORS:20191014-080803922", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191014-080803922", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP05(2021)084", "primary_object": { "basename": "1811.07884.pdf", "url": "https://authors.library.caltech.edu/records/tbg1f-ft873/files/1811.07884.pdf" }, "related_objects": [ { "basename": "Gukov2021_Article_4-manifoldsAndTopologicalModul.pdf", "url": "https://authors.library.caltech.edu/records/tbg1f-ft873/files/Gukov2021_Article_4-manifoldsAndTopologicalModul.pdf" } ], "pub_year": "2021", "author_list": "Gukov, Sergei; Pei, Du; et al." }, { "id": "https://authors.library.caltech.edu/records/fbad7-znn76", "eprint_id": 106264, "eprint_status": "archive", "datestamp": "2023-08-20 02:28:32", "lastmod": "2026-03-28 23:16:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Walter's theorem for fusion systems", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.\n\nReceived 1 April 2019; revised 25 June 2020; published online 23 October 2020.\n\nThis work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.", "abstract": "We determine the saturated 2\u2010fusion systems in which the centralizer of some fully centralized involution contains a component that is the 2\u2010fusion system of a large group of Lie type over a field of odd order.", "date": "2021-04", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "122", "number": "4", "publisher": "London Mathematical Society", "pagerange": "569-615", "id_number": "CaltechAUTHORS:20201023-130934536", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201023-130934536", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.12386", "pub_year": "2021", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/bbzca-e5238", "eprint_id": 108138, "eprint_status": "archive", "datestamp": "2023-08-20 02:30:39", "lastmod": "2026-03-28 22:47:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00f6nig-Tobias", "name": { "family": "K\u00f6nig", "given": "Tobias" } }, { "id": "Kova\u0159\u00edk-Hynek", "name": { "family": "Kova\u0159\u00edk", "given": "Hynek" }, "orcid": "0000-0003-3647-8447" } ] }, "title": "Energy asymptotics in the three-dimensional Brezis\u2013Nirenberg problem", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 09 October 2020. Accepted 25 January 2021. Published 19 February 2021. \n\nThis paper may be reproduced, in its entirety, for non-commercial purposes. Partial support through US National Science Foundation Grants DMS-1363432 and DMS-1954995 (R.L.F.), Studienstiftung des deutschen Volkes (T.K.) and Gruppo Nazionale per Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) (H.K.) is acknowledged. \n\nCommunicated by Andrea Malchiodi.\n\n

Published - Frank2021_Article_EnergyAsymptoticsInTheThree-di.pdf

Submitted - 1908.01331.pdf

", "abstract": "For a bounded open set \u03a9\u2282\u211d\u00b3 we consider the minimization problem\n\nS(a + V) = inf|[0\u2261u\u2208H\u00b9\u2080(\u03a9) [\u222b_\u03a9(|\u2207u|\u00b2 + (a + \u03f5V)|u|\u00b2) dx]/(\u222b_\u03a9 u\u2076 dx)^(1/3)]\n\ninvolving the critical Sobolev exponent. The function a is assumed to be critical in the sense of Hebey and Vaugon. Under certain assumptions on a and V we compute the asymptotics of S(a+V)\u2212S as \u03f5 \u2192 0+, where S is the Sobolev constant. (Almost) minimizers concentrate at a point in the zero set of the Robin function corresponding to a and we determine the location of the concentration point within that set. We also show that our assumptions are almost necessary to have S(a + \u03f5V) < S for all sufficiently small \u03f5 > 0.", "date": "2021-04", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "60", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 58", "id_number": "CaltechAUTHORS:20210222-100903531", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210222-100903531", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Studienstiftung des Deutschen Volkes" }, { "agency": "Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-021-01929-3", "primary_object": { "basename": "1908.01331.pdf", "url": "https://authors.library.caltech.edu/records/bbzca-e5238/files/1908.01331.pdf" }, "related_objects": [ { "basename": "Frank2021_Article_EnergyAsymptoticsInTheThree-di.pdf", "url": "https://authors.library.caltech.edu/records/bbzca-e5238/files/Frank2021_Article_EnergyAsymptoticsInTheThree-di.pdf" } ], "pub_year": "2021", "author_list": "Frank, Rupert L.; K\u00f6nig, Tobias; et al." }, { "id": "https://authors.library.caltech.edu/records/mw1cw-44196", "eprint_id": 108807, "eprint_status": "archive", "datestamp": "2023-10-03 22:41:46", "lastmod": "2026-03-29 22:04:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-Jacob-S", "name": { "family": "Christiansen", "given": "Jacob S." }, "orcid": "0000-0002-3417-8574" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-Maxim", "name": { "family": "Zinchenko", "given": "Maxim" }, "orcid": "0000-0002-9559-0650" } ] }, "title": "Remarks on periodic Jacobi matrices on trees", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 Published under license by AIP Publishing. \n\nSubmitted: 18 October 2020; Accepted: 19 March 2021; Published Online: 13 April 2021. \n\nJ.S.C. and M.Z. would like to thank F. Harrison and E. Mantovan for the hospitality of Caltech where some of this work was done. This work was partially supported by the Swedish Research Council (VR) under Grant No. 2018-03500 (J.S.C.), the NSF grant, No. DMS-1665526 (B.S.), and the Simons Foundation grant, No. CGM-581256 (M.Z.). \n\nData Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.\n\n

Published - 042101_1_online.pdf

Submitted - 2010-01701.pdf

", "abstract": "We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well-known gap in the spectrum of the Laplacian on the upper half-plane with a hyperbolic metric. We make some conjectures about antibound states and make an interesting observation for the so-called rg-model where the underlying graph has r red and g green vertices and where any two vertices of different colors are connected by a single edge.", "date": "2021-04", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "62", "number": "4", "publisher": "American Institute of Physics", "pagerange": "Art. No. 042101", "id_number": "CaltechAUTHORS:20210423-080608586", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210423-080608586", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Research Council", "grant_number": "2018-03500" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Simons Foundation", "grant_number": "CGM-581256" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/5.0033702", "primary_object": { "basename": "042101_1_online.pdf", "url": "https://authors.library.caltech.edu/records/mw1cw-44196/files/042101_1_online.pdf" }, "related_objects": [ { "basename": "2010-01701.pdf", "url": "https://authors.library.caltech.edu/records/mw1cw-44196/files/2010-01701.pdf" } ], "pub_year": "2021", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/7mpwp-5j216", "eprint_id": 106721, "eprint_status": "archive", "datestamp": "2023-08-20 02:29:07", "lastmod": "2026-03-28 20:44:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benjamin-Nathan", "name": { "family": "Benjamin", "given": "Nathan" }, "orcid": "0000-0003-3661-6563" }, { "id": "Keller-Christoph-A", "name": { "family": "Keller", "given": "Christoph A." }, "orcid": "0000-0003-2592-2012" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Zadeh-Ida-G", "name": { "family": "Zadeh", "given": "Ida G." }, "orcid": "0000-0002-8803-0823" } ] }, "title": "On rational points in CFT moduli spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal Field Theory, Sigma Models", "note": "\u00a9 2021 The Authors.\nThis article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.\nArticle funded by SCOAP3.\n\nReceived: January 10, 2021;\nAccepted: March 2, 2021;\nPublished: April 8, 2021.\n\nWe thank C. Bachas, D. Gepner, K. Narain, C. Vafa, and K. Wendland for interesting\ndiscussions. The work of N.B. is supported in part by the Simons Foundation Grant\nNo. 488653. The work of C.A.K. is supported in part by the Simons Foundation Grant\nNo. 629215. The work of H.O. is supported in part by U.S. Department of Energy grant\nDE-SC0011632, by the World Premier International Research Center Initiative, MEXT,\nJapan, by JSPS Grant-in-Aid for Scientific Research 17K05407 and 20K03965, and by\nJSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. N.B. and H.O.\nthank the Aspen Center for Theoretical Physics, which is supported by the National Science\nFoundation grant PHY-1607611, where part of this work was done.\n\n

Published - Benjamin2021_Article_OnRationalPointsInCFTModuliSpa.pdf

Submitted - 2011.07062.pdf

", "abstract": "Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there. We first study the bosonic sigma-model with S1 target space in detail and uncover hitherto unknown features. We find for instance that the vanishing of the twist gap, though true for the S1 example, does not automatically follow from enhanced symmetry points being dense in the moduli space. We then explore the supersymmetric sigma-model on K3 by perturbing away from the torus orbifold locus. Though we do not reach a definite conclusion on the distribution of enhanced symmetry points in the K3 moduli space, we make several observations on how chiral currents can emerge and disappear under conformal perturbation theory.", "date": "2021-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 67", "id_number": "CaltechAUTHORS:20201118-103403846", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201118-103403846", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "488653" }, { "agency": "Simons Foundation", "grant_number": "629215" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "17K05407" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20K03965" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2020-050", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2021)067", "primary_object": { "basename": "2011.07062.pdf", "url": "https://authors.library.caltech.edu/records/7mpwp-5j216/files/2011.07062.pdf" }, "related_objects": [ { "basename": "Benjamin2021_Article_OnRationalPointsInCFTModuliSpa.pdf", "url": "https://authors.library.caltech.edu/records/7mpwp-5j216/files/Benjamin2021_Article_OnRationalPointsInCFTModuliSpa.pdf" } ], "pub_year": "2021", "author_list": "Benjamin, Nathan; Keller, Christoph A.; et al." }, { "id": "https://authors.library.caltech.edu/records/1nt9d-yhc77", "eprint_id": 110991, "eprint_status": "archive", "datestamp": "2023-08-20 02:37:29", "lastmod": "2026-03-28 21:10:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benjamini-Itai", "name": { "family": "Benjamini", "given": "Itai" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Large, lengthy graphs look locally like lines", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. \n\nReceived 5 July 2019; revised 23 September 2020; published online 25 November 2020. \n\nWe thank Jonathan Hermon and Matthew Tointon for helpful comments on a draft. We also thank the anonymous referee for their helpful suggestions.\n\n

Accepted Version - 1905.00316.pdf

", "abstract": "We apply the theory of unimodular random rooted graphs to study the metric geometry of large, finite, bounded degree graphs whose diameter is proportional to their volume. We prove that for a positive proportion of the vertices of such a graph, there exists a mesoscopic scale on which the graph looks like R in the sense that the rescaled ball is close to a line segment in the Gromov\u2013Hausdorff metric.", "date": "2021-04", "date_type": "published", "publication": "Bulletin of the Lindon Mathematical Society", "volume": "53", "number": "2", "publisher": "Wiley", "pagerange": "482-492", "id_number": "CaltechAUTHORS:20210922-193307537", "issn": "1469-2120", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307537", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/blms.12436", "primary_object": { "basename": "1905.00316.pdf", "url": "https://authors.library.caltech.edu/records/1nt9d-yhc77/files/1905.00316.pdf" }, "pub_year": "2021", "author_list": "Benjamini, Itai and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/b9ndr-ppw42", "eprint_id": 106619, "eprint_status": "archive", "datestamp": "2023-08-22 09:24:06", "lastmod": "2026-03-29 18:18:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Hsin-Po-Shen", "name": { "family": "Hsin", "given": "Po-Shen" }, "orcid": "0000-0002-4764-1476" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" } ] }, "title": "Generalized global symmetries of T[M] theories. Part I", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories; Field Theories in Higher Dimensions; Global Symmetries; Topological Field Theories", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: November 12, 2020; Revised: March 21, 2021; Accepted: March 22, 2021; Published: April 23, 2021. \n\nWe would like to thank Dan Freed, Anton Kapustin, Pavel Putrov, Nathan Seiberg, Cumrun Vafa, Juven Wang, Edward Witten, and Shing-Tung Yau for illuminating discussions and comments. We would like to especially thank Nikita Sopenko for participation at the early stage of this project. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The work of P.-S. H. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award. The work of D.P. is supported by the Center for Mathematical Sciences and Applications at Harvard University, and by an NSF grant DMS-0932078, administered by the Mathematical Sciences Research Institute while the author was in residence at MSRI for the program \"Holomorphic differentials in mathematics and physics\" during the Fall of 2019.\n\n

Published - Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf

Accepted Version - 2010.15890.pdf

", "abstract": "We study reductions of 6d theories on a d-dimensional manifold M_d, focusing on the interplay between symmetries, anomalies, and dynamics of the resulting (6 \u2212 d)-dimensional theory T[M_d]. We refine and generalize the notion of \"polarization\" to polarization on M_d, which serves to fix the spectrum of local and extended operators in T[M_d]. Another important feature of theories T[M_d] is that they often possess higher-group symmetries, such as 2-group and 3-group symmetries. We study the origin of such symmetries as well as physical implications including symmetry breaking and symmetry enhancement in the renormalization group flow. To better probe the IR physics, we also investigate the 't Hooft anomaly of 5d Chern-Simons matter theories. The present paper focuses on developing the general framework as well as the special case of d = 0 and 1, while an upcoming paper will discuss the case of d = 2, 3 and 4.", "date": "2021-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 232", "id_number": "CaltechAUTHORS:20201111-130432310", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201111-130432310", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664227" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-0932078" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2020-045", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2021)232", "primary_object": { "basename": "2010.15890.pdf", "url": "https://authors.library.caltech.edu/records/b9ndr-ppw42/files/2010.15890.pdf" }, "related_objects": [ { "basename": "Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf", "url": "https://authors.library.caltech.edu/records/b9ndr-ppw42/files/Gukov2021_Article_GeneralizedGlobalSymmetriesOfT.pdf" } ], "pub_year": "2021", "author_list": "Gukov, Sergei; Hsin, Po-Shen; et al." }, { "id": "https://authors.library.caltech.edu/records/fw0kr-yvv69", "eprint_id": 103470, "eprint_status": "archive", "datestamp": "2023-08-22 09:22:09", "lastmod": "2026-03-28 20:43:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carlen-Eric-A", "name": { "family": "Carlen", "given": "Eric A." }, "orcid": "0000-0003-2613-187X" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Ivanisvili-Paata", "name": { "family": "Ivanisvili", "given": "Paata" } }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Inequalities for L\u1d56-Norms that Sharpen the Triangle Inequality and Complement Hanner's Inequality", "ispublished": "pub", "full_text_status": "public", "keywords": "L\u1d56 space; Minkowski's inequality; Convexity", "note": "\u00a9 The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived 06 November 2019; Published 25 May 2020. \n\nThis paper may be reproduced, in its entirety, for non-commercial purposes. Work partially supported by NSF grants DMS-1501007 and DMS-1764254 (E.A.C.), DMS-1363432 (R.L.F.), DMS-1856486 (P.I.), PHY-1265118 (E.H.L.). \n\nOpen Access funding provided by Projekt DEAL. We thank Anthony Carbery for useful correspondence.\n\n

Published - Carlen2021_Article_InequalitiesForLPLp-NormsThatS.pdf

Submitted - 1807.05599.pdf

", "abstract": "In 2006 Carbery raised a question about an improvement on the na\u00efve norm inequality \u2225f+g\u2225^p_p \u2264 2^(p\u22121)(\u2225f\u2225^p_p+\u2225g\u2225^p_p) for two functions f and g in L\u1d56 of any measure space. When f=g this is an equality, but when the supports of f and g are disjoint the factor 2^(p\u22121) is not needed. Carbery's question concerns a proposed interpolation between the two situations for p > 2 with the interpolation parameter measuring the overlap being \u2225fg\u2225_(p/2). Carbery proved that his proposed inequality holds in a special case. Here, we prove the inequality for all functions and, in fact, we prove an inequality of this type that is stronger than the one Carbery proposed. Moreover, our stronger inequalities are valid for all real p \u2260 0.", "date": "2021-04", "date_type": "published", "publication": "Journal of Geometric Analysis", "volume": "31", "number": "4", "publisher": "Springer-Verlag", "pagerange": "4051-4073", "id_number": "CaltechAUTHORS:20200526-144324896", "issn": "1050-6926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200526-144324896", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1501007" }, { "agency": "NSF", "grant_number": "DMS-1764254" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1856486" }, { "agency": "NSF", "grant_number": "PHY-1265118" }, { "agency": "Projekt DEAL" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s12220-020-00425-y", "primary_object": { "basename": "Carlen2021_Article_InequalitiesForLPLp-NormsThatS.pdf", "url": "https://authors.library.caltech.edu/records/fw0kr-yvv69/files/Carlen2021_Article_InequalitiesForLPLp-NormsThatS.pdf" }, "related_objects": [ { "basename": "1807.05599.pdf", "url": "https://authors.library.caltech.edu/records/fw0kr-yvv69/files/1807.05599.pdf" } ], "pub_year": "2021", "author_list": "Carlen, Eric A.; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/swz3a-s1691", "eprint_id": 108754, "eprint_status": "archive", "datestamp": "2023-08-22 09:29:55", "lastmod": "2026-03-29 19:40:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "R. L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Larson-Simon", "name": { "family": "Larson", "given": "S." }, "orcid": "0000-0002-0057-8211" } ] }, "title": "Two Consequences of Davies' Hardy Inequality", "ispublished": "pub", "full_text_status": "public", "keywords": "Hardy inequality; Dirichlet problem; eigenvalues", "note": "\u00a9 Pleiades Publishing, Ltd., 2021. Russian Text \u00a9 The Author(s), 2021, published in Funktsional'nyi Analiz i Ego Prilozheniya, 2021. \n\nReceived 06 December 2020; Revised 06 December 2020; Accepted 30 December 2020; Published 08 November 2021; Issue Date April 2021. \n\nR. L. F. acknowledges the support of U. S. National Science Foundation, grants DMS-1363432 and DMS-1954995. S. L. acknowledges the support of the Knut and Alice Wallenberg Foundation, grant KAW 2018.0281. \n\nIn memory of M. Z. Solomyak, on the occasion of his 90th birthday.\n\n

Submitted - 2011.11830.pdf

", "abstract": "Davies' version of the Hardy inequality gives a lower bound for the Dirichlet integral of a function vanishing on the boundary of a domain in terms of the integral of the squared function with a weight containing the averaged distance to the boundary. This inequality is applied to easily derive two classical results of spectral theory, E. Lieb's inequality for the first eigenvalue of the Dirichlet Laplacian and G. Rozenblum's estimate for the spectral counting function of the Laplacian in an unbounded domain in terms of the number of disjoint balls of preset size whose intersection with the domain is large enough.", "date": "2021-04", "date_type": "published", "publication": "Functional Analysis and Its Applications", "volume": "55", "number": "2", "publisher": "Springer", "pagerange": "174-177", "id_number": "CaltechAUTHORS:20210416-094618696", "issn": "0016-2663", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210416-094618696", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1954995" }, { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW 2018.0281" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/S0016266321020106", "primary_object": { "basename": "2011.11830.pdf", "url": "https://authors.library.caltech.edu/records/swz3a-s1691/files/2011.11830.pdf" }, "pub_year": "2021", "author_list": "Frank, R. L. and Larson, S." }, { "id": "https://authors.library.caltech.edu/records/9z0yx-4qq83", "eprint_id": 109347, "eprint_status": "archive", "datestamp": "2023-08-22 09:20:04", "lastmod": "2026-03-29 16:18:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-Pavel", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Klyuev-Daniil", "name": { "family": "Klyuev", "given": "Daniil" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" }, { "id": "Stryker-Douglas", "name": { "family": "Stryker", "given": "Douglas" } } ] }, "title": "Twisted Traces and Positive Forms on Quantized Kleinian Singularities of Type A", "ispublished": "pub", "full_text_status": "public", "keywords": "star-product; orthogonal polynomial; quantization; trace", "note": "\u00a9 2021 The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License. \n \nReceived September 22, 2020, in final form March 08, 2021; Published online March 25, 2021. \n\nThis paper is a contribution to the Special Issue on Representation Theory and Integrable Systems in honor\nof Vitaly Tarasov on the 60th birthday and Alexander Varchenko on the 70th birthday. The full collection is\navailable at https://www.emis.de/journals/SIGMA/Tarasov-Varchenko.html. \n\nThe work of P.E. was partially supported by the NSF grant DMS-1502244. P.E. is grateful to Anton Kapustin for introducing him to the topic of this paper, and to Chris Beem, Mykola Dedushenko and Leonardo Rastelli for useful discussions. E.R. would like to thank Nicholas Witte for pointing out the reference [12].\n\n

Published - sigma21-029.pdf

Accepted Version - 2009.09437.pdf

", "abstract": "Following [Beem C., Peelaers W., Rastelli L., Comm. Math. Phys. 354 (2017), 345-392] and [Etingof P., Stryker D., SIGMA 16 (2020), 014, 28 pages], we undertake a detailed study of twisted traces on quantizations of Kleinian singularities of type A_(n\u22121). In particular, we give explicit integral formulas for these traces and use them to determine when a trace defines a positive Hermitian form on the corresponding algebra. This leads to a classification of unitary short star-products for such quantizations, a problem posed by Beem, Peelaers and Rastelli in connection with 3-dimensional superconformal field theory. In particular, we confirm their conjecture that for n\u22644 a unitary short star-product is unique and compute its parameter as a function of the quantization parameters, giving exact formulas for the numerical functions by Beem, Peelaers and Rastelli. If n=2, this, in particular, recovers the theory of unitary spherical Harish-Chandra bimodules for sl\u2082. Thus the results of this paper may be viewed as a starting point for a generalization of the theory of unitary Harish-Chandra bimodules over enveloping algebras of reductive Lie algebras [Vogan Jr. D.A., Annals of Mathematics Studies, Vol. 118, Princeton University Press, Princeton, NJ, 1987] to more general quantum algebras. Finally, we derive recurrences to compute the coefficients of short star-products corresponding to twisted traces, which are generalizations of discrete Painlev\u00e9 systems.", "date": "2021-03-25", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "17", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 29", "id_number": "CaltechAUTHORS:20210602-134422197", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210602-134422197", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1502244" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/sigma.2021.029", "primary_object": { "basename": "2009.09437.pdf", "url": "https://authors.library.caltech.edu/records/9z0yx-4qq83/files/2009.09437.pdf" }, "related_objects": [ { "basename": "sigma21-029.pdf", "url": "https://authors.library.caltech.edu/records/9z0yx-4qq83/files/sigma21-029.pdf" } ], "pub_year": "2021", "author_list": "Etingof, Pavel; Klyuev, Daniil; et al." }, { "id": "https://authors.library.caltech.edu/records/54q7t-dfp96", "eprint_id": 108731, "eprint_status": "archive", "datestamp": "2023-08-20 02:19:05", "lastmod": "2026-03-28 23:11:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bartholdi-Laurent", "name": { "family": "Bartholdi", "given": "Laurent" } }, { "id": "Hann-Caruthers-Wade", "name": { "family": "Hann-Caruthers", "given": "Wade" } }, { "id": "Josyula-Maya", "name": { "family": "Josyula", "given": "Maya" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Yariv-L", "name": { "family": "Yariv", "given": "Leeat" } } ] }, "title": "Equitable Voting Rules", "ispublished": "pub", "full_text_status": "public", "keywords": "May's theorem, equity, symmetry, group theory", "note": "\u00a9 2021 The Econometric Society. \n\nCo-editor Bart Lipman handled this manuscript. Manuscript received 1 February, 2019; final version accepted 29 August, 2020; available online 3 September, 2020. \n\nWe thank Wolfgang Pesendorfer for useful comments. Tamuz gratefully acknowledges financial support from the Simons Foundation, through Grant 419427. Yariv gratefully acknowledges financial support from the NSF, through Grant SES-1629613.\n\n

Published - ECTA17032.pdf

Accepted Version - 1811.01227.pdf

Submitted - equitable.pdf

", "abstract": "May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.", "date": "2021-03-15", "date_type": "published", "publication": "Econometrica", "volume": "89", "number": "2", "publisher": "Blackwell Publishing", "pagerange": "563-589", "id_number": "CaltechAUTHORS:20210414-131421263", "issn": "0012-9682", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210414-131421263", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "NSF", "grant_number": "SES-1629613" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3982/ecta17032", "primary_object": { "basename": "1811.01227.pdf", "url": "https://authors.library.caltech.edu/records/54q7t-dfp96/files/1811.01227.pdf" }, "related_objects": [ { "basename": "ECTA17032.pdf", "url": "https://authors.library.caltech.edu/records/54q7t-dfp96/files/ECTA17032.pdf" }, { "basename": "equitable.pdf", "url": "https://authors.library.caltech.edu/records/54q7t-dfp96/files/equitable.pdf" } ], "pub_year": "2021", "author_list": "Bartholdi, Laurent; Hann-Caruthers, Wade; et al." }, { "id": "https://authors.library.caltech.edu/records/44cpt-j4p70", "eprint_id": 108717, "eprint_status": "archive", "datestamp": "2023-08-20 02:18:57", "lastmod": "2026-03-28 22:53:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Manolescu-Ciprian", "name": { "family": "Manolescu", "given": "Ciprian" } } ] }, "title": "A two-variable series for knot complements", "ispublished": "pub", "full_text_status": "public", "keywords": "WRT invariants, BPS states, Dehn surgery, resurgence, colored Jones polynomial", "note": "\u00a9 2021 European Mathematical Society. Published by EMS Press. This work is licensed under a CC BY 4.0 license. \n\nReceived June 7, 2019. Published online: 2021-03-15. \n\nSergei Gukovwas supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. DMS 1664240. \n\nCiprian Manolescu was supported by the National Science Foundation under Grant No. DMS-1708320.\n\n

Published - QT-2021-012-001-01.pdf

Accepted Version - 1904.06057.pdf

", "abstract": "The physical 3d N=2 theory T[Y] was previously used to predict the existence of some 3-manifold invariants Za(q) that take the form of power series with integer coefficients, converging in the unit disk. Their radial limits at the roots of unity should recover the Witten\u2013Reshetikhin\u2013Turaev invariants. In this paper we discuss how, for complements of knots in S\u00b3, the analogue of the invariants Za(q) should be a two-variable series F_K(x,q) obtained by parametric resurgence from the asymptotic expansion of the colored Jones polynomial. The terms in this series should satisfy a recurrence given by the quantum A-polynomial. Furthermore, there is a formula that relates F_K(x,q) to the invariants Za(q) for Dehn surgeries on the knot. We provide explicit calculations of F_K(x,q) in the case of knots given by negative definite plumbings with an unframed vertex, such as torus knots. We also find numerically the first terms in the series for the figure-eight knot, up to any desired order, and use this to understand Za(q) for some hyperbolic 3-manifolds.", "date": "2021-03-15", "date_type": "published", "publication": "Quantum Topology", "volume": "12", "number": "1", "publisher": "European Mathematical Society", "pagerange": "1-109", "id_number": "CaltechAUTHORS:20210413-133913817", "issn": "1663-487X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210413-133913817", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "NSF", "grant_number": "DMS-1708320" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/QT/145", "primary_object": { "basename": "1904.06057.pdf", "url": "https://authors.library.caltech.edu/records/44cpt-j4p70/files/1904.06057.pdf" }, "related_objects": [ { "basename": "QT-2021-012-001-01.pdf", "url": "https://authors.library.caltech.edu/records/44cpt-j4p70/files/QT-2021-012-001-01.pdf" } ], "pub_year": "2021", "author_list": "Gukov, Sergei and Manolescu, Ciprian" }, { "id": "https://authors.library.caltech.edu/records/a5e1r-de367", "eprint_id": 108790, "eprint_status": "archive", "datestamp": "2023-08-20 02:19:11", "lastmod": "2026-03-29 17:55:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dodelson-Matthew", "name": { "family": "Dodelson", "given": "Matthew" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Singularities of thermal correlators at strong coupling", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3. \n\nReceived 10 December 2020; accepted 24 February 2021; published 24 March 2021. \n\nWe thank P. Di Vecchia, V. Hubeny, T. Jacobson, E. Martinec, D. Meltzer, M. Mirbabayi, M. Rangamani, G. Sarosi, S. Shenker, D. Stanford, E. Silverstein, and N. Warner for discussion. The work of H.\u2009O. is supported in part by U.S. Department of Energy Grant No. DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research 17K05407 and 20K03965, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. H.\u2009O. thanks the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant No. PHY-1607611, where part of this work was done. The work of M.\u2009D. is supported by JSPS KAKENHI Grant No. 20K14465.\n\n

Published - PhysRevD.103.066018.pdf

Accepted Version - 2010.09734.pdf

", "abstract": "We analyze the singularities of the two-point function in a conformal field theory at finite temperature. In a free theory, the only singularity is along the boundary light cone. In the holographic limit, a new class of singularities emerges since two boundary points can be connected by a nontrivial null geodesic in the bulk, encircling the photon sphere of the black hole. We show that these new singularities are resolved by tidal effects due to the black hole curvature, by solving the string world sheet theory in the Penrose limit. Singularities in the asymptotically flat black hole geometry are also discussed.", "date": "2021-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "103", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066018", "id_number": "CaltechAUTHORS:20210421-153703789", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210421-153703789", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "17K05407" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20K03965" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20K14465" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/physrevd.103.066018", "primary_object": { "basename": "2010.09734.pdf", "url": "https://authors.library.caltech.edu/records/a5e1r-de367/files/2010.09734.pdf" }, "related_objects": [ { "basename": "PhysRevD.103.066018.pdf", "url": "https://authors.library.caltech.edu/records/a5e1r-de367/files/PhysRevD.103.066018.pdf" } ], "pub_year": "2021", "author_list": "Dodelson, Matthew and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/2ayzz-p1011", "eprint_id": 107157, "eprint_status": "archive", "datestamp": "2023-08-22 09:15:54", "lastmod": "2026-03-28 20:45:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Walter's basic theorem for fusion systems", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Finite simple groups; Fusion systems", "note": "\u00a9 2020 Elsevier. \n\nReceived 13 September 2018, Available online 8 December 2020. \n\nCommunicated by Markus Linckelmann. \n\nThis work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.", "abstract": "This is the first of two papers determining the saturated 2-fusion systems in which the centralizer of some fully centralized involution contains a component that is the 2-fusion system of a large group of Lie type over a field of odd order.", "date": "2021-03-15", "date_type": "published", "publication": "Journal of Algebra", "volume": "570", "publisher": "Elsevier", "pagerange": "595-610", "id_number": "CaltechAUTHORS:20201217-124921798", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201217-124921798", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2020.11.018", "pub_year": "2021", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/xg694-vvk07", "eprint_id": 110829, "eprint_status": "archive", "datestamp": "2023-08-20 02:10:34", "lastmod": "2026-03-10 00:02:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Enumeration of holomorphic cylinders in log\n Calabi\u2013Yau surfaces, II : Positivity, integrality and the gluing formula", "ispublished": "pub", "full_text_status": "public", "keywords": "cylinder, enumerative geometry, nonarchimedean geometry, Berkovich space, Gromov\u2013Witten, Calabi\u2013Yau", "note": "\u00a9\u20092021 MSP. \n\nReceived: 5 September 2016. Revised: 17 November 2019. Accepted: 21 February 2020. Published: 2 March 2021. \n\nI am very grateful to Maxim Kontsevich for sharing with me many ideas. I am equally grateful to Vladimir Berkovich, Antoine Chambert-Loir, Mark Gross, Bernd Siebert and Michael Temkin for valuable discussions. The smoothness argument in Section 5 I learned from Sean Keel. I would like to thank him in particular. This research was partially conducted during the period the author served as a Clay Research Fellow.\n\n

Accepted Version - 1608.07651.pdf

", "abstract": "We prove three fundamental properties of counting holomorphic cylinders in log Calabi\u2013Yau surfaces: positivity, integrality and the gluing formula. Positivity and integrality assert that the numbers of cylinders, defined via virtual techniques, are in fact nonnegative integers. The gluing formula roughly says that cylinders can be glued together to form longer cylinders, and the number of longer cylinders equals the product of the numbers of shorter cylinders. Our approach uses Berkovich geometry, tropical geometry, deformation theory and the ideas in the proof of associativity relations of Gromov\u2013Witten invariants by Maxim Kontsevich. These three properties provide evidence for a conjectural relation between counting cylinders and the broken lines of Gross, Hacking and Keel.", "date": "2021-03-02", "date_type": "published", "publication": "Geometry & Topology", "volume": "25", "number": "1", "publisher": "Mathematical Sciences Publishers", "pagerange": "1-46", "id_number": "CaltechAUTHORS:20210914-164412666", "issn": "1364-0380", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412666", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/gt.2021.25.1", "primary_object": { "basename": "1608.07651.pdf", "url": "https://authors.library.caltech.edu/records/xg694-vvk07/files/1608.07651.pdf" }, "pub_year": "2021", "author_list": "Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/9fh52-1es68", "eprint_id": 108398, "eprint_status": "archive", "datestamp": "2023-08-22 09:05:51", "lastmod": "2026-04-16 01:39:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Zhang-Pengfei-PHYSICS", "name": { "family": "Zhang", "given": "Pengfei" }, "orcid": "0000-0002-7408-0918" }, { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "An obstacle to sub-AdS holography for SYK-like models", "ispublished": "pub", "full_text_status": "public", "keywords": "1/N Expansion; AdS-CFT Correspondence", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: December 16, 2020; Revised: January 22, 2021; Accepted: January 28, 2021; Published: March 9, 2021. \n\nWe acknowledge Hui Zhai for collaboration in the early stages of this project. We thank Douglas Stanford for helpful discussions. Y.G. is supported by the Gordon and Betty Moore Foundation EPiQS Initiative through Grant (GBMF-4306), and by the Simons Foundation through the \"It from Qubit\" program\". A.K. is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. P.Z. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.\n\n

Published - Zhang2021_Article_AnObstacleToSub-AdSHolographyF.pdf

Submitted - 2012.01620.pdf

", "abstract": "We argue that \"stringy\" effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.", "date": "2021-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 94", "id_number": "CaltechAUTHORS:20210311-125528811", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210311-125528811", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation", "grant_number": "GBMF-4306" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep03(2021)094", "primary_object": { "basename": "2012.01620.pdf", "url": "https://authors.library.caltech.edu/records/9fh52-1es68/files/2012.01620.pdf" }, "related_objects": [ { "basename": "Zhang2021_Article_AnObstacleToSub-AdSHolographyF.pdf", "url": "https://authors.library.caltech.edu/records/9fh52-1es68/files/Zhang2021_Article_AnObstacleToSub-AdSHolographyF.pdf" } ], "pub_year": "2021", "author_list": "Zhang, Pengfei; Gu, Yingfei; et al." }, { "id": "https://authors.library.caltech.edu/records/ha7zw-g7z24", "eprint_id": 105620, "eprint_status": "archive", "datestamp": "2023-08-20 02:01:06", "lastmod": "2026-03-28 21:08:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Seiringer-Robert", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals, Inc. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. \n\nIssue Online: 17 January 2021; Version of Record online: 28 September 2020. \n\nPartial support through National Science Foundation Grant\nDMS-1363432 (R.L.F.) and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 694227; R.S.), is acknowledged.\n\n

Published - cpa.21944.pdf

Accepted Version - 1902.02489.pdf

", "abstract": "We consider the Fr\u00f6hlich polaron model in the strong coupling limit. It is well\u2010known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem.", "date": "2021-03", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "74", "number": "3", "publisher": "Wiley", "pagerange": "544-588", "id_number": "CaltechAUTHORS:20200928-152152135", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200928-152152135", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "European Research Council (ERC)", "grant_number": "694227" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/cpa.21944", "primary_object": { "basename": "1902.02489.pdf", "url": "https://authors.library.caltech.edu/records/ha7zw-g7z24/files/1902.02489.pdf" }, "related_objects": [ { "basename": "cpa.21944.pdf", "url": "https://authors.library.caltech.edu/records/ha7zw-g7z24/files/cpa.21944.pdf" } ], "pub_year": "2021", "author_list": "Frank, Rupert L. and Seiringer, Robert" }, { "id": "https://authors.library.caltech.edu/records/0d47f-80551", "eprint_id": 108541, "eprint_status": "archive", "datestamp": "2023-08-20 02:04:47", "lastmod": "2026-04-16 01:40:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dadras-Pouria", "name": { "family": "Dadras", "given": "Pouria" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Perturbative calculations of entanglement entropy", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence, Black Holes, 2D Gravity", "note": "\u00a9 2021 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.\nArticle funded by SCOAP3.\n\nReceived: December 11, 2020;\nAccepted: February 5, 2021;\nPublished: March 22, 2021.\n\nWe thank Douglas Stanford, Juan Maldacena, Pengfei Zhang, and Yiming Chen for useful\ndiscussions. We gratefully acknowledge the support by the Simons Foundation under\ngrant 376205. A.K. is also supported by the Simons Foundation through the \"It from\nQubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF\nFrontier center funded in part by the Gordon and Betty Moore Foundation.\n\n

Published - Dadras-Kitaev2021_Article_PerturbativeCalculationsOfEnta.pdf

Submitted - 2011.09622.pdf

", "abstract": "This paper is an attempt to extend the recent understanding of the Page curve for evaporating black holes to more general systems coupled to a heat bath. Although calculating the von Neumann entropy by the replica trick is usually a challenge, we have identified two solvable cases. For the initial section of the Page curve, we sum up the perturbation series in the system-bath coupling \u03ba; the most interesting contribution is of order 2s, where s is the number of replicas. For the saturated regime, we consider the effect of an external impulse on the entropy at a later time and relate it to OTOCs. A significant simplification occurs in the maximal chaos case such that the effect may be interpreted in terms of an intermediate object, analogous to the branching surface of a replica wormhole.", "date": "2021-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2021", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 198", "id_number": "CaltechAUTHORS:20210324-090318969", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210324-090318969", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep03(2021)198", "primary_object": { "basename": "2011.09622.pdf", "url": "https://authors.library.caltech.edu/records/0d47f-80551/files/2011.09622.pdf" }, "related_objects": [ { "basename": "Dadras-Kitaev2021_Article_PerturbativeCalculationsOfEnta.pdf", "url": "https://authors.library.caltech.edu/records/0d47f-80551/files/Dadras-Kitaev2021_Article_PerturbativeCalculationsOfEnta.pdf" } ], "pub_year": "2021", "author_list": "Dadras, Pouria and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/5k8hv-4ts49", "eprint_id": 107121, "eprint_status": "archive", "datestamp": "2023-08-22 08:55:03", "lastmod": "2026-03-30 05:33:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Ferber-Asaf", "name": { "family": "Ferber", "given": "Asaf" } } ] }, "title": "Lower bounds for multicolor Ramsey numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey numbers; Monochromatic cliques", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 24 September 2020, Revised 25 November 2020, Accepted 26 November 2020, Available online 9 December 2020. \n\nResearch supported in part by NSF grants DMS-1954395 and DMS-1953799. \n\nWe are extremely grateful to Vishesh Jain and Wojciech Samotij for reading an early draft of this paper and offering several suggestions which improved the presentation. We also owe a debt to Noga Alon and Anurag Bishnoi, both of whom pointed out the constraint on the dimension of isotropic subspaces, thereby improving the bound in our original posting.\n\n

Submitted - 2009.10458.pdf

", "abstract": "We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed number of colors greater than two.", "date": "2021-02-12", "date_type": "published", "publication": "Advances in Mathematics", "volume": "378", "publisher": "Elsevier", "pagerange": "Art. No. 107528", "id_number": "CaltechAUTHORS:20201216-111908862", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201216-111908862", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1954395" }, { "agency": "NSF", "grant_number": "DMS-1953799" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2020.107528", "primary_object": { "basename": "2009.10458.pdf", "url": "https://authors.library.caltech.edu/records/5k8hv-4ts49/files/2009.10458.pdf" }, "pub_year": "2021", "author_list": "Conlon, David and Ferber, Asaf" }, { "id": "https://authors.library.caltech.edu/records/m2zh4-t7w53", "eprint_id": 108043, "eprint_status": "archive", "datestamp": "2023-08-20 01:43:23", "lastmod": "2026-03-09 21:31:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eischen-Ellen", "name": { "family": "Eischen", "given": "E." } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "E." } } ] }, "title": "p-adic families of automorphic forms in the \u00b5-ordinary setting", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2021 Johns Hopkins University Press. \n\nManuscript received January 19, 2018; revised January 28, 2019. \n\nResearch of the first author supported in part by NSF grant DMS-1559609 and NSF CAREER Grant DMS-1751281. \n\nWe thank H. Hida for feedback on the initial idea for this project. We are also very grateful to E. de Shalit and E. Goren for helpful feedback on the first version of this paper, which led to key improvements. Our work on this paper benefitted from conversations with several additional mathematicians concerning topics closely related to this paper. E.M. thanks B. Moonen for a discussion about his earlier work on which portions of this paper rely significantly, and she thanks M.-H. Nicole for a discussion about his work with W. Goldring on the \u00b5-ordinary Hasse invariant. We also thank E. Rains for alerting us to the Littlewood\u2013Richardson rule mentioned in Section 2.4.1, and we thank M. Harris for helpful feedback about references. We are grateful to J. Fintzen and I. Varma for conversations concerning the collaboration [EFMV18], whose influence is seen here. We thank Caltech and the University of Oregon for hosting us during this collaboration.\n\n

Accepted Version - 1710.01864.pdf

", "abstract": "We develop a theory of p-adic automorphic forms on unitary groups that allows p-adic interpolation in families and holds for all primes p that do not ramify in the reflex field E of the associated unitary Shimura variety. If the ordinary locus is nonempty (a condition only met if p splits completely in E), we recover Hida's theory of p-adic automorphic forms, which is defined over the ordinary locus. More generally, we work over the \u00b5-ordinary locus, which is open and dense. \n\nBy eliminating the splitting condition on p, our framework should allow many results employing Hida's theory to extend to infinitely many more primes. We also provide a construction of p-adic families of automorphic forms that uses differential operators constructed in the paper. Our approach is to adapt the methods of Hida and Katz to the more general \u00b5-ordinary setting, while also building on papers of each author. Along the way, we encounter some unexpected challenges and subtleties that do not arise in the ordinary setting.", "date": "2021-02", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "143", "number": "1", "publisher": "Johns Hopkins University Press", "pagerange": "1-52", "id_number": "CaltechAUTHORS:20210212-133815628", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210212-133815628", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1559609" }, { "agency": "NSF", "grant_number": "DMS-1751281" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1353/ajm.2021.0006", "primary_object": { "basename": "1710.01864.pdf", "url": "https://authors.library.caltech.edu/records/m2zh4-t7w53/files/1710.01864.pdf" }, "pub_year": "2021", "author_list": "Eischen, E. and Mantovan, E." }, { "id": "https://authors.library.caltech.edu/records/c9dkm-rs921", "eprint_id": 71957, "eprint_status": "archive", "datestamp": "2023-08-20 01:36:35", "lastmod": "2026-03-30 07:19:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harel-Matan", "name": { "family": "Harel", "given": "Matan" } }, { "id": "Mossel-Elchanan", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Strack-Philipp", "name": { "family": "Strack", "given": "Philipp" }, "orcid": "0000-0002-7960-9243" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Rational Groupthink", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2020. \n\nPublished by Oxford University Press on behalf of the President and Fellows of Harvard College. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). \n\nPublished: 08 July 2020. \n\nWe thank seminar audiences in Berkeley, Berlin, Bonn, Caltech, Chicago, D\u00fcsseldorf, Duke, Harvard, Medell\u0131n, Microsoft Research New England, MIT, Montreal, NYU, Penn State, Pittsburgh, Princeton, San Diego, UPenn, USC, Washington University, and Yale, as well as Nageeb Ali, Ben Brooks, Dirk Bergemann, Kim Border, Federico Echenique, Wade Hann-Caruthers, Benjamin Golub, RainieHeck, Paul Heidhues, Shachar Kariv, Navin Kartik, StevenMorris, Luciano Pomatto, Larry Samuelson, Lones Smith, Juuso Toikka, Leeat Yariv, and others for insightful comments and discussions. Matan Harel was partially supported by the IDEX grant of Paris-Saclay. Elchanan Mossel is supported by ONR grant N00014-16-1-2227 and NSF grant CCF 1320105. Omer Tamuz was supported by a grant from the Simons Foundation (#419427).\n\n

Published - qjaa026.pdf

Submitted - 1412.7172v1.pdf

Submitted - 1412.7172v2.pdf

Submitted - 1412.7172v3.pdf

Submitted - 1412.7172v4.pdf

Submitted - 1412.7172v5.pdf

Submitted - 1412.7172v6.pdf

Submitted - 1412.7172v7.pdf

Supplemental Material - qjaa026_online_appendix.pdf

", "abstract": "We study how long-lived rational agents learn from repeatedly observing a private signal and each others' actions. With normal signals, a group of any size learns more slowly than just four agents who directly observe each others' private signals in each period. Similar results apply to general signal structures. We identify rational groupthink\u2014in which agents ignore their private signals and choose the same action for long periods of time\u2014as the cause of this failure of information aggregation.", "date": "2021-02", "date_type": "published", "publication": "Quarterly Journal of Economics", "volume": "136", "number": "1", "publisher": "Oxford University Press", "pagerange": "621-668", "id_number": "CaltechAUTHORS:20161111-135545798", "issn": "0033-5533", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-135545798", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Paris-Saclay" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-16-1-2227" }, { "agency": "NSF", "grant_number": "CCF-1320105" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/qje/qjaa026", "primary_object": { "basename": "1412.7172v6.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v6.pdf" }, "related_objects": [ { "basename": "1412.7172v7.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v7.pdf" }, { "basename": "qjaa026_online_appendix.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/qjaa026_online_appendix.pdf" }, { "basename": "1412.7172v1.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v1.pdf" }, { "basename": "1412.7172v5.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v5.pdf" }, { "basename": "qjaa026.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/qjaa026.pdf" }, { "basename": "1412.7172v2.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v2.pdf" }, { "basename": "1412.7172v3.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v3.pdf" }, { "basename": "1412.7172v4.pdf", "url": "https://authors.library.caltech.edu/records/c9dkm-rs921/files/1412.7172v4.pdf" } ], "pub_year": "2021", "author_list": "Harel, Matan; Mossel, Elchanan; et al." }, { "id": "https://authors.library.caltech.edu/records/sm0tq-p8w54", "eprint_id": 95610, "eprint_status": "archive", "datestamp": "2023-08-20 01:36:57", "lastmod": "2026-03-29 20:56:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Merz-Konstantin", "name": { "family": "Merz", "given": "Konstantin" } }, { "id": "Siedentop-Heinz", "name": { "family": "Siedentop", "given": "Heinz" } } ] }, "title": "Equivalence of Sobolev Norms Involving Generalized Hardy Operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2019. Published by Oxford University Press. \nThis article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model).\n\nReceived: 24 July 2018;\nRevision received: 12 March 2019;\nAccepted: 17 May 2019;\nPublished: 09 July 2019.\n\nThe authors are very grateful to an anonymous referee for many helpful remarks and suggestions.\n\nFunding:\nThis work was supported by the Deutsche Forschungsgemeinschaft [grant SI 348/15-1 to H.S. and EXC-2111 390814868 to R.L.F., K.M., H.S.] and the U.S. National Science Foundation [grant DMS-1363432 to R.L.F.].\n\n

Submitted - 1807.09027.pdf

", "abstract": "We consider the fractional Schr\u00f6dinger operator with Hardy potential and critical or subcritical coupling constant. This operator generates a natural scale of homogeneous Sobolev spaces, which we compare with the ordinary homogeneous Sobolev spaces. As a byproduct, we obtain generalized and reversed Hardy inequalities for this operator. Our results extend those obtained recently for ordinary (non-fractional) Schr\u00f6dinger operators and have an important application in the treatment of large relativistic atoms.", "date": "2021-02", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2021", "number": "3", "publisher": "Oxford University Press", "pagerange": "2284-2303", "id_number": "CaltechAUTHORS:20190520-135826551", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-135826551", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "SI 348/15-1" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111 390814868" }, { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnz135", "primary_object": { "basename": "1807.09027.pdf", "url": "https://authors.library.caltech.edu/records/sm0tq-p8w54/files/1807.09027.pdf" }, "pub_year": "2021", "author_list": "Frank, Rupert L.; Merz, Konstantin; et al." }, { "id": "https://authors.library.caltech.edu/records/jfxe1-xbm62", "eprint_status": "archive", "datestamp": "2026-01-15 00:36:44", "lastmod": "2026-03-28 20:46:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Zhao", "given": "Yufei" }, "orcid": "0000-0002-1995-3755" } ] }, "title": "Common and Sidorenko Linear Equations", "ispublished": "pub", "full_text_status": "public", "abstract": "

A linear equation with coefficients in $\\mathbb{F}_q$ is common if the number of monochromatic solutions in any two-coloring of $\\mathbb{F}_q^{\\,n}$ is asymptotically (as $n \\to \\infty$) at least the number expected in a random two-coloring. The linear equation is Sidorenko if the number of solutions in any dense subset of $\\mathbb{F}_q^{\\,n}$ is asymptotically at least the number expected in a random set of the same density. In this paper, we characterize those linear equations which are common, and those which are Sidorenko. The main novelty is a construction based on choosing random Fourier coefficients that shows that certain linear equations do not have these properties. This solves problems posed in a paper of Saad and Wolf.

", "date": "2021-01-20", "date_type": "published", "publication": "The Quarterly Journal of Mathematics", "volume": "72", "number": "4", "publisher": "Oxford University Press (OUP)", "pagerange": "1223-1234", "issn": "0033-5606", "official_url": "https://authors.library.caltech.edu/records/jfxe1-xbm62", "funders": { "items": [ { "agency": "Packard Fellowship and NSF", "grant_number": "DMS-1855635" }, { "agency": "MIT Solomon Buchsbaum Fund and Sloan Research Fellowship", "grant_number": "DMS-1764176" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/qmath/haaa068", "pub_year": "2021", "author_list": "Fox, Jacob; Pham, Huy Tuan; et al." }, { "id": "https://authors.library.caltech.edu/records/x70d0-23195", "eprint_id": 100882, "eprint_status": "archive", "datestamp": "2023-08-20 01:10:54", "lastmod": "2026-03-30 05:22:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mu-Xiaosheng", "name": { "family": "Mu", "given": "Xiaosheng" }, "orcid": "0000-0002-2868-5182" }, { "id": "Pomatto-L", "name": { "family": "Pomatto", "given": "Luciano" }, "orcid": "0000-0002-4331-8436" }, { "id": "Strack-Philipp", "name": { "family": "Strack", "given": "Philipp" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "From Blackwell Dominance in Large Samples to R\u00e9nyi Divergences and Back Again", "ispublished": "pub", "full_text_status": "public", "keywords": "Comparison of experiments, stochastic dominance, divergences", "note": "\u00a9 2021 The Econometric Society. \n\nManuscript received 5 August, 2019; final version accepted 4 September, 2020; available online 11 September, 2020. \n\nWe are grateful to the coeditor and three referees for their comments and suggestions. In addition, we would like to thank Kim Border, Laura Doval, Federico Echenique, Tobias Fritz, Drew Fudenberg, George Mailath, Massimo Marinacci, Margaret Meyer, Marco Ottaviani, and Peter Norman S\u00f8rensen for helpful discussions. Xiaosheng Mu acknowledges the hospitality of Columbia University and the Cowles Foundation at Yale University, which hosted him during parts of this research. Philipp Strack was supported by a Sloan research fellowship. Omer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan research fellowship, and a BSF award (#2018397).\n\n

Published - ECTA17548.pdf

Accepted Version - 1906.02838.pdf

", "abstract": "We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher R\u00e9nyi divergences.", "date": "2021-01", "date_type": "published", "publication": "Econometrica", "volume": "89", "number": "1", "publisher": "Econometric Society", "pagerange": "475-506", "id_number": "CaltechAUTHORS:20200124-080643011", "issn": "1468-0262", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-080643011", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Cowles Foundation for Research in Economics" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2018397" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3982/ECTA17548", "primary_object": { "basename": "1906.02838.pdf", "url": "https://authors.library.caltech.edu/records/x70d0-23195/files/1906.02838.pdf" }, "related_objects": [ { "basename": "ECTA17548.pdf", "url": "https://authors.library.caltech.edu/records/x70d0-23195/files/ECTA17548.pdf" } ], "pub_year": "2021", "author_list": "Mu, Xiaosheng; Pomatto, Luciano; et al." }, { "id": "https://authors.library.caltech.edu/records/ahg63-7tj61", "eprint_id": 116053, "eprint_status": "archive", "datestamp": "2023-08-20 01:10:07", "lastmod": "2026-03-08 18:14:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "Matthias" }, "orcid": "0000-0002-4523-9467" }, { "id": "Morin-Baptiste", "name": { "family": "Morin", "given": "Baptiste" } } ] }, "title": "Compatibility of Special Value Conjectures with the Functional Equation of Zeta Functions", "ispublished": "pub", "full_text_status": "public", "keywords": "arithmetic schemes, zeta-values, functional equation, Weil-\u00e9tale cohomology", "note": "CC BY 4.0. \n\nWe would like to thank S. Lichtenbaum for many indirect contributions to this project. Our realization that his Conjecture 0.1 in [16] could be proven using the ideas of T. Saito in [23] was at the origin of this article (but in fact such a proof had already been carried out by T. Saito himself in [24][Cor. 4.9], see Thm. 3.3 below). Lichtenbaum's preprint [17] has considerable overlap with our article in that he also formulates a conjecture on special values of \u03b6(X, s) and proves compatibility with the functional equation. Despite differences in language, and the fact that all results of [17] are only up to powers of 2, we believe our approaches are largely equivalent. The first version of [17] was posted in April 2017 and the authors recall discussing an explicit formula for C(X, n) among each other at around the same time. However, to the best of our knowledge we never communicated with Lichtenbaum about specifics of special value conjectures, and Lichtenbaum and us arrived at our respective formulations independently. \n\nWe would also like to thank Spencer Bloch for interesting discussions related to C(X, n). \n\nThe second author was supported by ANR-15-CE40-0002-01. The first author was supported by collaboration grant 522885 from the Simons foundation.\n\n

Published - 10012165000.pdf

Submitted - 2005.04829.pdf

", "abstract": "We prove that the special value conjecture for the Zeta function \u03b6(X, s) of a proper, regular arithmetic scheme X that we formulated in [8] is compatible with the functional equation of \u03b6(X, s) provided that the rational factor C(X, n) we were not able to compute previously has the simple explicit form given in the introduction below.", "date": "2021", "date_type": "published", "publication": "Documenta Mathematica", "volume": "26", "publisher": "Deutsche Mathematiker-Vereinigung", "pagerange": "1633-1677", "id_number": "CaltechAUTHORS:20220802-839169000", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220802-839169000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Agence Nationale de la Recherche (ANR)", "grant_number": "ANR-15-CE40-0002-01" }, { "agency": "Simons Foundation", "grant_number": "522885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "10012165000.pdf", "url": "https://authors.library.caltech.edu/records/ahg63-7tj61/files/10012165000.pdf" }, "related_objects": [ { "basename": "2005.04829.pdf", "url": "https://authors.library.caltech.edu/records/ahg63-7tj61/files/2005.04829.pdf" } ], "pub_year": "2021", "author_list": "Flach, Matthias and Morin, Baptiste" }, { "id": "https://authors.library.caltech.edu/records/ngt4x-7vd02", "eprint_id": 107664, "eprint_status": "archive", "datestamp": "2023-08-22 08:05:27", "lastmod": "2026-03-29 17:40:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lee-Chul-hee", "name": { "family": "Lee", "given": "Chul-hee" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Warnaar-S-Ole", "name": { "family": "Warnaar", "given": "S. Ole" }, "orcid": "0000-0002-9786-0175" } ] }, "title": "An Elliptic Hypergeometric Function Approach to Branching Rules", "ispublished": "pub", "full_text_status": "public", "keywords": "branching formulas; elliptic hypergeometric series; elliptic Selberg integrals; interpolation functions; Koornwinder polynomials; Littlewood identities; Macdonald polynomials", "note": "\u00a9 2020 National Academy of Sciences of Ukraine. \n\nThis paper is a contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum\nField Theory. The full collection is available at https://www.emis.de/journals/SIGMA/elliptic-integrablesystems.html. \n\nWe thank one of the referees of our paper for suggesting we compare the branching rule (1.12a) with [15, Conjectures 9.12 and 9.13] by Hoshino and Shiraishi. This work was supported by the Australian Research Council Discovery Grant DP170102648 and a KIAS Individual Grant (MG067302) at Korea Institute for Advanced Study.\n\n

Published - sigma20-142.pdf

Accepted Version - 2007.03174.pdf

", "abstract": "We prove Macdonald-type deformations of a number of well-known classical branching rules by employing identities for elliptic hypergeometric integrals and series. We also propose some conjectural branching rules and allied conjectures exhibiting a novel type of vanishing behaviour involving partitions with empty 2-cores.", "date": "2020-12-23", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "16", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 142", "id_number": "CaltechAUTHORS:20210122-141416267", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210122-141416267", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council", "grant_number": "DP170102648" }, { "agency": "Korea Institute for Advanced Study", "grant_number": "MG067302" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/sigma.2020.142", "primary_object": { "basename": "sigma20-142.pdf", "url": "https://authors.library.caltech.edu/records/ngt4x-7vd02/files/sigma20-142.pdf" }, "related_objects": [ { "basename": "2007.03174.pdf", "url": "https://authors.library.caltech.edu/records/ngt4x-7vd02/files/2007.03174.pdf" } ], "pub_year": "2020", "author_list": "Lee, Chul-hee; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/2jfc3-n2a32", "eprint_id": 103783, "eprint_status": "archive", "datestamp": "2023-08-20 01:02:48", "lastmod": "2026-03-30 05:10:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hsin-Po-Shen", "name": { "family": "Hsin", "given": "Po-Shen" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Thorngren-Ryan", "name": { "family": "Thorngren", "given": "Ryan" }, "orcid": "0000-0001-9433-3399" } ] }, "title": "Berry phase in quantum field theory: Diabolical points and boundary phenomena", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Physical Society. \n\nReceived 6 July 2020; accepted 11 November 2020; published 9 December 2020. \n\nWe thank Dominic Else, Tobias Holder, Raquel Queiroz, Nathan Seiberg, Ruben Verresen, and Adar Sharon for discussions. A.K. is grateful to Lev Spodyneiko for a collaboration on a closely related project. The work is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the Simons Foundation through the Simons Investigator Award.\n\n

Published - PhysRevB.102.245113.pdf

Submitted - 2004.10758.pdf

", "abstract": "We study aspects of the Berry phase in gapped many-body quantum systems by means of effective field theory. Once the parameters are promoted to space-time-dependent background fields, such adiabatic phases are described by Wess-Zumino-Witten (WZW) and similar terms. In the presence of symmetries, there are also quantized invariants capturing generalized Thouless pumps. Consideration of these terms provides constraints on the phase diagram of many-body systems, implying the existence of gapless points in the phase diagram, which are stable for topological reasons. We describe such diabolical points, realized by free fermions and gauge theories in various dimensions, which act as sources of \"higher Berry curvature\" and are protected by the quantization of the corresponding WZW terms or Thouless pump terms. These are analogous to Weyl nodes in a semimetal band structure. We argue that in the presence of a boundary, there are boundary diabolical points\u2014parameter values where the boundary gap closes\u2014which occupy arcs ending at the bulk diabolical points. Thus the boundary has an \"anomaly in the space of couplings\" in the sense of [C. Cordova, D. S. Freed, H. T. Lam, and N. Seiberg, SciPost Phys. 8, 001 (2020) and SciPost Phys. 8, 002 (2020)]. Consideration of the topological effective action for the parameters also provides some new checks on conjectured infrared dualities and deconfined quantum criticality in 2+1d.", "date": "2020-12-15", "date_type": "published", "publication": "Physical Review B", "volume": "102", "number": "24", "publisher": "American Physical Society", "pagerange": "Art. No. 245113", "id_number": "CaltechAUTHORS:20200609-073406092", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200609-073406092", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.102.245113", "primary_object": { "basename": "PhysRevB.102.245113.pdf", "url": "https://authors.library.caltech.edu/records/2jfc3-n2a32/files/PhysRevB.102.245113.pdf" }, "related_objects": [ { "basename": "2004.10758.pdf", "url": "https://authors.library.caltech.edu/records/2jfc3-n2a32/files/2004.10758.pdf" } ], "pub_year": "2020", "author_list": "Hsin, Po-Shen; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/t1bkm-w7d03", "eprint_id": 105313, "eprint_status": "archive", "datestamp": "2023-08-22 07:56:46", "lastmod": "2026-03-29 18:10:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00f6nig-T", "name": { "family": "K\u00f6nig", "given": "Tobias" } }, { "id": "Tang-Hanli", "name": { "family": "Tang", "given": "Hanli" }, "orcid": "0000-0001-8060-9884" } ] }, "title": "Classification of solutions of an equation related to a conformal log Sobolev inequality", "ispublished": "pub", "full_text_status": "public", "keywords": "Log-Sobolev inequality; Classification of solutions; Conformal invariance; Method of moving spheres", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 19 March 2020, Revised 16 August 2020, Accepted 21 August 2020, Available online 3 September 2020. \n\nThe first author is grateful to M. Zhu for a correspondence in May 2012 on the topic of this paper. Partial support through US National Science Foundation grant DMS-1363432 (R.L.F.), Studienstiftung des Deutschen Volkes (T.K.) and National Natural Science Foundation of China (Grant No. 11701032) (H.T.) is acknowledged.\n\n

Submitted - 2003.08135.pdf

", "abstract": "We classify all finite energy solutions of an equation which arises as the Euler\u2013Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to Beckner. Our proof uses an extension of the method of moving spheres from R^n to S^n and a classification result of Li and Zhu. Along the way we prove a small volume maximum principle and a strong maximum principle for the underlying operator which is closely related to the logarithmic Laplacian.", "date": "2020-12-02", "date_type": "published", "publication": "Advances in Mathematics", "volume": "375", "publisher": "Elsevier", "pagerange": "Art. No. 107395", "id_number": "CaltechAUTHORS:20200910-141623696", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200910-141623696", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Studienstiftung des Deutschen Volkes" }, { "agency": "National Natural Science Foundation of China", "grant_number": "11701032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2020.107395", "primary_object": { "basename": "2003.08135.pdf", "url": "https://authors.library.caltech.edu/records/t1bkm-w7d03/files/2003.08135.pdf" }, "pub_year": "2020", "author_list": "Frank, Rupert L.; K\u00f6nig, Tobias; et al." }, { "id": "https://authors.library.caltech.edu/records/cny0p-qk635", "eprint_id": 103231, "eprint_status": "archive", "datestamp": "2023-08-20 00:30:55", "lastmod": "2026-03-30 06:53:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" }, "orcid": "0000-0002-8380-0921" } ] }, "title": "Fusion systems with alternating J\u2010components", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. \n\nIssue Online: 03 December 2020; Version of Record online: 14 May 2020; Manuscript revised: 10 February 2020; Manuscript received: 05 June 2019. \n\nThis work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.", "abstract": "We essentially determine the saturated 2\u2010fusion systems of J\u2010component type in which the centralizer of some fully centralized involution of maximal 2\u2010rank contains a component that is the 2\u2010fusion system of an alternating group A_n for some n \u2a7e 8.", "date": "2020-12", "date_type": "published", "publication": "Journal of the London Mathematical Society", "volume": "102", "number": "3", "publisher": "London Mathematical Society", "pagerange": "905-956", "id_number": "CaltechAUTHORS:20200515-104035073", "issn": "0024-6107", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200515-104035073", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/jlms.12335", "pub_year": "2020", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/scafr-q3881", "eprint_id": 105284, "eprint_status": "archive", "datestamp": "2023-08-22 07:45:08", "lastmod": "2026-03-30 08:44:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Short proofs of some extremal results\u00a0III", "ispublished": "pub", "full_text_status": "public", "keywords": "extremal graph theory; Ramsey theory; random graphs", "note": "\u00a9 2020 Wiley Periodicals LLC. \n\nIssue Online: 25 October 2020; Version of Record online: 30 August 2020; Manuscript accepted: 02 June 2020; Manuscript received: 20 October 2019. \n\nThis research was supported by the ERC Starting Grant, 676632 (D.C.). NSF Award, DMS\u20101855635. Alfred P. Sloan Fellowship (J.F.), SNSF grant, 200021\u2010175573 (B.S.). \n\nSection 2 was first written in May 2015, predating a recent paper of Geneson [41] showing that T_k \u2264 k^(5/2+o(1)). More recently J. Balogh, W. Linz and L. Mattos [9] independently investigated the question of estimating T_k and showed that T_k = k^(2+o(1)) (which is slightly weaker than Corollary 2.4). We would like to thank Kevin Ford for some helpful discussions on this theme and also thank the anonymous referees for their careful reading of the paper and useful suggestions.\n\n

Submitted - 1910.08661.pdf

", "abstract": "We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short.", "date": "2020-12", "date_type": "published", "publication": "Random Structures & Algorithms", "volume": "57", "number": "4", "publisher": "Wiley", "pagerange": "958-982", "id_number": "CaltechAUTHORS:20200909-070916091", "issn": "1042-9832", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200909-070916091", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "NSF", "grant_number": "DMS\u20101855635" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021\u2010175573" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.20953", "primary_object": { "basename": "1910.08661.pdf", "url": "https://authors.library.caltech.edu/records/scafr-q3881/files/1910.08661.pdf" }, "pub_year": "2020", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/f781n-d0219", "eprint_id": 98055, "eprint_status": "archive", "datestamp": "2023-08-22 07:43:58", "lastmod": "2026-03-28 20:44:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Das-Shagnik", "name": { "family": "Das", "given": "Shagnik" } }, { "id": "Lee-Joonkyung", "name": { "family": "Lee", "given": "Joonkyung" } }, { "id": "M\u00e9sz\u00e1ros-T", "name": { "family": "M\u00e9sz\u00e1ros", "given": "Tam\u00e1s" } } ] }, "title": "Ramsey games near the critical threshold", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey theory; random graphs; positional games", "note": "\u00a9 2020 The Authors. Random Structures & Algorithms published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. \n\nIssue Online: 25 October 2020; Version of Record online: 17 October 2020; Manuscript accepted: 22 April 2020; Manuscript received: 08 August 2019. \n\nThis research was supported by the Deutsche Forschungsgemeinschaft (DFG) project 415310276; the German\u2010Israeli Foundation for Scientific Research and Development, GIF grant G\u20101347\u2010304.6/2016 [S.D.]. The Dahlem Research School, DRS Fellowship Program and the Berlin Mathematics Research Center MATH+, project \"learning hypergraphs\" [T.M.]. The European Research Council (ERC) starting grant RanDM 676632 [D.C.] and ERC consolidator grant PEPCo 724903 [J.L.]. Open access funding enabled and organized by Projekt DEAL. \n\nPart of this work was carried out while the third author visited the second and fourth authors at FU Berlin and he is grateful for their hospitality. Open access funding enabled and organized by Projekt DEAL.\n\n

Published - rsa.20959.pdf

Submitted - 1908.02991.pdf

", "abstract": "A well\u2010known result of R\u00f6dl and Ruci\u0144ski states that for any graph H there exists a constant C such that if p \u2265 Cn^(-1/m2(H)), then the random graph G_(n,\u2009p) is a.a.s. H\u2010Ramsey, that is, any 2\u2010coloring of its edges contains a monochromatic copy of H. Aside from a few simple exceptions, the corresponding 0\u2010statement also holds, that is, there exists c\u2009>\u20090 such that whenever p \u2264 Cn^(-1/m2(H)) the random graph Gn,\u2009p is a.a.s. not H\u2010Ramsey. We show that near this threshold, even when G_(n,\u2009p) is not H\u2010Ramsey, it is often extremely close to being H\u2010Ramsey. More precisely, we prove that for any constant c\u2009>\u20090 and any strictly 2\u2010balanced graph H, if p \u2265 Cn^(-1/m2(H)), then the random graph G_(n,\u2009p) a.a.s. has the property that every 2\u2010edge\u2010coloring without monochromatic copies of H cannot be extended to an H\u2010free coloring after \u03c9(1) extra random edges are added. This generalizes a result by Friedgut, Kohayakawa, R\u00f6dl, Ruci\u0144ski, and Tetali, who in 2002 proved the same statement for triangles, and addresses a question raised by those authors. We also extend a result of theirs on the three\u2010color case and show that these theorems need not hold when H is not strictly 2\u2010balanced.", "date": "2020-12", "date_type": "published", "publication": "Random Structures and Algorithms", "volume": "57", "number": "4", "publisher": "Wiley", "pagerange": "940-957", "id_number": "CaltechAUTHORS:20190820-162204728", "issn": "1042-9832", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190820-162204728", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "415310276" }, { "agency": "German-Israeli Foundation for Research and Development", "grant_number": "G-1347-304.6/2016" }, { "agency": "Dahlem Research School" }, { "agency": "Berlin Mathematics Research Center" }, { "agency": "European Research Council (ERC)", "grant_number": "RanDM 676632" }, { "agency": "European Research Council (ERC)", "grant_number": "PEPCo 724903" }, { "agency": "Projekt DEAL" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.20959", "primary_object": { "basename": "1908.02991.pdf", "url": "https://authors.library.caltech.edu/records/f781n-d0219/files/1908.02991.pdf" }, "related_objects": [ { "basename": "rsa.20959.pdf", "url": "https://authors.library.caltech.edu/records/f781n-d0219/files/rsa.20959.pdf" } ], "pub_year": "2020", "author_list": "Conlon, David; Das, Shagnik; et al." }, { "id": "https://authors.library.caltech.edu/records/ty32r-s8w85", "eprint_id": 110992, "eprint_status": "archive", "datestamp": "2023-08-20 00:44:13", "lastmod": "2026-03-30 05:33:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Curien-Nicolas", "name": { "family": "Curien", "given": "Nicolas" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Nachmias-Asaf", "name": { "family": "Nachmias", "given": "Asaf" }, "orcid": "0000-0002-4852-5645" } ] }, "title": "Geometric and spectral properties of causal maps", "ispublished": "pub", "full_text_status": "public", "keywords": "Random trees, random walks, spectral dimension", "note": "\u00a9 2020 EMS Publishing House. \n\nNC acknowledges support from the Institut Universitaire de France, ANR Graal (ANR-14-CE25-0014), ANR Liouville (ANR-15-CE40-0013) and ERC GeoBrown. TH and AN were supported by ISF grant 1207/15 and ERC grant 676970 RandGeom. TH was also supported by a Microsoft Research PhD Fellowship and he thanks Tel Aviv University and Universit\u00e9 Paris-Sud Orsay for their hospitality during visits in which this work was carried out. TH also thanks Jian Ding for bringing the problem of resistance growth in the CDT to his attention. Lastly, we warmly thank the anonymous referees for many valuable comments on the manuscript.\n\n

Accepted Version - 1710.03137.pdf

", "abstract": "We study the random planar map obtained from a critical, finite variance, Galton\u2013Watson plane tree by adding the horizontal connections between successive vertices at each level. This random graph is closely related to the well-known causal dynamical triangulation that was introduced by Ambj\u00f8rn and Loll and has been studied extensively by physicists. We prove that the horizontal distances in the graph are smaller than the vertical distances, but only by a subpolynomial factor: The diameter of the set of vertices at level n is both o(n) and n^(1\u2212o(1)). This enables us to prove that the spectral dimension of the infinite version of the graph is almost surely equal to 2, and consequently the random walk is diffusive almost surely. We also initiate an investigation of the case in which the offspring distribution is critical and belongs to the domain of attraction of an \u03b1-stable law for \u03b1 \u2208 (1,2), for which our understanding is much less complete.", "date": "2020-12", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "22", "number": "12", "publisher": "European Mathematical Society", "pagerange": "3997-4024", "id_number": "CaltechAUTHORS:20210922-193307624", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307624", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-14-CE25-0014" }, { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-15-CE40-0013" }, { "agency": "European Research Council (ERC)", "grant_number": "740943" }, { "agency": "Israel Science Foundation", "grant_number": "1207/15" }, { "agency": "European Research Council (ERC)", "grant_number": "676970" }, { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/jems/1001", "primary_object": { "basename": "1710.03137.pdf", "url": "https://authors.library.caltech.edu/records/ty32r-s8w85/files/1710.03137.pdf" }, "pub_year": "2020", "author_list": "Curien, Nicolas; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/ave15-h5f50", "eprint_id": 111028, "eprint_status": "archive", "datestamp": "2023-08-20 00:25:03", "lastmod": "2026-03-09 02:35:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "New critical exponent inequalities for percolation and the random cluster model", "ispublished": "pub", "full_text_status": "public", "keywords": "percolation, random-cluster model, differential inequality, critical exponent, scaling relations, subcritical", "note": "\u00a9 2020 Mathematical Sciences Publishers. \n\nReceived 24 Oct 2019. Revised 20 Feb 2020. Accepted 24 Feb 2020. \n\nWe thank Hugo Duminil-Copin and Geoffrey Grimmett for helpful discussions.\n\n

Submitted - 1901.10363.pdf

", "abstract": "We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion (Ann. of Math. (2) 189:1 (2019), 75\u201399) to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin\u2013Kasteleyn random cluster model. This differential inequality has a similar form to that derived for Bernoulli percolation by Menshikov (Dokl. Akad. Nauk 288:6 (1986), 1308\u20131311) but with the important difference that it describes the distribution of the volume of a cluster rather than of its radius. We apply this differential inequality to prove the following: \n\n1. The critical exponent inequalities \u03b3 \u2264 \u03b4 \u2212 1 and \u0394 \u2264 \u03b3 + 1 hold for percolation and the random cluster model on any transitive graph. These inequalities are new even in the context of Bernoulli percolation on Z^d, and are saturated in mean-field for Bernoulli percolation and for the random cluster model with q \u2208 [1,2). \n\n2. The volume of a cluster has an exponential tail in the entire subcritical phase of the random cluster model on any transitive graph. This proof also applies to infinite-range models, where the result is new even in the Euclidean setting.", "date": "2020-11-19", "date_type": "published", "publication": "Probability and Mathematical Physics", "volume": "1", "number": "1", "publisher": "Mathematical Sciences Publishers", "pagerange": "147-165", "id_number": "CaltechAUTHORS:20210924-201102398", "issn": "2690-1005", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-201102398", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/pmp.2020.1.147", "primary_object": { "basename": "1901.10363.pdf", "url": "https://authors.library.caltech.edu/records/ave15-h5f50/files/1901.10363.pdf" }, "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/ws4nr-5nm95", "eprint_id": 106429, "eprint_status": "archive", "datestamp": "2023-08-20 00:18:17", "lastmod": "2026-04-16 01:40:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lunkin-A-V", "name": { "family": "Lunkin", "given": "A.\u2009V." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A.\u2009Yu." }, "orcid": "0000-0002-5777-642X" }, { "id": "Feigel'man-M-V", "name": { "family": "Feigel'man", "given": "M.\u2009V." }, "orcid": "0000-0002-7114-5296" } ] }, "title": "Perturbed Sachdev-Ye-Kitaev Model: A Polaron in the Hyperbolic Plane", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Physical Society. \n\nReceived 5 July 2020; accepted 2 October 2020; published 3 November 2020. \n\nM.\u2009V.\u2009F. is grateful to L.\u2009B. Ioffe, A. Kamenev, V.\u2009E. Kravtsov, and K.\u2009S. Tikhonov for useful discussions. Research of A.\u2009V.\u2009L. was partially supported by the Foundation for Advancement of Theoretical Physics and Mathematics \"Basis\" and Basic research program of HSE.\u2009A.\u2009K. is supported by the Simons Foundation under Grant No. 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation.\n\n

Published - PhysRevLett.125.196602.pdf

Submitted - 2006.14535.pdf

Supplemental Material - SM.pdf

", "abstract": "We study the Sachdev-Ye-Kitaev (SYK\u2084) model with a weak SYK\u2082 term of magnitude \u0393 beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/N \u226a \u0393 \u226a J/\u221aN, fluctuations of the Schwarzian mode are suppressed, and the SYK\u2084 mean-field solution remains valid beyond the timescale t\u2080 \u223c N/J up to t\u2217\u223cJ/\u0393\u00b2. The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2\u03c0T, but its prefactor scales as T at low temperatures T \u2264 \u0393.", "date": "2020-11-06", "date_type": "published", "publication": "Physical Review Letters", "volume": "125", "number": "19", "publisher": "American Physical Society", "pagerange": "Art. No. 196602", "id_number": "CaltechAUTHORS:20201104-130324443", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201104-130324443", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Foundation for Advancement of Theoretical Physics" }, { "agency": "National Research University (Russia)" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute of Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/physrevlett.125.196602", "primary_object": { "basename": "2006.14535.pdf", "url": "https://authors.library.caltech.edu/records/ws4nr-5nm95/files/2006.14535.pdf" }, "related_objects": [ { "basename": "PhysRevLett.125.196602.pdf", "url": "https://authors.library.caltech.edu/records/ws4nr-5nm95/files/PhysRevLett.125.196602.pdf" }, { "basename": "SM.pdf", "url": "https://authors.library.caltech.edu/records/ws4nr-5nm95/files/SM.pdf" } ], "pub_year": "2020", "author_list": "Lunkin, A.\u2009V.; Kitaev, A.\u2009Yu.; et al." }, { "id": "https://authors.library.caltech.edu/records/v7tqh-4ec92", "eprint_id": 81753, "eprint_status": "archive", "datestamp": "2023-08-22 07:12:37", "lastmod": "2026-03-09 23:04:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Elliptic Double Affine Hecke Algebras", "ispublished": "pub", "full_text_status": "public", "keywords": "elliptic curves; Hecke algebras; noncommutative deformations", "note": "\u00a9 2020 the Authors. Creative Commons Attribution-ShareAlike License \n\nReceived December 19, 2019, in final form October 16, 2020; Published online November 05, 2020. \n\nThis paper is a contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum\nField Theory. The full collection is available at https://www.emis.de/journals/SIGMA/elliptic-integrablesystems.html. \n\nThe author would particularly like to thank P. Etingof both for asking the original seed question\n(with an important assist from A. Okounkov!) and hosting the author's sabbatical at MIT (which the author would also like to thank, naturally) where much of the basic approach was worked out, with great assistance from conversations with not only Etingof but also (regarding various geometrical issues) B. Poonen. Thanks also go to T. Graber and E. Mantovan for helpful and encouraging conversations regarding the constructions of Section 2 as well as various general algebraic geometric questions, and to O. Chalykh for asking some fruitful questions about residue conditions. The author's work presented here was supported in part by grants from the National Science Foundation, DMS-1001645 and DMS-1500806.\n\n

Published - sigma20-111.pdf

Submitted - 1709.02989.pdf

", "abstract": "We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra. As an application, we use a variant of the C_n version of the construction to construct a flat noncommutative deformation of the nth symmetric power of any rational surface with a smooth anticanonical curve, and give a further construction which conjecturally is a corresponding deformation of the Hilbert scheme of points.", "date": "2020-11-05", "date_type": "published", "publication": "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)", "volume": "16", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 111", "id_number": "CaltechAUTHORS:20170922-134529235", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170922-134529235", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1001645" }, { "agency": "NSF", "grant_number": "DMS-1500806" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2020.111", "primary_object": { "basename": "1709.02989.pdf", "url": "https://authors.library.caltech.edu/records/v7tqh-4ec92/files/1709.02989.pdf" }, "related_objects": [ { "basename": "sigma20-111.pdf", "url": "https://authors.library.caltech.edu/records/v7tqh-4ec92/files/sigma20-111.pdf" } ], "pub_year": "2020", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/c2t20-f0d81", "eprint_id": 98102, "eprint_status": "archive", "datestamp": "2023-08-22 07:09:02", "lastmod": "2026-03-30 06:28:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "The 2-fusion system of an almost simple group", "ispublished": "pub", "full_text_status": "public", "keywords": "Finite groups; Fusion systems", "note": "\u00a9 2019 Elsevier Inc. \n\nReceived 11 February 2019, Available online 22 August 2019. \n\nThis work was partially supported by DMS NSF-1265587 and DMS NSF-1601063.", "abstract": "We show that, under suitable local constraints, the 2-fusion system of an almost simple finite group is almost simple.", "date": "2020-11-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "561", "publisher": "Elsevier", "pagerange": "5-16", "id_number": "CaltechAUTHORS:20190822-100100397", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190822-100100397", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-1601063" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2019.08.017", "pub_year": "2020", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/hbkkk-d8404", "eprint_id": 98032, "eprint_status": "archive", "datestamp": "2023-08-20 00:00:36", "lastmod": "2026-03-30 05:58:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Tidor-J", "name": { "family": "Tidor", "given": "Jonathan" } }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" } } ] }, "title": "Hypergraph expanders of all uniformities from Cayley graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. \n\nIssue Online: 21 July 2020; Version of Record online: 21 July 2020; Manuscript revised: 17 February 2020; Manuscript received: 18 September 2018. \n\nD. Conlon was supported by a Royal Society University Research Fellowship and ERC Starting Grant 676632. J. Tidor was supported by an MIT Presidential Fellowship. Y. Zhao was supported by NSF Awards DMS-1764176 and DMS-1362326 and the MIT Solomon Buchsbaum Fund. \n\nThis paper was partially written while the first author was visiting the California Institute of Technology as a Moore Distinguished Scholar and he is extremely grateful for their kind support.\n\n

Submitted - 1809.06342.pdf

", "abstract": "Hypergraph expanders are hypergraphs with surprising, non\u2010intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of 3\u2010uniform hypergraph expanders with polylogarithmic degree. We generalize this construction, giving a simple construction of r\u2010uniform hypergraph expanders for all r \u2a7e 3.", "date": "2020-11", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "121", "number": "5", "publisher": "London Mathematical Society", "pagerange": "1311-1336", "id_number": "CaltechAUTHORS:20190819-170932806", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-170932806", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "Massachusetts Institute of Technology (MIT)" }, { "agency": "NSF", "grant_number": "DMS-1764176" }, { "agency": "NSF", "grant_number": "DMS-1362326" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.12371", "primary_object": { "basename": "1809.06342.pdf", "url": "https://authors.library.caltech.edu/records/hbkkk-d8404/files/1809.06342.pdf" }, "pub_year": "2020", "author_list": "Conlon, David; Tidor, Jonathan; et al." }, { "id": "https://authors.library.caltech.edu/records/6590x-xqw57", "eprint_id": 96805, "eprint_status": "archive", "datestamp": "2023-08-22 07:02:55", "lastmod": "2026-03-30 04:50:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Basu-Pathikrit", "name": { "family": "Basu", "given": "Pathikrit" } }, { "id": "Chatterjee-Kalyan", "name": { "family": "Chatterjee", "given": "Kalyan" } }, { "id": "Hoshino-Tetsuya", "name": { "family": "Hoshino", "given": "Tetsuya" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Repeated Coordination with Private Learning", "ispublished": "pub", "full_text_status": "public", "keywords": "Coordination; Repeated games; Private learning; Learning from actions; Common learning", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 23 March 2019, Revised 1 August 2020, Accepted 19 August 2020, Available online 28 August 2020. \n\nWe thank Nageeb Ali, Sylvain Chassang, Drew Fudenberg, George Mailath, Manuel Mueller-Frank, Roger Myerson, Philipp Strack, Adam Wierman, and Yuichi Yamamoto for comments. We are grateful to the editor, Xavier Vives, and two anonymous referees for valuable suggestions. This work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).\n\n

Submitted - 1809.00051.pdf

", "abstract": "We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et al., 2008), but do not coordinate in every equilibrium. We show that there exist stable equilibria in which players can overcome unfavorable signal realizations and eventually coordinate on the correct action, for any discount factor. For high discount factors, we show that in addition players can also achieve efficient payoffs.", "date": "2020-11", "date_type": "published", "publication": "Journal of Economic Theory", "volume": "190", "publisher": "Elsevier", "pagerange": "Art. No. 105106", "id_number": "CaltechAUTHORS:20190628-075628753", "issn": "0022-0531", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190628-075628753", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jet.2020.105106", "primary_object": { "basename": "1809.00051.pdf", "url": "https://authors.library.caltech.edu/records/6590x-xqw57/files/1809.00051.pdf" }, "pub_year": "2020", "author_list": "Basu, Pathikrit; Chatterjee, Kalyan; et al." }, { "id": "https://authors.library.caltech.edu/records/6ky39-9jb76", "eprint_id": 106591, "eprint_status": "archive", "datestamp": "2023-08-20 00:07:50", "lastmod": "2026-03-28 23:22:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Franco-Sebasti\u00e1n", "name": { "family": "Franco", "given": "Sebasti\u00e1n" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Lee-Sangmin", "name": { "family": "Lee", "given": "Sangmin" } }, { "id": "Seong-Rak-Kyeong", "name": { "family": "Seong", "given": "Rak-Kyeong" } }, { "id": "Sparks-James", "name": { "family": "Sparks", "given": "James" } } ] }, "title": "\"Lagrangian disks\" in M-theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Brane Dynamics in Gauge Theories, D-branes, M-Theory, Supersymmetric Gauge Theory", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.\nArticle funded by SCOAP3.\n\nReceived: April 26, 2020; Revised: September 11, 2020; Accepted: September 27, 2020; Published: November 10, 2020. \n\nIt is pleasure to thank Robert Bryant, Lorenzo Foscolo, Sheldon Katz, Rafe Mazzeo, Jeffrey Meier, Grigory Mikhalkin, and Nathan Seiberg for useful discussions. The work of S.F. is supported by the National Science Foundation grant PHY-1820721. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.L. is supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1402-08.\n\n

Published - 2020_Article_.pdf

Submitted - 1910.01645.pdf

", "abstract": "While the study of bordered (pseudo-)holomorphic curves with boundary on Lagrangian submanifolds has a long history, a similar problem that involves (special) Lagrangian submanifolds with boundary on complex surfaces appears to be largely overlooked in both physics and math literature. We relate this problem to geometry of coassociative submanifolds in G\u2082 holonomy spaces and to Spin(7) metrics on 8-manifolds with T\u00b2 fibrations. As an application to physics, we propose a large class of brane models in type IIA string theory that generalize brane brick models on the one hand and 2d theories T[M\u2084] on the other.", "date": "2020-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 33", "id_number": "CaltechAUTHORS:20201110-123837447", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201110-123837447", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1820721" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Samsung Science and Technology Foundation", "grant_number": "SSTF-BA1402-08" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/jhep11(2020)033", "primary_object": { "basename": "1910.01645.pdf", "url": "https://authors.library.caltech.edu/records/6ky39-9jb76/files/1910.01645.pdf" }, "related_objects": [ { "basename": "2020_Article_.pdf", "url": "https://authors.library.caltech.edu/records/6ky39-9jb76/files/2020_Article_.pdf" } ], "pub_year": "2020", "author_list": "Franco, Sebasti\u00e1n; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/s777e-ew214", "eprint_id": 110993, "eprint_status": "archive", "datestamp": "2023-08-19 23:54:48", "lastmod": "2026-03-09 02:35:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "The L\u00b2 boundedness condition in nonamenable percolation", "ispublished": "pub", "full_text_status": "public", "keywords": "Critical exponents, nonamenable, percolation", "note": "\u00a9 2020 The author(s). Creative Commons Attribution 4.0 International License. \n\nReceived: 12 April 2019; Accepted: 22 September 2020; Published: 2020. First available in Project Euclid: 16 October 2020. \n\nWe thank Gady Kozma for helpful discussions on interpolation theory of operators, and thank Asaf Nachmias for comments on a draft. We also thank the anonymous referees for their careful reading and helpful comments.\n\n

Published - 20-EJP525.pdf

Accepted Version - 1904.05804.pdf

", "abstract": "Let G = (V,E) be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. In recent work, we conjectured that if G is nonamenable then the matrix of critical connection probabilities T_(p_c) (u,v) = \u2119_(p_c) (u\u2194v) is bounded as an operator T_(p_c) : L\u00b2(V)\u2192L\u00b2(V) and proved that this conjecture holds for several classes of graphs. We also noted in that work that the conjecture implies two older conjectures, namely that percolation on transitive nonamenable graphs always has a nontrivial nonuniqueness phase, and that critical percolation on the same class of graphs has mean-field critical behaviour. \n\nIn this paper we further investigate the consequences of the L\u00b2 boundedness conjecture. In particular, we prove that the following hold for all transitive graphs: i) The two-point function decays exponentially in the distance for all p < p_(2\u21922); ii) If p_c < p_(2\u21922), then the critical exponent governing the extrinsic diameter of a critical cluster is 1; iii) Below p_(2\u21922), percolation is \"ballistic\" in the sense that the intrinsic distance between two points is exponentially unlikely to be much larger than their extrinsic distance; iv) If p_c < p_(2\u21922), then \u2016T_(p_c) \u2016_(q\u2192q) \u224d (q\u22121)\u22121 and p_(q\u2192q) \u2212 p_c \u224d q \u2212 1 as q\u21931. v) If p_c < p_(2\u21922), then various 'multiple-arm' events have probabilities comparable to the upper bound given by the BK inequality. In particular, the probability that the origin is a trifurcation point is of order (p \u2212 p_c)\u00b3 as p \u2193 p_c. All of these results are new even in the Gromov hyperbolic case. \n\nFinally, we apply these results together with duality arguments to compute the critical exponents governing the geometry of intrinsic geodesics at the uniqueness threshold of percolation in the hyperbolic plane.", "date": "2020-10-16", "date_type": "published", "publication": "Electronic Journal of Probability", "volume": "25", "publisher": "Electronic Journal of Probability", "pagerange": "Art. No. 127", "id_number": "CaltechAUTHORS:20210922-193307690", "issn": "1083-6489", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307690", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/20-ejp525", "primary_object": { "basename": "20-EJP525.pdf", "url": "https://authors.library.caltech.edu/records/s777e-ew214/files/20-EJP525.pdf" }, "related_objects": [ { "basename": "1904.05804.pdf", "url": "https://authors.library.caltech.edu/records/s777e-ew214/files/1904.05804.pdf" } ], "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/mn1pw-1xa26", "eprint_id": 107492, "eprint_status": "archive", "datestamp": "2023-08-19 23:54:30", "lastmod": "2026-03-28 20:51:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Kim-Seunghyeok", "name": { "family": "Kim", "given": "Seunghyeok" } }, { "id": "Pistoia-Angela", "name": { "family": "Pistoia", "given": "Angela" } } ] }, "title": "Non-degeneracy for the critical Lane\u2013Emden system", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 by the authors. \n\nReceived by the editors September 22, 2019, and, in revised form, May 17, 2020. \n\nThe first author was partially supported by US National Science Foundation grant DMS-1363432. \n\nThe second author was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF2017R1C1B5076384). \n\nThe third author was partially supported by Fondi di Ateneo \"Sapienza\" Universit\u00e0 di Roma (Italy). \n\nThe authors appreciate the valuable comments and suggestions of two anonymous referees on an earlier version of this paper.\n\n

Submitted - 1908.11122.pdf

", "abstract": "We prove the non-degeneracy for the critical Lane\u2013Emden system \n\n\u2212\u0394U = V^p, \u2212\u0394V = U^q, U,V >0 in R^N \n\nfor all N \u2265 3 and p, q > 0 such that 1/(p+1) + 1/(q+1) = (N\u22122)/N. We show that all solutions to the linearized system around a ground state must arise from the symmetries of the critical Lane\u2013Emden system provided that they belong to the corresponding energy space or they tend to zero at infinity.", "date": "2020-10-16", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "149", "number": "1", "publisher": "American Mathematical Society", "pagerange": "265-278", "id_number": "CaltechAUTHORS:20210114-143038456", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210114-143038456", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "National Research Foundation of Korea", "grant_number": "NRF2017R1C1B5076384" }, { "agency": "Fondi di Ateneo \"Sapienza\" Universit\u00e0 di Roma" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/proc/15217", "primary_object": { "basename": "1908.11122.pdf", "url": "https://authors.library.caltech.edu/records/mn1pw-1xa26/files/1908.11122.pdf" }, "pub_year": "2020", "author_list": "Frank, Rupert L.; Kim, Seunghyeok; et al." }, { "id": "https://authors.library.caltech.edu/records/3gath-fpn47", "eprint_id": 103228, "eprint_status": "archive", "datestamp": "2023-08-22 06:57:49", "lastmod": "2026-03-28 20:46:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Gang-Zhou", "name": { "family": "Gang", "given": "Zhou" }, "orcid": "0000-0002-1649-1823" } ] }, "title": "A non-linear adiabatic theorem for the one-dimensional Landau\u2013Pekar equations", "ispublished": "pub", "full_text_status": "public", "keywords": "Polaron; Adiabatic theorem; Dispersive estimates", "note": "\u00a9 2020 Elsevier Inc. \n\nReceived 20 June 2019, Accepted 28 April 2020, Available online 14 May 2020. \n\nThe first author would like to thank Benjamin Schlein and Robert Seiringer for interesting discussions. Partial support through US National Science Foundation grant DMS-1363432 and through German Research Foundation grant EXC-2111 390814868 (R.L.F.) is acknowledged.\n\n

Submitted - 1906.07908.pdf

", "abstract": "We discuss a one-dimensional version of the Landau\u2013Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schr\u00f6dinger equation with time-dependent potential are a key technical ingredient in our proof.", "date": "2020-10-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "279", "number": "7", "publisher": "Elsevier", "pagerange": "Art. No. 108631", "id_number": "CaltechAUTHORS:20200515-091132161", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200515-091132161", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111 390814868" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2020.108631", "primary_object": { "basename": "1906.07908.pdf", "url": "https://authors.library.caltech.edu/records/3gath-fpn47/files/1906.07908.pdf" }, "pub_year": "2020", "author_list": "Frank, Rupert L. and Gang, Zhou" }, { "id": "https://authors.library.caltech.edu/records/m8n9v-j1t44", "eprint_id": 110996, "eprint_status": "archive", "datestamp": "2023-08-19 23:43:18", "lastmod": "2026-03-30 04:32:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Non-intersection of transient branching random walks", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived: 7 October 2019 / Revised: 6 February 2020 / Published online: 25 February 2020. \n\nWe thank Itai Benjamini, Jonathan Hermon, Asaf Nachmias, and Elisabetta Candellero for useful discussions. In particular, we thank Asaf for discussions that led to a substantially simpler proof of Theorem 3.3. We also thank the anonymous referee for their careful reading and helpful suggestions.\n\n

Published - Hutchcroft2020_Article_Non-intersectionOfTransientBra.pdf

Accepted Version - 1910.01018.pdf

", "abstract": "Let G be a Cayley graph of a nonamenable group with spectral radius \u03c1 < 1. It is known that branching random walk on G with offspring distribution \u03bc is transient, i.e., visits the origin at most finitely often almost surely, if and only if the expected number of offspring \u03bc[bar] satisfies \u03bc[bar] \u2264 \u03c1 \u2212 1. Benjamini and M\u00fcller (2010) conjectured that throughout the transient supercritical phase 1< \u03bc[bar] \u2264 \u03c1 \u2212 1, and in particular at the recurrence threshold \u03bc[bar] = \u03c1 \u2212 1, the trace of the branching random walk is tree-like in the sense that it is infinitely-ended almost surely on the event that the walk survives forever. This is essentially equivalent to the assertion that two independent copies of the branching random walk intersect at most finitely often almost surely. We prove this conjecture, along with several other related conjectures made by the same authors. \n\nA central contribution of this work is the introduction of the notion of local unimodularity, which we expect to have several further applications in the future.", "date": "2020-10", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "178", "number": "1-2", "publisher": "Springer", "pagerange": "1-23", "id_number": "CaltechAUTHORS:20210922-193307881", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307881", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-020-00964-z", "primary_object": { "basename": "1910.01018.pdf", "url": "https://authors.library.caltech.edu/records/m8n9v-j1t44/files/1910.01018.pdf" }, "related_objects": [ { "basename": "Hutchcroft2020_Article_Non-intersectionOfTransientBra.pdf", "url": "https://authors.library.caltech.edu/records/m8n9v-j1t44/files/Hutchcroft2020_Article_Non-intersectionOfTransientBra.pdf" } ], "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/0an9f-d4t30", "eprint_id": 110995, "eprint_status": "archive", "datestamp": "2023-08-19 23:43:12", "lastmod": "2026-03-29 17:43:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gwynne-Ewain", "name": { "family": "Gwynne", "given": "Ewain" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Anomalous diffusion of random walk on random planar maps", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived: 5 September 2018 / Revised: 21 May 2020 / Published online: 20 July 2020. \n\nWe thank two anonymous referees for helpful comments on an earlier version of this manuscript. We thank Marie Albenque, Nina Holden, Jason Miller, Asaf Nachmias, and Xin Sun for helpful discussions. We thank Asaf in particular for bringing the maximal versions of the Markov-type inequalities to our attention. This work was initiated during a visit by TH to MIT, whom he thanks for their hospitality.\n\n

Published - Gwynne-Hutchcroft2020_Article_AnomalousDiffusionOfRandomWalk.pdf

Accepted Version - 1807.01512.pdf

", "abstract": "We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most n^(1/4 + o_n(1)) in n units of time. Together with the complementary lower bound proven by Gwynne and Miller (2017) this shows that the typical graph distance displacement of the walk after n steps is n^(1/4 + o_n(1)), as conjectured by Benjamini and Curien (2013). More generally, we show that the simple random walks on a certain family of random planar maps in the \u03b3-Liouville quantum gravity (LQG) universality class for \u03b3\u2208(0,2)---including spanning tree-weighted maps, bipolar-oriented maps, and mated-CRT maps---typically travels graph distance n^(1/d_\u03b3 + o_n(1)) in n units of time, where d\u03b3 is the growth exponent for the volume of a metric ball on the map, which was shown to exist and depend only on \u03b3 by Ding and Gwynne (2018). Since d_\u03b3 > 2, this shows that the simple random walk on each of these maps is subdiffusive. \n\nOur proofs are based on an embedding of the random planar maps under consideration into C wherein graph distance balls can be compared to Euclidean balls modulo subpolynomial errors. This embedding arises from a coupling of the given random planar map with a mated-CRT map together with the relationship of the latter map to SLE-decorated LQG.", "date": "2020-10", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "178", "number": "1-2", "publisher": "Springer", "pagerange": "567-611", "id_number": "CaltechAUTHORS:20210922-193307816", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307816", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-020-00986-7", "primary_object": { "basename": "1807.01512.pdf", "url": "https://authors.library.caltech.edu/records/0an9f-d4t30/files/1807.01512.pdf" }, "related_objects": [ { "basename": "Gwynne-Hutchcroft2020_Article_AnomalousDiffusionOfRandomWalk.pdf", "url": "https://authors.library.caltech.edu/records/0an9f-d4t30/files/Gwynne-Hutchcroft2020_Article_AnomalousDiffusionOfRandomWalk.pdf" } ], "pub_year": "2020", "author_list": "Gwynne, Ewain and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/w8j7r-3fk10", "eprint_id": 110994, "eprint_status": "archive", "datestamp": "2023-08-19 23:43:06", "lastmod": "2026-03-29 18:23:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Nonuniqueness and mean-field criticality for percolation on nonunimodular transitive graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Mathematical Society. \n\nReceived by the editors November 29, 2017, and, in revised form, July 9, 2019, and February 23, 2020. \n\nThis work mainly took place while the author was a Ph.D. student at the University of British Columbia, during which time he was supported by a Microsoft Research Ph.D. Fellowship. \n\nThe author thanks Nicolas Curien, Hugo Duminil-Copin, Matan Harel, Aran Raoufi, and Yinon Spinka for useful discussions, particularly during a visit by the author to the IHES in March 2017. He also thanks Omer Angel, Gady Kozma, Russ Lyons, and Asaf Nachmias for several helpful discussions, and also Russ Lyons for catching some typos in a previous version. Finally, we thank the three anonymous referees and Pengfei Tang for their close reading and detailed comments, which have greatly improved the paper.\n\n

Accepted Version - 1711.02590.pdf

", "abstract": "We study Bernoulli bond percolation on nonunimodular quasi-transitive graphs, and more generally graphs whose automorphism group has a nonunimodular quasi-transitive subgroup. We prove that percolation on any such graph has a nonempty phase in which there are infinite light clusters, which implies the existence of a nonempty phase in which there are infinitely many infinite clusters. That is, we show that p_c < p_h < P_u for any such graph. This answers a question of H\u00e4ggstr\u00f6m, Peres, and Schonmann (1999), and verifies the nonunimodular case of a well-known conjecture of Benjamini and Schramm (1996). We also prove that the triangle condition holds at criticality on any such graph, which implies that various critical exponents exist and take their mean-field values. \n\n\nAll our results apply, for example, to the product T_k x Z^d of a k-regular tree with Z^d for k \u2265 3 and d \u2265 1, for which these results were previously known only for large k. Furthermore, our methods also enable us to establish the basic topological features of the phase diagram for anisotropic percolation on such products, in which tree edges and Z^d edges are given different retention probabilities. These features had only previously been established for d = 1, k large.", "date": "2020-10", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "33", "number": "4", "publisher": "American Mathematical Society", "pagerange": "1101-1165", "id_number": "CaltechAUTHORS:20210922-193307757", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307757", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/jams/953", "primary_object": { "basename": "1711.02590.pdf", "url": "https://authors.library.caltech.edu/records/w8j7r-3fk10/files/1711.02590.pdf" }, "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/bkvxa-xz107", "eprint_id": 89664, "eprint_status": "archive", "datestamp": "2023-08-19 23:32:17", "lastmod": "2026-03-29 20:15:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dedushenko-M", "name": { "family": "Dedushenko", "given": "Mykola" }, "orcid": "0000-0002-9273-7602" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Nakajima-Hiraku", "name": { "family": "Nakajima", "given": "Hiraku" } }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Ye-Ke", "name": { "family": "Ye", "given": "Ke" }, "orcid": "0000-0002-2978-2013" } ] }, "title": "3d TQFTs from Argyres\u2013Douglas theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 IOP Publishing Ltd. \n\nReceived 24 February 2020; Revised 27 August 2020; Accepted 2 September 2020; Published 8 October 2020. \n\nWe thank J E Andersen, B Feigin, L Fredrickson, K Maruyoshi and N Nekrasov for interesting discussions. The work of MD, SG, DP and KY was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of MD was also supported by the Sherman Fairchild Foundation. The work of SG was also supported by the National Science Foundation under Grant No. NSF DMS 1664240. The work of DP was also supported in part by the center of excellence grant 'Center for Quantum Geometry of Moduli Space' from the Danish National Research Foundation (DNRF95) and the Center for Mathematical Sciences and Applications. The research of HN was supported in part by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and by JSPS Grant No. 16H06335.\n\n

Submitted - 1809.04638.pdf

", "abstract": "We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres\u2013Douglas theories on S\u00b9 \u00d7 M\u2083 with a non-trivial holonomy of a discrete global symmetry along the S\u00b9. For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern\u2013Simons and Rozansky\u2013Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the (G\u2082)\u2081 and (F\u2084)\u2081 Chern\u2013Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d N = 2 theory. We test our proposal by applying localization techniques to the conjectural N = 1 UV Lagrangian descriptions of the (A\u2081, A\u2082), (A\u2081, A\u2083) and (A\u2081, D\u2083) theories.", "date": "2020-10", "date_type": "published", "publication": "Journal of Physics A: Mathematical and General", "volume": "53", "number": "43", "publisher": "IOP", "pagerange": "Art. No. 43LT01", "id_number": "CaltechAUTHORS:20180915-165620259", "issn": "0305-4470", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180915-165620259", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "16H06335" } ] }, "other_numbering_system": { "items": [ { "id": "2018-033", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1751-8121/abb481", "primary_object": { "basename": "1809.04638.pdf", "url": "https://authors.library.caltech.edu/records/bkvxa-xz107/files/1809.04638.pdf" }, "pub_year": "2020", "author_list": "Dedushenko, Mykola; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/gdfsz-5f343", "eprint_id": 78994, "eprint_status": "archive", "datestamp": "2023-08-19 23:32:08", "lastmod": "2026-03-30 05:56:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Burton-P-J", "name": { "family": "Burton", "given": "Peter J." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Weak containment of measure-preserving group actions", "ispublished": "pub", "full_text_status": "public", "keywords": "measure-preserving group actions, weak containment, weak equivalence", "note": "\u00a9 2019 Cambridge University Press. \n\nReceived 10 August 2018 and accepted in revised form 24 February 2019. Published online by Cambridge University Press: 17 April 2019.\n\n

Published - weak_containment_of_measurepreserving_group_actions.pdf

Submitted - 1611.07921.pdf

", "abstract": "This paper concerns the study of the global structure of measure-preserving actions of countable groups on standard probability spaces. Weak containment is a hierarchical notion of complexity of such actions, motivated by an analogous concept in the theory of unitary representations. This concept gives rise to an associated notion of equivalence of actions, called weak equivalence, which is much coarser than the notion of isomorphism (conjugacy). It is well understood now that, in general, isomorphism is a very complex notion, a fact which manifests itself, for example, in the lack of any reasonable structure in the space of actions modulo isomorphism. On the other hand, the space of weak equivalence classes is quite well behaved. Another interesting fact that relates to the study of weak containment is that many important parameters associated with actions, such as the type, cost, and combinatorial parameters, turn out to be invariants of weak equivalence and in fact exhibit desirable monotonicity properties with respect to the pre-order of weak containment, a fact that can be useful in certain applications. There has been quite a lot of activity in this area in the last few years, and our goal in this paper is to provide a survey of this work.", "date": "2020-10", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "40", "number": "10", "publisher": "Cambridge University Press", "pagerange": "2681-2733", "id_number": "CaltechAUTHORS:20170712-090422831", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-090422831", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/etds.2019.26", "primary_object": { "basename": "1611.07921.pdf", "url": "https://authors.library.caltech.edu/records/gdfsz-5f343/files/1611.07921.pdf" }, "related_objects": [ { "basename": "weak_containment_of_measurepreserving_group_actions.pdf", "url": "https://authors.library.caltech.edu/records/gdfsz-5f343/files/weak_containment_of_measurepreserving_group_actions.pdf" } ], "pub_year": "2020", "author_list": "Burton, Peter J. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/ya229-k3e62", "eprint_id": 100889, "eprint_status": "archive", "datestamp": "2023-08-19 23:32:49", "lastmod": "2026-03-29 20:37:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conley-C-T", "name": { "family": "Conley", "given": "Clinton T." } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Unfriendly colorings of graphs with finite average degree", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. \n\nReceived 13 March 2019; published online 9 May 2020. \n\nClinton T. Conley was supported by NSF grant DMS-1500906. Omer Tamuz was supported by a grant from the Simons Foundation (#419427).\n\n

Published - plms.12345.pdf

Submitted - 1903.05268.pdf

", "abstract": "In an unfriendly coloring of a graph the color of every node mismatches that of the majority of its neighbors. We show that every probability measure preserving Borel graph with finite average degree admits a Borel unfriendly coloring almost everywhere. We also show that every bounded degree Borel graph of subexponential growth admits a Borel unfriendly coloring.", "date": "2020-10", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "121", "number": "4", "publisher": "London Mathematical Society", "pagerange": "828-832", "id_number": "CaltechAUTHORS:20200124-090354536", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200124-090354536", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1500906" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms.12345", "primary_object": { "basename": "plms.12345.pdf", "url": "https://authors.library.caltech.edu/records/ya229-k3e62/files/plms.12345.pdf" }, "related_objects": [ { "basename": "1903.05268.pdf", "url": "https://authors.library.caltech.edu/records/ya229-k3e62/files/1903.05268.pdf" } ], "pub_year": "2020", "author_list": "Conley, Clinton T. and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/q9x5v-3h166", "eprint_id": 105750, "eprint_status": "archive", "datestamp": "2023-08-19 23:36:05", "lastmod": "2026-03-28 20:56:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Sopenko-N", "name": { "family": "Sopenko", "given": "Nikita" }, "orcid": "0000-0002-8479-1924" } ] }, "title": "Hall conductance and the statistics of flux insertions in gapped interacting lattice systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Published under license by AIP Publishing. \n\nSubmitted: 24 July 2020; Accepted: 30 August 2020; Published Online: 1 October 2020. \n\nThis research was supported, in part, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award. N.S. gratefully acknowledges the support of the Dominic Orr Fellowship at Caltech. \n\nData Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.\n\n

Published - 5.0022944.pdf

Submitted - 2006.14151.pdf

", "abstract": "We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems that are in the same gapped phase. We provide a rigorous version of Laughlin's flux-insertion argument, which shows that for short-range entangled systems, the Hall conductance is an integer multiple of e\u00b2/h. We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e\u00b2/h. Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.", "date": "2020-10", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "61", "number": "10", "publisher": "American Institute of Physics", "pagerange": "Art. No. 101901", "id_number": "CaltechAUTHORS:20201002-092331999", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201002-092331999", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "Dominic Orr Graduate Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/5.0022944", "primary_object": { "basename": "2006.14151.pdf", "url": "https://authors.library.caltech.edu/records/q9x5v-3h166/files/2006.14151.pdf" }, "related_objects": [ { "basename": "5.0022944.pdf", "url": "https://authors.library.caltech.edu/records/q9x5v-3h166/files/5.0022944.pdf" } ], "pub_year": "2020", "author_list": "Kapustin, Anton and Sopenko, Nikita" }, { "id": "https://authors.library.caltech.edu/records/td2t2-y4867", "eprint_id": 95606, "eprint_status": "archive", "datestamp": "2023-08-19 23:05:01", "lastmod": "2026-03-30 05:02:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Larson-Simon", "name": { "family": "Larson", "given": "Simon" }, "orcid": "0000-0002-0057-8211" } ] }, "title": "Two-term spectral asymptotics for the Dirichlet Laplacian in a Lipschitz domain", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Walter de Gruyter GmbH, Berlin/Boston. \n\nReceived: 2019-02-26; Revised: 2019-05-12; Published Online: 2019-08-15. \n\nU.S. National Science Foundation grant DMS-1363432 (R.L.F.) and Swedish Research Council grant no. 2012-3864 (S.L.) is acknowledged.\n\n

Submitted - 1901.09771.pdf

", "abstract": "We prove a two-term Weyl-type asymptotic formula for sums of eigenvalues of the Dirichlet Laplacian in a bounded open set with Lipschitz boundary. Moreover, in the case of a convex domain we obtain a universal bound which correctly reproduces the first two terms in the asymptotics.", "date": "2020-09", "date_type": "published", "publication": "Journal f\u00fcr die reine und angewandte Mathematik", "volume": "2020", "number": "766", "publisher": "De Gruyter", "pagerange": "195-228", "id_number": "CaltechAUTHORS:20190520-133710218", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-133710218", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Swedish Research Council", "grant_number": "2012-3864" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2019-0019", "primary_object": { "basename": "1901.09771.pdf", "url": "https://authors.library.caltech.edu/records/td2t2-y4867/files/1901.09771.pdf" }, "pub_year": "2020", "author_list": "Frank, Rupert L. and Larson, Simon" }, { "id": "https://authors.library.caltech.edu/records/cf8rb-yre64", "eprint_id": 105543, "eprint_status": "archive", "datestamp": "2023-08-19 23:12:11", "lastmod": "2026-03-30 06:39:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chun-Sungbong", "name": { "family": "Chun", "given": "Sungbong" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Park-Sunghyuk", "name": { "family": "Park", "given": "Sunghyuk" }, "orcid": "0000-0002-6132-0871" }, { "id": "Sopenko-N", "name": { "family": "Sopenko", "given": "Nikita" } } ] }, "title": "3d-3d correspondence for mapping tori", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal Field Models in String Theory, Supersymmetric Effective Theories, Topological Field Theories", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: June 29, 2020. Accepted: August 25, 2020. Published: September 23, 2020. \n\nArticle funded by SCOAP3. \n\nIt is pleasure to thank Ian Agol, Francesco Benini, Miranda Cheng, Francesca Ferrari, Michael Freedman, Sarah Harrison, Jeremy Lovejoy, Ciprian Manolescu, Satoshi Nawata, Du Pei, Pavel Putrov, Larry Rolen, Nathan Seiberg, Cumrun Vafa, and Christian Zickert for help and suggestions. The work of S.C. was supported by the US Department of Energy under grant DE-SC0010008. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.P. is supported by Kwanjeong Educational Foundation. N.S. gratefully acknowledges the support of the Dominic Orr Graduate Fellowship at Caltech.\n\n

Published - Chun2020_Article_3d-3dCorrespondenceForMappingT.pdf

Accepted Version - 1911.08456.pdf

", "abstract": "One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [M\u2083] \u2014 or, rather, a \"collection of SCFTs\" as we refer to it in the paper \u2014 for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M\u2083 and, secondly, is not limited to a particular supersymmetric partition function of T [M\u2083]. In particular, we propose to describe such \"collection of SCFTs\" in terms of 3d N = 2 gauge theories with \"non-linear matter\" fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [M\u2083], and propose new tools to compute more recent q-series invariants \u1e90 (M\u2083) in the case of manifolds with b\u2081 > 0. Although we use genus-1 mapping tori as our \"case study,\" many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.", "date": "2020-09", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 152", "id_number": "CaltechAUTHORS:20200925-091915393", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200925-091915393", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "SCOAP3" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0010008" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Kwanjeong Educational Foundation" }, { "agency": "Dominic Orr Graduate Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "2019-048", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/jhep09(2020)152", "primary_object": { "basename": "1911.08456.pdf", "url": "https://authors.library.caltech.edu/records/cf8rb-yre64/files/1911.08456.pdf" }, "related_objects": [ { "basename": "Chun2020_Article_3d-3dCorrespondenceForMappingT.pdf", "url": "https://authors.library.caltech.edu/records/cf8rb-yre64/files/Chun2020_Article_3d-3dCorrespondenceForMappingT.pdf" } ], "pub_year": "2020", "author_list": "Chun, Sungbong; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/ba2tq-frh31", "eprint_id": 110997, "eprint_status": "archive", "datestamp": "2023-08-19 23:13:52", "lastmod": "2026-03-30 06:16:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Pete-G\u00e1bor", "name": { "family": "Pete", "given": "G\u00e1bor" } } ] }, "title": "Kazhdan groups have cost 1", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. \n\nReceived: 26 October 2018 / Accepted: 16 February 2020 / Published online: 2 April 2020. \n\nOpen access funding provided by Alfr\u00e9d R\u00e9nyi Institute of Mathematics. We are grateful to Mikl\u00f3s Ab\u00e9rt for many helpful discussions, to MFO, Oberwolfach, where this work was conceived, and to Damien Gaboriau and Russ Lyons for comments on the manuscript. We also thank the anonymous referees for their thorough reading and helpful comments. The work of GP was supported by the ERC Consolidator Grant 772466 \"NOISE\", and by the Hungarian National Research, Development and Innovation Office, NKFIH Grant K109684.\n\n

Published - Hutchcroft-Pete2020_Article_KazhdanGroupsHaveCost1.pdf

Accepted Version - 1810.11015.pdf

", "abstract": "We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.", "date": "2020-09", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "221", "number": "3", "publisher": "Springer", "pagerange": "873-891", "id_number": "CaltechAUTHORS:20210922-193307950", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193307950", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfr\u00e9d R\u00e9nyi Institute of Mathematics" }, { "agency": "European Research Council (ERC)", "grant_number": "772466" }, { "agency": "Hungarian National Research, Development, and Innovation Office (NKFIH)", "grant_number": "K109684" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-020-00967-6", "primary_object": { "basename": "1810.11015.pdf", "url": "https://authors.library.caltech.edu/records/ba2tq-frh31/files/1810.11015.pdf" }, "related_objects": [ { "basename": "Hutchcroft-Pete2020_Article_KazhdanGroupsHaveCost1.pdf", "url": "https://authors.library.caltech.edu/records/ba2tq-frh31/files/Hutchcroft-Pete2020_Article_KazhdanGroupsHaveCost1.pdf" } ], "pub_year": "2020", "author_list": "Hutchcroft, Tom and Pete, G\u00e1bor" }, { "id": "https://authors.library.caltech.edu/records/82180-98g80", "eprint_id": 95127, "eprint_status": "archive", "datestamp": "2023-08-19 23:04:56", "lastmod": "2026-03-29 22:05:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" }, "orcid": "0000-0002-9559-0650" } ] }, "title": "Asymptotics of Chebyshev Polynomials. IV. Comments on the Complex Case", "ispublished": "pub", "full_text_status": "public", "keywords": "Chebyshev polynomials, Lemniscates, Zero Counting Measures, Totik\u2013Widom upper bound", "note": "\u00a9 2020 Springer. \n\nReceived 27 December 2018; Revised 04 February 2019; Published 12 November 2020. \n\nResearch supported in part by Project Grant DFF-4181-00502 from the Danish Council for Independent Research and by the Swedish Research Council (VR) Grant No. 2018-03500. \n\nResearch supported in part by NSF grants DMS-1265592 and DMS-1665526 and in part by Israeli BSF Grant No. 2014337. \n\nResearch supported in part by Simons Foundation grant CGM-581256.\n\n

Submitted - 1812.10667.pdf

", "abstract": "We make a number of comments on Chebyshev polynomials for general compact subsets of the complex plane. We focus on two aspects: asymptotics of the zeros and explicit Totik\u2013Widom upper bounds on their norms.", "date": "2020-09", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "141", "number": "1", "publisher": "Hebrew University Magnes Press", "pagerange": "207-223", "id_number": "CaltechAUTHORS:20190501-093308068", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190501-093308068", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Danish Council for Independent Research", "grant_number": "DFF-4181-00502" }, { "agency": "Swedish Research Council", "grant_number": "2018-03500" }, { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" }, { "agency": "Simons Foundation", "grant_number": "CGM-581256" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s11854-020-0120-9", "primary_object": { "basename": "1812.10667.pdf", "url": "https://authors.library.caltech.edu/records/82180-98g80/files/1812.10667.pdf" }, "pub_year": "2020", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/6htd4-g6y52", "eprint_id": 100564, "eprint_status": "archive", "datestamp": "2023-08-22 06:07:32", "lastmod": "2026-03-30 05:54:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avni-N", "name": { "family": "Avni", "given": "Nir" } }, { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Periodic Jacobi Matrices on Trees", "ispublished": "pub", "full_text_status": "public", "keywords": "Jacobi matrices; Trees; Spectral theory", "note": "\u00a9 2020 Elsevier Inc. \n\nResearch supported in part by NSF grant DMS-1902041. \n\nResearch supported in part by Israeli BSF Grant No. 2014337. and Israel Science Foundation Grant No. 399/16. \n\nResearch supported in part by NSF grant DMS-1665526 and in part by Israeli BSF Grant No. 2014337.\n\n

Submitted - 1911.02612.pdf

", "abstract": "We begin the systematic study of the spectral theory of periodic Jacobi matrices on trees including a formal definition. The most significant result that appears here for the first time is that these operators have no singular continuous spectrum. We review important previous results of Sunada and Aomoto and present several illuminating examples. We present many open problems and conjectures that we hope will stimulate further work.", "date": "2020-08-26", "date_type": "published", "publication": "Advances in Mathematics", "volume": "370", "publisher": "Elsevier", "pagerange": "Art. No. 107241", "id_number": "CaltechAUTHORS:20200108-134956957", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200108-134956957", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1902041" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" }, { "agency": "Israel Science Foundation", "grant_number": "399/16" }, { "agency": "NSF", "grant_number": "DMS-1665526" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.aim.2020.107241", "primary_object": { "basename": "1911.02612.pdf", "url": "https://authors.library.caltech.edu/records/6htd4-g6y52/files/1911.02612.pdf" }, "pub_year": "2020", "author_list": "Avni, Nir; Breuer, Jonathan; et al." }, { "id": "https://authors.library.caltech.edu/records/nezma-weh48", "eprint_id": 108042, "eprint_status": "archive", "datestamp": "2023-08-19 22:59:59", "lastmod": "2026-03-29 20:27:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" }, { "id": "Zahl-Joshua", "name": { "family": "Zahl", "given": "Joshua" } } ] }, "title": "A Kakeya maximal function estimate in four dimensions using planebrushes", "ispublished": "pub", "full_text_status": "public", "keywords": "Kakeya problem", "note": "\u00a9 2021 EMS Publishing House.\n\nSupported by NSF grant DMS 1565904.\n\nSupported by an NSERC Discovery grant. \n\nThe authors would like to thank Keith Rogers and the anonymous referees for comments and corrections on an earlier version of this manuscript.\n\n

Submitted - 1902.00989.pdf

", "abstract": "We obtain an improved Kakeya maximal function estimate in R\u2074 using a new geometric argument called the planebrush. A planebrush is a higher dimensional analogue of Wolff's hairbrush, which gives effective control on the size of Besicovitch sets when the lines through a typical point concentrate into a plane. When Besicovitch sets do not have this property, the existing trilinear estimates of Guth\u2013Zahl can be used to bound the size of a Besicovitch set. In particular, we establish a maximal function estimate in R\u2074 at dimension 3.059. As a consequence, every Besicovitch set in R\u2074 must have Hausdorff dimension at least 3.059.", "date": "2020-08-20", "date_type": "published", "publication": "Revista Matem\u00e1tica Iberoamericana", "volume": "37", "number": "1", "publisher": "European Mathematical Society", "pagerange": "317-359", "id_number": "CaltechAUTHORS:20210212-133815036", "issn": "0213-2230", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210212-133815036", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1565904" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/rmi/1219", "primary_object": { "basename": "1902.00989.pdf", "url": "https://authors.library.caltech.edu/records/nezma-weh48/files/1902.00989.pdf" }, "pub_year": "2020", "author_list": "Katz, Nets Hawk and Zahl, Joshua" }, { "id": "https://authors.library.caltech.edu/records/mtj5r-2fp93", "eprint_id": 102982, "eprint_status": "archive", "datestamp": "2023-08-19 22:57:14", "lastmod": "2026-03-28 23:04:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Andriolo-S", "name": { "family": "Andriolo", "given": "Stefano" }, "orcid": "0000-0003-0965-3967" }, { "id": "Huang-Tzu-Chen", "name": { "family": "Huang", "given": "Tzu-Chen" }, "orcid": "0000-0002-8738-7695" }, { "id": "Noumi-Toshifumi", "name": { "family": "Noumi", "given": "Toshifumi" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Shiu-Gary", "name": { "family": "Shiu", "given": "Gary" }, "orcid": "0000-0003-1308-5202" } ] }, "title": "Duality and axionic weak gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 The author(s).Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3. \n\nReceived 27 May 2020; accepted 29 June 2020; published 12 August 2020. \n\nWe would like to thank Yu-tin Huang and Pablo Soler for valuable discussions and comments on the earlier version of the draft. S.\u2009A. is supported by \"Fondazione Angelo Della Riccia\" Fellowship. T.\u2009N. is supported in part by JSPS KAKENHI Grants No. JP17H02894, No. JP18K13539 and No. JP20H01902, and MEXT KAKENHI Grant No. JP18H04352. The work of H.\u2009O. is supported in part by U.\u2009S. Department of Energy (DOE) Grant No. DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. G.\u2009S. is supported in part by the DOE Grant No. DE-SC0017647 and the Kellett Award of the University of Wisconsin. T.\u2009N. and G.\u2009S. gratefully acknowledge the hospitality of the Kavli Institute for Theoretical Physics (supported by NSF PHY-1748958) while part of this work was completed. H.\u2009O. thanks the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant No. PHY-1607611, where part of this work was done.\n\n

Published - PhysRevD.102.046008.pdf

Submitted - 2004.13721.pdf

", "abstract": "The axionic weak gravity conjecture predicts the existence of instantons whose actions are less than their charges in appropriate units. We show that the conjecture is satisfied for the axion-dilaton-gravity system if we assume duality constraints on the higher derivative corrections in addition to positivity bounds which follow from unitarity, analyticity, and locality of UV scattering amplitudes. On the other hand, the conjecture does not follow if we assume the positivity bounds only. This presents an example where derivation of the weak gravity conjecture requires more detailed UV information than the consistency of scattering amplitudes.", "date": "2020-08-15", "date_type": "published", "publication": "Physical Review D", "volume": "102", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 046008", "id_number": "CaltechAUTHORS:20200504-141139669", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200504-141139669", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "JP17H02894" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "JP18K13539" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "JP20H01902" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "JP18H04352" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0017647" }, { "agency": "NSF", "grant_number": "PHY-1748958" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2020-007", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.102.046008", "primary_object": { "basename": "2004.13721.pdf", "url": "https://authors.library.caltech.edu/records/mtj5r-2fp93/files/2004.13721.pdf" }, "related_objects": [ { "basename": "PhysRevD.102.046008.pdf", "url": "https://authors.library.caltech.edu/records/mtj5r-2fp93/files/PhysRevD.102.046008.pdf" } ], "pub_year": "2020", "author_list": "Andriolo, Stefano; Huang, Tzu-Chen; et al." }, { "id": "https://authors.library.caltech.edu/records/egyte-aws08", "eprint_id": 104752, "eprint_status": "archive", "datestamp": "2023-08-19 22:52:36", "lastmod": "2026-03-18 00:00:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Castelvecchi-D", "name": { "family": "Castelvecchi", "given": "Davide" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The mathematician who helped to reshape physics", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2020 Springer Nature Limited.", "abstract": "Barry Simon linked a phenomenon that had shocked physicists to topology, the branch of mathematics that studies shapes.", "date": "2020-08-06", "date_type": "published", "publication": "Nature", "volume": "584", "number": "7819", "publisher": "Nature Publishing Group", "pagerange": "20-20", "id_number": "CaltechAUTHORS:20200805-100854001", "issn": "0028-0836", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200805-100854001", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/d41586-020-02297-2", "pub_year": "2020", "author_list": "Castelvecchi, Davide and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/4meq0-wgk36", "eprint_id": 110827, "eprint_status": "archive", "datestamp": "2023-08-19 22:51:45", "lastmod": "2026-03-30 08:44:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Porta-Mauro", "name": { "family": "Porta", "given": "Mauro" }, "orcid": "0000-0002-1239-3409" }, { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Representability theorem in derived analytic geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "Representability, deformation theory, analytic cotangent complex, derived geometry, rigid analytic geometry, complex geometry, derived stacks", "note": "\u00a9 2020 EMS Publishing House. \n\nDate: April 5, 2017 (Revised on July 31, 2020). \n\nWe are very grateful to Antoine Chambert-Loir, Maxim Kontsevich, Jacob Lurie, Tony Pantev, Marco Robalo, Nick Rozenblyum, Carlos Simpson, Bertrand To\u00ebn and Gabriele Vezzosi for valuable discussions. The authors would also like to thank each other for the joint effort. Various stages of this research received supports from the Clay Mathematics Institute, Simons Foundation grant number 347070, Fondation Sciences Math\u00e9matiques de Paris, and from the Ky Fan and Yu-Fen Fan Membership Fund and the S.-S. Chern Endowment Fund of the Institute for Advanced Study.\n\n

Accepted Version - 1704.01683.pdf

", "abstract": "We prove the representability theorem in derived analytic geometry. The theorem asserts that an analytic moduli functor is a derived analytic stack if and only if it is compatible with Postnikov towers, has a global analytic cotangent complex, and its truncation is an analytic stack. Our result applies to both derived complex analytic geometry and derived nonarchimedean analytic geometry (rigid analytic geometry). The representability theorem is of both philosophical and practical importance in derived geometry. The conditions of representability are natural expectations for a moduli functor. So the theorem confirms that the notion of derived analytic space is natural and sufficiently general. On the other hand, the conditions are easy to verify in practice. So the theorem enables us to enhance various classical moduli spaces with derived structures, thus providing plenty of down-to-earth examples of derived analytic spaces. For the purpose of proof, we study analytification, square-zero extensions, analytic modules and cotangent complexes in the context of derived analytic geometry. We will explore applications of the representability theorem in our subsequent works. In particular, we will establish the existence of derived mapping stacks via the representability theorem.", "date": "2020-08-04", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "22", "number": "12", "publisher": "European Mathematical Society", "pagerange": "3867-3951", "id_number": "CaltechAUTHORS:20210914-164412497", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412497", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "347070" }, { "agency": "Fondation Sciences Math\u00e9matiques de Paris" }, { "agency": "Ky Fan and Yu-Fen Fan Membership Fund" }, { "agency": "Institute for Advanced Study" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JEMS/998", "primary_object": { "basename": "1704.01683.pdf", "url": "https://authors.library.caltech.edu/records/4meq0-wgk36/files/1704.01683.pdf" }, "pub_year": "2020", "author_list": "Porta, Mauro and Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/ac4wy-sjs56", "eprint_id": 66622, "eprint_status": "archive", "datestamp": "2023-08-22 05:48:06", "lastmod": "2026-03-29 15:40:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Willett-B", "name": { "family": "Willett", "given": "Brian" } }, { "id": "Yaakov-I", "name": { "family": "Yaakov", "given": "Itamar" } } ] }, "title": "Tests of Seiberg-like Dualities in Three Dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal Field Theory; Duality in Gauge Field Theories; Extended Super-symmetry; Supersymmetric Gauge Theory", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: July 22, 2020; Accepted: July 23, 2020; Published: August 24, 2020. \n\nWe would like to thank Eric Rains for very helpful input on evaluating some of the matrix integrals, as well as Alexei Borodin. This work was supported in part by the DOE grant DE-FG02-92ER40701.\n\n

Published - Kapustin2020_Article_TestsOfSeiberg-likeDualitiesIn.pdf

Submitted - 1012.4021.pdf

", "abstract": "We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N = 3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N = 4 gauge theories realized by monopole operators.", "date": "2020-08", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "8", "publisher": "Springer", "pagerange": "Art. No. 114", "id_number": "CaltechAUTHORS:20160503-142729844", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-142729844", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP08(2020)114", "primary_object": { "basename": "1012.4021.pdf", "url": "https://authors.library.caltech.edu/records/ac4wy-sjs56/files/1012.4021.pdf" }, "related_objects": [ { "basename": "Kapustin2020_Article_TestsOfSeiberg-likeDualitiesIn.pdf", "url": "https://authors.library.caltech.edu/records/ac4wy-sjs56/files/Kapustin2020_Article_TestsOfSeiberg-likeDualitiesIn.pdf" } ], "pub_year": "2020", "author_list": "Kapustin, Anton; Willett, Brian; et al." }, { "id": "https://authors.library.caltech.edu/records/ckkgn-4qb79", "eprint_id": 101674, "eprint_status": "archive", "datestamp": "2023-08-19 21:52:43", "lastmod": "2026-03-29 21:24:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Spodyneiko-L", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "Higher-dimensional generalizations of the Berry curvature", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Physical Society. \n\nReceived 20 February 2020; accepted 14 May 2020; published 11 June 2020. \n\nA.K. would like to thank D. Freed, M. Freedman, M. Hopkins, A. Kitaev. G. Moore, and C. Teleman for discussions of family invariants of gapped systems and related issues, and P.-S. Hsin and R. Thorngren for collaboration on a related project. We are especially grateful to A. Kitaev for reading a preliminary draft of the paper and pointing out an error. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award.\n\n

Published - PhysRevB.101.235130.pdf

Submitted - 2001.03454.pdf

", "abstract": "A family of finite-dimensional quantum systems with a nondegenerate ground state gives rise to a closed two-form on the parameter space, the curvature of the Berry connection. Its integral over a surface detects the presence of degeneracy points inside the volume enclosed by the surface. We seek generalizations of the Berry curvature to gapped many-body systems in D spatial dimensions which can detect gapless or degenerate points in the phase diagram of a system. Field theory predicts that in spatial dimension D the analog of the Berry curvature is a closed (D+2)-form on the parameter space (the Wess-Zumino-Witten form). We construct such closed forms for arbitrary families of gapped interacting lattice systems in all dimensions. We show that whenever the integral of the Wess-Zumino-Witten form over a (D+2)-dimensional surface in the parameter space is nonzero, there must be gapless edge modes for at least one value of the parameters. These edge modes arise even when the bulk system is in a trivial phase for all values of the parameters and are protected by the nontrivial topology of the phase diagram.", "date": "2020-06-15", "date_type": "published", "publication": "Physical Review B", "volume": "101", "number": "23", "publisher": "American Physical Society", "pagerange": "Art. No. 235130", "id_number": "CaltechAUTHORS:20200303-084023611", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200303-084023611", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.101.235130", "primary_object": { "basename": "2001.03454.pdf", "url": "https://authors.library.caltech.edu/records/ckkgn-4qb79/files/2001.03454.pdf" }, "related_objects": [ { "basename": "PhysRevB.101.235130.pdf", "url": "https://authors.library.caltech.edu/records/ckkgn-4qb79/files/PhysRevB.101.235130.pdf" } ], "pub_year": "2020", "author_list": "Kapustin, Anton and Spodyneiko, Lev" }, { "id": "https://authors.library.caltech.edu/records/zk5t7-7fb65", "eprint_id": 103267, "eprint_status": "archive", "datestamp": "2023-08-22 05:00:42", "lastmod": "2026-03-28 21:11:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Y-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Quantum Statistical Mechanics of the Absolute Galois Group", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum statistical mechanics; dessins d'enfant; absolute Galois group; Drinfeld-Ihara involution; quasi-triangular quasi-Hopf algebras", "note": "\u00a9 2020 The Author(s) under the terms of the Creative Commons Attribution-ShareAlike License. \n \nReceived August 01, 2019, in final form April 15, 2020; Published online May 05, 2020. \n\nThis paper is a contribution to the Special Issue on Integrability, Geometry, Moduli in honor of Motohico Mulase\nfor his 65th birthday. The full collection is available at https://www.emis.de/journals/SIGMA/Mulase.html. \n\nThe second named author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593. \n\nWe thank the anonymous referees for several very useful comments that significantly improve the paper, and Lieven Le Bruyn for his suggestions in a series of mails that helped us to avoid ambiguities.\n\n

Published - sigma20-038.pdf

Accepted Version - 1907.13545.pdf

", "abstract": "We present possible extensions of the quantum statistical mechanical formulation of class field theory to the non-abelian case, based on the action of the absolute Galois group on Grothendieck's dessins d'enfant, the embedding in the Grothendieck-Teichm\u00fcller group, and the Drinfeld-Ihara involution.", "date": "2020-05-05", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "16", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 038", "id_number": "CaltechAUTHORS:20200518-092511147", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200518-092511147", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/sigma.2020.038", "primary_object": { "basename": "1907.13545.pdf", "url": "https://authors.library.caltech.edu/records/zk5t7-7fb65/files/1907.13545.pdf" }, "related_objects": [ { "basename": "sigma20-038.pdf", "url": "https://authors.library.caltech.edu/records/zk5t7-7fb65/files/sigma20-038.pdf" } ], "pub_year": "2020", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/cqd0v-w8754", "eprint_id": 111000, "eprint_status": "archive", "datestamp": "2023-08-19 21:18:18", "lastmod": "2026-03-29 19:51:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Indistinguishability of collections of trees in the uniform spanning forest", "ispublished": "pub", "full_text_status": "public", "keywords": "ergodicity, Indistinguishability, Liouville, Uniform spanning forest, Zero-one law", "note": "\u00a9 2020 Institut Henri Poincar\u00e9. \n\nReceived: 16 October 2018; Revised: 19 February 2019; Accepted: 25 March 2019; Published: May 2020. First available in Project Euclid: 16 March 2020. \n\nThis work took place while the author was an intern at Microsoft Research, Redmond.\n\n

Submitted - 1810.06382.pdf

", "abstract": "We prove the following indistinguishability theorem for k-tuples of trees in the uniform spanning forest of Z^d: Suppose that A is a property of a k-tuple of components that is stable under finite modifications of the forest. Then either every k-tuple of distinct trees has property A almost surely, or no k-tuple of distinct trees has property A almost surely. This generalizes the indistinguishability theorem of the author and Nachmias (2016), which applied to individual trees. Our results apply more generally to any graph that has the Liouville property and for which every component of the USF is one-ended.", "date": "2020-05", "date_type": "published", "publication": "Annales de l'Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques", "volume": "56", "number": "2", "publisher": "Institut Henri Poincar\u00e9", "pagerange": "917-927", "id_number": "CaltechAUTHORS:20210922-193308155", "issn": "0246-0203", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193308155", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/19-AIHP988", "primary_object": { "basename": "1810.06382.pdf", "url": "https://authors.library.caltech.edu/records/cqd0v-w8754/files/1810.06382.pdf" }, "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/d2qn7-4t233", "eprint_id": 110998, "eprint_status": "archive", "datestamp": "2023-08-19 21:18:14", "lastmod": "2026-03-29 20:05:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Locality of the critical probability for transitive graphs of exponential growth", "ispublished": "pub", "full_text_status": "public", "keywords": "Benjamini\u2013Schramm convergence, Critical exponents, critical probability, exponential growth, locality, Nonamenable groups, percolation", "note": "\u00a9 2020 Institute of Mathematical Statistics. \n\nReceived: 1 August 2018; Revised: 1 April 2019; Published: May 2020. First available in Project Euclid: 17 June 2020. \n\nWe thank Jonathan Hermon for many helpful discussions, and for his careful reading of an earlier version of this manuscript. This paper also greatly benefited from discussions with Vincent Tassion on rewriting the Aizenman-Kesten-Newman uniqueness proof with martingale techniques, which took place at the Isaac Newton Institute during the RGM follow up workshop. We also thank Itai Benjamini, Hugo Duminil-Copin, Gady Kozma, Russ Lyons, Sebastien Martineau, Asaf Nachmias, and an anonymous referee for comments on earlier versions of the paper.\n\n

Accepted Version - 1808.08940.pdf

", "abstract": "Around 2008, Schramm conjectured that the critical probabilities for Bernoulli bond percolation satisfy the following continuity property: If (G_n)_(n \u2265 1) is a sequence of transitive graphs converging locally to a transitive graph G and limsup_(n \u2192 \u221e)p_c(G_n) < 1, then p_c(G_n) \u2192 p_c(G) as n \u2192 \u221e. We verify this conjecture under the additional hypothesis that there is a uniform exponential lower bound on the volume growth of the graphs in question. The result is new even in the case that the sequence of graphs is uniformly nonamenable. \n\nIn the unimodular case, this result is obtained as a corollary to the following theorem of independent interest: For every g > 1 and M < \u221e, there exist positive constants C = C(g,M) and \u03b4 = \u03b4(g,M) such that if G is a transitive unimodular graph with degree at most M and growth gr(G):= inf_(r \u2265 1)|B(o,r)|^(1/r) \u2265 g, then P_(p_c)(|K_o| \u2265 n) \u2264 C_n^(\u2212\u03b4) for every n \u2265 1, where K_o is the cluster of the root vertex o. The proof of this inequality makes use of new universal bounds on the probabilities of certain two-arm events, which hold for every unimodular transitive graph.", "date": "2020-05", "date_type": "published", "publication": "Annals of Probability", "volume": "48", "number": "3", "publisher": "Institute of Mathematical Statistics", "pagerange": "1352-1371", "id_number": "CaltechAUTHORS:20210922-193308018", "issn": "0091-1798", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193308018", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/19-AOP1395", "primary_object": { "basename": "1808.08940.pdf", "url": "https://authors.library.caltech.edu/records/d2qn7-4t233/files/1808.08940.pdf" }, "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/yz2f6-maw09", "eprint_id": 103384, "eprint_status": "archive", "datestamp": "2023-08-19 21:13:22", "lastmod": "2026-03-28 23:25:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Mueller-Frank-M", "name": { "family": "Mueller-Frank", "given": "Manuel" } }, { "id": "Sly-A", "name": { "family": "Sly", "given": "Allan" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Social Learning Equilibria", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 The Econometric Society.\n\n

Supplemental Material - ecta200153-sup-0001-Supplement.pdf

", "abstract": "We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce social learning equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.", "date": "2020-05", "date_type": "published", "publication": "Econometrica", "volume": "88", "number": "3", "publisher": "Econometric Society", "pagerange": "1235-1267", "id_number": "CaltechAUTHORS:20200521-152747894", "issn": "0012-9682", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200521-152747894", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministerio de Econom\u00eda y Competitividad (MINECO)" }, { "agency": "NSF" }, { "agency": "Office of Naval Research (ONR)" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3982/ecta16465", "primary_object": { "basename": "ecta200153-sup-0001-Supplement.pdf", "url": "https://authors.library.caltech.edu/records/yz2f6-maw09/files/ecta200153-sup-0001-Supplement.pdf" }, "pub_year": "2020", "author_list": "Mossel, Elchanan; Mueller-Frank, Manuel; et al." }, { "id": "https://authors.library.caltech.edu/records/m9xak-tca52", "eprint_id": 94501, "eprint_status": "archive", "datestamp": "2023-08-19 21:08:04", "lastmod": "2026-03-28 23:10:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Pomatto-L", "name": { "family": "Pomatto", "given": "Luciano" }, "orcid": "0000-0002-4331-8436" }, { "id": "Strack-P", "name": { "family": "Strack", "given": "Philipp" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Stochastic Dominance Under Independent Noise", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 by The University of Chicago. \n\nAccepted: July 22, 2019. Electronically published April 6, 2020. \n\nWe are grateful to the editor and the referees for their comments and suggestions. We also thank Kim Border, Simone Cerreia-Vioglio, Jak\u0161a Cvitanic, Ed Green, Elliot Lipnowski, Massimo Marinacci, Doron Ravid, and Xiaosheng Mu as well as seminar audiences at the Workshop on Information and Social Economics at Caltech, the University of Chile, Princeton University, and the Stony Brook International Conference on Game Theory. All errors and omissions are our own. Tamuz was supported by a grant from the Simons Foundation (419427).\n\n

Accepted Version - fosd.pdf

Submitted - 1807.06927.pdf

", "abstract": "Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g., uninsurable labor risk, house price risk) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second-order stochastic dominance and show how they lead to a novel and elementary axiomatization of mean-variance preferences.", "date": "2020-05", "date_type": "published", "publication": "Journal of Political Economy", "volume": "128", "number": "5", "publisher": "University of Chicago Press", "pagerange": "1877-1900", "id_number": "CaltechAUTHORS:20190405-101226198", "issn": "0022-3808", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190405-101226198", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1086/705555", "primary_object": { "basename": "1807.06927.pdf", "url": "https://authors.library.caltech.edu/records/m9xak-tca52/files/1807.06927.pdf" }, "related_objects": [ { "basename": "fosd.pdf", "url": "https://authors.library.caltech.edu/records/m9xak-tca52/files/fosd.pdf" } ], "pub_year": "2020", "author_list": "Pomatto, Luciano; Strack, Philipp; et al." }, { "id": "https://authors.library.caltech.edu/records/pq6ca-68465", "eprint_id": 95604, "eprint_status": "archive", "datestamp": "2023-08-19 21:02:51", "lastmod": "2026-03-28 21:07:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carlen-E-A", "name": { "family": "Carlen", "given": "Eric A." }, "orcid": "0000-0003-2613-187X" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Inequalities that sharpen the triangle inequality for sums of N functions in L^p", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 by Institut Mittag-Leffler. \n\nReceived 26 March 2019; Received revised 14 July 2019; Accepted 25 November 2019; Published 23 April 2020. \n\nWork partially supported by NSF grants DMS-1501007 (E.A.C.) and DMS-1363432 (R.L.F.).\n\n

Submitted - 1902.04399.pdf

", "abstract": "We study L^p inequalities that sharpen the triangle inequality for sums of N functions in L^p.", "date": "2020-04-23", "date_type": "published", "publication": "Arkiv f\u00f6r Matematik", "volume": "58", "number": "1", "publisher": "Royal Swedish Academy of Sciences", "pagerange": "57-69", "id_number": "CaltechAUTHORS:20190520-133118107", "issn": "0004-2080", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-133118107", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1501007" }, { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ARKIV.2020.v58.n1.a4", "primary_object": { "basename": "1902.04399.pdf", "url": "https://authors.library.caltech.edu/records/pq6ca-68465/files/1902.04399.pdf" }, "pub_year": "2020", "author_list": "Carlen, Eric A.; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/g8t8s-r6903", "eprint_id": 85187, "eprint_status": "archive", "datestamp": "2023-08-19 21:02:43", "lastmod": "2026-03-29 19:53:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ballinger-W", "name": { "family": "Ballinger", "given": "William" } }, { "id": "Hsu-Chloe Ching-Yun", "name": { "family": "Hsu", "given": "Chloe Ching-Yun" }, "orcid": "0000-0002-7743-3168" }, { "id": "Mackey-W", "name": { "family": "Mackey", "given": "Wyatt" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Ochse-T", "name": { "family": "Ochse", "given": "Tynan" } }, { "id": "Vafaee-F", "name": { "family": "Vafaee", "given": "Faramarz" } } ] }, "title": "The prism manifold realization problem", "ispublished": "pub", "full_text_status": "public", "keywords": "prism manifold, Dehn surgery, changemaker", "note": "\u00a9 2020 Mathematical Sciences Publishers. \n\nReceived: 17 May 2018; Revised: 6 June 2019; Accepted: 24 June 2019; Published: 23 April 2020. \n\nNi was partially supported by NSF grant number DMS-1252992 and an Alfred P Sloan Research Fellowship. Ballinger, Hsu, Mackey and Ochse were supported by Caltech's Summer Undergraduate Research Fellowships (SURF) program. Ballinger also wishes to thank Samuel P and Frances Krown for their generous support through the SURF program. We are grateful to John Berge for sending us the preprint [2] and some useful programs. We thank Zhengyuan Shang for finding a typo in Table 3. We thank the referee for a very thorough review.\n\n

Published - agt-v20-n2-p06-s.pdf

Submitted - 1612.04921.pdf

", "abstract": "The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in S\u00b3. In recent years, the realization problem for C\u2013, T\u2013, O\u2013 and I\u2013type spherical manifolds has been solved, leaving the D\u2013type manifolds (also known as the prism manifolds) as the only remaining case. Every prism manifold can be parametrized as P(p,q) for a pair of relatively prime integers p>1 and q. We determine a list of prism manifolds P(p,q) that can possibly be realized by positive integral surgeries on knots in S\u00b3 when q<0. Based on the forthcoming work of Berge and Kang, we are confident that this list is complete. The methodology undertaken to obtain the classification is similar to that of Greene for lens spaces.", "date": "2020-04-23", "date_type": "published", "publication": "Algebraic and Geometric Topology", "volume": "20", "publisher": "Geometry & Topology Publications", "pagerange": "757-816", "id_number": "CaltechAUTHORS:20180308-070142351", "issn": "1472-2747", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180308-070142351", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/agt.2020.20.757", "primary_object": { "basename": "1612.04921.pdf", "url": "https://authors.library.caltech.edu/records/g8t8s-r6903/files/1612.04921.pdf" }, "related_objects": [ { "basename": "agt-v20-n2-p06-s.pdf", "url": "https://authors.library.caltech.edu/records/g8t8s-r6903/files/agt-v20-n2-p06-s.pdf" } ], "pub_year": "2020", "author_list": "Ballinger, William; Hsu, Chloe Ching-Yun; et al." }, { "id": "https://authors.library.caltech.edu/records/zyqtd-0nm36", "eprint_id": 95609, "eprint_status": "archive", "datestamp": "2023-08-19 21:01:54", "lastmod": "2026-03-30 07:32:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Emmert-L", "name": { "family": "Emmert", "given": "Lukas" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00f6nig-T", "name": { "family": "K\u00f6nig", "given": "Tobias" } } ] }, "title": "Liquid Drop Model for Nuclear Matter in the Dilute Limit", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 by the authors. \n\nReceived by the editors July 12, 2019; accepted for publication (in revised form) February 12, 2020; published electronically April 22, 2020. \n\nThe work of the second author was partially supported by the National Science Foundation grant DMS-1363432.\n\n

Published - 19m1274420.pdf

Submitted - 1807.11904.pdf

", "abstract": "We consider the liquid drop model for nuclei interacting with a neutralizing homogeneous background of electrons. The regime we are interested in is when the fraction between the electronic and the nuclear charge densities is small. We show that in this dilute limit the thermodynamic ground state energy is given to leading order by that of an isolated nucleus.", "date": "2020-04-22", "date_type": "published", "publication": "SIAM Journal on Mathematical Analysis", "volume": "52", "number": "2", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "1980-1999", "id_number": "CaltechAUTHORS:20190520-135621604", "issn": "0036-1410", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-135621604", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/19M1274420", "primary_object": { "basename": "1807.11904.pdf", "url": "https://authors.library.caltech.edu/records/zyqtd-0nm36/files/1807.11904.pdf" }, "related_objects": [ { "basename": "19m1274420.pdf", "url": "https://authors.library.caltech.edu/records/zyqtd-0nm36/files/19m1274420.pdf" } ], "pub_year": "2020", "author_list": "Emmert, Lukas; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/53wvv-vm244", "eprint_id": 101220, "eprint_status": "archive", "datestamp": "2023-08-19 20:43:41", "lastmod": "2026-03-30 06:51:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fathizadeh-Farzad", "name": { "family": "Fathizadeh", "given": "Farzad" }, "orcid": "0000-0002-7863-4009" }, { "id": "Kafkoulis-Yeorgia", "name": { "family": "Kafkoulis", "given": "Yeorgia" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson\u2013Walker Cosmologies", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Springer Nature Switzerland AG. \n\nFirst Online: 10 February 2020. \n\nThe first author acknowledges the support from the Marie Curie/SER Cymru II Cofund Research Fellowship 663830-SU-008 and thanks the Perimeter Institute for Theoretical Physics for their hospitality in July 2018 and their excellent environment where this work was partially carried out. The second author was partially supported by a Gantvoort Scholarship, a Mr. and Mrs. Robert C. Loschke Summer Undergraduate Research Fellowship, and a Taussky-Todd Prize. The third author was partially supported by NSF Grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics.\n\n

Submitted - 1811.02972.pdf

", "abstract": "We obtain an explicit formula for the full expansion of the spectral action on Robertson\u2013Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman\u2013Kac formula. We then apply this result to the case of multifractal Packed Swiss Cheese Cosmology models obtained from an arrangement of Robertson\u2013Walker spacetimes along an Apollonian sphere packing. Using Mellin transforms, we show that the asymptotic expansion of the spectral action contains the same terms as in the case of a single Robertson\u2013Walker spacetime, but with zeta-regularized coefficients, given by values at integers of the zeta function of the fractal string of the radii of the sphere packing, as well as additional log-periodic correction terms arising from the poles (off the real line) of this zeta function.", "date": "2020-04", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "21", "number": "4", "publisher": "Springer", "pagerange": "1329-1382", "id_number": "CaltechAUTHORS:20200211-084519645", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200211-084519645", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Marie Curie Fellowship", "grant_number": "663830-SU-008" }, { "agency": "Gantvoort Scholarship" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Taussky-Todd Prize" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-020-00894-5", "primary_object": { "basename": "1811.02972.pdf", "url": "https://authors.library.caltech.edu/records/53wvv-vm244/files/1811.02972.pdf" }, "pub_year": "2020", "author_list": "Fathizadeh, Farzad; Kafkoulis, Yeorgia; et al." }, { "id": "https://authors.library.caltech.edu/records/2kwzk-b1v64", "eprint_id": 102500, "eprint_status": "archive", "datestamp": "2023-08-19 20:45:03", "lastmod": "2026-03-29 16:39:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "Trialities of minimally supersymmetric 2d gauge theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories, Supersymmetric Gauge Theory,\nSupersymmetry and Duality, Sigma Models", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: January 27, 2020; Accepted: March 25, 2020; Published: April 14, 2020. \n\nWe would like to thank Francesco Benini, Mykola Dedushenko, Shiraz Minwalla, Cumrun Vafa, Edward Witten for fruitful discussions. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of D.P. is supported by NSF Grant DMS-1440140 while in residence at the Mathematical Sciences Research Institute in Berkeley, California during the Fall 2019 semester, and by the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95).\n\n

Published - Gukov2020_Article_TrialitiesOfMinimallySupersymm.pdf

Submitted - 1910.13455.pdf

", "abstract": "We study dynamics of two-dimensional N = (0, 1) supersymmetric gauge theories. In particular, we propose that there is an infrared triality between certain triples of theories with orthogonal and symplectic gauge groups. The proposal is supported by matching of anomalies and elliptic genera. This triality can be viewed as a (0, 1) counterpart of the (0, 2) triality proposed earlier by two of the authors and A. Gadde. We also describe the relation between global anomalies in gauge theoretic and sigma-model descriptions, filling in a gap in the present literature.", "date": "2020-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 079", "id_number": "CaltechAUTHORS:20200413-094559729", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200413-094559729", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "NSF", "grant_number": "DMS-1440140" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2020)079", "primary_object": { "basename": "1910.13455.pdf", "url": "https://authors.library.caltech.edu/records/2kwzk-b1v64/files/1910.13455.pdf" }, "related_objects": [ { "basename": "Gukov2020_Article_TrialitiesOfMinimallySupersymm.pdf", "url": "https://authors.library.caltech.edu/records/2kwzk-b1v64/files/Gukov2020_Article_TrialitiesOfMinimallySupersymm.pdf" } ], "pub_year": "2020", "author_list": "Gukov, Sergei; Pei, Du; et al." }, { "id": "https://authors.library.caltech.edu/records/prt2v-4dz74", "eprint_id": 102669, "eprint_status": "archive", "datestamp": "2023-08-19 20:45:44", "lastmod": "2026-03-30 14:01:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Larson-Simon", "name": { "family": "Larson", "given": "Simon" }, "orcid": "0000-0002-0057-8211" } ] }, "title": "On the error in the two-term Weyl formula for the Dirichlet Laplacian", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Published under license by AIP Publishing. \n\nSubmitted: 13 January 2020; Accepted: 24 March 2020; Published Online: 20 April 2020. \n\nWe would like to dedicate this paper to the memory of Jean Bourgain. The U.S. National Science Foundation (Grant No. DMS-1363432) (R.L.F.) and Knut and Alice Wallenberg Foundation (Grant No. KAW 2018.0281) (S.L.) are acknowledged. The authors also wish to thank Institut Mittag-Leffler, where part of this work was carried out. \n\nData sharing is not applicable to this article as no new data were created or analyzed in this study.\n\n

Published - 1.5145003.pdf

Submitted - 2001.01876.pdf

", "abstract": "We study the optimality of the remainder term in the two-term Weyl law for the Dirichlet Laplacian within the class of Lipschitz regular subsets of R^d. In particular, for the short-time asymptotics of the trace of the heat kernel, we prove that the error term cannot be made quantitatively better than little-o of the second term.", "date": "2020-04", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "61", "number": "4", "publisher": "American Institute of Physics", "pagerange": "Art. No. 043504", "id_number": "CaltechAUTHORS:20200420-145908047", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200420-145908047", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Knut and Alice Wallenberg Foundation", "grant_number": "KAW 2018.0281" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.5145003", "primary_object": { "basename": "2001.01876.pdf", "url": "https://authors.library.caltech.edu/records/prt2v-4dz74/files/2001.01876.pdf" }, "related_objects": [ { "basename": "1.5145003.pdf", "url": "https://authors.library.caltech.edu/records/prt2v-4dz74/files/1.5145003.pdf" } ], "pub_year": "2020", "author_list": "Frank, Rupert L. and Larson, Simon" }, { "id": "https://authors.library.caltech.edu/records/e8jy9-czd04", "eprint_id": 102405, "eprint_status": "archive", "datestamp": "2023-08-19 20:34:52", "lastmod": "2026-03-29 21:29:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benjamin-N", "name": { "family": "Benjamin", "given": "Nathan" }, "orcid": "0000-0003-3661-6563" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Shao-Shu-Heng", "name": { "family": "Shao", "given": "Shu-Heng" }, "orcid": "0000-0003-1294-2786" }, { "id": "Wang-Yifan", "name": { "family": "Wang", "given": "Yifan" }, "orcid": "0000-0001-9965-9777" } ] }, "title": "Twist Gap and Global Symmetry in Two Dimensions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3.\n\nReceived 14 March 2020; accepted 13 May 2020; published 26 May 2020.\n\nWe thank Igor Klebanov, Petr Kravchuk, Ying-Hsuan Lin, Juan Maldacena, and Xi Yin for interesting discussions. The work of N.\u2009B. is supported in part by the Simons Foundation Grant No. 488653. The work of H.\u2009O. is supported in part by U.S. Department of Energy Grant No. DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. The work of S.-H.\u2009S. is supported by the Simons Collaboration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (Grant No. 651440, N.\u2009S.). The work of Y.\u2009W. is supported in part by the U.S. NSF under Grant No. PHY-1620059 and by the Simons Foundation Grant No. 488653. We thank the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant No. PHY-1607611, where this work was initiated.\n\n

Published - PhysRevD.101.106026.pdf

Submitted - 2003.02844.pdf

", "abstract": "We show that every compact, unitary two-dimensional conformal field theory with an Abelian conserved current has vanishing twist gap for charged primary fields with respect to the u(1)\u00d7Virasoro algebra. This means that either the chiral algebra is enhanced by a charged primary field with zero twist or there is an infinite family of charged primary fields that accumulate to zero twist.", "date": "2020-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "101", "number": "10", "publisher": "American Physical Society", "pagerange": "Art. No. 106026", "id_number": "CaltechAUTHORS:20200408-133007156", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200408-133007156", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "488653" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "Simons Foundation", "grant_number": "651440" }, { "agency": "NSF", "grant_number": "PHY-1620059" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2020-002", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.101.106026", "primary_object": { "basename": "2003.02844.pdf", "url": "https://authors.library.caltech.edu/records/e8jy9-czd04/files/2003.02844.pdf" }, "related_objects": [ { "basename": "PhysRevD.101.106026.pdf", "url": "https://authors.library.caltech.edu/records/e8jy9-czd04/files/PhysRevD.101.106026.pdf" } ], "pub_year": "2020", "author_list": "Benjamin, Nathan; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/39b33-r3y64", "eprint_id": 101142, "eprint_status": "archive", "datestamp": "2023-08-19 20:34:24", "lastmod": "2026-03-29 21:26:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dodelson-M", "name": { "family": "Dodelson", "given": "Matthew" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "The High Energy Behavior of Mellin Amplitudes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3. \n\nReceived 20 December 2019; accepted 12 February 2020; published 12 March 2020. \n\nWe thank C. Cardona, J. Maldacena, J. Penedones, J. Silva, D. Simmons-Duffin, and A. Zhiboedov for discussions. This work is supported in part by the World Premier International Research Center Initiative, MEXT, Japan. The work of H.\u2009O. is also supported in part by U.S. Department of Energy Grant No. DE-SC0011632, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. H.\u2009O. thanks the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant No. PHY-1607611, where part of this work was done.\n\n

Published - PhysRevD.101.066008.pdf

Submitted - 1911.05274.pdf

", "abstract": "In any consistent massive quantum field theory there are well-known bounds on scattering amplitudes at high energies. In conformal field theory there is no scattering amplitude, but the Mellin amplitude is a well-defined object analogous to the scattering amplitude. We prove bounds at high energies on Mellin amplitudes in conformal field theories, valid under certain technical assumptions. Such bounds are derived by demanding the absence of spurious singularities in position space correlators. We also conjecture a stronger bound, based on evidence from several explicit examples.", "date": "2020-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "101", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066008", "id_number": "CaltechAUTHORS:20200205-143527298", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200205-143527298", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2019-049", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.101.066008", "primary_object": { "basename": "1911.05274.pdf", "url": "https://authors.library.caltech.edu/records/39b33-r3y64/files/1911.05274.pdf" }, "related_objects": [ { "basename": "PhysRevD.101.066008.pdf", "url": "https://authors.library.caltech.edu/records/39b33-r3y64/files/PhysRevD.101.066008.pdf" } ], "pub_year": "2020", "author_list": "Dodelson, Matthew and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/7003j-mxf28", "eprint_id": 100200, "eprint_status": "archive", "datestamp": "2023-08-22 04:08:36", "lastmod": "2026-03-30 07:43:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Y-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Nori Diagrams and Persistent Homology", "ispublished": "pub", "full_text_status": "public", "keywords": "Persistent homology; Nori diagrams; Nori motives; Thin categories; Model structures", "note": "\u00a9 2019 Springer Nature Switzerland AG. \n\nReceived 14 February 2019; Revised 21 October 2019; Accepted 30 October 2019; First Online 22 November 2019. \n\nWe thank Jack Morava for suggesting the question of model structures for persistent homology discussed in Sect. 6. The second author is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593, by the FQXi Grant FQXi-RFP-1 804, and by the Perimeter Institute for Theoretical Physics.\n\n

Submitted - 1901.10301.pdf

", "abstract": "Recently, it was found that there is a remarkable intuitive similarity between studies in theoretical computer science dealing with large data sets on the one hand, and categorical methods of topology and geometry in pure mathematics, on the other. In this article, we treat the key notion of persistency from computer science in the algebraic geometric context involving Nori motivic constructions and related methods. We also discuss model structures for persistent topology.", "date": "2020-03", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "14", "publisher": "Springer", "pagerange": "77-102", "id_number": "CaltechAUTHORS:20191205-092818459", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191205-092818459", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Foundational Questions Institute (FQXI)", "grant_number": "RFP-1 804" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-019-00422-7", "primary_object": { "basename": "1901.10301.pdf", "url": "https://authors.library.caltech.edu/records/7003j-mxf28/files/1901.10301.pdf" }, "pub_year": "2020", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/h8w30-qk348", "eprint_id": 95608, "eprint_status": "archive", "datestamp": "2023-08-19 20:06:46", "lastmod": "2026-03-28 20:51:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borrelli-W", "name": { "family": "Borrelli", "given": "William" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Sharp decay estimates for critical Dirac equations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 by the authors. \n\nReceived by editor(s): December 11, 2018; Received by editor(s) in revised form: March 21, 2019, July 3, 2019, and July 28, 2019; Published electronically: December 10, 2019. \n\nU.S. National Science Foundation grant DMS-1363432 (R.L.F.) is acknowledged.\n\n

Published - S0002-9947-2019-07958-8.pdf

Submitted - 1809.01417.pdf

", "abstract": "We prove sharp pointwise decay estimates for critical Dirac equations on R^n with n \u2265 2. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited states with an explicit asymptotic behavior. Moreover, we provide some classification results both for ground states and for excited states.", "date": "2020-03", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "373", "number": "3", "publisher": "American Mathematical Society", "pagerange": "2045-2070", "id_number": "CaltechAUTHORS:20190520-135426746", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-135426746", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/7958", "primary_object": { "basename": "1809.01417.pdf", "url": "https://authors.library.caltech.edu/records/h8w30-qk348/files/1809.01417.pdf" }, "related_objects": [ { "basename": "S0002-9947-2019-07958-8.pdf", "url": "https://authors.library.caltech.edu/records/h8w30-qk348/files/S0002-9947-2019-07958-8.pdf" } ], "pub_year": "2020", "author_list": "Borrelli, William and Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/n7nss-psj53", "eprint_id": 98036, "eprint_status": "archive", "datestamp": "2023-08-19 19:57:07", "lastmod": "2026-03-30 13:43:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Books versus triangles at the extremal density", "ispublished": "pub", "full_text_status": "public", "keywords": "extremal graph theory, Rademacher-type theorems, books", "note": "\u00a9 2020 Society for Industrial and Applied Mathematics. \n\nReceived by the editors May 14, 2019; accepted for publication (in revised form) October 22, 2019; published electronically February 12, 2020. \n\nThe first author's research was supported by ERC Starting Grant 676632. The second author's research was supported by a Packard Fellowship and by NSF Career Award DMS-1352121. The third author's research was supported in part by SNSF grant 200021-175573. \n\nWe are grateful to Shagnik Das and Nina Kam\u010dev for helpful conversations and are particularly indebted to Shagnik for writing up an early draft of section 3. We would also like to thank the anonymous referees for their detailed and insightful reports.\n\n

Published - 19m1261766.pdf

Submitted - 1905.05312.pdf

", "abstract": "A celebrated result of Mantel shows that every graph on n vertices with [n\u00b2/4] + 1 edges must contain a triangle. A robust version of this result, due to Rademacher, says that there\nmust, in fact, be at least [n/2] triangles in any such graph. Another strengthening, due to the\ncombined efforts of many authors starting with Erd\u0151s, says that any such graph must have an edge\nwhich is contained in at least n/6 triangles. Following Mubayi, we study the interplay between\nthese two results, that is, between the number of triangles in such graphs and their book number,\nthe largest number of triangles sharing an edge. Among other results, Mubayi showed that for any\n1/6 \u2264 \u03b2 < 1/4 there is \u03b3 > 0 such that any graph on n vertices with at least [n\u00b2/4] +1 edges and book number at most \u03b2n contains at least (\u03b3 - o(1))n\u00b3 triangles. He also asked for a more precise\nestimate for \u03b3 in terms of \u03b2. We make a conjecture about this dependency and prove this conjecture\nfor \u03b2 = 1/6 and for 0.2495 \u2264 \u03b2 < 1/4, thereby answering Mubayi's question in these ranges.", "date": "2020-02-12", "date_type": "published", "publication": "SIAM Journal on Discrete Mathematics", "volume": "34", "number": "1", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "385-398", "id_number": "CaltechAUTHORS:20190819-170946478", "issn": "0895-4801", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-170946478", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-175573" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/19M1261766", "primary_object": { "basename": "19m1261766.pdf", "url": "https://authors.library.caltech.edu/records/n7nss-psj53/files/19m1261766.pdf" }, "related_objects": [ { "basename": "1905.05312.pdf", "url": "https://authors.library.caltech.edu/records/n7nss-psj53/files/1905.05312.pdf" } ], "pub_year": "2020", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/rtzsw-gpe56", "eprint_id": 103269, "eprint_status": "archive", "datestamp": "2023-08-19 19:53:44", "lastmod": "2026-03-30 07:41:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Holographic Codes on Bruhat-Tits buildings and Drinfeld Symmetric Spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Arithmetical physics, AdS/CFT holography, p-adic,\nBruhat\u2013Tits buildings, Drinfeld symmetric spaces", "note": "\u00a9 2020 by International Press of Boston, Inc. \n\nReceived 29 January 2018; Published 6 February 2020. \n\nDedicated to Yuri Manin on the occasion of his 80th birthday. \n\nThe author thanks Matthew Heydeman, Sarthak Parikh, and Ingmar Saberi for many very useful discussions and an ongoing collaboration on several topics discussed in this paper, and especially Sarthak Parikh for suggesting several improvements to the paper. The author is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics.\n\n

Published - PAMQ-2020-0016-0001-a001.pdf

Submitted - 1801.09623.pdf

", "abstract": "This paper is based on the author's talk at the Arbeitstagung 2017. It discusses some general approaches to the construction of classical and quantum holographic codes on Bruhat\u2013Tits trees and buildings and on Drinfeld symmetric spaces, in the context of the p-adic AdS/CFT correspondence.", "date": "2020-02-06", "date_type": "published", "publication": "Pure and Applied Mathematics Quarterly", "volume": "16", "number": "1", "publisher": "International Press", "pagerange": "1-33", "id_number": "CaltechAUTHORS:20200518-094042414", "issn": "1558-8602", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200518-094042414", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/PAMQ.2020.v16.n1.a1", "primary_object": { "basename": "1801.09623.pdf", "url": "https://authors.library.caltech.edu/records/rtzsw-gpe56/files/1801.09623.pdf" }, "related_objects": [ { "basename": "PAMQ-2020-0016-0001-a001.pdf", "url": "https://authors.library.caltech.edu/records/rtzsw-gpe56/files/PAMQ-2020-0016-0001-a001.pdf" } ], "pub_year": "2020", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/yjd75-2ph48", "eprint_id": 101578, "eprint_status": "archive", "datestamp": "2023-08-22 03:51:57", "lastmod": "2026-04-16 01:40:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Sachdev-S", "name": { "family": "Sachdev", "given": "Subir" }, "orcid": "0000-0002-2432-7070" }, { "id": "Tarnopolsky-G", "name": { "family": "Tarnopolsky", "given": "Grigory" } } ] }, "title": "Notes on the complex Sachdev-Ye-Kitaev model", "ispublished": "pub", "full_text_status": "public", "keywords": "Holography and condensed matter physics (AdS/CMT); AdS-CFT Correspondence; Models of Quantum Gravity", "note": "\u00a9 2020 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: November 13, 2019; Accepted: February 4, 2020; Published: February 25, 2020. \n\nWe thank Wenbo Fu, Antoine Georges, Simone Giombi, Luca Iliesiu, Igor Klebanov, Sung-Sik Lee, Juan Maldacena, Olivier Parcollet, Xiao-Liang Qi, Shinsei Ryu, Wei Song, Douglas Stanford and Cenke Xu for useful discussions. Y.G. is supported by the Gordon and Betty\nMoore Foundation EPiQS Initiative through Grant (GBMF-4306) and DOE grant, DE-SC0019030. A.K. is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. S.S. and G.T. are supported by DOE grant, DE-SC0019030. G.T. acknowledges support from the MURI grant W911NF-14-1-0003 from ARO and by DOE grant DE-SC0007870. This work was performed in part at KITP, University of California, Santa Barbara supported by the NSF under grant PHY-1748958.\n\n

Published - Gu2020_Article_NotesOnTheComplexSachdev-Ye-Ki.pdf

Submitted - 1910.14099.pdf

", "abstract": "We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N\u2009\u226b\u20091 flavors and a global U(1) charge. We provide a general definition of the charge in the (G, \u03a3) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.", "date": "2020-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2020", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 157", "id_number": "CaltechAUTHORS:20200226-133542550", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200226-133542550", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation", "grant_number": "GBMF-4306" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0019030" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute of Quantum Information and Matter (IQIM)" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-14-1-0003" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0007870" }, { "agency": "NSF", "grant_number": "PHY-1748958" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/jhep02(2020)157", "primary_object": { "basename": "1910.14099.pdf", "url": "https://authors.library.caltech.edu/records/yjd75-2ph48/files/1910.14099.pdf" }, "related_objects": [ { "basename": "Gu2020_Article_NotesOnTheComplexSachdev-Ye-Ki.pdf", "url": "https://authors.library.caltech.edu/records/yjd75-2ph48/files/Gu2020_Article_NotesOnTheComplexSachdev-Ye-Ki.pdf" } ], "pub_year": "2020", "author_list": "Gu, Yingfei; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/agh1q-xw932", "eprint_id": 73923, "eprint_status": "archive", "datestamp": "2023-08-22 03:43:44", "lastmod": "2026-03-29 19:45:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "BPS spectra and 3-manifold invariants", "ispublished": "pub", "full_text_status": "public", "keywords": "BPS spectrum; 3-manifold; invariant; knot", "note": "\u00a9 2020 World Scientific Publishing Company. \n\nReceived 7 January 2020; Accepted 13 January 2020; Published 17 March 2020. \n\nWe would like to thank J. E. Andersen, M. Aganagic, F. Benini, C. Cordova, A.Gadde, E. Gorsky,K. Hori,H. Kim, S. Nawata,M. Romo, S. Shakirov, L. Rozansky and K. Ye for useful comments and discussions. The work of S.G. and D.P. is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. In addition, the work of D.P. is supported by the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95). P.P. gratefully acknowledges the support from Marvin L. Goldberger Fellowship and the DOE Grant DE-SC0009988. The research of C.V. is supported in part by NSF grant PHY-1067976. This work was performed in part (by P.P.) at Aspen Center for Physics which is supported by National Science Foundation grant PHY-1066293. The authors would like to thank Simons Center for Geometry and Physics and the organisers of the Simons Summer Workshop 2016, where the work on the project has begun, for generous hospitality.\n\n

Submitted - 1701.06567v1.pdf

", "abstract": "We provide a physical definition of new homological invariants H_a(M\u2083) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M\u2083 times a 2-disk, D\u00b2, whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N=2 theory T[M\u2083]: D\u00b2\u00d7S\u00b9 half-index, S\u00b2\u00d7S\u00b9 superconformal index, and S\u00b2\u00d7S\u00b9 topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern\u2013Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M\u2083. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.", "date": "2020-02", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "29", "number": "2", "publisher": "World Scientific Publishing", "pagerange": "Art. No. 2040003", "id_number": "CaltechAUTHORS:20170201-100930550", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170201-100930550", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Marvin L. Goldberger Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "NSF", "grant_number": "PHY-1066293" } ] }, "other_numbering_system": { "items": [ { "id": "2016-039", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0218216520400039", "primary_object": { "basename": "1701.06567v1.pdf", "url": "https://authors.library.caltech.edu/records/agh1q-xw932/files/1701.06567v1.pdf" }, "pub_year": "2020", "author_list": "Gukov, Sergei; Pei, Du; et al." }, { "id": "https://authors.library.caltech.edu/records/nm5e3-25081", "eprint_id": 78991, "eprint_status": "archive", "datestamp": "2023-08-19 19:42:34", "lastmod": "2026-03-30 16:40:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Biringer-I", "name": { "family": "Biringer", "given": "Ian" } }, { "id": "Bowen-L", "name": { "family": "Bowen", "given": "Lewis" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Invariant random subgroups of semidirect products", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Cambridge University Press.\n\nReceived 4 March 2017 and accepted in revised form 17 May 2018.\n\nWe thank the referee for a careful reading of the paper, a number of useful comments, and the suggestion to combine our work with [4] to give a proof of the Nevo\u2013Stuck\u2013Zimmer theorem for SL_n(Z), as described in Remark 1 above. The first author was supported in part by NSF grant DMS-1611851 and CAREER Award DMS-1654114. The second author was supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274. The third author's work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).\n\n

Submitted - 1703.01282.pdf

", "abstract": "We study invariant random subgroups (IRSs) of semidirect products G=A\u22ca\u0393. In particular, we characterize all IRSs of parabolic subgroups of SL_d(R), and show that all ergodic IRSs of R^d\u22caSL_d(R) are either of the form R^d\u22caK for some IRS of SL_d(R), or are induced from IRSs of \u039b\u22caSL(\u039b), where \u039b", "date": "2020-02", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "40", "number": "2", "publisher": "Cambridge University Press", "pagerange": "353-366", "id_number": "CaltechAUTHORS:20170712-084843331", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-084843331", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1611851" }, { "agency": "NSF", "grant_number": "DMS-1654114" }, { "agency": "NSF", "grant_number": "DMS-0968762" }, { "agency": "NSF", "grant_number": "DMS-0954606" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2008274" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/etds.2018.46", "primary_object": { "basename": "1703.01282.pdf", "url": "https://authors.library.caltech.edu/records/nm5e3-25081/files/1703.01282.pdf" }, "pub_year": "2020", "author_list": "Biringer, Ian; Bowen, Lewis; et al." }, { "id": "https://authors.library.caltech.edu/records/7dw4y-4c316", "eprint_id": 111020, "eprint_status": "archive", "datestamp": "2023-08-19 19:50:32", "lastmod": "2026-03-29 13:55:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Universality of high-dimensional spanning forests and sandpiles", "ispublished": "pub", "full_text_status": "public", "keywords": "Uniform spanning tree \u00b7 Uniform spanning forest \u00b7 Random interlacements \u00b7 Mean-field \u00b7 Critical exponents \u00b7 Anomalous diffusion", "note": "\u00a9 The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 11 April 2018 / Revised: 22 May 2019 / Published online: 5 June 2019. \n\nWe thank Martin Barlow, Antal J\u00e1rai, and Perla Sousi for helpful discussions, and thank Russ Lyons for catching some typos. I also thank the two anonymous referees for their close and careful reading of the paper; their comments and suggestions have greatly improved the paper. Much of this work took place while the author was a Ph.D. student at the University of British Columbia, during which time he was supported by a Microsoft Research Ph.D. Fellowship.\n\n

Published - Hutchcroft2020_Article_UniversalityOfHigh-dimensional.pdf

Accepted Version - 1804.04120.pdf

", "abstract": "We prove that the wired uniform spanning forest exhibits mean-field behaviour on a very large class of graphs, including every transitive graph of at least quintic volume growth and every bounded degree nonamenable graph. Several of our results are new even in the case of Z^d, d \u2265 5. In particular, we prove that every tree in the forest has spectral dimension 4/3 and walk dimension 3 almost surely, and that the critical exponents governing the intrinsic diameter and volume of the past of a vertex in the forest are 1 and 1/2 respectively. (The past of a vertex in the uniform spanning forest is the union of the vertex and the finite components that are disconnected from infinity when that vertex is deleted from the forest.) We obtain as a corollary that the critical exponent governing the extrinsic diameter of the past is 2 on any transitive graph of at least five dimensional polynomial growth, and is 1 on any bounded degree nonamenable graph. We deduce that the critical exponents describing the diameter and total number of topplings in an avalanche in the Abelian sandpile model are 2 and 1/2 respectively for any transitive graph with polynomial growth of dimension at least five, and are 1 and 1/2 respectively for any bounded degree nonamenable graph. In the case of Z^d, d \u2265 5, some of our results regarding critical exponents recover earlier results of Bhupatiraju et al. (Electron J Probab 22(85):51, 2017). In this case, we improve upon their results by showing that the tail probabilities in question are described by the appropriate power laws to within constant-order multiplicative errors, rather than the polylogarithmic-order multiplicative errors present in that work.", "date": "2020-02", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "176", "number": "1-2", "publisher": "Springer", "pagerange": "533-597", "id_number": "CaltechAUTHORS:20210923-213625943", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210923-213625943", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-019-00923-3", "primary_object": { "basename": "1804.04120.pdf", "url": "https://authors.library.caltech.edu/records/7dw4y-4c316/files/1804.04120.pdf" }, "related_objects": [ { "basename": "Hutchcroft2020_Article_UniversalityOfHigh-dimensional.pdf", "url": "https://authors.library.caltech.edu/records/7dw4y-4c316/files/Hutchcroft2020_Article_UniversalityOfHigh-dimensional.pdf" } ], "pub_year": "2020", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/hng26-3je06", "eprint_id": 96481, "eprint_status": "archive", "datestamp": "2023-08-19 19:35:34", "lastmod": "2026-03-30 08:42:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Spodyneiko-L", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 American Physical Society. \n\nReceived 9 October 2019; revised manuscript received 14 January 2020; published 31 January 2020. \n\nWe thank Y.-A. Chen for participation in the early stages of this work and M. Hastings, H. Watanabe, A. Kitaev, and H. Edelsbrunner for discussions. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award.\n\n

Published - PhysRevB.101.045137.pdf

Submitted - 1905.06488.pdf

", "abstract": "We derive a Kubo-like formula for the thermal Hall conductance of a 2d lattice systems which is free from ambiguities associated with the definition of energy magnetization. We use it to define a relative topological invariant of gapped 2d lattice systems at zero temperature. Up to a numerical factor, it can be identified with the difference of chiral central charges for the corresponding edge modes. This establishes the bulk-boundary correspondence for the chiral central charge. We also show that for any local commuting projector Hamiltonian, the relative chiral central charge vanishes, while for free fermionic systems, it is related to the zero-temperature electric Hall conductance via the Wiedemann-Franz law.", "date": "2020-01-15", "date_type": "published", "publication": "Physical Review B", "volume": "101", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 045137", "id_number": "CaltechAUTHORS:20190617-151316187", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190617-151316187", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.101.045137", "primary_object": { "basename": "1905.06488.pdf", "url": "https://authors.library.caltech.edu/records/hng26-3je06/files/1905.06488.pdf" }, "related_objects": [ { "basename": "PhysRevB.101.045137.pdf", "url": "https://authors.library.caltech.edu/records/hng26-3je06/files/PhysRevB.101.045137.pdf" } ], "pub_year": "2020", "author_list": "Kapustin, Anton and Spodyneiko, Lev" }, { "id": "https://authors.library.caltech.edu/records/kgfmj-vq924", "eprint_id": 91400, "eprint_status": "archive", "datestamp": "2023-08-19 19:18:57", "lastmod": "2026-03-09 02:41:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Fidkowski-L", "name": { "family": "Fidkowski", "given": "Lukasz" }, "orcid": "0000-0002-9313-7799" } ] }, "title": "Local Commuting Projector Hamiltonians and the Quantum Hall Effect", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Springer-Verlag GmbH Germany, part of Springer Nature. \n\nReceived 21 October 2018; Accepted 25 February 2019; Published 09 May 2019.\n\n

Submitted - 1810.07756.pdf

", "abstract": "We prove that neither Integer nor Fractional Quantum Hall Effects with nonzero Hall conductivity are possible in gapped systems described by Local Commuting Projector Hamiltonians.", "date": "2020-01", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "373", "number": "1", "publisher": "Springer", "pagerange": "763-769", "id_number": "CaltechAUTHORS:20181203-110141167", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181203-110141167", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-019-03444-1", "primary_object": { "basename": "1810.07756.pdf", "url": "https://authors.library.caltech.edu/records/kgfmj-vq924/files/1810.07756.pdf" }, "pub_year": "2020", "author_list": "Kapustin, Anton and Fidkowski, Lukasz" }, { "id": "https://authors.library.caltech.edu/records/reagx-64650", "eprint_id": 110999, "eprint_status": "archive", "datestamp": "2023-08-19 19:27:19", "lastmod": "2026-03-09 02:34:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Holroyd-Alexander-E", "name": { "family": "Holroyd", "given": "Alexander E." } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Levy-Avi", "name": { "family": "Levy", "given": "Avi" } } ] }, "title": "Mallows permutations and finite dependence", "ispublished": "pub", "full_text_status": "public", "keywords": "finite dependence, Proper coloring, random permutation", "note": "\u00a9 2020 Institute of Mathematical Statistics. \n\nReceived: 1 June 2017; Revised: 1 January 2019; Published: January 2020. First available in Project Euclid: 25 March 2020. \n\nAL and TH were supported by internships at Microsoft Research while portions of this work were completed. TH was also supported by a Microsoft Research PhD fellowship.\n\n

Submitted - 1706.09526.pdf

", "abstract": "We use the Mallows permutation model to construct a new family of stationary finitely dependent proper colorings of the integers. We prove that these colorings can be expressed as finitary factors of i.i.d. processes with finite mean coding radii. They are the first colorings known to have these properties. Moreover, we prove that the coding radii have exponential tails, and that the colorings can also be expressed as functions of countable-state Markov chains. We deduce analogous existence statements concerning shifts of finite type and higher-dimensional colorings.", "date": "2020-01", "date_type": "published", "publication": "Annals of Probability", "volume": "48", "number": "1", "publisher": "Institute of Mathematical Statistics", "pagerange": "343-379", "id_number": "CaltechAUTHORS:20210922-193308087", "issn": "0091-1798", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193308087", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/19-AOP1363", "primary_object": { "basename": "1706.09526.pdf", "url": "https://authors.library.caltech.edu/records/reagx-64650/files/1706.09526.pdf" }, "pub_year": "2020", "author_list": "Holroyd, Alexander E.; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/dz2fj-0rp70", "eprint_id": 100543, "eprint_status": "archive", "datestamp": "2023-08-19 19:22:47", "lastmod": "2026-03-09 02:17:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feigin-Boris", "name": { "family": "Feigin", "given": "Boris" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "VOA[M\u2084]", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2020 Published under license by AIP Publishing. \n\nSubmitted: 15 April 2019; Accepted: 5 November 2019; Published Online: 6 January 2020. \n\nThis paper is part of the Special Collection: XIXth International Congress on Mathematical Physics. \n\nWe would like to thank A. Braverman, K. Costello, T. Creutzig, J. Fuchs, A. Gadde, J. Meier, H. Nakajima, N. Paquette, P. Putrov, M. Rapcak, C. Schweigert, J. Teschner, R. Thomas, and E. Witten for valuable discussions and inspiration and F. Ferrari and S. Lee for comments on the manuscript. We also wish to thank the anonymous referee for very useful feedback and many insightful comments. The work of B.F. has been funded by the Russian Academic Excellence Project No. 5-100. The research of B.F. has also been supported by the Russian Science Foundation, Grant Project No. 16-11-10316. The work of S.G. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and in part by the National Science Foundation under Grant No. NSF DMS 1664240.\n\n

Published - 1.5100059.pdf

", "abstract": "We take a peek at a general program that associates vertex (or chiral) algebras to smooth 4-manifolds in such a way that operations on algebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corresponding algebras.", "date": "2020-01", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "61", "number": "1", "publisher": "American Institute of Physics", "pagerange": "Art. No. 012302", "id_number": "CaltechAUTHORS:20200107-142933165", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200107-142933165", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Academic Excellence Project (RAEP)", "grant_number": "5-100" }, { "agency": "Russian Science Foundation", "grant_number": "16-11-10316" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.5100059", "primary_object": { "basename": "1.5100059.pdf", "url": "https://authors.library.caltech.edu/records/dz2fj-0rp70/files/1.5100059.pdf" }, "pub_year": "2020", "author_list": "Feigin, Boris and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/z0gyd-rmz37", "eprint_id": 100596, "eprint_status": "archive", "datestamp": "2023-08-19 19:17:18", "lastmod": "2026-03-17 23:59:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Merz-Konstantin", "name": { "family": "Merz", "given": "Konstantin" } }, { "id": "Siedentop-Heinz", "name": { "family": "Siedentop", "given": "Heinz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Proof of the Strong Scott Conjecture for Chandrasekhar Atoms", "ispublished": "pub", "full_text_status": "public", "keywords": "heavy atoms, ground state density, relativistic Coulomb system, Scott conjecture", "note": "\u00a9 2020 Yokohama Publishers.\n\nManuscript received July 10, 2019; revised November 20, 2020.\n\nDedicated to Yakov Sinai on the occasion of his 85th birthday. \n\nThe authors acknowledge partial support by the U.S. National Science Foundation through grants DMS-1363432 (R.L.F.) and DMS-1665526 (B.S.), by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through grant SI 348/15-1 (H.S.) and through Germany's Excellence Strategy EXC-2111 390814868 (R.L.F., K.M., H.S.) and by the Israeli BSF through grant No. 2014337 (B.S.).\n\n

Accepted Version - 1907.04894v2.pdf

Submitted - p347.pdf

", "abstract": "We consider a large neutral atom of atomic number Z, taking relativistic effects into account by assuming the dispersion relation \u221ac\u00b2p\u00b2+c\u2074. We study the behavior of the one-particle ground state density on the length scale Z\u207b\u00b9 in the limit Z,c\u2192\u221e keeping Z/c fixed and find that the spherically averaged density as well as all individual angular momentum densities separately converge to the relativistic hydrogenic ones. This proves the generalization of the strong Scott conjecture for relativistic atoms and shows, in particular, that relativistic effects occur close to the nucleus. Along the way we prove upper bounds on the relativistic hydrogenic density.", "date": "2020", "date_type": "published", "publication": "Pure and Applied Functional Analysis", "volume": "5", "number": "6", "publisher": "Yokohama Publishers", "pagerange": "1319-1356", "id_number": "CaltechAUTHORS:20200109-110319953", "issn": "2189-3764", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200109-110319953", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "SI 348/15-1" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111 390814868" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.48550/arXiv.1907.04894", "primary_object": { "basename": "1907.04894v2.pdf", "url": "https://authors.library.caltech.edu/records/z0gyd-rmz37/files/1907.04894v2.pdf" }, "related_objects": [ { "basename": "p347.pdf", "url": "https://authors.library.caltech.edu/records/z0gyd-rmz37/files/p347.pdf" } ], "pub_year": "2020", "author_list": "Frank, Rupert L.; Merz, Konstantin; et al." }, { "id": "https://authors.library.caltech.edu/records/dcwj6-3zf74", "eprint_id": 117600, "eprint_status": "archive", "datestamp": "2023-08-22 03:22:35", "lastmod": "2026-03-09 23:57:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" } } ] }, "title": "Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology", "note": "I am grateful to my advisor Fernando Cod\u00e1 Marques for his support and his helpful remarks. I also thank Ian Agol for sharing his former thoughts about these questions related to the study of singularities, and Otis Chodosh, John Lott and Richard Bamler for their interest. \n\nThe author was supported by NSF-DMS-1509027.", "abstract": "We construct spherical space forms (S\u00b3/\u0393,g) with positive scalar curvature and containing no stable embedded minimal surfaces such that the following happens along the Ricci flow starting at (S\u00b3/\u0393,g): a stable embedded minimal 2\u2013sphere appears and a nontrivial singularity occurs. We also give in dimension 3 a general construction of Type I neckpinching and clarify the relationship between stable spheres and nontrivial Type I singularities of the Ricci flow. Some symmetry assumptions prevent the appearance of stable spheres, and this has consequences on the types of singularities which can occur for metrics with these symmetries.", "date": "2019-12-30", "date_type": "published", "publication": "Geometry & Topology", "volume": "23", "number": "7", "publisher": "Mathematical Sciences Publishers", "pagerange": "3501-3535", "id_number": "CaltechAUTHORS:20221026-539155000.13", "issn": "1364-0380", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221026-539155000.13", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1509027" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/gt.2019.23.3501", "pub_year": "2019", "author_list": "Song, Antoine" }, { "id": "https://authors.library.caltech.edu/records/wghbv-c2k62", "eprint_id": 90324, "eprint_status": "archive", "datestamp": "2023-08-19 19:08:44", "lastmod": "2026-03-31 05:29:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Yu-An", "name": { "family": "Chen", "given": "Yu-An" }, "orcid": "0000-0002-8810-9355" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Bosonization in three spatial dimensions and a 2-form gauge theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 American Physical Society. \n\nReceived 7 September 2019; revised manuscript received 21 November 2019; published 16 December 2019. \n\nY.-A.C. thanks Djordje Radicevic for many very helpful discussions. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. A.K. was also supported by the Simons Investigator Award.\n\n

Published - PhysRevB.100.245127.pdf

Submitted - 1807.07081.pdf

", "abstract": "We describe a 3d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 3d spatial lattice to a 2-form Z\u2082 gauge theory with an unusual Gauss law. An important property of this map is that it preserves the locality of the Hamiltonian. The map depends explicitly on the choice of a spin structure of the spatial manifold. We give examples of 3d bosonic systems dual to free fermions. We also describe the corresponding Euclidean lattice models, which is analogous to the Steenrod square term in (3+1)D [compared to the Chern-Simon term in (2+1)D].", "date": "2019-12-15", "date_type": "published", "publication": "Physical Review B", "volume": "100", "number": "24", "publisher": "American Physical Society", "pagerange": "Art. No. 245127", "id_number": "CaltechAUTHORS:20181022-110515479", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181022-110515479", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.100.245127", "primary_object": { "basename": "1807.07081.pdf", "url": "https://authors.library.caltech.edu/records/wghbv-c2k62/files/1807.07081.pdf" }, "related_objects": [ { "basename": "PhysRevB.100.245127.pdf", "url": "https://authors.library.caltech.edu/records/wghbv-c2k62/files/PhysRevB.100.245127.pdf" } ], "pub_year": "2019", "author_list": "Chen, Yu-An and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/p2ny4-2hm61", "eprint_id": 85190, "eprint_status": "archive", "datestamp": "2023-08-19 19:08:38", "lastmod": "2026-03-31 14:54:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Vafaee-F", "name": { "family": "Vafaee", "given": "Faramarz" } } ] }, "title": "Null surgery on knots in L-spaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 American Mathematical Society. \n\nReceived by the editors May 12, 2017, and, in revised form, January 9, 2018, and January 12, 2018. Published electronically: September 23, 2019. \n\nThe first author was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship. The second author was partially supported by an NSF Simons travel grant. \n\nWe are grateful to Kenneth Baker for pointing out Remark 3.2 to us, to Matthew Hedden for his input to Proposition 1.7, to Tye Lidman for helpful conversations, and to Jacob Rasmussen for pointing out a mistake in an earlier draft. We thank the referee for valuable remarks and a thoughtful review.\n\n

Submitted - 1608.07050.pdf

", "abstract": "Let K be a knot in an L-space Y with a Dehn surgery to a surface bundle over S\u00b9. We prove that K is rationally fibered, that is, the knot complement admits a fibration over S\u00b9. As part of the proof, we show that if K C Y has a Dehn surgery to S\u00b9 x S\u00b2, then K is rationally fibered. In the case that K admits some S\u00b9 x S\u00b2 surgery, K is Floer simple, that is, the rank of HFK(Y,K) is equal to the order of H\u2081(Y). By combining the latter two facts, we deduce that the induced contact structure on the ambient manifold Y is tight. In a different direction, we show that if K is a knot in an L-space Y, then any Thurston norm minimizing rational Seifert surface for K extends to a Thurston norm minimizing surface in the manifold obtained by the null surgery on K (i.e., the unique surgery on K with b\u2081 > 0).", "date": "2019-12-15", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "372", "number": "12", "publisher": "American Mathematical Society", "pagerange": "8279-8306", "id_number": "CaltechAUTHORS:20180308-071823523", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180308-071823523", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/7510", "primary_object": { "basename": "1608.07050.pdf", "url": "https://authors.library.caltech.edu/records/p2ny4-2hm61/files/1608.07050.pdf" }, "pub_year": "2019", "author_list": "Ni, Yi and Vafaee, Faramarz" }, { "id": "https://authors.library.caltech.edu/records/1f0pv-rf491", "eprint_id": 99832, "eprint_status": "archive", "datestamp": "2023-08-19 18:55:11", "lastmod": "2026-03-31 14:24:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frisch-J", "name": { "family": "Frisch", "given": "Joshua" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Vahidi-Ferdowsi-P", "name": { "family": "Vahidi Ferdowsi", "given": "Pooya" } } ] }, "title": "Strong amenability and the infinite conjugacy class property", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Springer-Verlag GmbH Germany, part of Springer Nature. \n\nReceived: 16 March 2018; Accepted: 7 June 2019; Published online: 13 July 2019. \n\nThis work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz), and by NSF Grant DMS-1464475. \n\nWe would like to thank Benjamin Weiss and Andrew Zucker for correcting mistakes in earlier drafts of this paper, and to likewise thank an anonymous referee for many corrections and suggestions. We would also like to thank Yair Hartman and Mehrdad Kalantar\nfor drawing our attention to the relation of our results to the unique trace property of group von Neumann algebras.\n\n

Submitted - 1801.04024.pdf

", "abstract": "A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable discrete group is strongly amenable if and only if none of its quotients have the infinite conjugacy class property.", "date": "2019-12", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "218", "number": "3", "publisher": "Springer", "pagerange": "833-851", "id_number": "CaltechAUTHORS:20191114-102021413", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191114-102021413", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "NSF", "grant_number": "DMS-1464475" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-019-00896-z", "primary_object": { "basename": "1801.04024.pdf", "url": "https://authors.library.caltech.edu/records/1f0pv-rf491/files/1801.04024.pdf" }, "pub_year": "2019", "author_list": "Frisch, Joshua; Tamuz, Omer; et al." }, { "id": "https://authors.library.caltech.edu/records/4zn03-g1969", "eprint_id": 86785, "eprint_status": "archive", "datestamp": "2023-08-22 03:04:41", "lastmod": "2026-03-31 05:29:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carrillo-Jos\u00e9-Antonio", "name": { "family": "Carrillo", "given": "Jos\u00e9 A." }, "orcid": "0000-0001-8819-4660" }, { "id": "Delgadino-Mat\u00edas-G", "name": { "family": "Delgadino", "given": "Mat\u00edas G." } }, { "id": "Dolbeault-Jean", "name": { "family": "Dolbeault", "given": "Jean" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hoffmann-Franca", "name": { "family": "Hoffmann", "given": "Franca" }, "orcid": "0000-0002-1182-5521" } ] }, "title": "Reverse Hardy-Littlewood-Sobolev inequalities", "ispublished": "pub", "full_text_status": "public", "keywords": "Reverse Hardy\u2013Littlewood\u2013Sobolev inequalities; Interpolation; Symmetrization; Concentration; Minimizer; Existence of optimal functions; Regularity; Uniqueness; Euler\u2013Lagrange equations; Free energy; Nonlinear diffusion; Mean field equations; Nonlinear springs; Measure valued solutions", "note": "Crown Copyright \u00a9 2019 Published by Elsevier Masson SAS. \n\nReceived 12 July 2018, Available online 10 September 2019. \n\nThis research has been partially supported by the projects EFI, contract ANR-17-CE40-0030 (J.D.) and Kibord, contract ANR-13-BS01-0004 (J.D., F.H.) of the French National Research Agency (ANR), and by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.). The research stay of F.H. in Paris in December 2017 was partially supported by the Simons Foundation and by Mathematisches Forschungsinstitut Oberwolfach. Some of the preliminary investigations were done at the Institute Mittag-Leffler during the fall program Interactions between Partial Differential Equations & Functional Inequalities. The authors thank J.A. Carrillo for preliminary discussions which took place there and R.L.F. thanks the University Paris-Dauphine for hospitality in February 2018.\n\n

Submitted - 1803.06151.pdf

", "abstract": "This paper is devoted to a new family of reverse Hardy\u2013Littlewood\u2013Sobolev inequalities which involve a power law kernel with positive exponent. We investigate the range of the admissible parameters and the properties of the optimal functions. A striking open question is the possibility of concentration which is analyzed and related with free energy functionals and nonlinear diffusion equations involving mean field drifts.", "date": "2019-12", "date_type": "published", "publication": "Journal de Math\u00e9matiques Pures et Appliqu\u00e9es", "volume": "132", "publisher": "Elsevier", "pagerange": "133-165", "id_number": "CaltechAUTHORS:20180604-111058055", "issn": "0021-7824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180604-111058055", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-17-CE40-0030" }, { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-13-BS01-0004" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Simons Foundation" }, { "agency": "Mathematisches Forschungsinstitut Oberwolfach" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.matpur.2019.09.001", "primary_object": { "basename": "1803.06151.pdf", "url": "https://authors.library.caltech.edu/records/4zn03-g1969/files/1803.06151.pdf" }, "pub_year": "2019", "author_list": "Carrillo, Jos\u00e9 A.; Delgadino, Mat\u00edas G.; et al." }, { "id": "https://authors.library.caltech.edu/records/hstwa-7v470", "eprint_id": 100563, "eprint_status": "archive", "datestamp": "2023-08-19 18:46:39", "lastmod": "2026-03-31 15:20:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jitomirskaya-S-Ya", "name": { "family": "Jitomirskaya", "given": "Svetlana" } }, { "id": "Molchanovsimon-S", "name": { "family": "Molchanovsimon", "given": "Stanislav" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Vainberg-B", "name": { "family": "Vainberg", "given": "Boris" } } ] }, "title": "Alexander Gordon", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 European Mathematical Society. \n\nPublished online: 2019-11-18\n\n

Draft - lxvi.pdf

", "abstract": "Alexander (Sasha) Gordon, died in Chicago on May 13, 2019, after a long illness. Sasha was a brilliant mathematician, author of a number of beautiful and original results in diverse fields of spectral theory and other areas of analysis. His insights were behind some of the foundations of almost periodic operators as well as the theme of genericity of singular continuous spectrum developed by B. Simon\nand collaborators. Born in Kharkov, Ukraine, on May 10, 1947, Sasha has had an unusual path in mathematics. At the time of his death, he was an associate professor of mathematics at UNCC. His life story can be viewed as a triumph of human and mathematical spirit over the circumstances.", "date": "2019-11-18", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "9", "number": "4", "publisher": "European Mathematical Society", "pagerange": "1157-1164", "id_number": "CaltechAUTHORS:20200108-134330154", "issn": "1664-039X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200108-134330154", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4171/JST/293", "primary_object": { "basename": "lxvi.pdf", "url": "https://authors.library.caltech.edu/records/hstwa-7v470/files/lxvi.pdf" }, "pub_year": "2019", "author_list": "Jitomirskaya, Svetlana; Molchanovsimon, Stanislav; et al." }, { "id": "https://authors.library.caltech.edu/records/0tjaf-j5g56", "eprint_id": 90635, "eprint_status": "archive", "datestamp": "2023-08-19 18:44:09", "lastmod": "2026-03-31 05:30:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Yu-An", "name": { "family": "Chen", "given": "Yu-An" }, "orcid": "0000-0002-8810-9355" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Turzillo-A", "name": { "family": "Turzillo", "given": "Alex" }, "orcid": "0000-0003-4293-4293" }, { "id": "You-Minyoung", "name": { "family": "You", "given": "Minyoung" } } ] }, "title": "Free and interacting short-range entangled phases of fermions: Beyond the tenfold way", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 American Physical Society. \n\nReceived 3 September 2019; revised manuscript received 3 November 2019; published 18 November 2019. \n\nA.T. is grateful to N. Strickland, M. Grant, and M. Wendt for their answers to the MathOverflow question Ref. [23]. This research was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of A.K. was partly performed at the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-1607611. A.K. was also supported by the Simons Investigator Award.\n\n

Published - PhysRevB.100.195128.pdf

Submitted - 1809.04958.pdf

", "abstract": "We extend the periodic table of phases of free fermions in the tenfold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary symmetry G in an arbitrary dimension. The classification is described as a function of the real representation theory of \nG and the data of the original periodic table. We also systematically study in low dimensions the relationship between the free invariants and the invariants of short-range entangled interacting phases of fermions. Namely we determine whether a given symmetry protected phase of free fermions is destabilized by sufficiently strong interactions or it remains stable even in the presence of interactions. We also determine which interacting fermionic phases cannot be realized by free fermions. Examples of both destabilized free phases and intrinsically interacting phases are common in all dimensions.", "date": "2019-11-15", "date_type": "published", "publication": "Physical Review B", "volume": "100", "number": "19", "publisher": "American Physical Society", "pagerange": "Art. No. 195128", "id_number": "CaltechAUTHORS:20181105-095310279", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181105-095310279", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.100.195128", "primary_object": { "basename": "1809.04958.pdf", "url": "https://authors.library.caltech.edu/records/0tjaf-j5g56/files/1809.04958.pdf" }, "related_objects": [ { "basename": "PhysRevB.100.195128.pdf", "url": "https://authors.library.caltech.edu/records/0tjaf-j5g56/files/PhysRevB.100.195128.pdf" } ], "pub_year": "2019", "author_list": "Chen, Yu-An; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/94psq-dhd56", "eprint_id": 95605, "eprint_status": "archive", "datestamp": "2023-08-19 18:39:40", "lastmod": "2026-03-31 05:52:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00f6nig-T", "name": { "family": "K\u00f6nig", "given": "Tobias" } } ] }, "title": "Singular solutions to a semilinear biharmonic equation with a general critical nonlinearity", "ispublished": "pub", "full_text_status": "public", "keywords": "Biharmonic equation, singular solutions, method of moving planes", "note": "\u00a9 2019 EMS Publishing House. \n\nPublished online: 2019-11-05. \n\nPartial support through US National Science Foundation grant DMS-1363432 (R.L.F.) and Studienstiftung des deutschen Volkes (T.K.) is acknowledged.\n\n

Submitted - 1903.02385.pdf

", "abstract": "We consider positive solutions u of the semilinear biharmonic equation \u0394\u00b2u = |x|\u2212^(n+4)/2g(|x|^(n\u22124)/2u) in R^n\u2216{0} with non-removable singularities at the origin. Under natural assumptions on the nonlinearity g, we show that |x|^(n\u22124)/2u is a periodic function of ln|x| and we classify all such solutions.", "date": "2019-11-05", "date_type": "published", "publication": "Rendiconti Lincei - Matematica e Applicazioni", "volume": "30", "number": "4", "publisher": "European Mathematical Society", "pagerange": "817-846", "id_number": "CaltechAUTHORS:20190520-133342030", "issn": "1120-6330", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-133342030", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Studienstiftung des deutschen Volkes" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/RLM/871", "primary_object": { "basename": "1903.02385.pdf", "url": "https://authors.library.caltech.edu/records/94psq-dhd56/files/1903.02385.pdf" }, "pub_year": "2019", "author_list": "Frank, Rupert L. and K\u00f6nig, Tobias" }, { "id": "https://authors.library.caltech.edu/records/crpct-nzd05", "eprint_id": 66609, "eprint_status": "archive", "datestamp": "2023-08-19 18:24:07", "lastmod": "2026-03-31 05:06:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "Exact Solutions of 2d Supersymmetric Gauge Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: October 20, 2019; Accepted: November 2, 2019; Published: November 29, 2019. \n\nWe would like to thank D. Gaiotto, B. Jia, I. Melnikov, V. Schomerus, and E. Sharpe for useful discussions. A.G. would also like to thank the Kavli Institute for Theoretical Physics for providing a hospitable and enjoyable work environment during the late stages of this project. The work of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02. The work of P.P. is supported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - Gadde2019_Article_ExactSolutionsOf2dSupersymmetr.pdf

Submitted - 1404.5314.pdf

", "abstract": "We study dynamics of two-dimensional non-abelian gauge theories with N = (0, 2) supersymmetry that include N = (0, 2) supersymmetric QCD and its generaliza- tions. In particular, we present the phase diagram of N = (0, 2) SQCD and determine its massive and low-energy spectrum. We find that the theory has no mass gap, a nearly constant distribution of massive states, and lots of massless states that in general flow to an interacting CFT. For a range of parameters where supersymmetry is not dynamically broken at low energies, we give a complete description of the low-energy physics in terms of 2d N = (0, 2) SCFTs using anomaly matching and modular invariance. Our construction provides a vast landscape of new N = (0, 2) SCFTs which, for small values of the central charge, could be used for building novel heterotic models with no moduli and, for large values of the central charge, could be dual to AdS\u2083 string vacua.", "date": "2019-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 174", "id_number": "CaltechAUTHORS:20160503-085246813", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-085246813", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "John A. McCone Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "PHY-1050729" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP11(2019)174", "primary_object": { "basename": "1404.5314.pdf", "url": "https://authors.library.caltech.edu/records/crpct-nzd05/files/1404.5314.pdf" }, "related_objects": [ { "basename": "Gadde2019_Article_ExactSolutionsOf2dSupersymmetr.pdf", "url": "https://authors.library.caltech.edu/records/crpct-nzd05/files/Gadde2019_Article_ExactSolutionsOf2dSupersymmetr.pdf" } ], "pub_year": "2019", "author_list": "Gadde, Abhijit; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/9cr5s-8ps38", "eprint_id": 95607, "eprint_status": "archive", "datestamp": "2023-08-19 18:26:33", "lastmod": "2026-03-31 15:54:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Pushnitski-Alexander", "name": { "family": "Pushnitski", "given": "Alexander" }, "orcid": "0000-0001-5622-7210" } ] }, "title": "Schatten class conditions for functions of Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Springer Nature Switzerland AG. \n\nFirst Online: 09 September 2019. \n\nPartial support by U.S. National Science Foundation DMS-1363432 (R.L.F.) is acknowledged. A.P. is grateful to Caltech for hospitality.\n\n

Submitted - 1901.05789.pdf

", "abstract": "We consider the difference f(H\u2081)\u2212f(H\u2080), where H\u2080 = \u2212\u0394 and H\u2081 = \u2212\u0394+V are the free and the perturbed Schr\u00f6dinger operators in L\u00b2(R^d), and V is a real-valued short range potential. We give a sharp sufficient condition for this difference to belong to a given Schatten class S_p, depending on the rate of decay of the potential and on the smoothness of f (stated in terms of the membership in a Besov class). In particular, for p > 1 we allow for some unbounded functions f.", "date": "2019-11", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "20", "number": "11", "publisher": "Springer", "pagerange": "3543-3562", "id_number": "CaltechAUTHORS:20190520-133945892", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-133945892", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-019-00838-8", "primary_object": { "basename": "1901.05789.pdf", "url": "https://authors.library.caltech.edu/records/9cr5s-8ps38/files/1901.05789.pdf" }, "pub_year": "2019", "author_list": "Frank, Rupert L. and Pushnitski, Alexander" }, { "id": "https://authors.library.caltech.edu/records/mcd2a-8fa05", "eprint_id": 111004, "eprint_status": "archive", "datestamp": "2023-08-19 18:09:52", "lastmod": "2026-03-31 15:55:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Peres-Yuval", "name": { "family": "Peres", "given": "Yuval" }, "orcid": "0000-0001-5456-6323" } ] }, "title": "The component graph of the uniform spanning forest: transitions in dimensions 9,10,11, ...", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 30 June 2017 / Revised: 4 October 2018 / Published online: 23 November 2018. \n\nThis work was carried out while T.H. was an intern at Microsoft Research, Redmond. T.H. thanks Mathav Murugan for many useful discussions on heat kernel estimates. We thank Omer Angel for his comments on an earlier draft of this manuscript, and thank the anonymous referee for many helpful comments and corrections.\n\n

Published - Hutchcroft-Peres2019_Article_TheComponentGraphOfTheUniformS.pdf

Submitted - 1702.05780.pdf

", "abstract": "We prove that the uniform spanning forests of Z^d and Z^\u2113 have qualitatively different connectivity properties whenever \u2113 > d \u2265 4. In particular, we consider the graph formed by contracting each tree of the uniform spanning forest down to a single vertex, which we call the component graph. We introduce the notion of ubiquitous subgraphs and show that the set of ubiquitous subgraphs of the component graph changes whenever the dimension changes and is above 8. To separate dimensions 5, 6, 7, and 8, we prove a similar result concerning ubiquitous subhypergraphs in the component hypergraph. Our result sharpens a theorem of Benjamini, Kesten, Peres, and Schramm, who proved that the diameter of the component graph increases by one every time the dimension increases by four.", "date": "2019-10", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "175", "number": "1-2", "publisher": "Springer", "pagerange": "141-208", "id_number": "CaltechAUTHORS:20210922-193309372", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309372", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-018-0884-3", "primary_object": { "basename": "1702.05780.pdf", "url": "https://authors.library.caltech.edu/records/mcd2a-8fa05/files/1702.05780.pdf" }, "related_objects": [ { "basename": "Hutchcroft-Peres2019_Article_TheComponentGraphOfTheUniformS.pdf", "url": "https://authors.library.caltech.edu/records/mcd2a-8fa05/files/Hutchcroft-Peres2019_Article_TheComponentGraphOfTheUniformS.pdf" } ], "pub_year": "2019", "author_list": "Hutchcroft, Tom and Peres, Yuval" }, { "id": "https://authors.library.caltech.edu/records/k8e0q-x5c22", "eprint_id": 99305, "eprint_status": "archive", "datestamp": "2023-08-22 02:36:57", "lastmod": "2026-03-31 04:50:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cheng-Miranda-C-N", "name": { "family": "Cheng", "given": "Miranda C. N." } }, { "id": "Chun-Sungbong", "name": { "family": "Chun", "given": "Sungbong" } }, { "id": "Ferrari-F", "name": { "family": "Ferrari", "given": "Francesca" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Harrison-S-M", "name": { "family": "Harrison", "given": "Sarah M." } } ] }, "title": "3d modularity", "ispublished": "pub", "full_text_status": "public", "keywords": "Chern-Simons Theories; Conformal Field Theory; M-Theory; Nonperturbative Effects", "note": "\u00a9 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: June 18, 2019; Accepted: August 27, 2019; Published: October 3, 2019. \n\nWe thank D. Adamovic, T. Creutzig, T. Dimofte, J. Duncan, P. Etingof, B. Feigin, D. Kazhdan, S. L\u00f6brich, C. Manolescu, D. Pei, P. Putrov, L. Rolen, C. Schweigert, C. Vafa and D. Zagier for helpful discussions. The work of M.C. is supported by ERC starting grant H2020 ERC StG #640159. S.C. and S.G. are supported by the Walter Burke Institute for Theoretical Physics, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664240. The work of S.C. is also supported in part by Samsung Scholarship. The work of S.G. is also supported in part by Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No. 14.641.31.0001. The work of F.F. is supported in part by the MIUR-SIR grant RBSI1471GJ \"Quantum Field Theories at Strong Coupling: Exact Computations and Applications\". S.H. is supported by the National Science and Engineering Council of Canada, an FRQNT new university researchers start-up grant, and the Canada Research Chairs program. M.C. would also like to thank LPTHE, Jussieu Paris, for hospitality during the final stage of this work.\n\n

Published - Cheng2019_Article_3dModularity.pdf

Submitted - 1809.10148.pdf

", "abstract": "We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d N = 2 theories where such structures a priori are not manifest. These modular structures include: mock modular forms, SL(2,\u2124) Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.", "date": "2019-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 10", "id_number": "CaltechAUTHORS:20191016-132239333", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191016-132239333", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "640159" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "Samsung Scholarship" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "14.641.31.0001" }, { "agency": "Ministero dell'Istruzione, dell'Universita e della Ricerca (MIUR)", "grant_number": "RBSI1471GJ" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Fonds de recherche du Qu\u00e9bec - Nature et technologies (FRQNT)" }, { "agency": "Canada Research Chairs Program" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/jhep10(2019)010", "primary_object": { "basename": "1809.10148.pdf", "url": "https://authors.library.caltech.edu/records/k8e0q-x5c22/files/1809.10148.pdf" }, "related_objects": [ { "basename": "Cheng2019_Article_3dModularity.pdf", "url": "https://authors.library.caltech.edu/records/k8e0q-x5c22/files/Cheng2019_Article_3dModularity.pdf" } ], "pub_year": "2019", "author_list": "Cheng, Miranda C. N.; Chun, Sungbong; et al." }, { "id": "https://authors.library.caltech.edu/records/cddrf-m4404", "eprint_id": 97017, "eprint_status": "archive", "datestamp": "2023-08-19 17:52:22", "lastmod": "2026-03-31 05:55:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benjamin-N", "name": { "family": "Benjamin", "given": "Nathan" }, "orcid": "0000-0003-3661-6563" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Shao-Shu-Heng", "name": { "family": "Shao", "given": "Shu-Heng" }, "orcid": "0000-0003-1294-2786" }, { "id": "Wang-Yifan", "name": { "family": "Wang", "given": "Yifan" }, "orcid": "0000-0001-9965-9777" } ] }, "title": "Light-cone modular bootstrap and pure gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3. \n\nReceived 7 July 2019; published 23 September 2019. \n\nWe thank S. Collier, T. Hartman, S. Kachru, Z. Komargodski, Y.-H. Lin, R. Mahajan, A. Maloney, H. Maxfield, D. Mazac, B. Mukhametzhanov, E. Perlmutter, L. Rastelli, D. Simmons-Duffin, D. Stanford, H. Verlinde, and E. Witten for interesting discussions. We thank T. Hartman, C. Keller, A. Maloney, H. Maxfield, and X. Yin for comments on a draft. The work of N. B. is supported in part by the Simons Foundation Grant No. 488653. The work of H. O. is supported in part by U.S. Department of Energy Grant No. DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. The work of S. H. S. is supported by the National Science Foundation Grant No. PHY-1606531 and by the Roger Dashen Membership. The work of Y.W. is supported in part by the U.S. NSF under Grant No. PHY-1620059 and by the Simons Foundation Grant No. 488653. N. B. and H. O. thank the Aspen Center for Theoretical Physics, which is supported by the National Science Foundation Grant No. PHY-1607611, where part of this work was done.\n\n

Published - PhysRevD.100.066029.pdf

Submitted - 1906.04184.pdf

", "abstract": "We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the light-cone limit. By recursively solving the modular crossing equations associated with different PSL(2,Z) elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over PSL(2,Z) elements, whose leading term generalizes the usual Cardy formula to a wider regime. Rather curiously, the contribution to the density of states from the vacuum becomes negative in a specific limit, which can be canceled by that from a nonvacuum Virasoro primary whose twist is no bigger than c\u22121/16. This suggests a new upper bound of c\u22121/16 on the twist gap in any c>1 compact, unitary conformal field theory with a vacuum, which would in particular imply that pure AdS_3 gravity does not exist. We confirm this negative density of states in the pure gravity partition function by Maloney, Witten, and Keller. We generalize our discussion to theories with N=(1,1) supersymmetry and find similar results.", "date": "2019-09-15", "date_type": "published", "publication": "Physical Review D", "volume": "100", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066029", "id_number": "CaltechAUTHORS:20190709-155709037", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190709-155709037", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "488653" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1606531" }, { "agency": "NSF", "grant_number": "PHY-1620059" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2019-020", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.100.066029", "primary_object": { "basename": "1906.04184.pdf", "url": "https://authors.library.caltech.edu/records/cddrf-m4404/files/1906.04184.pdf" }, "related_objects": [ { "basename": "PhysRevD.100.066029.pdf", "url": "https://authors.library.caltech.edu/records/cddrf-m4404/files/PhysRevD.100.066029.pdf" } ], "pub_year": "2019", "author_list": "Benjamin, Nathan; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/4264h-6jw70", "eprint_id": 111003, "eprint_status": "archive", "datestamp": "2023-08-19 17:51:37", "lastmod": "2026-03-31 05:33:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Nachmias-Asaf", "name": { "family": "Nachmias", "given": "Asaf" }, "orcid": "0000-0002-4852-5645" } ] }, "title": "Uniform spanning forests of planar graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. \n\nReceived 24 January 2018; accepted 3 March 2019. \n\nTH thanks Tel Aviv University and both authors thank the Issac Newton Institute, where part of this work was carried out, for their hospitality. We also thank Tyler Helmuth for finding several typos in an earlier version of this manuscript. Images of circle packings were created with Ken Stephenson's CirclePack software [51]. This project was supported by ERC starting grant RADNGEOM 676970.\n\n

Published - uniform-spanning-forests-of-planar-graphs.pdf

Submitted - 1603.07320.pdf

", "abstract": "We prove that the free uniform spanning forest of any bounded degree proper plane graph is connected almost surely, answering a question of Benjamini, Lyons, Peres and Schramm. We provide a quantitative form of this result, calculating the critical exponents governing the geometry of the uniform spanning forests of transient proper plane graphs with bounded degrees and codegrees. We find that the same exponents hold universally over this entire class of graphs provided that measurements are made using the hyperbolic geometry of their circle packings rather than their usual combinatorial geometry.", "date": "2019-09-13", "date_type": "published", "publication": "Forum Mathetmatics, Sigma", "volume": "7", "publisher": "Cambridge University Press", "pagerange": "Art. No. e29", "id_number": "CaltechAUTHORS:20210922-193309305", "issn": "2050-5094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309305", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "676970" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/fms.2019.14", "primary_object": { "basename": "1603.07320.pdf", "url": "https://authors.library.caltech.edu/records/4264h-6jw70/files/1603.07320.pdf" }, "related_objects": [ { "basename": "uniform-spanning-forests-of-planar-graphs.pdf", "url": "https://authors.library.caltech.edu/records/4264h-6jw70/files/uniform-spanning-forests-of-planar-graphs.pdf" } ], "pub_year": "2019", "author_list": "Hutchcroft, Tom and Nachmias, Asaf" }, { "id": "https://authors.library.caltech.edu/records/m6mec-31e56", "eprint_id": 111002, "eprint_status": "archive", "datestamp": "2023-08-19 17:41:35", "lastmod": "2026-03-31 15:36:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Self-avoiding walk on nonunimodular transitive graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Bubble diagram, mean-field, nonamenable, Nonunimodular, Self-avoiding walk, transitive graph", "note": "\u00a9 2019 Institute of Mathematical Statistics. \n\nReceived: 1 September 2017; Revised: 1 June 2018; Published: September 2019. First available in Project Euclid: 22 October 2019. \n\nThis work was carried out while the author was an intern at Microsoft Research, Redmond. We thank Omer Angel for improving Lemma 3.4 by a factor of 4. We also thank Tyler Helmuth for helpful discussions, and thank Gordon Slade and Hugo Duminil-Copin for comments on an earlier draft, and thank the anonymous referee for several helpful suggestions.\n\n

Accepted Version - 1709.10515.pdf

", "abstract": "We study self-avoiding walk on graphs whose automorphism group has a transitive nonunimodular subgroup. We prove that self-avoiding walk is ballistic, that the bubble diagram converges at criticality, and that the critical two-point function decays exponentially in the distance from the origin. This implies that the critical exponent governing the susceptibility takes its mean-field value, and hence that the number of self-avoiding walks of length n is comparable to the nth power of the connective constant. We also prove that the same results hold for a large class of repulsive walk models with a self-intersection based interaction, including the weakly self-avoiding walk. All of these results apply in particular to the product T_k \u00d7 Z^d of a k-regular tree (k \u2265 3) with Z^d, for which these results were previously only known for large k.", "date": "2019-09", "date_type": "published", "publication": "Annals of Probability", "volume": "47", "number": "5", "publisher": "Institute of Mathematical Statistics", "pagerange": "2801-2829", "id_number": "CaltechAUTHORS:20210922-193309236", "issn": "0091-1798", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309236", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/18-AOP1322", "primary_object": { "basename": "1709.10515.pdf", "url": "https://authors.library.caltech.edu/records/m6mec-31e56/files/1709.10515.pdf" }, "pub_year": "2019", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/q05gg-p4716", "eprint_id": 95072, "eprint_status": "archive", "datestamp": "2023-08-22 02:20:09", "lastmod": "2026-03-31 15:15:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-Elliott-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Periodic energy minimizers for a one-dimensional liquid drop model", "ispublished": "pub", "full_text_status": "public", "keywords": "Liquid drop model; Coulomb system; Periodicity; Thermodynamic limit", "note": "\u00a9 2019 The Author(s). \n\nReceived: 19 August 2018; Revised: 14 March 2019; Accepted: 1 April 2019; First Online: 29 April 2019. \n\nCompliance with ethical standards. \n\nOn behalf of all authors, the corresponding author states that there is no conflict of interest. \n\nU.S. National Science Foundation Grants DMS-1363432 (R.L.F.) and PHY-1265118 (E.H.L.) are acknowledged.\n\n

Submitted - 1808.06172.pdf

", "abstract": "We reprove a result by Ren and Wei concerning the periodicity of minimizers of a one-dimensional liquid drop model in the neutral case. Our proof works for general boundary conditions and also in the non-neutral case.", "date": "2019-09", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "109", "number": "9", "publisher": "Springer", "pagerange": "2069-2081", "id_number": "CaltechAUTHORS:20190429-123953827", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190429-123953827", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-019-01171-1", "primary_object": { "basename": "1808.06172.pdf", "url": "https://authors.library.caltech.edu/records/q05gg-p4716/files/1808.06172.pdf" }, "pub_year": "2019", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/09pcx-arn97", "eprint_id": 95590, "eprint_status": "archive", "datestamp": "2023-08-19 17:17:04", "lastmod": "2026-03-31 16:05:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Spodyneiko-L", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "Absence of Energy Currents in an Equilibrium State and Chiral Anomalies", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 American Physical Society. \n\nReceived 27 April 2019; revised manuscript received 21 May 2019; published 6 August 2019. \n\nA. K. is grateful to H. Watanabe for a discussion of Bloch's theorem. This research was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DESC0011632. A. K. was also supported by the Simons Investigator Award.\n\n

Published - PhysRevLett.123.060601.pdf

Submitted - 1904.05491.pdf

", "abstract": "A long time ago, Bloch showed that in a system of interacting nonrelativistic particles the net particle-number current must vanish in any equilibrium state. Bloch's argument does not generalize easily to the energy current. We devise an alternative argument which proves the vanishing of the net energy currents in equilibrium states of lattice systems as well as systems of nonrelativistic particles with finite-range potential interactions. We discuss some applications of these results. In particular, we show that neither a one-dimensional (1D) lattice system nor a 1D system of nonrelativistic particles with finite-range potential interactions can flow to a conformal field theory with unequal left-moving and right-moving central charges.", "date": "2019-08-09", "date_type": "published", "publication": "Physical Review Letters", "volume": "123", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 060601", "id_number": "CaltechAUTHORS:20190520-091208855", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-091208855", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.123.060601", "primary_object": { "basename": "1904.05491.pdf", "url": "https://authors.library.caltech.edu/records/09pcx-arn97/files/1904.05491.pdf" }, "related_objects": [ { "basename": "PhysRevLett.123.060601.pdf", "url": "https://authors.library.caltech.edu/records/09pcx-arn97/files/PhysRevLett.123.060601.pdf" } ], "pub_year": "2019", "author_list": "Kapustin, Anton and Spodyneiko, Lev" }, { "id": "https://authors.library.caltech.edu/records/4z5mg-qag42", "eprint_id": 95597, "eprint_status": "archive", "datestamp": "2023-08-22 02:06:32", "lastmod": "2026-03-31 06:01:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Pushnitski-A", "name": { "family": "Pushnitski", "given": "Alexander" } } ] }, "title": "Kato smoothness and functions of perturbed self-adjoint operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Kato smoothness; Schatten classes; Double operator integrals", "note": "\u00a9 2019 Elsevier Inc. \n\nReceived 25 January 2019, Revised 25 April 2019, Accepted 27 April 2019, Available online 20 May 2019.\n\n

Submitted - 1901.04731.pdf

", "abstract": "We consider the difference f(H_1)\u2212f(H_0) for self-adjoint operators H0 and H1acting in a Hilbert space. We establish a new class of estimates for the operator norm and the Schatten class norms of this difference. Our estimates utilise ideas of scattering theory and involve conditions on H_0 and H_1 in terms of the Kato smoothness. They allow for a much wider class of functions f (including some unbounded ones) than previously available results. As an important technical tool, we propose a new notion of Schatten class valued smoothness and develop a new framework for double operator integrals.", "date": "2019-07-31", "date_type": "published", "publication": "Advances in Mathematics", "volume": "351", "publisher": "Elsevier", "pagerange": "343-387", "id_number": "CaltechAUTHORS:20190520-102006314", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-102006314", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2019.05.002", "primary_object": { "basename": "1901.04731.pdf", "url": "https://authors.library.caltech.edu/records/4z5mg-qag42/files/1901.04731.pdf" }, "pub_year": "2019", "author_list": "Frank, Rupert L. and Pushnitski, Alexander" }, { "id": "https://authors.library.caltech.edu/records/5qpfg-kkk58", "eprint_id": 95603, "eprint_status": "archive", "datestamp": "2023-08-19 16:28:34", "lastmod": "2026-03-31 15:46:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Non-spherical equilibrium shapes in the liquid drop model", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Published under license by AIP Publishing. \n\nSubmitted: 11 March 2019; Accepted: 15 June 2019; Published Online: 16 July 2019. \n\nThe author is grateful for the invitation to give a talk at the ICMP 2018 in Montreal. He thanks T. K\u00f6nig for comments on an early version of the manuscript. Partial support from the US National Science Foundation (Grant No. DMS-1363432) is acknowledged.\n\n

Published - 1.5095603.pdf

Submitted - 1903.04344.pdf

", "abstract": "We prove the existence of a family of volume-constrained critical points of the liquid drop functional, which are cylindrically but not spherically symmetric. This family bifurcates from the ball and exchanges stability with it. We justify a formula of Bohr and Wheeler for the energy of these sets.", "date": "2019-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "60", "number": "7", "publisher": "American Institute of Physics", "pagerange": "Art. No. 071506", "id_number": "CaltechAUTHORS:20190520-132849818", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190520-132849818", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.5095603", "primary_object": { "basename": "1.5095603.pdf", "url": "https://authors.library.caltech.edu/records/5qpfg-kkk58/files/1.5095603.pdf" }, "related_objects": [ { "basename": "1903.04344.pdf", "url": "https://authors.library.caltech.edu/records/5qpfg-kkk58/files/1903.04344.pdf" } ], "pub_year": "2019", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/t636j-2fq90", "eprint_id": 97403, "eprint_status": "archive", "datestamp": "2023-08-19 16:32:46", "lastmod": "2026-03-31 05:35:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frisch-J", "name": { "family": "Frisch", "given": "Joshua" } }, { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Vahidi-Ferdowsi-P", "name": { "family": "Vahidi Ferdowsi", "given": "Pooya" } } ] }, "title": "Choquet-Deny groups and the infinite conjugacy class property", "ispublished": "pub", "full_text_status": "public", "keywords": "Furstenberg-Poisson boundary, random walks, harmonic functions", "note": "\u00a9 2019 Department of Mathematics, Princeton University. \n\nJ. Frisch was supported by NSF Grant DMS-1464475. Y. Hartman was partially supported by the Israel Science Foundation (grant No. 1175/18). He is grateful for the support of Northwestern University, where he was a postdoctoral fellow when most of this research was conducted. O. Tamuz was supported by a grant from the Simons Foundation (#419427).\n\n

Submitted - 1802.00751.pdf

", "abstract": "A countable discrete group G is called Choquet-Deny if for every non-degenerate probability measure \u03bc on G, it holds that all bounded \u03bc-harmonic functions are constant. We show that a finitely generated group G is Choquet-Deny if and only if it is virtually nilpotent. For general countable discrete groups, we show that G is Choquet-Deny if and only if none of its quotients has the infinite conjugacy class property. Moreover, when G is not Choquet-Deny, then this is witnessed by a symmetric, finite entropy, non-degenerate measure.", "date": "2019-07", "date_type": "published", "publication": "Annals of Mathematics", "volume": "190", "number": "1", "publisher": "Princeton University", "pagerange": "307-320", "id_number": "CaltechAUTHORS:20190725-090144871", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190725-090144871", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1464475" }, { "agency": "Israel Science Foundation", "grant_number": "1175/18" }, { "agency": "Northwestern University" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2019.190.1.5", "primary_object": { "basename": "1802.00751.pdf", "url": "https://authors.library.caltech.edu/records/t636j-2fq90/files/1802.00751.pdf" }, "pub_year": "2019", "author_list": "Frisch, Joshua; Hartman, Yair; et al." }, { "id": "https://authors.library.caltech.edu/records/js1vh-fqt50", "eprint_id": 95119, "eprint_status": "archive", "datestamp": "2023-08-22 01:52:06", "lastmod": "2026-03-30 23:53:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mart\u00ednez\u2013Finkelshtein-A", "name": { "family": "Mart\u00ednez\u2013Finkelshtein", "given": "Andrei" } }, { "id": "Simanek-B", "name": { "family": "Simanek", "given": "Brian" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Poncelet's theorem; Blaschke products; OPUC; POPUC; Numerical range", "note": "\u00a9 2019 Elsevier. \n\nReceived 31 October 2018, Revised 27 March 2019, Accepted 7 April 2019, Available online 30 April 2019. \n\nCommunicated by D. Stroock. \n\nResearch supported in part by the Spanish Government and the European Regional Development Fund (grant MTM2017-89941-P), Junta de Andaluc\u00eda (research group FQM-229 and Instituto Interuniversitario Carlos I de F\u00edsica Te\u00f3rica y Computacional), and by the University of Almer\u00eda (Campus de Excelencia Internacional del Mar CEIMAR). \n\nResearch supported in part by NSF grant DMS-1665526 and in part by Israeli BSF Grant No. 2014337. \n\nB.S. would like to thank Fritz Gesztesy and Lance Littlejohn for the invitation to visit Baylor where our collaboration was begun.\n\n

Accepted Version - 1810.13357.pdf

", "abstract": "There has been considerable recent literature connecting Poncelet's theorem to ellipses, Blaschke products and numerical ranges, summarized, for example, in the recent book [16]. We show how those results can be understood using ideas from the theory of orthogonal polynomials on the unit circle (OPUC) and, in turn, can provide new insights to the theory of OPUC.", "date": "2019-06-20", "date_type": "published", "publication": "Advances in Mathematics", "volume": "349", "publisher": "Elsevier", "pagerange": "992-1035", "id_number": "CaltechAUTHORS:20190430-104322593", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190430-104322593", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministerio de Ciencia e Innovaci\u00f3n (MCINN)", "grant_number": "MTM2017-89941-P" }, { "agency": "European Regional Development Fund" }, { "agency": "Junta de Andaluc\u00eda", "grant_number": "FQM-229" }, { "agency": "Instituto Interuniversitario Carlos I de F\u00edsica Te\u00f3rica y Computacional" }, { "agency": "University of Almer\u00eda" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.aim.2019.04.027", "primary_object": { "basename": "1810.13357.pdf", "url": "https://authors.library.caltech.edu/records/js1vh-fqt50/files/1810.13357.pdf" }, "pub_year": "2019", "author_list": "Mart\u00ednez\u2013Finkelshtein, Andrei; Simanek, Brian; et al." }, { "id": "https://authors.library.caltech.edu/records/exzam-6kr78", "eprint_id": 111005, "eprint_status": "archive", "datestamp": "2023-08-19 16:09:37", "lastmod": "2026-03-31 16:02:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Percolation on hyperbolic graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: October 18, 2018. Accepted: March 25, 2019. \n\nWe thank Omer Angel and Jonathan Hermon for helpful discussions. We also thank Itai Benjamini, Elisabetta Candellero, Jonathan Hermon, Gady Kozma, Russ Lyons, Asaf Nachmias, Vincent Tassion, and Henry Wilton for useful comments on earlier versions of the manuscript. We thank Asaf Nachmias in particular for his careful reading of the technical parts of the paper.\n\n

Published - Hutchcroft2019_Article_PercolationOnHyperbolicGraphs.pdf

Accepted Version - 1804.10191.pdf

", "abstract": "We prove that Bernoulli bond percolation on any nonamenable, Gromov hyperbolic, quasi-transitive graph has a phase in which there are infinitely many infinite clusters, verifying a well-known conjecture of Benjamini and Schramm (1996) under the additional assumption of hyperbolicity. In other words, we show that p_c < p_u for any such graph. Our proof also yields that the triangle condition \u2207_p-c < \u221e holds at criticality on any such graph, which is known to imply that several critical exponents exist and take their mean-field values. This gives the first family of examples of one-ended groups all of whose Cayley graphs are proven to have mean-field critical exponents for percolation.", "date": "2019-06", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "29", "number": "3", "publisher": "Springer", "pagerange": "766-810", "id_number": "CaltechAUTHORS:20210922-193309440", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309440", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-019-00498-0", "primary_object": { "basename": "1804.10191.pdf", "url": "https://authors.library.caltech.edu/records/exzam-6kr78/files/1804.10191.pdf" }, "related_objects": [ { "basename": "Hutchcroft2019_Article_PercolationOnHyperbolicGraphs.pdf", "url": "https://authors.library.caltech.edu/records/exzam-6kr78/files/Hutchcroft2019_Article_PercolationOnHyperbolicGraphs.pdf" } ], "pub_year": "2019", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/pdq5s-axw36", "eprint_id": 93186, "eprint_status": "archive", "datestamp": "2023-08-19 16:00:26", "lastmod": "2026-03-31 15:56:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Gamma spaces and information", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Elsevier B.V. \n\nReceived 3 September 2018, Revised 5 February 2019, Accepted 5 February 2019, Available online 21 February 2019. \n\nThe author is extremely grateful to Tobias Fritz for many useful discussions and for providing many comments and suggestions. She also thanks Paolo Aluffi, Tom Leinster, and Jack Morava for helpful comments. The author is partially supported by NSF grant DMS-1707882, and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics.\n\n

Submitted - 1807.05314.pdf

", "abstract": "We investigate the role of Segal's Gamma-spaces in the context of classical and quantum information, based on categories of finite probabilities with stochastic maps and density matrices with quantum channels. The information loss functional extends to the setting of probabilistic Gamma-spaces considered here. The Segal construction of connective spectra from Gamma-spaces can be used in this setting to obtain spectra associated to certain categories of gapped systems.", "date": "2019-06", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "140", "publisher": "Elsevier", "pagerange": "26-55", "id_number": "CaltechAUTHORS:20190222-112740050", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190222-112740050", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2019.02.004", "primary_object": { "basename": "1807.05314.pdf", "url": "https://authors.library.caltech.edu/records/pdq5s-axw36/files/1807.05314.pdf" }, "pub_year": "2019", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/mqmcj-qeh56", "eprint_id": 97055, "eprint_status": "archive", "datestamp": "2023-08-19 16:05:18", "lastmod": "2026-03-31 14:47:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Yu-I", "name": { "family": "Manin", "given": "Yu. I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "M." }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Asymptotic bounds for spherical codes", "ispublished": "pub", "full_text_status": "public", "keywords": "error-correcting codes, spherical codes, asymptotic bounds", "note": "\u00a9 2019 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. \n\nReceived 27 November 2017. \n\nThe second author is supported by NSF grant DMS-1707882 and NSERC grant RGPIN-2018-04937.\n\n

Submitted - 1801.01552.pdf

", "abstract": "The set of all error-correcting codes C over a fixed finite alphabet F of cardinality q determines the set of code points in the unit square [0,1]^2 with coordinates (R(C), \u03b4(C)):= (relative transmission rate, relative minimal distance). The central problem of the theory of such codes consists in maximising simultaneously the transmission rate of the code and the relative minimum Hamming distance between two different code words. The classical approach to this problem explored in vast literature consists in inventing explicit constructions of \"good codes\" and comparing new classes of codes with earlier ones.\nA less classical approach studies the geometry of the whole set of code points (R, \u03b4) (with q fixed), at first independently of its computability properties, and only afterwards turning to problems of computability, analogies with statistical physics, and so on.\nThe main purpose of this article consists in extending this latter strategy to the domain of spherical codes.", "date": "2019-06", "date_type": "published", "publication": "Izvestiya: Mathematics", "volume": "83", "number": "3", "publisher": "IOP Publishing", "pagerange": "540-564", "id_number": "CaltechAUTHORS:20190711-104459099", "issn": "1064-5632", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190711-104459099", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1070/im8739", "primary_object": { "basename": "1801.01552.pdf", "url": "https://authors.library.caltech.edu/records/mqmcj-qeh56/files/1801.01552.pdf" }, "pub_year": "2019", "author_list": "Manin, Yu. I. and Marcolli, M." }, { "id": "https://authors.library.caltech.edu/records/7gg35-x8b57", "eprint_id": 78985, "eprint_status": "archive", "datestamp": "2023-08-22 01:39:27", "lastmod": "2026-03-31 05:58:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cornelissen-G", "name": { "family": "Cornelissen", "given": "Gunther" } }, { "id": "Li-Xin", "name": { "family": "Li", "given": "Xin" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Smit-H", "name": { "family": "Smit", "given": "Harry" }, "orcid": "0000-0001-9547-8282" } ] }, "title": "Reconstructing global fields from dynamics in the abelianized Galois group", "ispublished": "pub", "full_text_status": "public", "keywords": "Class field theory; Bost\u2013Connes system; Anabelian geometry; Neukirch\u2013Uchida theorem; L-series", "note": "\u00a9 The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nFirst Online 15 March 2019. \n\nThis paper supersedes [5], of which it is the second (and final) part, dealing with the dynamical systems aspects of the theory. The first part [6] dealt with physics aspects related to partition functions, and [8] is a companion paper, only containing number theoretical results. Part of this work was done whilst the first two authors enjoyed the hospitality of the University of Warwick (special thanks to Richard Sharp for making it possible).\n\n

Published - Cornelissen2019_Article_ReconstructingGlobalFieldsFrom.pdf

Submitted - 1706.04517.pdf

", "abstract": "We study a dynamical system induced by the Artin reciprocity map for a global field. We translate the conjugacy of such dynamical systems into various arithmetical properties that are equivalent to field isomorphism, relating it to anabelian geometry.", "date": "2019-06", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "25", "number": "6", "publisher": "Springer", "pagerange": "Art. No. 24", "id_number": "CaltechAUTHORS:20170712-082102987", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-082102987", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-019-0469-8", "primary_object": { "basename": "1706.04517.pdf", "url": "https://authors.library.caltech.edu/records/7gg35-x8b57/files/1706.04517.pdf" }, "related_objects": [ { "basename": "Cornelissen2019_Article_ReconstructingGlobalFieldsFrom.pdf", "url": "https://authors.library.caltech.edu/records/7gg35-x8b57/files/Cornelissen2019_Article_ReconstructingGlobalFieldsFrom.pdf" } ], "pub_year": "2019", "author_list": "Cornelissen, Gunther; Li, Xin; et al." }, { "id": "https://authors.library.caltech.edu/records/ctm7x-9at88", "eprint_id": 97836, "eprint_status": "archive", "datestamp": "2023-08-19 15:58:03", "lastmod": "2026-03-31 14:41:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Tower-type bounds for unavoidable patterns in words", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Copyright 2019 American Mathematical Society. \n\nReceived by the editors December 17, 2017, and, in revised form, November 4, 2018. Article electronically published on May 30, 2019. \n\nThe research of the first author was supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. The research of the second author was supported by a Packard Fellowship, by NSF Career Award DMS-1352121, and by an Alfred P. Sloan Fellowship. The research of the third author was supported in part by SNSF grant 200021-175573.\n\n

Submitted - 1704.03479.pdf

", "abstract": "A word \u03c9 is said to contain the pattern P if there is a way to substitute a nonempty word for each letter in P so that the resulting word is a subword of \u03c9. Bean, Ehrenfeucht, and McNulty and, independently, Zimin characterised the patterns P which are unavoidable, in the sense that any sufficiently long word over a fixed alphabet contains P. Zimin's characterisation says that a pattern is unavoidable if and only if it is contained in a Zimin word, where the Zimin words are defined by Z_1 = x_1 and Z_n = Z_n \u2212 1x_(n)Z_(n) \u2212 1. We study the quantitative aspects of this theorem, obtaining essentially tight tower-type bounds for the function f(n, q), the least integer such that any word of length f(n, q) over an alphabet of size q contains Z_(n). When n = 3, the first nontrivial case, we determine f(n, q) up to a constant factor, showing that f(3, q) = \u0398(2_(q)q!).", "date": "2019-05-30", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "publisher": "American Mathematical Society", "id_number": "CaltechAUTHORS:20190812-163000172", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000172", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-175573" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/7751", "primary_object": { "basename": "1704.03479.pdf", "url": "https://authors.library.caltech.edu/records/ctm7x-9at88/files/1704.03479.pdf" }, "pub_year": "2019", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/60w82-new60", "eprint_id": 95559, "eprint_status": "archive", "datestamp": "2023-08-19 15:53:43", "lastmod": "2026-03-31 13:23:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harlow-D", "name": { "family": "Harlow", "given": "Daniel" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Constraints on Symmetries from Holography", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n\nFunded by SCOAP3. \n\nReceived 26 October 2018; revised manuscript received 24 January 2019; published 17 May 2019. \n\nD.\u2009H. is supported by the U.S. Department of Energy Grants No. DE-SC0018944 and No. DE-SC0019127, the Simons Foundation as a member of the It from Qubit collaboration, and the MIT department of physics. H.\u2009O. is supported in part by U.S. Department of Energy Grant No. DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895.\n\n

Published - PhysRevLett.122.191601.pdf

Submitted - 1810.05337.pdf

", "abstract": "In this Letter we show that a set of old conjectures about symmetries in quantum gravity hold within the anti\u2013de Sitter/conformal field theory correspondence. These conjectures are that no global symmetries are possible, that internal gauge symmetries must come with dynamical objects that transform in all irreducible representations, and that internal gauge groups must be compact. These conjectures are not obviously true from a bulk perspective, they are nontrivial consequences of the nonperturbative consistency of the correspondence. More details of and background for these arguments are presented in an accompanying paper.", "date": "2019-05-17", "date_type": "published", "publication": "Physical Review Letters", "volume": "122", "number": "19", "publisher": "American Physical Society", "pagerange": "Art. No. 191601", "id_number": "CaltechAUTHORS:20190517-095643873", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190517-095643873", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0018944" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0019127" }, { "agency": "Simons Foundation" }, { "agency": "Massachusetts Institute of Technology (MIT)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "World Premier International Research Center Initiative" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.122.191601", "primary_object": { "basename": "1810.05337.pdf", "url": "https://authors.library.caltech.edu/records/60w82-new60/files/1810.05337.pdf" }, "related_objects": [ { "basename": "PhysRevLett.122.191601.pdf", "url": "https://authors.library.caltech.edu/records/60w82-new60/files/PhysRevLett.122.191601.pdf" } ], "pub_year": "2019", "author_list": "Harlow, Daniel and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/pxrsq-vyd35", "eprint_id": 100204, "eprint_status": "archive", "datestamp": "2023-08-19 15:48:06", "lastmod": "2026-03-30 20:15:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Quorning-V", "name": { "family": "Quorning", "given": "Vibeke" } } ] }, "title": "Co-induction and invariant random subgroups", "ispublished": "pub", "full_text_status": "public", "keywords": "Co-induction, invariant random subgroups, weak mixing, small cancellation", "note": "\u00a9 2019 European Mathematical Society. \n\nReceived August 10, 2018. Published online: 2019-05-07. \n\nASK was partially supported by NSF Grant DMS-1464475. \n\nVQ was partially supported by Lars Hesselholt's Niels Bohr Professorship. We would like to thank Simon Thomas for a number of useful comments and in particular for bringing up the relevance of small cancellation theory to certain aspects of our work. We also would like to thank an anonymous referee for many useful remarks and corrections.\n\n

Submitted - 1806.08590.pdf

", "abstract": "In this paper we develop a co-induction operation which transforms an invariant random subgroup of a group into an invariant random subgroup of a larger group.\nWe use this operation to construct new continuum size families of non-atomic, weakly mixing invariant random subgroups of certain classes of wreath products, HNN-extensions and free products with amalgamation. By use of small cancellation theory, we also construct a new continuum size family of non-atomic invariant random subgroups of F\u2082 which are all invariant and weakly mixing with respect to the action of Aut(F\u2082).\nMoreover, for amenable groups \u0393 \u2264 \u0394, we obtain that the standard co-induction operation from the space of weak equivalence classes of \u0393\u0393 to the space of weak equivalence classes of \u0394 is continuous if and only if [\u0394:\u0393] < \u221e or core \u0394(\u0393) is trivial. For general groups we obtain that the co-induction operation is not continuous when [\u0394:\u0393] = \u221e. This answers a question raised by Burton and Kechris in [17]. Independently such an answer was also obtained, using a different method, by Bernshteyn in [8].", "date": "2019-05-07", "date_type": "published", "publication": "Groups, Geometry, and Dynamics", "volume": "13", "number": "4", "publisher": "European Mathematical Society", "pagerange": "1151-1193", "id_number": "CaltechAUTHORS:20191205-100802061", "issn": "1661-7207", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191205-100802061", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1464475" }, { "agency": "University of Copenhagen" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/GGD/517", "primary_object": { "basename": "1806.08590.pdf", "url": "https://authors.library.caltech.edu/records/pxrsq-vyd35/files/1806.08590.pdf" }, "pub_year": "2019", "author_list": "Kechris, Alexander S. and Quorning, Vibeke" }, { "id": "https://authors.library.caltech.edu/records/dkhn3-n3274", "eprint_id": 71955, "eprint_status": "archive", "datestamp": "2023-08-19 15:32:46", "lastmod": "2026-03-31 14:11:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frisch-J", "name": { "family": "Frisch", "given": "Joshua" } }, { "id": "Schlank-T", "name": { "family": "Schlank", "given": "Tomer" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Normal amenable subgroups of the automorphism group of the full shift", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Cambridge University Press. \n\nReceived 5 January 2017 and accepted in revised form 26 June 2017. \n\nThis research was partially conducted at Microsoft Research, New England.\n\n

Submitted - 1512.00587.pdf

Submitted - 1512.00587v2.pdf

", "abstract": "We show that every normal amenable subgroup of the automorphism group of the full shift is contained in its center. This follows from the analysis of this group's Furstenberg topological boundary, through the construction of a minimal and strongly proximal action. We extend this result to higher dimensional full shifts. This also provides a new proof of Ryan's theorem and of the fact that these groups contain free groups.", "date": "2019-05", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "39", "number": "5", "publisher": "Cambridge University Press", "pagerange": "1290-1298", "id_number": "CaltechAUTHORS:20161111-133444186", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-133444186", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/etds.2017.72", "primary_object": { "basename": "1512.00587.pdf", "url": "https://authors.library.caltech.edu/records/dkhn3-n3274/files/1512.00587.pdf" }, "related_objects": [ { "basename": "1512.00587v2.pdf", "url": "https://authors.library.caltech.edu/records/dkhn3-n3274/files/1512.00587v2.pdf" } ], "pub_year": "2019", "author_list": "Frisch, Joshua; Schlank, Tomer; et al." }, { "id": "https://authors.library.caltech.edu/records/x43w2-e4p85", "eprint_id": 111006, "eprint_status": "archive", "datestamp": "2023-08-19 15:43:46", "lastmod": "2026-03-31 14:37:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Statistical physics on a product of trees", "ispublished": "pub", "full_text_status": "public", "keywords": "Bubble diagram, Ising model, mean-field, Nonamenable groups, Nonunimodular, Nonuniqueness, percolation, Triangle condition", "note": "\u00a9 2019 Institut Henri Poincar\u00e9. \n\nReceived: 13 December 2017; Revised: 17 March 2018; Accepted: 13 April 2018; Published: May 2019. First available in Project Euclid: 14 May 2019. \n\nWe thank Aran Raoufi for help with some references and for spotting a typo, and thank the anonymous referee for suggesting various minor improvements.\n\n

Accepted Version - 1712.04911.pdf

", "abstract": "Let G be the product of finitely many trees T\u2081 \u00d7 T\u2082 \u00d7 \u22ef \u00d7 T_N, each of which is regular with degree at least three. We consider Bernoulli bond percolation and the Ising model on this graph, giving a short proof that the model undergoes a second order phase transition with mean-field critical exponents in each case. The result concerning percolation recovers a result of Kozma (2013), while the result concerning the Ising model is new. \n\nWe also present a new proof, using similar techniques, of a lemma of Schramm concerning the decay of the critical two-point function along a random walk, as well as some generalizations of this lemma.", "date": "2019-05", "date_type": "published", "publication": "Annales de l'Institut Henri Poincar\u00e9, Probabilit\u00e9s et Statistiques", "volume": "55", "number": "2", "publisher": "Institut Henri Poincar\u00e9", "pagerange": "1001-1010", "id_number": "CaltechAUTHORS:20210922-193309508", "issn": "0246-0203", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309508", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/18-aihp906", "primary_object": { "basename": "1712.04911.pdf", "url": "https://authors.library.caltech.edu/records/x43w2-e4p85/files/1712.04911.pdf" }, "pub_year": "2019", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/wqm8m-dh040", "eprint_id": 110828, "eprint_status": "archive", "datestamp": "2023-08-19 15:43:42", "lastmod": "2026-03-31 04:43:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nicaise-Johannes", "name": { "family": "Nicaise", "given": "Johannes" }, "orcid": "0000-0001-6650-1498" }, { "id": "Xu-Chenyang", "name": { "family": "Xu", "given": "Chenyang" } }, { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "The non-archimedean SYZ fibration", "ispublished": "pub", "full_text_status": "public", "keywords": "mirror symmetry, non-archimedean geometry, minimal model program, Strominger-Yau-Zaslow conjecture", "note": "\u00a9 The Authors 2019. \n \nReceived 2 February 2018, accepted in final form 22 December 2018, published online 30 April 2019. \n\n\nJohannes Nicaise is supported by the ERC Starting Grant MOTZETA (project 306610) of the European Research Council, and by long term structural funding (Methusalem grant) of the Flemish Government. A part of the research leading to these results was carried out at the Freiburg Institute for Advanced Studies (FRIAS) with funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement number 609305. Chenyang Xu is supported by the National Science Fund for Distinguished Young Scholars (11425101), 'Algebraic Geometry'. Tony Yue Yu is supported by the Clay Mathematics Institute.\n\n

Accepted Version - 1802.00287.pdf

", "abstract": "We construct non-archimedean SYZ (Strominger\u2013Yau\u2013Zaslow) fibrations for maximally degenerate Calabi\u2013Yau varieties, and we show that they are affinoid torus fibrations away from a codimension-two subset of the base. This confirms a prediction by Kontsevich and Soibelman. We also give an explicit description of the induced integral affine structure on the base of the SYZ fibration. Our main technical tool is a study of the structure of minimal dlt (divisorially log terminal) models along one-dimensional strata.", "date": "2019-05", "date_type": "published", "publication": "Compositio Mathematica", "volume": "155", "number": "5", "publisher": "Foundation Compositio Mathematica", "pagerange": "953-972", "id_number": "CaltechAUTHORS:20210914-164412592", "issn": "0010-437X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412592", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "306610" }, { "agency": "Methusalem" }, { "agency": "Marie Curie Fellowship", "grant_number": "609305" }, { "agency": "National Science Fund for Distinguished Young Scholars", "grant_number": "11425101" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0010437X19007152", "primary_object": { "basename": "1802.00287.pdf", "url": "https://authors.library.caltech.edu/records/wqm8m-dh040/files/1802.00287.pdf" }, "pub_year": "2019", "author_list": "Nicaise, Johannes; Xu, Chenyang; et al." }, { "id": "https://authors.library.caltech.edu/records/bx64m-zpz40", "eprint_id": 117598, "eprint_status": "archive", "datestamp": "2023-08-22 01:31:54", "lastmod": "2026-03-31 14:58:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marques-Fernando-C", "name": { "family": "Marques", "given": "Fernando C." } }, { "id": "Neves-Andr\u00e9", "name": { "family": "Neves", "given": "Andr\u00e9" } }, { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" } } ] }, "title": "Equidistribution of minimal hypersurfaces for generic metrics", "ispublished": "pub", "full_text_status": "public", "keywords": "General Mathematics", "note": "The first author is partly supported by NSF-DMS-1509027 and NSF DMS-1311795. The second author is partly supported by NSF DMS-1710846 and EPSRC Programme Grant EP/K00865X/1. The third author is supported by NSF-DMS-1509027.", "abstract": "For almost all Riemannian metrics (in the C\u221e Baire sense) on a closed manifold M\u207f\u207a\u00b9, 3 \u2264 (n+1) \u2264 7, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3):963\u2013972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven by Liokumovich et al. (Ann Math 187(3):933\u2013961, 2018).", "date": "2019-05", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "216", "number": "2", "publisher": "Springer", "pagerange": "421-443", "id_number": "CaltechAUTHORS:20221026-539148000.11", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221026-539148000.11", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1509027" }, { "agency": "NSF", "grant_number": "DMS-1311795" }, { "agency": "NSF", "grant_number": "DMS-1710846" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/K00865X/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-018-00850-5", "pub_year": "2019", "author_list": "Marques, Fernando C.; Neves, Andr\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/apz8k-z2d79", "eprint_id": 95895, "eprint_status": "archive", "datestamp": "2023-08-22 01:30:59", "lastmod": "2026-04-16 01:41:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Suh-S-Josephine", "name": { "family": "Suh", "given": "S. Josephine" }, "orcid": "0000-0003-2393-6883" } ] }, "title": "Statistical mechanics of a two-dimensional black hole", "ispublished": "pub", "full_text_status": "public", "keywords": "2D Gravity; Black Holes; Models of Quantum Gravity; AdS-CFT Correspondence", "note": "\u00a9 2019 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: March 5, 2019; Accepted: May 20, 2019; Published: May 29, 2019.\n\nWe thank Daniel Jafferis, Juan Maldacena, Douglas Stanford, Herman Verlinde, and Zhenbin Yang for discussions. We gratefully acknowledge the support by the Simons Foundation through the \"It from Qubit\" program. A.K. is supported by the Simons Foundation under grant 376205 and by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.\n\n

Published - Kitaev-Suh2019_Article_StatisticalMechanicsOfATwo-dim.pdf

Submitted - 1808.07032.pdf

", "abstract": "The dynamics of a nearly-AdS_2 spacetime with boundaries is reduced to that of two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We demonstrate how wavefunctions for a two-sided black hole and a regularized notion of trace can be used to construct thermal partition functions, and more generally, arbitrary density matrices. We also obtain correlation functions of external operators.", "date": "2019-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 198", "id_number": "CaltechAUTHORS:20190529-161258314", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190529-161258314", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/JHEP05(2019)198", "primary_object": { "basename": "1808.07032.pdf", "url": "https://authors.library.caltech.edu/records/apz8k-z2d79/files/1808.07032.pdf" }, "related_objects": [ { "basename": "Kitaev-Suh2019_Article_StatisticalMechanicsOfATwo-dim.pdf", "url": "https://authors.library.caltech.edu/records/apz8k-z2d79/files/Kitaev-Suh2019_Article_StatisticalMechanicsOfATwo-dim.pdf" } ], "pub_year": "2019", "author_list": "Kitaev, Alexei and Suh, S. Josephine" }, { "id": "https://authors.library.caltech.edu/records/gnyqz-g3n51", "eprint_id": 86786, "eprint_status": "archive", "datestamp": "2023-08-19 15:24:19", "lastmod": "2026-03-31 05:55:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "R. L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "A." } } ] }, "title": "Bound on the number of negative eigenvalues of two-dimensional Schr\u00f6dinger operators on domains", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator, Dirichlet Laplacian, Neumann Laplacian, Trudinger inequality", "note": "\u00a9 2019 American Mathematical Society. \n\nReceived 8 Dec. 2017. Article electronically published on April 12, 2019. \n\nPartially supported by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.) and by a grant of the Russian Federation Government under the supervision of a leading scientist at the Siberian Federal University, grant no. 14.Y26.31.0006 (A.L.). \n\nThe authors are grateful to Timo Weidl for extensive discussions related to this material and to Grigori Rozenblum for many helpful remarks on the manuscript.\n\n

Submitted - 1712.03167.pdf

", "abstract": "A fundamental result of Solomyak says that the number of negative eigenvalues of a Schr\u00f6dinger operator on a two-dimensional domain is bounded from above by a constant times a certain Orlicz norm of the potential. Here it is shown that in the case of Dirichlet boundary conditions the constant in this bound can be chosen independently of the domain.", "date": "2019-04-12", "date_type": "published", "publication": "St. Petersburg Mathematical Journal", "volume": "30", "number": "3", "publisher": "American Mathematical Society", "pagerange": "573-589", "id_number": "CaltechAUTHORS:20180604-111721567", "isbn": "978-3-03719-175-0", "issn": "1061-0022", "book_title": "Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180604-111721567", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Russian Federation" }, { "agency": "Siberian Federal University", "grant_number": "14.Y26.31.0006" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Dittrich-J", "name": { "family": "Dittrich", "given": "Jaroslav" } }, { "id": "Kova\u0159\u00edk-H", "name": { "family": "Kova\u0159\u00edk", "given": "Hynek" } }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } } ] }, "doi": "10.1090/spmj/1559", "primary_object": { "basename": "1712.03167.pdf", "url": "https://authors.library.caltech.edu/records/gnyqz-g3n51/files/1712.03167.pdf" }, "pub_year": "2019", "author_list": "Frank, R. L. and Laptev, A." }, { "id": "https://authors.library.caltech.edu/records/qx2jr-s0k04", "eprint_id": 84927, "eprint_status": "archive", "datestamp": "2023-08-22 01:13:32", "lastmod": "2026-03-31 15:26:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Tosio Kato's work on non-relativistic quantum mechanics: part 2", "ispublished": "pub", "full_text_status": "public", "keywords": "Kato; Schr\u00f6dinger operators; Quantum mechanics", "note": "\u00a9 2018 The Author(s). This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. \n\nReceived: 8 November 2017; Revised: 18 January 2018; Accepted: 20 January 2018; First Online: 22 February 2018. \n\nResearch supported in part by NSF Grants DMS-1265592 and DMS-1665526 and in part by Israeli BSF Grant No. 2014337.\n\n

Published - s166436071950005x.pdf

", "abstract": "We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics in this second part include absence of embedded eigenvalues, trace class scattering, Kato smoothness, the quantum adiabatic theorem and Kato's ultimate Trotter Product Formula.", "date": "2019-04", "date_type": "published", "publication": "Bulletin of Mathematical Sciences", "volume": "9", "number": "1", "publisher": "World Scientific Publishing", "pagerange": "Art. No. 1950005", "id_number": "CaltechAUTHORS:20180222-132115517", "issn": "1664-3607", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180222-132115517", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s13373-018-0121-5", "primary_object": { "basename": "s166436071950005x.pdf", "url": "https://authors.library.caltech.edu/records/qx2jr-s0k04/files/s166436071950005x.pdf" }, "pub_year": "2019", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/bfn75-7bv79", "eprint_status": "archive", "datestamp": "2025-07-22 22:22:26", "lastmod": "2026-03-09 23:04:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "name": { "family": "Sam", "given": "Steven V." } } ] }, "title": "Vector bundles on genus 2 curves and trivectors", "ispublished": "pub", "full_text_status": "public", "keywords": "genus 2 curves; vector bundles; invariant theory; moduli spaces", "note": "

This journal is © Foundation Compositio Mathematica 2019. This article is distributed with Open Access under the terms of the Creative Commons Attribution Non-Commercial License, which permits non-commercial reuse, distribution, and reproduction in any medium, provided that the original work is properly cited. For commercial re-use, please contact the Foundation Compositio Mathematica.

\n\n

Steven V Sam was partially supported by a Miller research fellowship and NSF DMS-1500069.

", "abstract": "

Given a complex curve C of genus 2, there is a well-known relationship between the moduli space of rank 3 semistable bundles on C and a cubic hypersurface known as the Coble cubic. Some of the aspects of this are known to be related to the geometric
invariant theory of the third exterior power of a 9-dimensional complex vector space. We extend this relationship to arbitrary fields and study some of the connections to invariant theory, which will be studied more in-depth in a followup paper.

", "date": "2019-04", "date_type": "published", "publication": "Algebraic Geometry", "volume": "6", "number": "3", "publisher": "Foundation Compositio Mathematica", "pagerange": "328-345", "issn": "2313-1691", "official_url": "https://authors.library.caltech.edu/records/bfn75-7bv79", "funders": { "items": [ { "agency": "Miller Institute for Basic Research in Science" }, { "grant_number": "DMS-1500069" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.14231/AG-2019-016", "primary_object": { "basename": "2019-3-016.pdf", "url": "https://authors.library.caltech.edu/records/bfn75-7bv79/files/2019-3-016.pdf" }, "pub_year": "2019", "author_list": "Rains, Eric M. and Sam, Steven V." }, { "id": "https://authors.library.caltech.edu/records/228dv-bnt78", "eprint_id": 111007, "eprint_status": "archive", "datestamp": "2023-08-19 15:17:13", "lastmod": "2026-03-31 16:03:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Harmonic Dirichlet functions on planar graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Circle packing \u00b7 Planar graphs \u00b7 Harmonic functions \u00b7 Dirichlet space \u00b7 Electrical networks", "note": "\u00a9 The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.\n\nReceived: 26 July 2017 / Revised: 24 October 2018 / Accepted: 7 January 2019 / Published online: 30 January 2019. \n\nThe author was supported by a Microsoft Research PhD Fellowship. We thank the anonymous referees for their comments and corrections.\n\n

Published - Hutchcroft2019_Article_HarmonicDirichletFunctionsOnPl.pdf

Accepted Version - 1707.07751.pdf

", "abstract": "Benjamini and Schramm (Invent Math 126(3):565\u2013587, 1996) used circle packing to prove that every transient, bounded degree planar graph admits non-constant harmonic functions of finite Dirichlet energy. We refine their result, showing in particular that for every transient, bounded degree, simple planar triangulation T and every circle packing of T in a domain D, there is a canonical, explicit bounded linear isomorphism between the space of harmonic Dirichlet functions on T and the space of harmonic Dirichlet functions on D.", "date": "2019-04", "date_type": "published", "publication": "Discrete & Computational Geometry", "volume": "61", "number": "3", "publisher": "Springer", "pagerange": "479-506", "id_number": "CaltechAUTHORS:20210922-193309575", "issn": "0179-5376", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309575", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00454-019-00057-2", "primary_object": { "basename": "1707.07751.pdf", "url": "https://authors.library.caltech.edu/records/228dv-bnt78/files/1707.07751.pdf" }, "related_objects": [ { "basename": "Hutchcroft2019_Article_HarmonicDirichletFunctionsOnPl.pdf", "url": "https://authors.library.caltech.edu/records/228dv-bnt78/files/Hutchcroft2019_Article_HarmonicDirichletFunctionsOnPl.pdf" } ], "pub_year": "2019", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/5edh3-kv125", "eprint_id": 71953, "eprint_status": "archive", "datestamp": "2023-08-19 15:04:01", "lastmod": "2026-03-31 05:20:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Juschenko-K", "name": { "family": "Juschenko", "given": "Kate" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Vahidi-Ferdowsi-P", "name": { "family": "Vahidi Ferdowsi", "given": "Pooya" } } ] }, "title": "Thompson's group F is not strongly amenable", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Cambridge University Press. \n\nReceived 5 August 2016 and accepted in revised form 26 April 2017. \n\nThe authors would like to thank Eli Glasner and Benjamin Weiss for enlightening and encouraging conversations.\n\n

Submitted - 1607.04915.pdf

", "abstract": "We show that Thompson's group has a topological action on a compact metric space that is proximal and has no fixed points.", "date": "2019-04", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "39", "number": "4", "publisher": "Cambridge University Press", "pagerange": "925-929", "id_number": "CaltechAUTHORS:20161111-131006027", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-131006027", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/etds.2017.49", "primary_object": { "basename": "1607.04915.pdf", "url": "https://authors.library.caltech.edu/records/5edh3-kv125/files/1607.04915.pdf" }, "pub_year": "2019", "author_list": "Hartman, Yair; Juschenko, Kate; et al." }, { "id": "https://authors.library.caltech.edu/records/8s609-ppc69", "eprint_id": 84212, "eprint_status": "archive", "datestamp": "2023-08-19 14:54:01", "lastmod": "2026-03-31 00:24:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dedushenko-M", "name": { "family": "Dedushenko", "given": "Mykola" }, "orcid": "0000-0002-9273-7602" }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "IR duality in 2D N = (0,2) gauge theory with noncompact dynamics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2019 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. \n \nFunded by SCOAP3. \n \nReceived 12 February 2018; published 14 March 2019. \n \nWe thank M. Fluder, J. Heckman, D. Jafferis, D. Kutasov, N. Nekrasov, P. Putrov, J. Song for useful discussions. This work was supported by the Walter Burke Institute for Theoretical Physics and the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. The work of MD was also supported by the Sherman Fairchild Foundation. S. G. gratefully acknowledges support from Harvard University, where some of the research for this paper was performed during the fall 2017, as well as partial support by the National Science Foundation under Grants No. NSF PHY11-25915 and No. NSF DMS 1664240.\n\n

Published - PhysRevD.99.066005.pdf

Submitted - 1712.07659.pdf

", "abstract": "Searching for the simplest non-Abelian 2D gauge theory with N = (0,2) supersymmetry and nontrivial IR physics, we propose a new duality for SU(2) SQCD with N^f = 4 chiral flavors. The chiral algebra of this theory is found to be so(8)_(\u22122), the same as in 4D N = 2 SU(2) gauge theory with four hypermultiplets.", "date": "2019-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "99", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066005", "id_number": "CaltechAUTHORS:20180109-161412323", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180109-161412323", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "Harvard University" }, { "agency": "NSF", "grant_number": "PHY11-25915" }, { "agency": "NSF", "grant_number": "DMS-1664240" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2017-072", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.99.066005", "primary_object": { "basename": "1712.07659.pdf", "url": "https://authors.library.caltech.edu/records/8s609-ppc69/files/1712.07659.pdf" }, "related_objects": [ { "basename": "PhysRevD.99.066005.pdf", "url": "https://authors.library.caltech.edu/records/8s609-ppc69/files/PhysRevD.99.066005.pdf" } ], "pub_year": "2019", "author_list": "Dedushenko, Mykola and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/xjwf7-exd84", "eprint_id": 92160, "eprint_status": "archive", "datestamp": "2023-08-19 14:28:18", "lastmod": "2026-03-31 15:53:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Li-Wanlin", "name": { "family": "Li", "given": "Wanlin" } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" }, "orcid": "0000-0003-4521-2130" }, { "id": "Pries-Rachel", "name": { "family": "Pries", "given": "Rachel" }, "orcid": "0000-0001-5987-0324" }, { "id": "Tang-Yunqing", "name": { "family": "Tang", "given": "Yunqing" } } ] }, "title": "Newton polygons arising from special families of cyclic covers of the projective line", "ispublished": "pub", "full_text_status": "public", "keywords": "Curve, Cyclic cover, Jacobian, Abelian variety, Shimura variety, PEL-type, Moduli space, Reduction, p-Rank, Supersingular, Newton polygon, p-Divisible group, Kottwitz method, Dieudonn\u00e9 module, Ekedahl\u2013Oort type", "note": "\u00a9 2019 Springer Nature Switzerland AG. \n\nReceived: 17 May 2018; Accepted: 19 December 2018; Published: 9 January 2019.\n\nThis project began at the Women in Numbers 4 workshop at the Banff International Research Station. Pries was partially supported by NSF grant DMS-15-02227. We thank Liang Xiao, Xinwen Zhu, and Rong Zhou for discussions about the appendix and thank Liang Xiao for the detailed suggestions on the writing of the appendix. We would like to thank the referee for many helpful comments.\n\n

Submitted - 1805.06914.pdf

", "abstract": "By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. For each of these, we compute the Newton polygons, and the \u03bc-ordinary Ekedahl\u2013Oort type, occurring in the characteristic p reduction of the Shimura variety. We prove that all but a few of the Newton polygons appear on the open Torelli locus. As an application, we produce multiple new examples of Newton polygons and Ekedahl\u2013Oort types of Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for genus 5, 6, 7; fourteen new non-supersingular Newton polygons for genus 5\u20137; eleven new Ekedahl\u2013Oort types for genus 4\u20137 and, for all g \u2265 6, the Newton polygon with p-rank g\u22126 with slopes 1 / 6 and 5 / 6.", "date": "2019-03", "date_type": "published", "publication": "Research in Number Theory", "volume": "5", "number": "1", "publisher": "Springer Nature", "pagerange": "Art. No. 12", "id_number": "CaltechAUTHORS:20190109-095500540", "issn": "2522-0160", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190109-095500540", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-15-02227" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s40993-018-0149-3", "primary_object": { "basename": "1805.06914.pdf", "url": "https://authors.library.caltech.edu/records/xjwf7-exd84/files/1805.06914.pdf" }, "pub_year": "2019", "author_list": "Li, Wanlin; Mantovan, Elena; et al." }, { "id": "https://authors.library.caltech.edu/records/tyfa7-r1013", "eprint_id": 78986, "eprint_status": "archive", "datestamp": "2023-08-19 14:26:27", "lastmod": "2026-03-31 05:41:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cornelissen-Gunther", "name": { "family": "Cornelissen", "given": "Gunther" } }, { "id": "de-Smit-Bart", "name": { "family": "de Smit", "given": "Bart" } }, { "id": "Li-Xin", "name": { "family": "Li", "given": "Xin" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Smit-Harry", "name": { "family": "Smit", "given": "Harry" }, "orcid": "0000-0001-9547-8282" } ] }, "title": "Characterization of global fields by Dirichlet L-series", "ispublished": "pub", "full_text_status": "public", "keywords": "Class field theory, L-series, Arithmetic equivalence", "note": "\u00a9 The Author(s) 2018. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 24 April 2018 Accepted: 10 November 2018, Published online: 26 November 2018. \n\nPart of this work was done whilst the first and third author enjoyed the hospitality of the University of Warwick (special thanks to Richard Sharp for making it possible).\n\n

Published - Cornelissen2018_Article_CharacterizationOfGlobalFields.pdf

Submitted - 1706.04515.pdf

", "abstract": "We prove that two global fields are isomorphic if and only if there is an isomorphism of groups of Dirichlet characters that preserves L-series.", "date": "2019-03", "date_type": "published", "publication": "Research in Number Theory", "volume": "5", "number": "1", "publisher": "Springer Nature", "pagerange": "Art. No. 7", "id_number": "CaltechAUTHORS:20170712-082510174", "issn": "2522-0160", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-082510174", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Universiteit Utrecht" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s40993-018-0143-9", "primary_object": { "basename": "Cornelissen2018_Article_CharacterizationOfGlobalFields.pdf", "url": "https://authors.library.caltech.edu/records/tyfa7-r1013/files/Cornelissen2018_Article_CharacterizationOfGlobalFields.pdf" }, "related_objects": [ { "basename": "1706.04515.pdf", "url": "https://authors.library.caltech.edu/records/tyfa7-r1013/files/1706.04515.pdf" } ], "pub_year": "2019", "author_list": "Cornelissen, Gunther; de Smit, Bart; et al." }, { "id": "https://authors.library.caltech.edu/records/j57ra-ax211", "eprint_id": 78987, "eprint_status": "archive", "datestamp": "2023-08-22 00:44:42", "lastmod": "2026-03-31 16:18:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Feynman quadrics-motive of the massive sunset graph", "ispublished": "pub", "full_text_status": "public", "keywords": "Feynman integral; Motive; Period; Quadric; Prym variety", "note": "\u00a9 2018 Elsevier Inc. \n\nReceived 3 June 2017, Revised 18 December 2017, Accepted 19 June 2018, Available online 23 July 2018. \n\nMatilde Marcolli was supported by the NSF grant DMS-1707882 and NSERC grants RGPIN-2018-04937 and RGPAS-2018-522593. Gon\u00e7alo Tabuada was supported by the NSF CAREER Award #1350472 and by the Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2013 (Centro de Matem\u00e9tica e Aplica\u00e7\u00f5es). \n\nThe authors are grateful to the anonymous referee for his/her comments.\n\n

Submitted - 1705.10307.pdf

", "abstract": "We prove that the Feynman quadrics-motive of the massive sunset graph is \"generically\" not mixed-Tate. Moreover, we explicitly describe its \"extra\" complexity in terms of a Prym variety.", "date": "2019-02", "date_type": "published", "publication": "Journal of Number Theory", "volume": "195", "publisher": "Elsevier", "pagerange": "159-183", "id_number": "CaltechAUTHORS:20170712-083350725", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-083350725", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "NSF", "grant_number": "DMS-1350472" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "UID/MAT/00297/2013" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jnt.2018.06.001", "primary_object": { "basename": "1705.10307.pdf", "url": "https://authors.library.caltech.edu/records/j57ra-ax211/files/1705.10307.pdf" }, "pub_year": "2019", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/a8dc3-z4r02", "eprint_id": 92991, "eprint_status": "archive", "datestamp": "2023-08-22 00:49:26", "lastmod": "2026-04-16 01:39:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gu-Yingfei", "name": { "family": "Gu", "given": "Yingfei" }, "orcid": "0000-0001-8645-879X" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "On the relation between the magnitude and exponent of OTOCs", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence; 1/N Expansion; Models of Quantum Gravity", "note": "\u00a9 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: January 15, 2019; Accepted: February 8, 2019; Published: February 13, 2019. \n\nWe thank David Huse, Juan Maldacena, Xiao-Liang Qi, Subir Sachdev, Steve Shenker, Douglas Stanford, Josephine Suh and Ashvin Vishwanath for useful discussions. Y.G. is supported by the Gordon and Betty Moore Foundation EPiQS Initiative through Grant (GBMF-4306). A.K. is supported by the Simons Foundation under grant 376205 and through the \"It from Qubit\" program, as well as by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611, and at KITP, supported by the NSF grant PHY-1748958.\n\n

Published - Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf

Submitted - 1812.00120.pdf

", "abstract": "We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called \"branching time\". The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define \"strings\" in this context. As another application, we consider an SYK chain. If the coupling strength \u03b2J is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2\u03c0/\u03b2.", "date": "2019-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 75", "id_number": "CaltechAUTHORS:20190220-075207560", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190220-075207560", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation", "grant_number": "GBMF-4306" }, { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "It from Qubit Program" }, { "agency": "Institute of Quantum Information and Matter (IQIM)" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "NSF", "grant_number": "PHY-1748958" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/JHEP02(2019)075", "primary_object": { "basename": "1812.00120.pdf", "url": "https://authors.library.caltech.edu/records/a8dc3-z4r02/files/1812.00120.pdf" }, "related_objects": [ { "basename": "Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf", "url": "https://authors.library.caltech.edu/records/a8dc3-z4r02/files/Gu-Kitaev2019_Article_OnTheRelationBetweenTheMagnitu.pdf" } ], "pub_year": "2019", "author_list": "Gu, Yingfei and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/mb482-qbn50", "eprint_id": 90910, "eprint_status": "archive", "datestamp": "2023-08-19 13:50:35", "lastmod": "2026-03-31 16:13:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Palti-E", "name": { "family": "Palti", "given": "Eran" } }, { "id": "Shiu-G", "name": { "family": "Shiu", "given": "Gary" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Distance and de Sitter Conjectures on the Swampland", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). \n\nFunded by SCOAP3. \n\nReceived 29 October 2018, Accepted 13 November 2018, Available online 15 November 2018. \n\nWe would like to thank Prateek Agrawal, Tom Banks, Raphael Bousso, Clifford Cheung, Daniel Chung, Joe Conlon, Albion Lawrence, Toshifumi Noumi, Georges Obied, Misao Sasaki, and Pablo Soler for discussions. The work of GS is supported in part by the DOE grant DE-SC0017647 and the Kellett Award of the University of Wisconsin. The work of CV is supported in part by NSF grant PHY-1067976. The work of HO is supported in part by U.S. Department of Energy grant DE-SC0011632, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. HO also thanks the hospitality of the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1607611. We would like to thank the hospitality of Simons Center for Geometry and Physics, where this work was initiated during the 2018 Simons Summer workshop.\n\n

Published - 1-s2.0-S037026931830858X-main.pdf

Submitted - 1810.05506.pdf

", "abstract": "Among Swampland conditions, the distance conjecture characterizes the geometry of scalar fields and the de Sitter conjecture constrains allowed potentials on it. We point out a connection between the distance conjecture and a refined version of the de Sitter conjecture in any parametrically controlled regime of string theory by using Bousso's covariant entropy bound. The refined version turns out to evade all counter-examples at scalar potential maxima that have been raised. We comment on the relation of our result to the Dine\u2013Seiberg problem.", "date": "2019-01-10", "date_type": "published", "publication": "Physics Letters B", "volume": "788", "publisher": "Elsevier", "pagerange": "180-184", "id_number": "CaltechAUTHORS:20181115-093945553", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181115-093945553", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0017647" }, { "agency": "University of Wisconsin" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1607611" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.physletb.2018.11.018", "primary_object": { "basename": "1810.05506.pdf", "url": "https://authors.library.caltech.edu/records/mb482-qbn50/files/1810.05506.pdf" }, "related_objects": [ { "basename": "1-s2.0-S037026931830858X-main.pdf", "url": "https://authors.library.caltech.edu/records/mb482-qbn50/files/1-s2.0-S037026931830858X-main.pdf" } ], "pub_year": "2019", "author_list": "Ooguri, Hirosi; Palti, Eran; et al." }, { "id": "https://authors.library.caltech.edu/records/rv1ak-ggt04", "eprint_id": 88624, "eprint_status": "archive", "datestamp": "2023-08-19 13:49:26", "lastmod": "2026-03-31 14:19:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Yuditskii-P", "name": { "family": "Yuditskii", "given": "Peter" } }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "Asymptotics of Chebyshev Polynomials, II. DCT Subsets of \u211d", "ispublished": "pub", "full_text_status": "public", "keywords": "Chebyshev polynomials, Widom conjecture, Parreau\u2013Widom set, Direct Cauchy Theorem, Totik\u2013Widom bound", "note": "\u00a9 2019 Duke University Press. \n\nReceived 19 March 2018. Revision received 27 August 2018. First published online 9 January 2019. \n\nJ.S.C.'s research was supported in part by project grant DFF-4181-00502 from the Danish Council for Independent Research, B.S.'s research was supported in part by National Science Foundation grants DMS-1265592 and DMS-1665526 and in part by United States\u2013Israel Binational Science Foundation grant 2014337, P.Y.'s research was supported by the Austrian Science Fund FWF, project P29363-N32, and M.Z.'s research was supported in part by Simons Foundation grant CGM-281971.\n\n

Submitted - 1709.06707.pdf

", "abstract": "We prove Szeg\u0151\u2013Widom asymptotics for the Chebyshev polynomials of a compact subset of \u211d which is regular for potential theory and obeys the Parreau\u2013Widom and DCT conditions.", "date": "2019-01-09", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "168", "number": "2", "publisher": "Duke University Press", "pagerange": "325-349", "id_number": "CaltechAUTHORS:20180807-124147489", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180807-124147489", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Danish Council for Independent Research", "grant_number": "DFF-4181-00502" }, { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" }, { "agency": "FWF Der Wissenschaftsfonds", "grant_number": "P29363-N32" }, { "agency": "Simons Foundation", "grant_number": "CGM-281971" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1215/00127094-2018-0045", "primary_object": { "basename": "1709.06707.pdf", "url": "https://authors.library.caltech.edu/records/rv1ak-ggt04/files/1709.06707.pdf" }, "pub_year": "2019", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/qqfbd-zpw07", "eprint_id": 97828, "eprint_status": "archive", "datestamp": "2023-08-22 00:37:31", "lastmod": "2026-03-08 03:40:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } } ] }, "title": "Lines in Euclidean Ramsey Theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Euclidean Ramsey theory; Probabilistic method", "note": "\u00a9 The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived 5 May 2017; revised 31 January 2018; accepted 25 February 2018; published online 23 March 2018. \n\nD. Conlon: Research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. J. Fox: Research supported by a Packard Fellowship and by NSF Career Award DMS-1352121. \n\nThis paper was written while both authors were visiting the Simons Institute for the Theory of Computing in Berkeley and we are grateful for their generous support. The authors would also like to thank Noga Alon and Ben Green for helpful discussions. Finally, we wish to thank David Ellis, Ron Graham and an anonymous referee for a number of useful comments and corrections. In particular, the anonymous referee was the one to point us to the paper by Szlam [14], helping us to greatly improve the results in the concluding remarks.\n\n

Submitted - 1705.02166.pdf

", "abstract": "Let \u2113_m be a sequence of m points on a line with consecutive points of distance one. For every natural number n, we prove the existence of a red/blue-coloring of E^n containing no red copy of \u2113_2 and no blue copy of \u2113_m for any m \u2265 2^(cn). This is best possible up to the constant c in the exponent. It also answers a question of Erd\u0151s et al. (J Comb Theory Ser A 14:341\u2013363, 1973). They asked if, for every natural number n, there is a set K \u2282 E^1 and a red/blue-coloring of E^n containing no red copy of \u2113_2 and no blue copy of K.", "date": "2019-01", "date_type": "published", "publication": "Discrete and Computational Geometry", "volume": "61", "number": "1", "publisher": "Springer", "pagerange": "218-225", "id_number": "CaltechAUTHORS:20190812-162959449", "issn": "0179-5376", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959449", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00454-018-9980-5", "primary_object": { "basename": "1705.02166.pdf", "url": "https://authors.library.caltech.edu/records/qqfbd-zpw07/files/1705.02166.pdf" }, "pub_year": "2019", "author_list": "Conlon, David and Fox, Jacob" }, { "id": "https://authors.library.caltech.edu/records/q15xy-ehs45", "eprint_id": 90740, "eprint_status": "archive", "datestamp": "2023-08-19 13:34:30", "lastmod": "2026-03-09 20:29:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" }, { "id": "Zahl-J", "name": { "family": "Zahl", "given": "Joshua" } } ] }, "title": "An improved bound on the Hausdorff dimension of Besicovitch sets in \u211d^3", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 American Mathematical Society. \n\nReceived by the editors May 20, 2017, and, in revised form, September 16, 2017, and May 21, 2018. Published electronically: August 29, 2018. \n\nThe first author was supported by NSF grants DMS 1266104 and DMS 1565904. The second author was supported by an NSERC Discovery grant. \n\nThe authors would like to thank Terry Tao, Daniel Di Benedetto, and the anonymous referee for helpful comments and suggestions to an earlier version of this manuscript.\n\n

Submitted - 1704.07210.pdf

", "abstract": "We prove that every Besicovitch set in \u211d^3 must have Hausdorff dimension at least 5/2 + \u03f5_0 for some small constant \u03f5_0 > 0. This follows from a more general result about the volume of unions of tubes that satisfies the Wolff axioms. Our proof grapples with a new \"almost counterexample\" to the Kakeya conjecture, which we call the SL_2 example; this object resembles a Besicovitch set that has Minkowski dimension 3 but Hausdorff dimension 5/2. We believe this example may be an interesting object for future study.", "date": "2019-01", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "32", "number": "1", "publisher": "American Mathematical Society", "pagerange": "195-259", "id_number": "CaltechAUTHORS:20181108-083518614", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181108-083518614", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1266104" }, { "agency": "NSF", "grant_number": "DMS-1565904" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/jams/907", "primary_object": { "basename": "1704.07210.pdf", "url": "https://authors.library.caltech.edu/records/q15xy-ehs45/files/1704.07210.pdf" }, "pub_year": "2019", "author_list": "Katz, Nets Hawk and Zahl, Joshua" }, { "id": "https://authors.library.caltech.edu/records/xcfv5-3k826", "eprint_id": 79009, "eprint_status": "archive", "datestamp": "2023-08-19 13:31:20", "lastmod": "2026-03-09 21:41:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fan-Wentao", "name": { "family": "Fan", "given": "Wentao" } }, { "id": "Fathizadeh-F", "name": { "family": "Fathizadeh", "given": "Farzad" }, "orcid": "0000-0002-7863-4009" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Modular forms in the spectral action of Bianchi IX gravitational instantons", "ispublished": "pub", "full_text_status": "public", "keywords": "Models of Quantum Gravity, Non-Commutative Geometry", "note": "\u00a9 2019 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: December 13, 2018; Revised: January 6, 2019; Accepted: January 22, 2019; Published: January 31, 2019. \n\nThe first author was supported by a Summer Undergraduate Research Fellowship at Caltech. The second author acknowledges the support from the Marie Curie/SER Cymru II Cofund Research Fellowship 663830-SU-008, and thanks the Institut des Hautes \u00c9tudes Scientifiques (I.H.E.S.) for an excellent environment and their hospitality in the Summer of 2015, where this work was partially carried out. The third author was partially supported by NSF grants DMS-1201512, PHY-1205440, DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics.\n\n

Published - Fan2019_Article_ModularFormsInTheSpectralActio.pdf

Submitted - 1511.05321.pdf

", "abstract": "We prove a modularity property for the heat kernel and the Seeley-deWitt coefficients of the heat kernel expansion for the Dirac-Laplacian on the Bianchi IX gravitational instantons. We prove, via an isospectrality result for the Dirac operators, that each term in the expansion is a vector-valued modular form, with an associated ordinary (meromorphic) modular form of weight 2. We discuss explicit examples related to well known modular forms. Our results show the existence of arithmetic structures in Euclidean gravity models based on the spectral action functional.", "date": "2019-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2019", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 234", "id_number": "CaltechAUTHORS:20170712-105237127", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-105237127", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Marie Curie Fellowship", "grant_number": "663830-SU-008" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP01(2019)234", "primary_object": { "basename": "1511.05321.pdf", "url": "https://authors.library.caltech.edu/records/xcfv5-3k826/files/1511.05321.pdf" }, "related_objects": [ { "basename": "Fan2019_Article_ModularFormsInTheSpectralActio.pdf", "url": "https://authors.library.caltech.edu/records/xcfv5-3k826/files/Fan2019_Article_ModularFormsInTheSpectralActio.pdf" } ], "pub_year": "2019", "author_list": "Fan, Wentao; Fathizadeh, Farzad; et al." }, { "id": "https://authors.library.caltech.edu/records/1wgr3-csa86", "eprint_id": 86788, "eprint_status": "archive", "datestamp": "2023-08-19 13:28:20", "lastmod": "2026-03-09 02:11:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hainzl-C", "name": { "family": "Hainzl", "given": "Christian" } }, { "id": "Langmann-E", "name": { "family": "Langmann", "given": "Edwin" } } ] }, "title": "The BCS critical temperature in a weak homogeneous magnetic field", "ispublished": "pub", "full_text_status": "public", "keywords": "Superconductivity, BCS theory, magnetic field", "note": "\u00a9 2019 European Mathematical Society. \n\nReceived June 18, 2017. \n\nWe are very grateful to Michael Loss, whose ideas played a crucial role in finding the proof of Lemma 29. E. L. would like to thank Yaron Kadem for helpful discussions. The authors would also like to thank an anonymous referee for carefully reading the paper and several remarks that helped us to improve the paper. Partial support by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.) and by Vetenskapsr\u00e5det through grant 2016-05167 (E.L.) is acknowledged.\n\n

Submitted - 1706.05686.pdf

", "abstract": "We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.", "date": "2019", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "9", "number": "3", "publisher": "European Mathematical Society", "pagerange": "1005-1062", "id_number": "CaltechAUTHORS:20180604-112611120", "issn": "1664-039X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180604-112611120", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Vetenskapsr\u00e5det", "grant_number": "2016-05167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JST/270", "primary_object": { "basename": "1706.05686.pdf", "url": "https://authors.library.caltech.edu/records/1wgr3-csa86/files/1706.05686.pdf" }, "pub_year": "2019", "author_list": "Frank, Rupert L.; Hainzl, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/jh0n8-9d140", "eprint_id": 86787, "eprint_status": "archive", "datestamp": "2023-08-19 13:28:11", "lastmod": "2026-03-09 02:11:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00f6nig-T", "name": { "family": "K\u00f6nig", "given": "Tobias" } } ] }, "title": "Classification of positive singular solutions to a nonlinear biharmonic equation with critical exponent", "ispublished": "pub", "full_text_status": "public", "keywords": "fourth-order equation, critical exponent, classification, periodic solutions", "note": "\u00a9 2019 Mathematical Sciences Publishers. \n \nReceived: 2 November 2017; Revised: 28 May 2018; Accepted: 30 July 2018; Published: 20 October 2018.\n\n

Published - apde-v12-n4-p08-s.pdf

Submitted - 1711.00776.pdf

", "abstract": "For n \u2265 5, we consider positive solutions u of the biharmonic equation \u0394^2u = u^((n+4)/(n\u22124)) on R^n\u2216{0}, with a nonremovable singularity at the origin. We show that \u2223\u2223x\u2223\u2223^((n\u22124)/2)u is a periodic function of ln|x| and we classify all periodic functions obtained in this way. This result is relevant for the description of the asymptotic behavior of local solutions near singularities and for the Q-curvature problem in conformal geometry.", "date": "2019", "date_type": "published", "publication": "Analysis & PDE", "volume": "12", "number": "4", "publisher": "Mathematical Sciences Publishers", "pagerange": "1101-1113", "id_number": "CaltechAUTHORS:20180604-112112515", "issn": "1948-206X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180604-112112515", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/apde.2019.12.1101", "primary_object": { "basename": "1711.00776.pdf", "url": "https://authors.library.caltech.edu/records/jh0n8-9d140/files/1711.00776.pdf" }, "related_objects": [ { "basename": "apde-v12-n4-p08-s.pdf", "url": "https://authors.library.caltech.edu/records/jh0n8-9d140/files/apde-v12-n4-p08-s.pdf" } ], "pub_year": "2019", "author_list": "Frank, Rupert L. and K\u00f6nig, Tobias" }, { "id": "https://authors.library.caltech.edu/records/qzf98-gbq57", "eprint_id": 89642, "eprint_status": "archive", "datestamp": "2023-08-19 12:56:39", "lastmod": "2026-04-01 02:46:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" }, { "id": "Rogers-Keith-M", "name": { "family": "Rogers", "given": "Keith M." } } ] }, "title": "On the polynomial Wolff axioms", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer Nature Switzerland AG 2018. \n\nReceived: March 8, 2018; Revised: June 6, 2018; Accepted: July 20, 2018; First Online: 14 September 2018. \n\nThe first author would like to thank Josh Zahl for helpful discussions. In particular the proof of Lemma 2.2 came from a conversation with him. The second author would like to thank Jonathan Hickman for helpful discussions regarding the application to restriction. \n\nSupported by NSF grant DMS 1565904 and by MINECO Grants SEV-2015-0554 and MTM2017- 85934-C3-1-P.\n\n

Accepted Version - 1802.09094

", "abstract": "We confirm a conjecture of Guth concerning the maximal number of \u03b4-tubes, with \u03b4-separated directions, contained in the \u03b4-neighborhood of a real algebraic variety. Modulo a factor of \u03b4^(\u2212\u03b5), we also prove Guth and Zahl's generalized version for semialgebraic sets. Although the applications are to be found in harmonic analysis, the proof will employ deep results from algebraic and differential geometry, including Tarski's projection theorem and Gromov's algebraic lemma.", "date": "2018-12", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "28", "number": "6", "publisher": "Springer", "pagerange": "1706-1716", "id_number": "CaltechAUTHORS:20180914-100924111", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180914-100924111", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1565904" }, { "agency": "Ministerio de Econom\u00eda, Industria y Competitividad (MINECO)", "grant_number": "SEV-2015-0554" }, { "agency": "Ministerio de Econom\u00eda, Industria y Competitividad (MINECO)", "grant_number": "MTM2017- 85934-C3-1-P" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-018-0466-7", "primary_object": { "basename": "1802.09094", "url": "https://authors.library.caltech.edu/records/qzf98-gbq57/files/1802.09094" }, "pub_year": "2018", "author_list": "Katz, Nets Hawk and Rogers, Keith M." }, { "id": "https://authors.library.caltech.edu/records/53g70-x7774", "eprint_id": 90555, "eprint_status": "archive", "datestamp": "2023-08-22 00:24:17", "lastmod": "2026-03-31 19:51:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fan-Wentao", "name": { "family": "Fan", "given": "Wentao" } }, { "id": "Fathizadeh-F", "name": { "family": "Fathizadeh", "given": "Farzad" }, "orcid": "0000-0002-7863-4009" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Motives and periods in Bianchi IX gravity models", "ispublished": "pub", "full_text_status": "public", "keywords": "Bianchi IX gravity model; Spectral action; Dirac\u2013Laplacian; Heat kernel expansion; Periods; Motives", "note": "\u00a9 2018 Springer Science+Business Media B.V., part of Springer Nature. \n\nReceived: 21 January 2018; Revised: 30 April 2018; Accepted: 1 May 2018; Published online: 7 May 2018. \n\nThe second author acknowledges support from the Marie Curie/SER Cymru II Cofund Research Fellowship 663830-SU-008. The third author acknowledges support from NSF Grant DMS-1707882, NSERC Discovery Grant RGPIN-2018-04937 and from the Perimeter Institute for Theoretical Physics.\n\n

Published - Fan2018_Article_MotivesAndPeriodsInBianchiIXGr.pdf

Submitted - 1709.08082.pdf

", "abstract": "We show that, when considering the anisotropic scaling factors and their derivatives as affine variables, the coefficients of the heat-kernel expansion of the Dirac\u2013Laplacian on SU(2) Bianchi IX metrics are algebro-geometric periods of motives of complements in affine spaces of unions of quadrics and hyperplanes. We show that the motives are mixed Tate and we provide an explicit computation of their Grothendieck classes.", "date": "2018-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "108", "number": "12", "publisher": "Springer", "pagerange": "2729-2747", "id_number": "CaltechAUTHORS:20181101-083114372", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181101-083114372", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Marie Curie Fellowship", "grant_number": "663830-SU-008" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-018-1096-6", "primary_object": { "basename": "1709.08082.pdf", "url": "https://authors.library.caltech.edu/records/53g70-x7774/files/1709.08082.pdf" }, "related_objects": [ { "basename": "Fan2018_Article_MotivesAndPeriodsInBianchiIXGr.pdf", "url": "https://authors.library.caltech.edu/records/53g70-x7774/files/Fan2018_Article_MotivesAndPeriodsInBianchiIXGr.pdf" } ], "pub_year": "2018", "author_list": "Fan, Wentao; Fathizadeh, Farzad; et al." }, { "id": "https://authors.library.caltech.edu/records/ysvq9-q6365", "eprint_id": 97817, "eprint_status": "archive", "datestamp": "2023-08-19 13:06:02", "lastmod": "2026-03-31 21:33:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Kim-Jeong-Han", "name": { "family": "Kim", "given": "Jeong Han" } }, { "id": "Lee-Choongbum", "name": { "family": "Lee", "given": "Choongbum" } }, { "id": "Lee-Joonkyung", "name": { "family": "Lee", "given": "Joonkyung" } } ] }, "title": "Some advances on Sidorenko's conjecture", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 London Mathematical Society. \n\nManuscript received 22 October 2015; manuscript revised 03 May 2018; version of Record online 27 June 2018; issue online 02 December 2018. \n\nThe first author was supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. The second author was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (MSIP) (NRF\u20102016R1A5A1008055) and Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF\u20102017R1E1A1A03070701), and KIAS internal Research Fund CG046002. This work was partially carried out while the second author was visiting Microsoft Research, Redmond and Microsoft Research, New England. The third author was supported by NSF Grant DMS\u20101362326. The fourth author was supported by the ILJU Foundation of Education and Culture and by ERC Starting Grant 676632. \n\nWe would like to thank Olaf Parczyk for sharing his Master's thesis with us. We would also like to thank Bal\u00e1zs Szegedy for a number of valuable discussions.\n\n

Submitted - 1510.06533.pdf

", "abstract": "A bipartite graph H is said to have Sidorenko's property if the probability that the uniform random mapping from V(H) to the vertex set of any graph G is a homomorphism is at least the product over all edges in H of the probability that the edge is mapped to an edge of G. In this paper, we provide three distinct families of bipartite graphs that have Sidorenko's property. First, using branching random walks, we develop an embedding algorithm which allows us to prove that bipartite graphs admitting a certain type of tree decomposition have Sidorenko's property. Second, we use the concept of locally dense graphs to prove that subdivisions of certain graphs, including cliques, have Sidorenko's property. Third, we prove that if H has Sidorenko's property, then the Cartesian product of H with an even cycle also has Sidorenko's property.", "date": "2018-12", "date_type": "published", "publication": "Journal of the London Mathematical Society", "volume": "98", "number": "3", "publisher": "London Mathematical Society", "pagerange": "593-608", "id_number": "CaltechAUTHORS:20190812-162958339", "issn": "0024-6107", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958339", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "National Research Foundation of Korea", "grant_number": "NRF\u20102016R1A5A1008055" }, { "agency": "National Research Foundation of Korea", "grant_number": "NRF-2017R1E1A1A03070701" }, { "agency": "Korea Institute for Advanced Study", "grant_number": "CG046002" }, { "agency": "Microsoft Research" }, { "agency": "NSF", "grant_number": "DMS-1362326" }, { "agency": "ILJU Foundation of Education and Culture" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/jlms.12142", "primary_object": { "basename": "1510.06533.pdf", "url": "https://authors.library.caltech.edu/records/ysvq9-q6365/files/1510.06533.pdf" }, "pub_year": "2018", "author_list": "Conlon, David; Kim, Jeong Han; et al." }, { "id": "https://authors.library.caltech.edu/records/hhdf1-6y806", "eprint_id": 86775, "eprint_status": "archive", "datestamp": "2023-08-19 12:54:28", "lastmod": "2026-03-31 19:55:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Sabin-Julien", "name": { "family": "Sabin", "given": "Julien" } } ] }, "title": "Extremizers for the Airy\u2013Strichartz inequality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Springer-Verlag GmbH Germany, part of Springer Nature. \n\nReceived: 11 December 2017; Revised: 30 April 2018; First Online: 02 June 2018. \n\nThe authors would like to thank Terence Tao for suggesting to look at this problem for general p and Diogo Oliveira e Silva, R\u00e9ne Quilodr\u00e1n and an anonymous referee for discussions concerning the Ap,R problem. Partial support through US National Science Foundation Grant DMS-1363432 (R.L.F.) is also acknowledged.\n\n

Submitted - 1712.04156.pdf

", "abstract": "We identify the compactness threshold for optimizing sequences of the Airy\u2013Strichartz inequality as an explicit multiple of the sharp constant in the Strichartz inequality. In particular, if the sharp constant in the Airy\u2013Strichartz inequality is strictly smaller than this multiple of the sharp constant in the Strichartz inequality, then there is an optimizer for the former inequality. Our result is valid for the full range of Airy\u2013Strichartz inequalities (except the endpoints) both in the diagonal and off-diagonal cases.", "date": "2018-12", "date_type": "published", "publication": "Mathematische Annalen", "volume": "372", "number": "3-4", "publisher": "Springer", "pagerange": "1121-1166", "id_number": "CaltechAUTHORS:20180604-091720191", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180604-091720191", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-018-1695-7", "primary_object": { "basename": "1712.04156.pdf", "url": "https://authors.library.caltech.edu/records/hhdf1-6y806/files/1712.04156.pdf" }, "pub_year": "2018", "author_list": "Frank, Rupert L. and Sabin, Julien" }, { "id": "https://authors.library.caltech.edu/records/tzm1n-21q89", "eprint_id": 90671, "eprint_status": "archive", "datestamp": "2023-08-19 12:51:44", "lastmod": "2026-03-31 22:51:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carlen-E-A", "name": { "family": "Carlen", "given": "Eric A." }, "orcid": "0000-0003-2613-187X" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Inequalities for quantum divergences and the Audenaert\u2013Datta conjecture", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 IOP Publishing Ltd. \n\nReceived 11 June 2018; Accepted 16 October 2018; Accepted Manuscript online 16 October 2018; Published 5 November 2018. \n\nUS National Science Foundation grants DMS-1363432 (RLF), DMS-1501007 (EAC), PHY-1265118 (EHL) are acknowledged.\n\n

Submitted - 1806.03985.pdf

", "abstract": "Given two density matrices \u03c1 and \u03c3, there are a number of different expressions that reduce to the \u03b1-R\u00e9nyi relative entropy of \u03c1 with respect to \u03c3 in the classical case; i.e. when \u03c1 and \u03c3 commute. Only those expressions for which the data processing inequality (DPI) is valid are of potential interest as quantum divergences in quantum information theory. Audenaert and Datta have made a conjecture on the validity of the DPI for an interesting family of quantum generalizations of the \u03b1-R\u00e9nyi relative entropies, the \u03b1 - z-R\u00e9nyi relative entropies. They and others have contributed to the partial solution of this conjecture. We review the problem, its context, and the methods that have been used to obtain the results that are known at present, presenting a unified treatment of developments that have unfolded in a number of different papers.", "date": "2018-11-30", "date_type": "published", "publication": "Journal of Physics A: Mathematical and Theoretical", "volume": "51", "number": "48", "publisher": "IOP", "pagerange": "Art. No. 483001", "id_number": "CaltechAUTHORS:20181106-123858044", "issn": "1751-8113", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181106-123858044", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1501007" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1751-8121/aae8a3", "primary_object": { "basename": "1806.03985.pdf", "url": "https://authors.library.caltech.edu/records/tzm1n-21q89/files/1806.03985.pdf" }, "pub_year": "2018", "author_list": "Carlen, Eric A.; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/bm5e1-e1120", "eprint_id": 87369, "eprint_status": "archive", "datestamp": "2023-09-22 22:46:08", "lastmod": "2026-04-01 00:02:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" } ] }, "title": "A Proof of Onsager's Conjecture", "ispublished": "pub", "full_text_status": "public", "keywords": "Euler equations, incompressible, weak solutions, Onsager conjecture, Onsager's conjecture, energy conservation, conservation of energy, dissipation, energy dissipation, regularity, anomalous dissipation, turbulence, fluid dynamics, convex integration, nonuniqueness", "note": "\u00a9 2018 Department of Mathematics, Princeton University. \n\nThe work of P. Isett is supported by the National Science Foundation under Award No. DMS-1402370 and DMS-1700312.\n\n

Submitted - 1608.08301.pdf

", "abstract": "For any \u03b1 < 1/3, we construct weak solutions to the 3D incompressible Euler equations in the class C_tC_^x\u03b1 that have nonempty, compact support in time on R \u00d7 T^3 and therefore fail to conserve the total kinetic energy. This result, together with the proof of energy conservation for \u03b1 < 1/3 due to [Eyink] and [Constantin, E, Titi], solves Onsager's conjecture that the exponent \u03b1 = 1/3 marks the threshold for conservation of energy for weak solutions in the class L_t^\u221eC_x^\u03b1. The previous best results were solutions in the classC_tC_x^\u03b1 for \u03b1 < 1/5, due to [Isett], and in the class L_t^1C_x^\u03b1 for \u03b1 < 1/3 due to [Buckmaster, De Lellis, Sz\u00e9kelyhidi], both based on the method of convex integration developed for the incompressible Euler equations by [De Lellis, Sz\u00e9kelyhidi]. The present proof combines the method of convex integration and a new \"Gluing Approximation\" technique. The convex integration part of the proof relies on the \"Mikado flows\" introduced by [Daneri, Sz\u00e9kelyhidi] and the framework of estimates developed in the author's previous work.", "date": "2018-11", "date_type": "published", "publication": "Annals of Mathematics", "volume": "188", "number": "3", "publisher": "Princeton University", "pagerange": "871-963", "id_number": "CaltechAUTHORS:20180627-075519807", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180627-075519807", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1402370" }, { "agency": "NSF", "grant_number": "DMS-1700312" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2018.188.3.4", "primary_object": { "basename": "1608.08301.pdf", "url": "https://authors.library.caltech.edu/records/bm5e1-e1120/files/1608.08301.pdf" }, "pub_year": "2018", "author_list": "Isett, Philip" }, { "id": "https://authors.library.caltech.edu/records/pq7tc-dzz93", "eprint_id": 77287, "eprint_status": "archive", "datestamp": "2023-08-19 12:04:45", "lastmod": "2026-03-31 19:25:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zeitouni-O", "name": { "family": "Zeitouni", "given": "Ofer" } } ] }, "title": "Large Deviations and Sum Rules for Spectral Theory - A Pedagogical Approach", "ispublished": "pub", "full_text_status": "public", "keywords": "Sum rules, large deviations, orthogonal polynomials", "note": "\u00a9 2018 European Mathematical Society. \n\nReceived August 4, 2016. Published online: 2018-10-22. \n\nResearch supported in part by Israeli BSF Grant No. 2014337. \n\nResearch supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2014337. Research supported in part by a grant from the Israel Science Foundation.\n\n

Submitted - p339.pdf

", "abstract": "This is a pedagogical exposition of the large deviation approach to sum rules pioneered by Gamboa, Nagel and Rouault. We'll explain how to use their ideas to recover the Szeg\u0151 and Killip\u2013Simon Theorems. The primary audience is spectral theorists and people working on orthogonal polynomials who have limited familiarity with the theory of large deviations.", "date": "2018-10-22", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "8", "number": "4", "publisher": "European Mathematical Society", "pagerange": "1551-1581", "id_number": "CaltechAUTHORS:20170509-081147843", "issn": "1664-039X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170509-081147843", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" }, { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "Israel Science Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4171/JST/235", "primary_object": { "basename": "p339.pdf", "url": "https://authors.library.caltech.edu/records/pq7tc-dzz93/files/p339.pdf" }, "pub_year": "2018", "author_list": "Breuer, Jonathan; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/v2xvg-61954", "eprint_id": 77289, "eprint_status": "archive", "datestamp": "2023-08-19 11:51:48", "lastmod": "2026-03-31 19:09:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zeitouni-O", "name": { "family": "Zeitouni", "given": "Ofer" } } ] }, "title": "Large Deviations and the Lukic Conjecture", "ispublished": "pub", "full_text_status": "public", "keywords": "sum rules, large deviations, orthogonal polynomials", "note": "\u00a9 2018 Duke University Press. \n\nReceived: 15 March 2017; Revised: 16 May 2018; First published online 3 October 2018. \n\nWe thank Peter Yuditskii for telling two of us about [8] and Fabrice Gamboa, Jan Nagel, and Alain Rouault for useful discussions. \n\nBreuer's work was partially supported by Israel Science Foundation grant 399/16 and by United States\u2013Israel Binational Science Foundation grant 2014337. Simon's work was partially supported by National Science Foundation grant DMS-1265592 and by United States\u2013Israel Binational Science Foundation grant 2014337. Zeitouni's work was partially supported by a grant from the Israel Science Foundation.\n\n

Submitted - 1703.00653.pdf

", "abstract": "We use the large deviation approach to sum rules pioneered by Gamboa, Nagel, and Rouault to prove higher-order sum rules for orthogonal polynomials on the unit circle. In particular, we prove one half of a conjectured sum rule of Lukic in the case of two singular points, one simple and one double. This is important because it is known that the conjecture of Simon fails in exactly this case, so this article provides support for the idea that Lukic's replacement for Simon's conjecture might be true.", "date": "2018-10-03", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "167", "number": "15", "publisher": "Duke University Press", "pagerange": "2857-2902", "id_number": "CaltechAUTHORS:20170509-082734416", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170509-082734416", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "399/16" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" }, { "agency": "NSF", "grant_number": "DMS-1265592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1215/00127094-2018-0027", "primary_object": { "basename": "1703.00653.pdf", "url": "https://authors.library.caltech.edu/records/v2xvg-61954/files/1703.00653.pdf" }, "pub_year": "2018", "author_list": "Breuer, Jonathan; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/9kz89-a8c13", "eprint_id": 117601, "eprint_status": "archive", "datestamp": "2023-08-22 00:08:37", "lastmod": "2026-03-31 17:58:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Song-Antoine", "name": { "family": "Song", "given": "Antoine" } } ] }, "title": "Embeddedness of least area minimal hypersurfaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Geometry and Topology; Algebra and Number Theory; Analysis", "note": "\u00a9 2018 Lehigh University. \n\nReceived: 17 February 2016; Published: October 2018. \n\nI am grateful to my advisor Fernando Cod\u00e1 Marques for bringing a version of the main question to my attention. I would like to thank him for his constant support, for stimulating discussions and for guiding me through the recent literature. I also want to thank Harold Rosenberg for a meaningful discussion.", "abstract": "In \"Simple closed geodesics on convex surfaces\" [J. Differential Geom., 36(3):517\u2013549, 1992], E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher dimensions, this result holds without assumptions on the curvature. More precisely, in a closed (n + 1)-manifold with 2 \u2264 n \u2264 6, a least area closed minimal hypersurface exists and any such hypersurface is embedded. \n\nAs an application, we give a short proof of the fact that if a closed three-manifold M has scalar curvature at least 6 and is not isometric to the round three-sphere, then M contains an embedded closed minimal surface of area less than 4\u03c0. This confirms a conjecture of F. C. Marques and A. Neves.", "date": "2018-10", "date_type": "published", "publication": "Journal of Differential Geometry", "volume": "110", "number": "2", "publisher": "International Press", "pagerange": "345-377", "id_number": "CaltechAUTHORS:20221026-539158000.15", "issn": "0022-040X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20221026-539158000.15", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/jdg/1538791246", "pub_year": "2018", "author_list": "Song, Antoine" }, { "id": "https://authors.library.caltech.edu/records/40548-8c694", "eprint_id": 111009, "eprint_status": "archive", "datestamp": "2023-08-22 00:01:49", "lastmod": "2026-04-01 02:28:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Holroyd-Alexander-E", "name": { "family": "Holroyd", "given": "Alexander E." } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Levy-Avi", "name": { "family": "Levy", "given": "Avi" } } ] }, "title": "Finitely dependent cycle coloring", "ispublished": "pub", "full_text_status": "public", "keywords": "proper coloring; finite dependence; block factor; necklace", "note": "\u00a9 2018 The Author(s). Creative Commons Attribution 4.0 International License. \n\nSubmitted to ECP on July 29, 2017, final version accepted on February 13, 2018. First available in Project Euclid: 15 September 2018. \n\nAL and TH were supported by internships at Microsoft Research while portions of this work were completed. TH was also supported by a Microsoft Research PhD fellowship.\n\n

Published - 18-ECP118.pdf

Submitted - 1707.09374.pdf

", "abstract": "We construct stationary finitely dependent colorings of the cycle which are analogous to the colorings of the integers recently constructed by Holroyd and Liggett. These colorings can be described by a simple necklace insertion procedure, and also in terms of an Eden growth model on a tree. Using these descriptions we obtain simpler and more direct proofs of the characterizations of the 1- and 2-color marginals.", "date": "2018-09-15", "date_type": "published", "publication": "Electronic Communications in Probability", "volume": "23", "publisher": "Institute of Mathematical Statistics and Bernoulli Society", "pagerange": "Art. No. 64", "id_number": "CaltechAUTHORS:20210922-193309713", "issn": "1083-589X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309713", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/18-ECP118", "primary_object": { "basename": "1707.09374.pdf", "url": "https://authors.library.caltech.edu/records/40548-8c694/files/1707.09374.pdf" }, "related_objects": [ { "basename": "18-ECP118.pdf", "url": "https://authors.library.caltech.edu/records/40548-8c694/files/18-ECP118.pdf" } ], "pub_year": "2018", "author_list": "Holroyd, Alexander E.; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/f998n-csy95", "eprint_id": 72535, "eprint_status": "archive", "datestamp": "2023-08-19 11:28:34", "lastmod": "2026-03-31 22:19:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Turzillo-A", "name": { "family": "Turzillo", "given": "Alex" }, "orcid": "0000-0003-4293-4293" }, { "id": "You-Minyoung", "name": { "family": "You", "given": "Minyoung" } } ] }, "title": "Spin Topological Field Theory and Fermionic Matrix Product States", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 American Physical Society. \n\nReceived 27 February 2018; published 4 September 2018. \n\nThe research of A.K. was supported by the U. S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the Simons Investigator Award.\n\n

Published - PhysRevB.98.125101.pdf

Submitted - 1610.10075.pdf

", "abstract": "We study state-sum constructions of G-equivariant spin topological quantum field theory (TQFTs) and their relationship to matrix product states. In the Neveu-Schwarz, Ramond, and twisted sectors, states of the TQFT are generalized matrix product states. Our results are applied to the classification of fermionic short-range-entangled phases with a unitary symmetry G to determine the group law on the set of such phases. Interesting subtleties appear when the total symmetry group is a nontrivial extension of G by fermion parity.", "date": "2018-09-15", "date_type": "published", "publication": "Physical Review B", "volume": "98", "number": "12", "publisher": "American Physical Society", "pagerange": "Art. No. 125101", "id_number": "CaltechAUTHORS:20161202-140551166", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161202-140551166", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.98.125101", "primary_object": { "basename": "PhysRevB.98.125101.pdf", "url": "https://authors.library.caltech.edu/records/f998n-csy95/files/PhysRevB.98.125101.pdf" }, "related_objects": [ { "basename": "1610.10075.pdf", "url": "https://authors.library.caltech.edu/records/f998n-csy95/files/1610.10075.pdf" } ], "pub_year": "2018", "author_list": "Kapustin, Anton; Turzillo, Alex; et al." }, { "id": "https://authors.library.caltech.edu/records/xf9ak-cr102", "eprint_id": 111019, "eprint_status": "archive", "datestamp": "2023-08-19 11:27:45", "lastmod": "2026-03-31 19:02:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Foxall-Eric", "name": { "family": "Foxall", "given": "Eric" } }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Junge-Matthew", "name": { "family": "Junge", "given": "Matthew" } } ] }, "title": "Coalescing random walk on unimodular graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "coalescing random walk, unimodular random graph, voter model", "note": "\u00a9 2018 The Author(s). Creative Commons Attribution 4.0 International License. \n\nReceived: 6 April 2018; Accepted: 2 May 2018; Published: 2018. First available in Project Euclid: 13 September 2018.\n\n

Published - 18-ECP136.pdf

Accepted Version - 1701.02653.pdf

", "abstract": "Coalescing random walk on a unimodular random rooted graph for which the root has finite expected degree visits each site infinitely often almost surely. A corollary is that an opinion in the voter model on such graphs has infinite expected lifetime. Additionally, we deduce an adaptation of our main theorem that holds uniformly for coalescing random walk on finite random unimodular graphs with degree distribution stochastically dominated by a probability measure with finite mean.", "date": "2018-09-13", "date_type": "published", "publication": "Electronic Communications in Probability", "volume": "23", "publisher": "Institute of Mathematical Statistics", "pagerange": "Art. No. 62", "id_number": "CaltechAUTHORS:20210923-184021815", "issn": "1083-589X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210923-184021815", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/18-ecp136", "primary_object": { "basename": "1701.02653.pdf", "url": "https://authors.library.caltech.edu/records/xf9ak-cr102/files/1701.02653.pdf" }, "related_objects": [ { "basename": "18-ECP136.pdf", "url": "https://authors.library.caltech.edu/records/xf9ak-cr102/files/18-ECP136.pdf" } ], "pub_year": "2018", "author_list": "Foxall, Eric; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/w61fx-hp647", "eprint_id": 66605, "eprint_status": "archive", "datestamp": "2023-08-19 11:23:33", "lastmod": "2026-03-31 20:22:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gorsky-E", "name": { "family": "Gorsky", "given": "Eugene" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sto\u0161i\u0107-M", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" } } ] }, "title": "Quadruply-graded colored homology of knots", "ispublished": "pub", "full_text_status": "public", "keywords": "knot homology, colored HOMFLYPT invariants, BPS invariants,\ndifferentials, Lie superalgebras", "note": "\u00a9 2018 Instytut Matematyczny PAN. \n\nReceived 28 October 2014; revised 21 February 2017. Published online 3 September 2018.\n\nWe are grateful to M. Abouzaid, M. Aganagic, J. M. Baptista, M. Bershtein, I. Cherednik, K. Costello, R. Elliot, P. Etingof, A. Gorsky, K. Hikami, M. Khovanov, B. Kim, A. N. Kirillov and A. A. Kirillov Jr., I. Losev, A. Morozov, H. Nakajima, A. Negu\u00b5, N. Nekrasov, A. Oblomkov, A. Okounkov, J. Rasmussen, L. Rozansky, S. Shakirov, V. Shende, C. Vafa, O. Viro, E. Witten, and C. Woodward for useful discussions. \n\nE.G. would like to thank California Institute of Technology and Kyoto Research Institute for Mathematical Sciences for hospitality. The research of E.G. is partially supported by the NSF grant DMS-1559338, grants RFBR-10-01-678, NSh-8462.2010.1, Simons Foundation and Russian Academic Excellence Project 5-100.\nS.G. would like to thank Instituto Superior T\u00e9cnico in Lisbon and the Simons Center for Geometry and Physics at Stony Brook for hospitality during the key stages of this work. The work of S.G. is supported in part by DOE grant DE-FG03-92-ER40701FG-02 and in part by NSF grant PHY-0757647. \n\nM.S. would like to thank the California Institute of Technology for hospitality while part of this work was done. The work of S.G. and M.S. was partially supported by ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\" funded by the European Research Council under the European Union Seventh Framework Programme. M.S. was also partially supported by the Portuguese Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia through the project PTDC/MAT/101503/2008, New Geometry and Topology, and\nby the Ministry of Science of Serbia, project no. 174012. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of the funding agencies.\n\n

Published - fm30-11-2017.pdf

Submitted - 1304.3481.pdf

", "abstract": "We conjecture the existence of four independent gradings in colored HOMFLYPT homology, and make qualitative predictions of various interesting structures and symmetries in the colored homology of arbitrary knots. We propose an explicit conjectural description for the rectangular colored homology of torus knots, and identify the new gradings in this context. While some of these structures have a natural interpretation in the physical realization of knot homologies based on counting supersymmetric configurations (BPS states, instantons, and vortices), others are completely new. They suggest new geometric and physical realizations of colored HOMFLYPT homology as the Hochschild homology of the category of branes in a Landau\u2013Ginzburg B-model or, equivalently, in the mirror A-model. Supergroups and supermanifolds are surprisingly ubiquitous in all aspects of this work.", "date": "2018-09-03", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "243", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "209-299", "id_number": "CaltechAUTHORS:20160503-082624275", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-082624275", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1559338" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "RFBR-10-01-678" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "NSh-8462.2010.1" }, { "agency": "Simons Foundation" }, { "agency": "Russian Academic Excellence Project (RAEP)", "grant_number": "5-100" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT/101503/2008" }, { "agency": "Ministry of Science (Serbia)", "grant_number": "174012" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4064/fm30-11-2017", "primary_object": { "basename": "1304.3481.pdf", "url": "https://authors.library.caltech.edu/records/w61fx-hp647/files/1304.3481.pdf" }, "related_objects": [ { "basename": "fm30-11-2017.pdf", "url": "https://authors.library.caltech.edu/records/w61fx-hp647/files/fm30-11-2017.pdf" } ], "pub_year": "2018", "author_list": "Gorsky, Eugene; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/ah2hj-4fp82", "eprint_id": 78988, "eprint_status": "archive", "datestamp": "2023-08-19 11:13:51", "lastmod": "2026-03-31 19:20:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Nies-A", "name": { "family": "Nies", "given": "Andr\u00e9" } }, { "id": "Tent-K", "name": { "family": "Tent", "given": "Katrin" } } ] }, "title": "The complexity of topological group isomorphism", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 The Association for Symbolic Logic. \n\nPublished online: 23 October 2018. \n\nThe first author was partially supported by NSF grant DMS 1464475. The second author was partially supported by the Marsden fund of New Zealand. The third author was supported by Sonderforschungsbereich 878 at Universit\u00e4t M\u00fcnster.\n\n

Submitted - 1705.08081.pdf

", "abstract": "We study the complexity of the topological isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Borel spaces. For profinite, locally compact, and Roelcke precompact groups, we show that the complexity is the same as the one of countable graph isomorphism. For oligomorphic groups, we merely establish this as an upper bound.", "date": "2018-09", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "83", "number": "3", "publisher": "Cambridge University Press", "pagerange": "1190-1203", "id_number": "CaltechAUTHORS:20170712-083759861", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-083759861", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1464475" }, { "agency": "Marsden Fund of New Zealand" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "Sonderforschungsbereich 878" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/jsl.2018.25", "primary_object": { "basename": "1705.08081.pdf", "url": "https://authors.library.caltech.edu/records/ah2hj-4fp82/files/1705.08081.pdf" }, "pub_year": "2018", "author_list": "Kechris, Alexander S.; Nies, Andr\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/jtkbd-2y576", "eprint_id": 77073, "eprint_status": "archive", "datestamp": "2023-09-28 19:37:17", "lastmod": "2026-03-31 21:49:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Nam-Phan-Th\u00e0nh", "name": { "family": "Nam", "given": "Phan Th\u00e0nh" }, "orcid": "0000-0001-7599-9742" }, { "id": "Van-Den-Bosch-H", "name": { "family": "Van Den Bosch", "given": "Hanne" }, "orcid": "0000-0002-5073-3515" } ] }, "title": "The Maximal Excess Charge in M\u00fcller Density-Matrix-Functional Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Springer International Publishing AG, part of Springer Nature. \n\nReceived: 04 December 2017; Accepted: 09 April 2018; First Online: 07 July 2018. \n\nThe authors are grateful to Heinz Siedentop for a motivating discussion. Partial support by U.S. National Science Foundation DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT\u2013PCHA/Doctorado Nacional/2014, Fondecyt Project # 116\u20130856 and Iniciativa Cient\u00edfica Milenio (Chile) through Millennium Nucleus RC\u2013120002 \"F\u00edsica Matem\u00e1tica\" (H.V.D.B.) is acknowledged.\n\n

Submitted - 1608_05625.pdf

", "abstract": "We consider an atom described by M\u00fcller theory, which is similar to Hartree\u2013Fock theory, but with a modified exchange term. We prove that a nucleus of charge Z can bind at most Z + C electrons, where C is a universal constant. Our proof proceeds by comparison with Thomas\u2013Fermi theory, and a key ingredient is a novel bound on the number of electrons far from the nucleus.", "date": "2018-09", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "19", "number": "9", "publisher": "Springer", "pagerange": "2839-2867", "id_number": "CaltechAUTHORS:20170428-155623144", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170428-155623144", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "FWF Der Wissenschaftsfonds", "grant_number": "P 27533-N27" }, { "agency": "Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (CONICYT)", "grant_number": "116-0856" }, { "agency": "Iniciativa Cient\u00edfica Milenio del Ministerio de Econom\u00eda, Fomento y Turismo", "grant_number": "RC-120002" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-018-0695-1", "primary_object": { "basename": "1608_05625.pdf", "url": "https://authors.library.caltech.edu/records/jtkbd-2y576/files/1608_05625.pdf" }, "pub_year": "2018", "author_list": "Frank, Rupert L.; Nam, Phan Th\u00e0nh; et al." }, { "id": "https://authors.library.caltech.edu/records/vpw4b-fp197", "eprint_id": 98078, "eprint_status": "archive", "datestamp": "2023-08-21 23:50:49", "lastmod": "2026-03-08 17:36:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aigner-Horev-E", "name": { "family": "Aigner-Horev", "given": "Elad" } }, { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "H\u00e0n-Hi\u1ec7p", "name": { "family": "H\u00e0n", "given": "Hi\u1ec7p" } }, { "id": "Person-Y", "name": { "family": "Person", "given": "Yury" } }, { "id": "Schacht-M", "name": { "family": "Schacht", "given": "Mathias" } } ] }, "title": "Quasirandomness in Hypergraphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Hypergraphs; quasirandom", "note": "\u00a9 The authors. Released under the CC BY-ND license (International 4.0). \n\nSubmitted: Dec 12, 2017; accepted Jul 24, 2018; published: Aug 24, 2018. \n\nThe second author was supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. The third author was supported by the FONDECYT Iniciaci\u00f3n grant 11150913 and by Millenium Nucleus Information and Coordination in Networks. The fourth author was supported by DFG grant PE 2299/1-1. The fifth author was supported by ERC Consolidator Grant 724903. \n\nWe are indebted to the anonymous referee for their careful review.\n\n

Published - EJC25.3.34.pdf

", "abstract": "A graph G is called quasirandom if it possesses typical properties of the corresponding random graph G(n, p) with the same edge density as G. A well-known theorem of Chung, Graham and Wilson states that, in fact, many such 'typical' properties are asymptotically equivalent and, thus, a graph G possessing one property immediately satisfies the others.\n\nIn recent years, more quasirandom graph properties have been found and extensions to hypergraphs have been explored. For the latter, however, there exist several distinct notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. The purpose of this paper is to give short purely combinatorial proofs of most of Towsner's results.", "date": "2018-08-24", "date_type": "published", "publication": "Electronic Journal of Combinatorics", "volume": "25", "number": "3", "publisher": "Electronic Journal of Combinatorics", "pagerange": "Art. No. P3.34", "id_number": "CaltechAUTHORS:20190821-110928639", "issn": "1077-8926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190821-110928639", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (FONDECYT)", "grant_number": "11150913" }, { "agency": "Millenium Nucleus Information and Coordination in Networks" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "PE 2299/1-1" }, { "agency": "European Research Council (ERC)", "grant_number": "724903" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "EJC25.3.34.pdf", "url": "https://authors.library.caltech.edu/records/vpw4b-fp197/files/EJC25.3.34.pdf" }, "pub_year": "2018", "author_list": "Aigner-Horev, Elad; Conlon, David; et al." }, { "id": "https://authors.library.caltech.edu/records/xpbhc-t0n54", "eprint_id": 110834, "eprint_status": "archive", "datestamp": "2023-08-19 10:58:21", "lastmod": "2026-03-31 22:15:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Gromov compactness in non-archimedean analytic geometry", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Walter de Gruyter GmbH 2016. \n\nPublished by De Gruyter January 14, 2016. \n\nI am very grateful to Maxim Kontsevich for inspirations and guidance. Special thanks to Antoine Chambert-Loir who provided me much advice and support. I appreciate valuable discussions with Ahmed Abbes, Denis Auroux, Pierrick Bousseau, Olivier Debarre, Antoine Ducros, Lie Fu, Ilia Itenberg, Fran\u00e7ois Loeser, Johannes Nicaise, Mauro Porta, Matthieu Romagny, Michael Temkin and Jean-Yves Welschinger. I would like to thank the referees for helpful comments.\n\n

Accepted Version - 1401.6452.pdf

", "abstract": "Gromov's compactness theorem for pseudo-holomorphic curves is a foundational result in symplectic geometry. It controls the compactness of the moduli space of pseudo-holomorphic curves with bounded area in a symplectic manifold. In this paper, we prove the analog of Gromov's compactness theorem in non-archimedean analytic geometry. We work in the framework of Berkovich spaces. First, we introduce a notion of K\u00e4hler structure in non-archimedean analytic geometry using metrizations of virtual line bundles. Second, we introduce formal stacks and non-archimedean analytic stacks. Then we construct the moduli stack of non-archimedean analytic stable maps using formal models, Artin's representability criterion and the geometry of stable curves. Finally, we reduce the non-archimedean problem to the known compactness results in algebraic geometry. The motivation of this paper is to provide the foundations for non-archimedean enumerative geometry.", "date": "2018-08-01", "date_type": "published", "publication": "Journal F\u00fcr Die Reine und Angewandte Mathematik", "volume": "2018", "number": "741", "publisher": "Walter de Gruyter", "pagerange": "179-210", "id_number": "CaltechAUTHORS:20210914-164413051", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164413051", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2015-0077", "primary_object": { "basename": "1401.6452.pdf", "url": "https://authors.library.caltech.edu/records/xpbhc-t0n54/files/1401.6452.pdf" }, "pub_year": "2018", "author_list": "Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/w63qa-xx947", "eprint_id": 81746, "eprint_status": "archive", "datestamp": "2023-08-21 23:44:01", "lastmod": "2026-03-31 19:13:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Warnaar-S-O", "name": { "family": "Warnaar", "given": "S. Ole" }, "orcid": "0000-0002-9786-0175" } ] }, "title": "A Nekrasov\u2013Okounkov formula for Macdonald polynomials", "ispublished": "pub", "full_text_status": "public", "keywords": "Hook-length formulas; Macdonald polynomials", "note": "\u00a9 2017 Springer Science+Business Media, LLC. \n\nReceived: 18 December 2016; Accepted: 09 September 2017; First Online: 22 September 2017. \n\nWork supported by the National Science Foundation (Grant Number DMS-1001645) and the Australian Research Council.\n\nThe second author is grateful to Masoud Kamgarpour for pointing out the papers of Hausel and Rodriguez-Villegas [22], and Hausel, Letellier and Rodriguez-Villegas [20, 21] on mixed Hodge polynomials, and to Dennis Stanton for helpful discussions on p-core partitions. We thank Fernando Rodriguez-Villegas for sending us a preliminary version of his paper [6] with Carlsson, which contains a different proof of Conjecture 1.1 based on the Carlsson\u2013Nekrasov\u2013Okounkov vertex operator [5]. We also thank Amer Iqbal for alerting us to the connection between our work and [24] and Jim Bryan for explaining the work of Waelder, which implies the elliptic Nekrasov\u2013Okounkov formula described in the appendix. We thank the two referees for their helpful comments and corrections.\n\n

Submitted - 1606.04613.pdf

", "abstract": "We prove a Macdonald polynomial analogue of the celebrated Nekrasov\u2013Okounkov hook-length formula from the theory of random partitions. As an application we obtain a proof of one of the main conjectures of Hausel and Rodriguez-Villegas from their work on mixed Hodge polynomials of the moduli space of stable Higgs bundles on Riemann surfaces.", "date": "2018-08", "date_type": "published", "publication": "Journal of Algebraic Combinatorics", "volume": "48", "number": "1", "publisher": "Springer", "pagerange": "1-30", "id_number": "CaltechAUTHORS:20170922-130437528", "issn": "0925-9899", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170922-130437528", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1001645" }, { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10801-017-0790-2", "primary_object": { "basename": "1606.04613.pdf", "url": "https://authors.library.caltech.edu/records/w63qa-xx947/files/1606.04613.pdf" }, "pub_year": "2018", "author_list": "Rains, Eric M. and Warnaar, S. Ole" }, { "id": "https://authors.library.caltech.edu/records/q3fsh-t7f69", "eprint_id": 63951, "eprint_status": "archive", "datestamp": "2023-08-19 10:26:33", "lastmod": "2026-04-01 02:16:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "McKinney-T", "name": { "family": "McKinney", "given": "Tristan" } }, { "id": "Rothstein-I-Z", "name": { "family": "Rothstein", "given": "Ira Z." }, "orcid": "0000-0002-3374-4212" } ] }, "title": "Wilsonian effective field theory of two-dimensional Van Hove singularities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 American Physical Society. \n\nReceived 30 January 2016; revised manuscript received 11 May 2018; published 17 July 2018. \n\nThis work was supported by DOE Contracts No. DE-SC0011632, No. DE-FG02-92ER40701, No. DOE-ER-40682-143, and No. DE-AC02-6CH03000. The authors gratefully acknowledge helpful conversations with J. Polchinski, M. Metlitskii, L. Motrunich, and I. Saberi. A.K. and T.M. are grateful to the Simons Center for Geometry and Physics for hospitality during various stages of this work. A.K. is also grateful to the Aspen Center for Physics, the Kavli Institute for Physics and Mathematics of the Universe, and Institut des Hautes Etudes Scientifiques for hospitality. I.Z.R. is grateful to the Caltech theory group for hospitality and to the Moore Foundation for support.\n\n

Published - PhysRevB.98.035122.pdf

Submitted - 1601.03150v1.pdf

", "abstract": "We study two-dimensional fermions with a short-range interaction in the presence of a Van Hove singularity. It is shown that this system can be consistently described by an effective field theory whose Fermi surface is subdivided into regions as defined by a factorization scale, and that the theory is renormalizable in the sense that all of the counterterms are well defined in the IR limit. The theory has the unusual feature that the renormalization-group equation for the coupling has an explicit dependence on the renormalization scale, much as in theories of Wilson lines. In contrast to the case of a round Fermi surface, there are multiple marginal interactions with nontrivial RG flow. The Cooper instability remains strongest in the BCS channel. We also show that the marginal Fermi-liquid scenario for the quasiparticle width is a robust consequence of the Van Hove singularity. Our results are universal in the sense that they do not depend on the detailed properties of the Fermi surface away from the singularity.", "date": "2018-07-15", "date_type": "published", "publication": "Physical Review B", "volume": "98", "number": "3", "publisher": "American Physical Society", "pagerange": "Art. No. 035122", "id_number": "CaltechAUTHORS:20160125-190842565", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160125-190842565", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DOE-ER-40682-143" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC02-6CH03000" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "2016-001", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.98.035122", "primary_object": { "basename": "1601.03150v1.pdf", "url": "https://authors.library.caltech.edu/records/q3fsh-t7f69/files/1601.03150v1.pdf" }, "related_objects": [ { "basename": "PhysRevB.98.035122.pdf", "url": "https://authors.library.caltech.edu/records/q3fsh-t7f69/files/PhysRevB.98.035122.pdf" } ], "pub_year": "2018", "author_list": "Kapustin, Anton; McKinney, Tristan; et al." }, { "id": "https://authors.library.caltech.edu/records/83b2d-z3434", "eprint_id": 81754, "eprint_status": "archive", "datestamp": "2023-08-19 10:24:12", "lastmod": "2026-03-31 22:13:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sam-S-V", "name": { "family": "Sam", "given": "Steven V." } } ] }, "title": "Invariant theory of \u22c0^3(9) and genus 2 curves", "ispublished": "pub", "full_text_status": "public", "keywords": "genus-2 curves, invariant theory, abelian surfaces, Selmer groups", "note": "\u00a9 2018 Mathematical Sciences Publishers. \n\nReceived: 22 February 2017; Revised: 30 October 2017; Accepted: 16 November 2017; Published: 11 July 2018. \n\nSS was partially supported by a Miller research fellowship and NSF DMS-1500069.\n\n

Published - ant-v12-n4-p05-p.pdf

Submitted - 1702.04840.pdf

", "abstract": "Previous work established a connection between the geometric invariant theory of the third exterior power of a 9-dimensional complex vector space and the moduli space of genus-2 curves with some additional data. We generalize this connection to arbitrary fields, and describe the arithmetic data needed to get a bijection between both sides of this story.", "date": "2018-07-11", "date_type": "published", "publication": "Algebra and Number Theory", "volume": "12", "number": "4", "publisher": "Mathematical Sciences Publishers", "pagerange": "935-957", "id_number": "CaltechAUTHORS:20170922-135107001", "issn": "1937-0652", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170922-135107001", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Miller Institute for Basic Research in Science" }, { "agency": "NSF", "grant_number": "DMS-1500069" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/ant.2018.12.935", "primary_object": { "basename": "1702.04840.pdf", "url": "https://authors.library.caltech.edu/records/83b2d-z3434/files/1702.04840.pdf" }, "related_objects": [ { "basename": "ant-v12-n4-p05-p.pdf", "url": "https://authors.library.caltech.edu/records/83b2d-z3434/files/ant-v12-n4-p05-p.pdf" } ], "pub_year": "2018", "author_list": "Rains, Eric M. and Sam, Steven V." }, { "id": "https://authors.library.caltech.edu/records/pz4qv-6pf59", "eprint_id": 87568, "eprint_status": "archive", "datestamp": "2023-08-19 10:13:22", "lastmod": "2026-04-16 01:39:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Poulin-D", "name": { "family": "Poulin", "given": "David" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Steiger-D-S", "name": { "family": "Steiger", "given": "Damian S." } }, { "id": "Hastings-M-B", "name": { "family": "Hastings", "given": "Matthew B." } }, { "id": "Troyer-M", "name": { "family": "Troyer", "given": "Matthias" } } ] }, "title": "Quantum Algorithm for Spectral Measurement with a Lower Gate Count", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 American Physical Society. \n\n(Received 22 December 2017; published 5 July 2018) \n\nWe thank Thomas H\u00e4ner for interesting discussions and Sergey Bravyi for feedback, and acknowledge support by the Swiss National Science Foundation, the NCCR QSIT, Canada's NSERC, Caltech's IQIM, and the Simons Foundation.\n\n

Published - PhysRevLett.121.010501.pdf

", "abstract": "We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.", "date": "2018-07-06", "date_type": "published", "publication": "Physical Review Letters", "volume": "121", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 010501", "id_number": "CaltechAUTHORS:20180705-150616687", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180705-150616687", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swiss National Science Foundation (SNSF)" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.121.010501", "primary_object": { "basename": "PhysRevLett.121.010501.pdf", "url": "https://authors.library.caltech.edu/records/pz4qv-6pf59/files/PhysRevLett.121.010501.pdf" }, "pub_year": "2018", "author_list": "Poulin, David; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/21ast-60592", "eprint_id": 111017, "eprint_status": "archive", "datestamp": "2023-08-19 10:08:37", "lastmod": "2026-03-31 19:18:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Angel-Omer", "name": { "family": "Angel", "given": "Omer" }, "orcid": "0000-0002-6451-8242" }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Nachmias-Asaf", "name": { "family": "Nachmias", "given": "Asaf" }, "orcid": "0000-0002-4852-5645" }, { "id": "Ray-Gourab", "name": { "family": "Ray", "given": "Gourab" } } ] }, "title": "Hyperbolic and Parabolic Unimodular Random Maps", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Springer. \n\nReceived: August 12, 2017. Accepted: February 27, 2018. \n\nOA was supported by NSERC and the Simons Foundation. TH was supported by a Microsoft Research PhD Fellowship. AN was supported by ISF grant 1207/15, and ERC starting grant 676970 RANDGEOM. GR was supported in part by EPSRC grant EP/I03372X/1. Part of this work was conducted at the Isaac Newton Institute in Cambridge, during the programme 'Random Geometry' supported by EPSRC Grant Number EP/K032208/1.\n\n

Accepted Version - 1612.08693.pdf

", "abstract": "We show that for infinite planar unimodular random rooted maps. many global geometric and probabilistic properties are equivalent, and are determined by a natural, local notion of average curvature. This dichotomy includes properties relating to amenability, conformal geometry, random walks, uniform and minimal spanning forests, and Bernoulli bond percolation. We also prove that every simply connected unimodular random rooted map is sofic, that is, a Benjamini\u2013Schramm limit of finite maps.", "date": "2018-07", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "28", "number": "4", "publisher": "Springer", "pagerange": "879-942", "id_number": "CaltechAUTHORS:20210923-184021127", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210923-184021127", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Simons Foundation" }, { "agency": "Microsoft Research" }, { "agency": "Israel Science Foundation", "grant_number": "1207/15" }, { "agency": "European Research Council (ERC)", "grant_number": "676970" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/I03372X/1" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/K032208/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-018-0446-y", "primary_object": { "basename": "1612.08693.pdf", "url": "https://authors.library.caltech.edu/records/21ast-60592/files/1612.08693.pdf" }, "pub_year": "2018", "author_list": "Angel, Omer; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/vv9pf-jbm87", "eprint_id": 85783, "eprint_status": "archive", "datestamp": "2023-08-21 23:25:36", "lastmod": "2026-03-31 19:20:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Yu-An", "name": { "family": "Chen", "given": "Yu-An" }, "orcid": "0000-0002-8810-9355" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Radi\u010devi\u0107-\u0110", "name": { "family": "Radi\u010devi\u0107", "given": "\u0110or\u0111e" } } ] }, "title": "Exact bosonization in two spatial dimensions and a new class of lattice gauge theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Bosonization; Lattice gauge theory; Spin systems", "note": "\u00a9 2018 Elsevier Inc. \n\nReceived 1 March 2018, Accepted 30 March 2018, Available online 11 April 2018. \n\nA. K. would like to thank T. Senthil for a discussion. The research of A. K. and Y. C. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632. A. K. was also supported by the Simons Investigator Award. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation.\n\n

Submitted - 1711.00515.pdf

", "abstract": "We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contain Chern\u2013Simons-like terms. Finally, we write down a fermionic dual of the gauged Ising model (the Fradkin-Shenker model).", "date": "2018-06", "date_type": "published", "publication": "Annals of Physics", "volume": "393", "publisher": "Elsevier", "pagerange": "234-253", "id_number": "CaltechAUTHORS:20180412-112218749", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180412-112218749", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aop.2018.03.024", "primary_object": { "basename": "1711.00515.pdf", "url": "https://authors.library.caltech.edu/records/vv9pf-jbm87/files/1711.00515.pdf" }, "pub_year": "2018", "author_list": "Chen, Yu-An; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/g5k83-d9494", "eprint_id": 81760, "eprint_status": "archive", "datestamp": "2023-08-19 08:55:49", "lastmod": "2026-03-31 17:59:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jordan-B-W", "name": { "family": "Jordan", "given": "Bruce W." } }, { "id": "Keeton-A-G", "name": { "family": "Keeton", "given": "Allan G." } }, { "id": "Poonen-B", "name": { "family": "Poonen", "given": "Bjorn" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Shepherd-Barron-N", "name": { "family": "Shepherd-Barron", "given": "Nicholas" } }, { "id": "Tate-J-T", "name": { "family": "Tate", "given": "John T." } } ] }, "title": "Abelian varieties isogenous to a power of an elliptic curve", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Authors 2018. \n\nPublished online: 21 March 2018. \n\nB.P. was supported in part by National Science Foundation grant DMS-1069236 and DMS-1601946 and grants from the Simons Foundation (#340694 and #402472 to Bjorn Poonen). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Simons Foundation. \n\nIt is a pleasure to thank Everett Howe, Tony Scholl, and Christopher Skinner for helpful discussions. We thank also the referees for valuable suggestions on the exposition.\n\n

Submitted - 1602.06237.pdf

", "abstract": "Let E be an elliptic curve over a field k. Let R:=End E. There is a functor Hom_R(\u2212,E) from the category of finitely presented torsion-free left R -modules to the category of abelian varieties isogenous to a power of E, and a functor Hom(\u2212,E) in the opposite direction. We prove necessary and sufficient conditions on E for these functors to be equivalences of categories. We also prove a partial generalization in which E is replaced by a suitable higher-dimensional abelian variety over F_p.", "date": "2018-05", "date_type": "published", "publication": "Compositio Mathematica", "volume": "154", "number": "5", "publisher": "Cambridge University Press", "pagerange": "934-959", "id_number": "CaltechAUTHORS:20170922-140322875", "issn": "0010-437X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170922-140322875", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1069236" }, { "agency": "NSF", "grant_number": "DMS-1601946" }, { "agency": "Simons Foundation", "grant_number": "340694" }, { "agency": "Simons Foundation", "grant_number": "402472" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0010437X17007990", "primary_object": { "basename": "1602.06237.pdf", "url": "https://authors.library.caltech.edu/records/g5k83-d9494/files/1602.06237.pdf" }, "pub_year": "2018", "author_list": "Jordan, Bruce W.; Keeton, Allan G.; et al." }, { "id": "https://authors.library.caltech.edu/records/z0v9j-1z604", "eprint_id": 79026, "eprint_status": "archive", "datestamp": "2023-08-19 08:55:37", "lastmod": "2026-03-31 20:06:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bernardara-Marcello", "name": { "family": "Bernardara", "given": "Marcello" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-Gon\u00e7alo", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Some remarks concerning Voevodsky's nilpotence conjecture", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Walter de Gruyter GmbH, Berlin/Boston. \n\nReceived: 2014-11-21; Published Online: 2015-11-28; Published in Print: 2018-05-01. \n\nG. Tabuada was partially supported by the National Science Foundation CAREER Award #1350472 and by the Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project grant UID/MAT/00297/2013 (Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es). M. Marcolli was partially supported by the NSF grants DMS-1201512 and PHY-1205440.\n\n

Submitted - 1403.0876.pdf

", "abstract": "In this article we extend Voevodsky's nilpotence conjecture from smooth projective schemes to the broader setting of smooth proper dg categories. Making use of this noncommutative generalization, we then address Voevodsky's original conjecture in the following cases: quadric fibrations, intersection of quadrics, linear sections of Grassmannians, linear sections of determinantal varieties, homological projective duals, and Moishezon manifolds.", "date": "2018-05", "date_type": "published", "publication": "Journal f\u00fcr die Reine und Angewandte Mathematik", "volume": "738", "publisher": "De Gruyter", "pagerange": "299-312", "id_number": "CaltechAUTHORS:20170712-145442721", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-145442721", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1350472" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "UID/MAT/00297/2013" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2015-0068", "primary_object": { "basename": "1403.0876.pdf", "url": "https://authors.library.caltech.edu/records/z0v9j-1z604/files/1403.0876.pdf" }, "pub_year": "2018", "author_list": "Bernardara, Marcello; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/xr8k2-9be11", "eprint_id": 97830, "eprint_status": "archive", "datestamp": "2023-08-19 09:04:44", "lastmod": "2026-03-31 18:04:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Hereditary quasirandomness without regularity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Cambridge Philosophical Society 2017. \n\nFirst published online 26 January 2017. \n\nConlon supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. Fox supported by a Packard Fellowship, by NSF Career Award DMS-1352121 and by an Alfred P. Sloan Fellowship. Sudakov supported by SNSF grant 200021-149111.\n\n

Submitted - 1611.02099.pdf

", "abstract": "A result of Simonovits and S\u00f3s states that for any fixed graph H and any \u03f5 > 0 there exists \u03b4 > 0 such that if G is an n-vertex graph with the property that every S \u2286 V(G) contains p^(e(H))|S|^(v(H)) \u00b1 \u03b4n^(v(H)) labelled copies of H, then G is quasirandom in the sense that every S \u2286 V(G) contains \u00bdp|S|^2 \u00b1 \u03f5n^2 edges. The original proof of this result makes heavy use of the regularity lemma, resulting in a bound on \u03b4^(\u22121) which is a tower of twos of height polynomial in \u03f5^(\u22121). We give an alternative proof of this theorem which avoids the regularity lemma and shows that \u03b4 may be taken to be linear in \u03f5 when H is a clique and polynomial in \u03f5 for general H. This answers a problem raised by Simonovits and S\u00f3s.", "date": "2018-05", "date_type": "published", "publication": "Mathematical Proceedings of the Cambridge Philosophical Society", "volume": "164", "number": "3", "publisher": "Cambridge University Press", "pagerange": "385-399", "id_number": "CaltechAUTHORS:20190812-162959631", "issn": "0305-0041", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959631", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0305004116001055", "primary_object": { "basename": "1611.02099.pdf", "url": "https://authors.library.caltech.edu/records/xr8k2-9be11/files/1611.02099.pdf" }, "pub_year": "2018", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/68vgr-vj392", "eprint_id": 86710, "eprint_status": "archive", "datestamp": "2023-08-21 23:17:49", "lastmod": "2026-04-16 01:39:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Suh-S-Josephine", "name": { "family": "Suh", "given": "S. Josephine" }, "orcid": "0000-0003-2393-6883" } ] }, "title": "The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual", "ispublished": "pub", "full_text_status": "public", "keywords": "2D Gravity; AdS-CFT Correspondence; Black Holes; Models of Quantum Gravity", "note": "\u00a9 The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: April 2, 2018; Accepted: May 22, 2018; Published: May 29, 2018. \n\nWe thank Juan Maldacena, Douglas Stanford, and Yingfei Gu for useful discussions. We gratefully acknowledge the support by the Simons Foundation through the \"It from Qubit\" program. A.K. is supported by the Simons Foundation under grant 376205 and by the Institute of Quantum Information and Matter, a NSF Frontier center funded in part by the Gordon and Betty Moore Foundation. The work of J.S. was supported in part by the Natural Sciences and Engineering Research Council of Canada and by the Simons Foundation through grant 376206. It was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.\n\n

Published - 10.1007_2FJHEP05_2018_183.pdf

Submitted - 1711.08467.pdf

", "abstract": "We give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.", "date": "2018-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2018", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 183", "id_number": "CaltechAUTHORS:20180530-110303978", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180530-110303978", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "376205" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Simons Foundation", "grant_number": "376206" }, { "agency": "NSF", "grant_number": "PHY-1607611" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/JHEP05(2018)183", "primary_object": { "basename": "10.1007_2FJHEP05_2018_183.pdf", "url": "https://authors.library.caltech.edu/records/68vgr-vj392/files/10.1007_2FJHEP05_2018_183.pdf" }, "related_objects": [ { "basename": "1711.08467.pdf", "url": "https://authors.library.caltech.edu/records/68vgr-vj392/files/1711.08467.pdf" } ], "pub_year": "2018", "author_list": "Kitaev, Alexei and Suh, S. Josephine" }, { "id": "https://authors.library.caltech.edu/records/s41jh-3gx85", "eprint_id": 77998, "eprint_status": "archive", "datestamp": "2023-08-19 08:28:28", "lastmod": "2026-03-31 22:53:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sun-Yi", "name": { "family": "Sun", "given": "Yi" } }, { "id": "Varchenko-A", "name": { "family": "Varchenko", "given": "Alexander" } } ] }, "title": "Affine Macdonald conjectures and special values of Felder\u2013Varchenko functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Springer International Publishing. \n\nPublished online: 27 April 2017. \n\nY.S. and A.V. thank the Max-Planck-Institut f\u00fcr Mathematik in Bonn for providing excellent working conditions. Y.S. thanks P. Etingof for many helpful discussions. E.M.R. was partially supported by NSF Grant DMS-1500806. This work was partially supported by a Junior Fellow award from the Simons Foundation to Yi Sun. A.V. was partially supported by NSF Grant DMS-1362924 and Simons Foundation Grant #336826.\n\n

Submitted - 1610.01917.pdf

", "abstract": "We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof\u2013Kirillov Jr. (Duke Math J 78(2):229\u2013256, 1995) and prove the first non-trivial cases of these conjectures. Our results provide a q-deformation of the computation of genus 1 conformal blocks via elliptic Selberg integrals by Felder\u2013Stevens\u2013Varchenko (Math Res Lett 10(5\u20136):671\u2013684, 2003). They allow us to give precise formulations for the affine Macdonald conjectures in the general case which are consistent with computer computations. Our method applies recent work of the second named author to relate these conjectures in the case of U_q(sl_2) to evaluations of certain theta hypergeometric integrals defined by Felder\u2013Varchenko (Int Math Res Not 21:1037\u20131055, 2004). We then evaluate the resulting integrals, which may be of independent interest, by well-chosen applications of the elliptic beta integral introduced by Spiridonov (Uspekhi Mat Nauk 56(1(337)):181\u2013182, 2001).", "date": "2018-04", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "24", "number": "2", "publisher": "Springer", "pagerange": "1549-1591", "id_number": "CaltechAUTHORS:20170607-102914977", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170607-102914977", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1500806" }, { "agency": "NSF", "grant_number": "DMS-1362924" }, { "agency": "Simons Foundation", "grant_number": "336826" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-017-0328-4", "primary_object": { "basename": "1610.01917.pdf", "url": "https://authors.library.caltech.edu/records/s41jh-3gx85/files/1610.01917.pdf" }, "pub_year": "2018", "author_list": "Rains, Eric M.; Sun, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/ksy17-y1b09", "eprint_id": 84928, "eprint_status": "archive", "datestamp": "2023-08-21 23:02:55", "lastmod": "2026-03-31 23:09:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Tosio Kato's work on non-relativistic quantum mechanics: part 1", "ispublished": "pub", "full_text_status": "public", "keywords": "Kato; Schr\u00f6dinger operators; Quantum mechanics", "note": "\u00a9 2018 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 8 November 2017; Revised: 18 January 2018; Accepted: 29 January 2018; First Online: 22 February 2018. \n\nB. Simon: Research supported in part by NSF Grants DMS-1265592 and DMS-1665526 and in part by Israeli BSF Grant No. 2014337.\n\n

Published - 10.1007_s13373-018-0118-0.pdf

Submitted - 1711.00528.pdf

", "abstract": "We review the work of Tosio Kato on the mathematics of non-relativistic quantum mechanics and some of the research that was motivated by this. Topics in this first part include analytic and asymptotic eigenvalue perturbation theory, Temple\u2013Kato inequality, self-adjointness results, and quadratic forms including monotone convergence theorems.", "date": "2018-04", "date_type": "published", "publication": "Bulletin of Mathematical Sciences", "volume": "8", "number": "1", "publisher": "Springer", "pagerange": "121-232", "id_number": "CaltechAUTHORS:20180222-133447211", "issn": "1664-3607", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180222-133447211", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s13373-018-0118-0", "primary_object": { "basename": "10.1007_s13373-018-0118-0.pdf", "url": "https://authors.library.caltech.edu/records/ksy17-y1b09/files/10.1007_s13373-018-0118-0.pdf" }, "related_objects": [ { "basename": "1711.00528.pdf", "url": "https://authors.library.caltech.edu/records/ksy17-y1b09/files/1711.00528.pdf" } ], "pub_year": "2018", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/qb77v-8wh17", "eprint_id": 78211, "eprint_status": "archive", "datestamp": "2023-08-19 08:28:38", "lastmod": "2026-03-31 17:59:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Demirel-Frank-S", "name": { "family": "Demirel-Frank", "given": "Semra" } }, { "id": "Shou-Laura", "name": { "family": "Shou", "given": "Laura" } } ] }, "title": "Trace formulas for Schr\u00f6dinger operators on star graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 21 February 2016; Accepted: 07 December 2016; First Online: 31 December 2016.\n\n

Published - 10.1007_2Fs13373-016-0097-y.pdf

Submitted - 1510.08408.pdf

", "abstract": "We derive trace formulas of the Buslaev\u2013Faddeev type for quantum star graphs. One of the new ingredients is high energy asymptotics of the perturbation determinant.", "date": "2018-04", "date_type": "published", "publication": "Bulletin of Mathematical Sciences", "volume": "8", "number": "1", "publisher": "Springer", "pagerange": "15-31", "id_number": "CaltechAUTHORS:20170614-125957633", "issn": "1664-3607", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170614-125957633", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s13373-016-0097-y", "primary_object": { "basename": "10.1007_2Fs13373-016-0097-y.pdf", "url": "https://authors.library.caltech.edu/records/qb77v-8wh17/files/10.1007_2Fs13373-016-0097-y.pdf" }, "related_objects": [ { "basename": "1510.08408.pdf", "url": "https://authors.library.caltech.edu/records/qb77v-8wh17/files/1510.08408.pdf" } ], "pub_year": "2018", "author_list": "Demirel-Frank, Semra and Shou, Laura" }, { "id": "https://authors.library.caltech.edu/records/2gx54-zxy05", "eprint_id": 84906, "eprint_status": "archive", "datestamp": "2023-08-19 08:30:13", "lastmod": "2026-03-31 23:20:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Jin-Tianling", "name": { "family": "Jin", "given": "Tianling" } }, { "id": "Xiong-Jingang", "name": { "family": "Xiong", "given": "Jingang" } } ] }, "title": "Minimizers for the fractional Sobolev inequality on domains", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Springer-Verlag GmbH Germany, part of Springer Nature.\n\nReceived: 20 August 2017; Accepted: 25 January 2018; First Online: 17 February 2018.\n\nPart of this work was done when T. J. was visiting California Institute of Technology as an Orr foundation Caltech-HKUST Visiting Scholar during 2015-2016. He would like to thank Professor Thomas Y. Hou for hosting his visit. He also thanks Professors Zhen-Qing Chen and Dong Li for useful discussions. Partial support through National Science Foundation, grant DMS-1363432 (R.L.F.), Hong Kong RGC grant ECS 26300716 (T.J.) and NSFC 11501034, a key project of NSFC 11631002 and NSFC 11571019, (J.X.) is acknowledged.\n\n

Submitted - 1707.00131.pdf

", "abstract": "We consider a version of the fractional Sobolev inequality in domains and study whether the best constant in this inequality is attained. For the half-space and a large class of bounded domains we show that a minimizer exists, which is in contrast to the classical Sobolev inequalities in domains.", "date": "2018-04", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "57", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 43", "id_number": "CaltechAUTHORS:20180221-110808137", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180221-110808137", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Hong Kong Research Grants Council", "grant_number": "ECS 26300716" }, { "agency": "National Natural Science Foundation of China (NSFC)", "grant_number": "11501034" }, { "agency": "National Natural Science Foundation of China (NSFC)", "grant_number": "11631002" }, { "agency": "National Natural Science Foundation of China (NSFC)", "grant_number": "11571019" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-018-1304-3", "primary_object": { "basename": "1707.00131.pdf", "url": "https://authors.library.caltech.edu/records/2gx54-zxy05/files/1707.00131.pdf" }, "pub_year": "2018", "author_list": "Frank, Rupert L.; Jin, Tianling; et al." }, { "id": "https://authors.library.caltech.edu/records/kvee1-jv190", "eprint_id": 110830, "eprint_status": "archive", "datestamp": "2023-08-19 08:38:29", "lastmod": "2026-04-01 02:46:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Porta-Mauro", "name": { "family": "Porta", "given": "Mauro" }, "orcid": "0000-0002-1239-3409" }, { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Derived non-archimedean analytic spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Derived geometry \u00b7 Rigid analytic geometry \u00b7 Non-archimedean geometry \u00b7 Berkovich space \u00b7 Analytic stack \u00b7 Higher stack \u00b7 Pregeometry \u00b7 Structured topos", "note": "\u00a9 2018 Springer. \n\nPublished 09 February 2017. Issue Date: April 2018. \n\nWe are grateful to Vladimir Berkovich, Antoine Chambert-Loir, Brian Conrad, Antoine Ducros, Bruno Klingler, Maxim Kontsevich, Jacob Lurie, Marco Robalo, Matthieu Romagny, Pierre Schapira, Carlos Simpson, Michael Temkin, Bertrand To\u00ebn and Gabriele Vezzosi for valuable discussions. The authors would also like to thank each other for the joint effort. This research was partially conducted during the period Mauro Porta was supported by Simons Foundation grant number 347070 and the group GNSAGA, and Tony Yue Yu served as a Clay Research Fellow.\n\n

Submitted - 1601.00859.pdf

", "abstract": "We propose a derived version of non-archimedean analytic geometry. Intuitively, a derived non-archimedean analytic space consists of an ordinary non-archimedean analytic space equipped with a sheaf of derived rings. Such a naive definition turns out to be insufficient. In this paper, we resort to the theory of pregeometries and structured topoi introduced by Jacob Lurie. We prove the following three fundamental properties of derived non-archimedean analytic spaces: \n\n(1) The category of ordinary non-archimedean analytic spaces embeds fully faithfully into the \u221e-category of derived non-archimedean analytic spaces. \n\n(2) The \u221e-category of derived non-archimedean analytic spaces admits fiber products. \n\n(3) The \u221e-category of higher non-archimedean analytic Deligne\u2013Mumford stacks embeds fully faithfully into the \u221e-category of derived non-archimedean analytic spaces. The essential image of this embedding is spanned by n-localic discrete derived non-archimedean analytic spaces. \n\nWe will further develop the theory of derived non-archimedean analytic geometry in our subsequent works. Our motivations mainly come from intersection theory, enumerative geometry and mirror symmetry.", "date": "2018-04", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "24", "number": "2", "publisher": "Springer", "pagerange": "609-665", "id_number": "CaltechAUTHORS:20210914-164412737", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412737", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "347070" }, { "agency": "Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA)" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-017-0310-1", "primary_object": { "basename": "1601.00859.pdf", "url": "https://authors.library.caltech.edu/records/kvee1-jv190/files/1601.00859.pdf" }, "pub_year": "2018", "author_list": "Porta, Mauro and Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/xm044-phe92", "eprint_id": 81764, "eprint_status": "archive", "datestamp": "2023-08-21 22:56:10", "lastmod": "2026-03-09 22:11:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Multivariate quadratic transformations and the interpolation kernel", "ispublished": "pub", "full_text_status": "public", "keywords": "quadratic transformations; elliptic special functions", "note": "\u00a9 2018 The Author(s). The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License. \n\nReceived September 12, 2017, in final form February 27, 2018; Published online March 08, 2018. \n\nThis paper is a contribution to the Special Issue on Elliptic Hypergeometric Functions and Their Applications.\nThe full collection is available at https://www.emis.de/journals/SIGMA/EHF2017.html \n\nThe author would particularly like to thank P. Etingof for an initial suggestion that taking p to be a formal variable might allow one to extend the W(E7) symmetry of the order 1 elliptic Selberg to W(E8); this turned out not to work (some symmetries are, indeed, gained, but at the expense of others), but led the author to a more general study of the formal limit. In addition, the author would like to thank D. Betea, M. Wheeler, and P. Zinn-Justin for discussions relating to Izergin-Korepin determinants and their elliptic analogues, and especially for discussions relating to Conjecture 1 of [1] (which led the author to consider the general case of the Littlewood kernel below). The author would also like to thank O. Warnaar for additional discussions related to the Macdonald polynomial limit. The author would finally like to thank H. Rosengren for providing extra motivation to finish writing the present work, as well as some helpful pointers to the vertex model literature. The author was partially supported by the National Science Foundation (grant number DMS-1001645).\n\n

Published - sigma18-019.pdf

Submitted - 1408.0305.pdf

", "abstract": "We prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the ''interpolation kernel'', an analytic continuation of the author's elliptic interpolation functions which plays a major role in the proof as well as acting as the kernel for a Fourier transform on certain elliptic double affine Hecke algebras (discussed in a later paper). In the process, we give a number of examples of a new approach to proving elliptic hypergeometric integral identities, by reduction to a Zariski dense subset of a formal neighborhood of the trigonometric limit.", "date": "2018-03-08", "date_type": "published", "publication": "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)", "volume": "14", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 019", "id_number": "CaltechAUTHORS:20170922-141735253", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170922-141735253", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1001645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2018.019", "primary_object": { "basename": "1408.0305.pdf", "url": "https://authors.library.caltech.edu/records/xm044-phe92/files/1408.0305.pdf" }, "related_objects": [ { "basename": "sigma18-019.pdf", "url": "https://authors.library.caltech.edu/records/xm044-phe92/files/sigma18-019.pdf" } ], "pub_year": "2018", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/gsa52-xsw68", "eprint_id": 79008, "eprint_status": "archive", "datestamp": "2023-08-19 08:11:35", "lastmod": "2026-03-09 21:10:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chen-Ruiyuan", "name": { "family": "Chen", "given": "Ruiyuan" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Structurable equivalence relations", "ispublished": "pub", "full_text_status": "public", "keywords": "countable Borel equivalence relations, structurability, Borel reductions", "note": "\u00a9 2018 Instytut Matematyczny PAN. \n\nReceived 28 June 2016; revised 23 June 2017. Published online 1 March 2018. \n\nResearch of R. Chen partially supported by NSERC PGS D. Research of A. S. Kechris partially supported by NSF Grants DMS-0968710 and DMS-1464475. We would like to thank Andrew Marks for many valuable suggestions and for allowing us to include Theorem 1.11 in this paper. We are also grateful to Anush Tserunyan for extensive comments and suggestions, including spotting and correcting an error in the original version of Lemma 8.3.\n\n

Published - fm428-7-2017.pdf

Submitted - 1606.01995.pdf

", "abstract": "For a class K of countable relational structures, a countable Borel equivalence relation E is said to be K-structurable if there is a Borel way to put a structure in K on each E-equivalence class. We study in this paper the global structure of the classes of K-structurable equivalence relations for various K. We show that K-structurability interacts well with several kinds of Borel homomorphisms and reductions commonly used in\nthe classification of countable Borel equivalence relations. We consider the poset of classes\nof K-structurable equivalence relations for various K, under inclusion, and show that it is a distributive lattice; this implies that the Borel reducibility preordering among countable Borel equivalence relations contains a large sublattice. Finally, we consider the effect on K-structurability of various model-theoretic properties of K. In particular, we characterize the K such that every K-structurable equivalence relation is smooth, answering a question of Marks.", "date": "2018-03-01", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "242", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "109-185", "id_number": "CaltechAUTHORS:20170712-102415675", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-102415675", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "NSF", "grant_number": "DMS-0968710" }, { "agency": "NSF", "grant_number": "DMS-1464475" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4064/fm428-7-2017", "primary_object": { "basename": "1606.01995.pdf", "url": "https://authors.library.caltech.edu/records/gsa52-xsw68/files/1606.01995.pdf" }, "related_objects": [ { "basename": "fm428-7-2017.pdf", "url": "https://authors.library.caltech.edu/records/gsa52-xsw68/files/fm428-7-2017.pdf" } ], "pub_year": "2018", "author_list": "Chen, Ruiyuan and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/ak4z3-yey29", "eprint_id": 111025, "eprint_status": "archive", "datestamp": "2023-08-19 08:11:19", "lastmod": "2026-03-31 22:54:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Interlacements and the wired uniform spanning forest", "ispublished": "pub", "full_text_status": "public", "keywords": "Spanning forests, random interlacements, unimodular random graphs, coarse geometry", "note": "\u00a9 2018 Institute of Mathematical Statistics. \n\nReceived December 2015; revised May 2017. \n\nThis work was carried out while the author was an intern at Microsoft Research, Redmond. We thank Omer Angel, Ori Gurel-Gurevich, Ander Holroyd, Russ Lyons, Asaf Nachmias and Yuval Peres for useful discussions. We also thank Tyler Helmuth for his careful reading of an earlier version of this manuscript, thank Perla Sousi for finding several typos, and thank both Russ Lyons and the anonymous referee for suggesting many corrections and improvements to the initial preprint.\n\n

Published - 17-AOP1203.pdf

Submitted - 1512.08509.pdf

", "abstract": "We extend the Aldous\u2013Broder algorithm to generate the wired uniform spanning forests (WUSFs) of infinite, transient graphs. We do this by replacing the simple random walk in the classical algorithm with Sznitman's random interlacement process. We then apply this algorithm to study the WUSF, showing that every component of the WUSF is one-ended almost surely in any graph satisfying a certain weak anchored isoperimetric condition, that the number of 'excessive ends' in the WUSF is nonrandom in any graph, and also that every component of the WUSF is one-ended almost surely in any transient unimodular random rooted graph. The first two of these results answer positively two questions of Lyons, Morris and Schramm [Electron. J. Probab. 13 (2008) 1702\u20131725], while the third extends a recent result of the author. \n\nFinally, we construct a counterexample showing that almost sure one-endedness of WUSF components is not preserved by rough isometries of the underlying graph, answering negatively a further question of Lyons, Morris and Schramm.", "date": "2018-03", "date_type": "published", "publication": "Annals of Probability", "volume": "46", "number": "2", "publisher": "Institute of Mathematical Statistics", "pagerange": "1170-1200", "id_number": "CaltechAUTHORS:20210924-190634891", "issn": "0091-1798", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-190634891", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/17-aop1203", "primary_object": { "basename": "1512.08509.pdf", "url": "https://authors.library.caltech.edu/records/ak4z3-yey29/files/1512.08509.pdf" }, "related_objects": [ { "basename": "17-AOP1203.pdf", "url": "https://authors.library.caltech.edu/records/ak4z3-yey29/files/17-AOP1203.pdf" } ], "pub_year": "2018", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/gq1az-jgw66", "eprint_id": 77090, "eprint_status": "archive", "datestamp": "2023-08-19 07:57:39", "lastmod": "2026-03-31 19:17:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Nam-Phan-Th\u00e0nh", "name": { "family": "Nam", "given": "Phan Th\u00e0nh" } }, { "id": "Van-Den-Bosch-H", "name": { "family": "Van Den Bosch", "given": "Hanne" } } ] }, "title": "The ionization conjecture in Thomas-Fermi-Dirac-von Weizs\u00e4cker theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Wiley Periodicals, Inc. \n\nIssue online: 17 January 2018; Version of record online:\n4 October 2017; Manuscript Received: June 2016. \n\nWe thank the referee for helpful suggestions which improved the presentation of the paper. Partial support by U.S. National Science Foundation DMS-1363432 (R.L.F.), Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.), CONICYT (Chile) through CONICYT\u2013PCHA/Doctorado Nacional/2014 and Iniciativa Cient\u00edfica Milenio (Chile) through Millenium Nucleus RC\u2013120002 \"F\u00edsica Matem\u00e1tica\" (H.V.D.B.) is acknowledged.\n\n

Submitted - 1606.07355.pdf

", "abstract": "We prove that in Thomas\u2013Fermi\u2013Dirac\u2013von Weizs\u00e4cker theory, a nucleus of charge Z\u2009>\u20090 can bind at most Z\u2009+\u2009C electrons, where C is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a by-product, gives bounds on the screened nuclear potential and the radius of the minimizer. A key ingredient of the proof is a novel technique to control the particles in the exterior region, which also applies to the liquid drop model with a nuclear background potential.", "date": "2018-03", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "71", "number": "3", "publisher": "Wiley", "pagerange": "577-614", "id_number": "CaltechAUTHORS:20170501-083145482", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-083145482", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "FWF Der Wissenschaftsfonds", "grant_number": "P 27533-N27" }, { "agency": "Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (CONICYT)" }, { "agency": "Iniciativa Cient\u00edfica Milenio", "grant_number": "RC-120002" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/cpa.21717", "primary_object": { "basename": "1606.07355.pdf", "url": "https://authors.library.caltech.edu/records/gq1az-jgw66/files/1606.07355.pdf" }, "pub_year": "2018", "author_list": "Frank, Rupert L.; Nam, Phan Th\u00e0nh; et al." }, { "id": "https://authors.library.caltech.edu/records/q2w3t-6td28", "eprint_id": 79011, "eprint_status": "archive", "datestamp": "2023-08-21 22:49:48", "lastmod": "2026-03-31 22:01:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Port-A", "name": { "family": "Port", "given": "Alexander" } }, { "id": "Gheorghita-I", "name": { "family": "Gheorghita", "given": "Iulia" } }, { "id": "Guth-D", "name": { "family": "Guth", "given": "Daniel" } }, { "id": "Clark-J-M", "name": { "family": "Clark", "given": "John M." } }, { "id": "Liang-Crystal", "name": { "family": "Liang", "given": "Crystal" } }, { "id": "Dasu-S", "name": { "family": "Dasu", "given": "Shival" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Persistent Topology of Syntax", "ispublished": "pub", "full_text_status": "public", "keywords": "Linguistics; Syntax; Persistent homology", "note": "\u00a9 2017 Springer International Publishing AG, part of Springer Nature. \n\nReceived: 15 December 2016; Revised: 8 December 2017; Accepted: 13 December 2017; First Online: 26 December 2017. \n\nThis work was performed within the activities of the last author's Mathematical and Computational Linguistics lab and CS101/Ma191 class at Caltech. The last author was partially supported by NSF Grants DMS-1007207, DMS-1201512, DMS-1707882, and PHY-1205440.\n\n

Submitted - 1507.05134.pdf

", "abstract": "We study the persistent homology of a data set of syntactic parameters of world languages. We show that, while homology generators behave erratically over the whole data set, non-trivial persistent homology appears when one restricts to specific language families. Different families exhibit different persistent homology. We focus on the cases of the Indo-European and the Niger\u2013Congo families, for which we compare persistent homology over different cluster filtering values. The persistent components appear to correspond to linguistic subfamilies, while the meaning, in historical linguistic terms, of the presence of persistent generators of the first homology is more mysterious. We investigate the possible significance of the persistent first homology generator that we find in the Indo-European family. We show that it is not due to the Anglo-Norman bridge (which is a lexical, not syntactic phenomenon), but is related instead to the position of Ancient Greek and the Hellenic branch within the Indo-European phylogenetic network.", "date": "2018-03", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "12", "number": "1", "publisher": "Springer Verlag", "pagerange": "33-50", "id_number": "CaltechAUTHORS:20170712-111147439", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-111147439", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-017-0329-x", "primary_object": { "basename": "1507.05134.pdf", "url": "https://authors.library.caltech.edu/records/q2w3t-6td28/files/1507.05134.pdf" }, "pub_year": "2018", "author_list": "Port, Alexander; Gheorghita, Iulia; et al." }, { "id": "https://authors.library.caltech.edu/records/9c6re-9k844", "eprint_id": 111024, "eprint_status": "archive", "datestamp": "2023-08-21 22:43:46", "lastmod": "2026-03-31 17:58:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "The Hammersley-Welsh bound for self-avoiding walk revisited", "ispublished": "pub", "full_text_status": "public", "keywords": "self-avoiding walk; Hammersley-Welsh", "note": "\u00a9 2018 The Author(s). Creative Commons Attribution 4.0 International License. \n\nSubmitted to ECP on August 31, 2017, final version accepted on October 19, 2017. First available in Project Euclid: 12 February 2018. \n\nThe author was supported by internships at Microsoft Research and a Microsoft Research PhD Fellowship. We thank Omer Angel, Hugo Duminil-Copin, Tyler Helmuth and Gordon Slade for comments on an earlier draft. Finally, we thank the anonymous referee for catching several errors in the preprint.\n\n

Published - 17-ECP94.pdf

Accepted Version - 1708.09460.pdf

", "abstract": "The Hammersley-Welsh bound (Quart. J. Math., 1962) states that the number c_n of length n self-avoiding walks on Z^d satisfies \n\nc_n \u2264 exp[O(n^(1/2))]\u03bc^n_c, \n\nwhere \u03bc_c = \u03bc_c(d) is the connective constant of Z^d. While stronger estimates have subsequently been proven for d \u2265 3, for d = 2 this has remained the best rigorous, unconditional bound available. In this note, we give a new, simplified proof of this bound, which does not rely on the combinatorial analysis of unfolding. We also prove a small, non-quantitative improvement to the bound, namely \n\nc_n \u2264 exp[o^(n^(1/2))] \u03bc^n_c. \n\nThe improved bound is obtained as a corollary to the sub-ballisticity theorem of Duminil-Copin and Hammond (Commun. Math. Phys., 2013). We also show that any quantitative form of that theorem would yield a corresponding quantitative improvement to the Hammersley-Welsh bound.", "date": "2018-02", "date_type": "published", "publication": "Electronic Communications in Probability", "volume": "23", "publisher": "Institute of Mathematical Statistics", "pagerange": "Art. No. 5", "id_number": "CaltechAUTHORS:20210924-184806499", "issn": "1083-589X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-184806499", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/17-ECP94", "primary_object": { "basename": "1708.09460.pdf", "url": "https://authors.library.caltech.edu/records/9c6re-9k844/files/1708.09460.pdf" }, "related_objects": [ { "basename": "17-ECP94.pdf", "url": "https://authors.library.caltech.edu/records/9c6re-9k844/files/17-ECP94.pdf" } ], "pub_year": "2018", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/ywftn-q2j47", "eprint_id": 68893, "eprint_status": "archive", "datestamp": "2023-08-19 07:31:49", "lastmod": "2026-04-01 00:09:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" }, { "id": "Yan-Wenbin", "name": { "family": "Yan", "given": "Wenbin" } }, { "id": "Ye-Ke", "name": { "family": "Ye", "given": "Ke" }, "orcid": "0000-0002-2978-2013" } ] }, "title": "Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Springer-Verlag GmbH Germany, part of Springer Nature. \n\nReceived: 24 July 2016; Accepted: 28 November 2017; First Online: 11 January 2018. \n\nWe thank J\u00f8rgen Ellegaard Andersen, Francesco Benini, Martin Fluder, Abhijit Gadde, Tam\u00e1s Hausel, Murat Kolo\u011flu, Pavel Putrov, Richard Wentworth, Ingmar Saberi, Jaewon Song, Andras Szenes and Masahito Yamazaki for helpful discussions related to this work. We would also like to thank the organizers of the Simons Summer Workshop 2015, where a significant portion of this project was completed. This work is funded by the DOE Grant DE-SC0011632, U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 (\"the GEAR Network\"), the Walter Burke Institute for Theoretical Physics, the center of excellence grant \"Center for Quantum Geometry of Moduli Space\" from the Danish National Research Foundation (DNRF95), and the Center of Mathematical Sciences and Applications at Harvard University.\n\n

Submitted - 1605.06528v2.pdf

Supplemental Material - 220_2017_3074_MOESM1_ESM.pdf

", "abstract": "In this paper, we show the equivalence between two seemingly distinct 2d TQFTs: one comes from the \"Coulomb branch index\" of the class SS theory T[\u03a3,G] on L(k,1)\u00d7S^1, the other is the LGLG \"equivariant Verlinde formula\", or equivalently partition function of LGCLGC complex Chern\u2013Simons theory on \u03a3\u00d7S^1. We first derive this equivalence using the M-theory geometry and show that the gauge groups appearing on the two sides are naturally G and its Langlands dual LGLG. When G is not simply-connected, we provide a recipe of computing the index of T[\u03a3,G] as summation over the indices of T[\u03a3,G] with non-trivial background 't Hooft fluxes, where G is the universal cover of G. Then we check explicitly this relation between the Coulomb index and the equivariant Verlinde formula for G=SU(2) or SO(3). In the end, as an application of this newly found relation, we consider the more general case where G is SU(N) or PSU(N) and show that equivariant Verlinde algebra can be derived using field theory via (generalized) Argyres\u2013Seiberg duality. We also attach a Mathematica notebook that can be used to compute the SU(3) equivariant Verlinde coefficients.", "date": "2018-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "357", "number": "3", "publisher": "Springer", "pagerange": "1215-1251", "id_number": "CaltechAUTHORS:20160707-133458529", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160707-133458529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1107452" }, { "agency": "NSF", "grant_number": "DMS-1107263" }, { "agency": "NSF", "grant_number": "DMS-1107367" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Danish National Research Foundation", "grant_number": "DNRF95" }, { "agency": "Harvard University" } ] }, "other_numbering_system": { "items": [ { "id": "2016-012", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-017-3074-8", "primary_object": { "basename": "220_2017_3074_MOESM1_ESM.pdf", "url": "https://authors.library.caltech.edu/records/ywftn-q2j47/files/220_2017_3074_MOESM1_ESM.pdf" }, "related_objects": [ { "basename": "1605.06528v2.pdf", "url": "https://authors.library.caltech.edu/records/ywftn-q2j47/files/1605.06528v2.pdf" } ], "pub_year": "2018", "author_list": "Gukov, Sergei; Pei, Du; et al." }, { "id": "https://authors.library.caltech.edu/records/2k02c-58033", "eprint_id": 85185, "eprint_status": "archive", "datestamp": "2023-08-19 07:21:30", "lastmod": "2026-03-31 23:26:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Zhang-Xingru", "name": { "family": "Zhang", "given": "Xingru" } } ] }, "title": "Finite Dehn surgeries on knots in S^3", "ispublished": "pub", "full_text_status": "public", "keywords": "finite Dehn surgery, Culler-Shalen norm, Heegaard Floer homology", "note": "\u00a9 2018 The Author(s). \n\nReceived: 22 November 2016. Revised: 20 June 2017. Accepted: 14 September 2017. Published: 10 January 2018. \n\nNi was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P Sloan Research Fellowship.\n\n

Submitted - 1607.05685.pdf

", "abstract": "We show that on a hyperbolic knot K in S^3, the distance between any two finite surgery slopes is at most 2, and consequently, there are at most three nontrivial finite surgeries. Moreover, in the case where K admits three nontrivial finite surgeries, K must be the pretzel knot P(\u22122,3,7). In the case where K admits two noncyclic finite surgeries or two finite surgeries at distance 2, the two surgery slopes must be one of ten or seventeen specific pairs, respectively. For D\u2013type finite surgeries, we improve a finiteness theorem due to Doig by giving an explicit bound on the possible resulting prism manifolds, and also prove that 4m and 4m + 4 are characterizing slopes for the torus knot T(2m + 1,2) for each m \u2265 1.", "date": "2018-01-10", "date_type": "published", "publication": "Algebraic & Geometric Topology", "volume": "18", "number": "1", "publisher": "Geometry & Topology Publications", "pagerange": "441-492", "id_number": "CaltechAUTHORS:20180307-130606037", "issn": "1472-2747", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180307-130606037", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/agt.2018.18.441", "primary_object": { "basename": "1607.05685.pdf", "url": "https://authors.library.caltech.edu/records/2k02c-58033/files/1607.05685.pdf" }, "pub_year": "2018", "author_list": "Ni, Yi and Zhang, Xingru" }, { "id": "https://authors.library.caltech.edu/records/perfm-31s26", "eprint_id": 96246, "eprint_status": "archive", "datestamp": "2023-08-19 07:12:34", "lastmod": "2026-03-18 00:01:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Tosio Kato's Work on Non-Relativistic Quantum Mechanics: A Brief Report", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2018 International Association of Mathematical Physics.", "abstract": "In 2017, we celebrated the 100th anniversary of the birth of Tosio Kato (August 25, 1917\u2013October 2, 1999), the founding father of the theory of Schr\u00f6dinger operators. There was a centennial held in Tokyo in his memory and honor in September. I decided to write a review article on his work in nonrelativistic quantum mechanics (NRQM), which, as we'll see, was only part of his opus. I originally guessed it would be about 80 pages but it turned out to be more than 210! It will appear in Bull. Math. Sci. Our intrepid newsletter editor asked if I could produce a Reader's Digest version for the newsletter and that is what this is. A version of this will appear in Analysis and Operator Theory \u2013 In Honor of Tosio Kato's 100th Birthday, a volume edited by Th. M. Rassias and V. Zagrebnov to be published by Springer. Since the longer article has an over 600 item bibliography, I will not provide any detailed references here but refer the reader to the full article. The rest of this introduction will say a little about Kato's life while the next will summarize some major themes in his work. I will then describe in some depth (but less detail than in my Bull. Math. Sci. article) five topics that were among the most important of Kato's contributions to NRQM.", "date": "2018-01", "date_type": "published", "publication": "IAMP News Bulletin", "publisher": "International Association of Mathematical Physics", "pagerange": "6-25", "id_number": "CaltechAUTHORS:20190610-130435055", "issn": "2304-7348", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190610-130435055", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "pub_year": "2018", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/tgbga-5zw88", "eprint_id": 78984, "eprint_status": "archive", "datestamp": "2023-08-21 22:27:34", "lastmod": "2026-03-09 23:58:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hann-Caruthers-W", "name": { "family": "Hann-Caruthers", "given": "Wade" } }, { "id": "Martynov-V-V", "name": { "family": "Martynov", "given": "Vadim V." } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "The speed of sequential asymptotic learning", "ispublished": "pub", "full_text_status": "public", "keywords": "Social learning; Herd behavior", "note": "\u00a9 2017 Elsevier Inc. \n\nReceived 7 March 2017, Revised 27 September 2017, Accepted 21 November 2017, Available online 1 December 2017. \n\nThe authors would like to thank Christophe Chamley, Gil Refael, Peter S\u00f8rensen, Philipp Strack, Ye Wang, Ivo Welch and Leeat Yariv for helpful comments and discussions. This work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).\n\n

Submitted - 1707.02689.pdf

", "abstract": "In the classical herding literature, agents receive a private signal regarding a binary state of nature, and sequentially choose an action, after observing the actions of their predecessors. When the informativeness of private signals is unbounded, it is known that agents converge to the correct action and correct belief. We study how quickly convergence occurs, and show that it happens more slowly than it does when agents observe signals. However, we also show that the speed of learning from actions can be arbitrarily close to the speed of learning from signals. In particular, the expected time until the agents stop taking the wrong action can be either finite or infinite, depending on the private signal distribution. In the canonical case of Gaussian private signals we calculate the speed of convergence precisely, and show explicitly that, in this case, learning from actions is significantly slower than learning from signals.", "date": "2018-01", "date_type": "published", "publication": "Journal of Economic Theory", "volume": "173", "publisher": "Elsevier", "pagerange": "383-409", "id_number": "CaltechAUTHORS:20170712-081145954", "issn": "0022-0531", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-081145954", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jet.2017.11.009", "primary_object": { "basename": "1707.02689.pdf", "url": "https://authors.library.caltech.edu/records/tgbga-5zw88/files/1707.02689.pdf" }, "pub_year": "2018", "author_list": "Hann-Caruthers, Wade; Martynov, Vadim V.; et al." }, { "id": "https://authors.library.caltech.edu/records/kg1dv-36j31", "eprint_id": 96198, "eprint_status": "archive", "datestamp": "2023-08-19 07:04:33", "lastmod": "2026-03-08 18:14:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "Matthias" }, "orcid": "0000-0002-4523-9467" }, { "id": "Baptiste-M", "name": { "family": "Baptiste", "given": "Morin" } } ] }, "title": "Weil-\u00c9tale Cohomology and Zeta-Values of Proper Regular Arithmetic Schemes", "ispublished": "pub", "full_text_status": "public", "keywords": "Zeta functions, Zeta-values, Weil-\u00e9tale cohomology, Arakelov theory", "note": "\u00a9 2018 Documenta Mathematica. Attribution 4.0 International (CC BY 4.0).\n\n

Published - 10011881000.pdf

Submitted - 1605.01277.pdf

", "abstract": "We give a conjectural description of the vanishing order and leading Taylor coefficient of the Zeta function of a proper, regular arithmetic scheme X at any integer n in terms of Weil-\u00e9tale cohomology complexes. This extends work of Lichtenbaum [65] and Geisser [36] for X of characteristic p, of Lichtenbaum [66] for X = Spec(O_F) and n = 0 where F is a number field, and of the second author for arbitrary X and n = 0 [72]. We show that our conjecture is compatible with the Tamagawa number conjecture of Bloch, Kato, Fontaine and Perrin-Riou [31] if X is smooth over Spec(O_F), and hence that it holds in cases where the Tamagawa number conjecture is known.", "date": "2018", "date_type": "published", "publication": "Documenta Mathematica", "volume": "23", "publisher": "Documenta Mathematica", "pagerange": "1425-1560", "id_number": "CaltechAUTHORS:20190607-083625026", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190607-083625026", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.25537/dm.2018v23.1425-1560", "primary_object": { "basename": "10011881000.pdf", "url": "https://authors.library.caltech.edu/records/kg1dv-36j31/files/10011881000.pdf" }, "related_objects": [ { "basename": "1605.01277.pdf", "url": "https://authors.library.caltech.edu/records/kg1dv-36j31/files/1605.01277.pdf" } ], "pub_year": "2018", "author_list": "Flach, Matthias and Baptiste, Morin" }, { "id": "https://authors.library.caltech.edu/records/z6f77-k3d83", "eprint_id": 89599, "eprint_status": "archive", "datestamp": "2023-08-19 07:03:48", "lastmod": "2026-03-09 02:11:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "A \"Liquid-Solid\" Phase Transition in a Simple Model for Swarming, Based on the \"No Flat-Spots\" Theorem for Subharmonic Functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 Indiana University Mathematics Journal. \n\nThe authors are grateful to Luis Silvestre and to Mikhail\nSodin for showing us how to prove Proposition A.1 for continuous and for L1 functions, respectively, to Almut Burchard and Paul Gauthier for their careful reading and many helpful comments, and to Haim Br\u00e9zis for references related to Proposition 2.1. Support by U.S. National Science Foundation grants DMS-1363432 (R.L.F.) and PHY-1265118 (E.H.L.) is acknowledged\n\n

Published - 7398.pdf

Submitted - 1607.07971.pdf

", "abstract": "We consider a family of non-local shape optimization\nproblems, which are motivated by a simple model for swarming\nand other self-assembly/aggregation models, and prove the existence of different phases for several of them. A technical key ingredient, which we establish, is that a strictly subharmonic function cannot be constant on a set of positive measure.", "date": "2018", "date_type": "published", "publication": "Indiana University Mathematics Journal", "volume": "67", "number": "4", "publisher": "Indiana University", "pagerange": "1547-1569", "id_number": "CaltechAUTHORS:20180912-155642789", "issn": "0022-2518", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180912-155642789", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1512/iumj.2018.67.7398", "primary_object": { "basename": "1607.07971.pdf", "url": "https://authors.library.caltech.edu/records/z6f77-k3d83/files/1607.07971.pdf" }, "related_objects": [ { "basename": "7398.pdf", "url": "https://authors.library.caltech.edu/records/z6f77-k3d83/files/7398.pdf" } ], "pub_year": "2018", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/h2y1r-w6590", "eprint_id": 79012, "eprint_status": "archive", "datestamp": "2023-08-19 07:02:08", "lastmod": "2026-03-09 21:30:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eischen-E", "name": { "family": "Eischen", "given": "Ellen" } }, { "id": "Fintzen-J", "name": { "family": "Fintzen", "given": "Jessica" } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } }, { "id": "Varma-I", "name": { "family": "Varma", "given": "Ila" } } ] }, "title": "Differential operators and families of automorphic forms on unitary groups of arbitrary signature", "ispublished": "pub", "full_text_status": "public", "keywords": "p-adic automorphic forms, differential operators, Maass operators, Shimura varieties", "note": "\u00a9 2018 FIZ Karlsruhe GmbH. Attribution 4.0 International (CC BY 4.0). \n\nReceived: January 1, 2017; Revised: August 31, 2017. \n\nWe would like to thank Ana Caraiani very much for contributing to initial conversations about topics in this paper. We would also like to thank the referee for a careful reading and helpful suggestions. \n\nE.E.'s research was partially supported by NSF Grants DMS-1249384 and DMS-1559609. J.F.'s research was partially supported by the Studienstiftung des deutschen Volkes. E.M.'s research was partially supported by NSF Grant DMS-1001077. I.V.'s research was partially supported by a National Defense Science and Engineering Fellowship and NSF Grant DMS-1502834.\n\n

Published - 10011761000.pdf

Submitted - 1511.06771.pdf

", "abstract": "In the 1970's, Serre exploited congruences between qexpansion\ncoefficients of Eisenstein series to produce p-adic families\nof Eisenstein series and, in turn, p-adic zeta functions. Partly through integration with more recent machinery, including Katz's approach to p-adic differential operators, his strategy has influenced four decades of developments. Prior papers employing Katz's and Serre's ideas exploiting differential operators and congruences to produce families of automorphic forms rely crucially on q-expansions of automorphic forms. The overarching goal of the present paper is to adapt the strategy to automorphic forms on unitary groups, which lack q-expansions when the signature is of the form (a, b), a \u2260 b. In particular, this paper completely removes the restrictions on the signature present in prior work. As intermediate steps, we achieve two key objectives. First, partly by carefully analyzing the action of the Young symmetrizer on Serre\u2013Tate expansions, we explicitly describe the action of differential operators on the Serre\u2013Tate expansions of automorphic forms on\nunitary groups of arbitrary signature. As a direct consequence, for\neach unitary group, we obtain congruences and families analogous to those studied by Katz and Serre. Second, via a novel lifting argument, we construct a p-adic measure taking values in the space of p-adic automorphic forms on unitary groups of any prescribed signature.\nWe relate the values of this measure to an explicit p-adic family\nof Eisenstein series. One application of our results is to the recently\ncompleted construction of p-adic L-functions for unitary groups by\nthe first named author, Harris, Li, and Skinner.", "date": "2018", "date_type": "published", "publication": "Documenta Mathematica", "volume": "23", "publisher": "Documenta Mathematica", "pagerange": "445-495", "id_number": "CaltechAUTHORS:20170712-123707950", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-123707950", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1249384" }, { "agency": "NSF", "grant_number": "DMS-1559609" }, { "agency": "Studienstiftung des deutschen Volkes" }, { "agency": "NSF", "grant_number": "DMS-1001077" }, { "agency": "National Defense Science and Engineering Graduate (NDSEG) Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1502834" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.25537/dm.2018v23.445-495", "primary_object": { "basename": "10011761000.pdf", "url": "https://authors.library.caltech.edu/records/h2y1r-w6590/files/10011761000.pdf" }, "related_objects": [ { "basename": "1511.06771.pdf", "url": "https://authors.library.caltech.edu/records/h2y1r-w6590/files/1511.06771.pdf" } ], "pub_year": "2018", "author_list": "Eischen, Ellen; Fintzen, Jessica; et al." }, { "id": "https://authors.library.caltech.edu/records/pqpa9-chj11", "eprint_id": 67954, "eprint_status": "archive", "datestamp": "2023-08-19 07:02:02", "lastmod": "2026-03-09 21:41:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Heydeman-Matthew", "name": { "family": "Heydeman", "given": "Matthew" }, "orcid": "0000-0001-7033-9075" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Saberi-Ingmar-A", "name": { "family": "Saberi", "given": "Ingmar A." } }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } } ] }, "title": "Tensor networks, p-adic fields, and algebraic curves: arithmetic and the AdS_3/CFT_2 correspondence", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 International Press.\n\nThe authors wish to thank N. Bao, H. Kim, M. Kolo\u011flu, T. McKinney, N. Hunter-Jones, B. Michel, M. M. N\u0103st\u0103sescu, H. Ooguri, and A. Turzillo for helpful conversations as this work was being prepared. I.A.S. is also grateful to the Partnership Mathematics and Physics of Universit\u00e4t Heidelberg, the University of Bristol, and the Gone Fishing meeting at the University of Colorado, Boulder for hospitality. We are especially grateful to the anonymous referee, for careful reading and thorough and useful comments. \n\nThe work of M.H., I.A.S., and B.S. is supported by the United States Department of Energy under the grant DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech. M.M. is partially supported by NSF grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics.\n\n

Submitted - 1605.07639v1.pdf

", "abstract": "One of the many remarkable properties of conformal field theory in two dimensions is its connection to algebraic geometry. Since every compact Riemann surface is a projective algebraic curve, many constructions of interest in physics (which a priori depend on the analytic structure of the spacetime) can be formulated in purely algebraic language. This opens the door to interesting generalizations, obtained by taking another choice of field: for instance, the p-adics. We generalize the AdS/CFT correspondence according to this principle; the result is a formulation of holography in which the bulk geometry is discrete\u2014the Bruhat\u2013Tits tree for PGL(2,Qp)\u2014but the group of bulk isometries nonetheless agrees with that of boundary conformal transformations and is not broken by discretization. We suggest that this forms the natural geometric setting for tensor networks that have been proposed as models of bulk reconstruction via quantum error correcting codes; in certain cases, geodesics in the Bruhat\u2013Tits tree reproduce those constructed using quantum error correction. Other aspects of holography also hold: Standard holographic results for massive free scalar fields in a fixed background carry over to the tree, whose vertical direction can be interpreted as a renormalization-group scale for modes in the boundary CFT. Higher-genus bulk geometries (the BTZ black hole and its generalizations) can be understood straightforwardly in our setting, and the Ryu\u2013Takayanagi formula for the entanglement entropy appears naturally.", "date": "2018", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "22", "number": "1", "publisher": "International Press", "pagerange": "93-176", "id_number": "CaltechAUTHORS:20160615-160129721", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160615-160129721", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPIN-2018-04937" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "RGPAS-2018-522593" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "other_numbering_system": { "items": [ { "id": "2016-013", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2018.v22.n1.a4", "primary_object": { "basename": "1605.07639v1.pdf", "url": "https://authors.library.caltech.edu/records/pqpa9-chj11/files/1605.07639v1.pdf" }, "pub_year": "2018", "author_list": "Heydeman, Matthew; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/fjteg-4ys50", "eprint_id": 97838, "eprint_status": "archive", "datestamp": "2023-08-19 07:04:37", "lastmod": "2026-03-08 17:40:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bukh-B", "name": { "family": "Bukh", "given": "Boris" } }, { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Rational exponents in extremal graph theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Extremal graph theory, bipartite graphs, algebraic constructions", "note": "\u00a9 2018 European Mathematical Society. \n\nPublished online: 2018-05-22. \n\nBukh research supported in part by a Sloan Research Fellowship, NSF grant DMS-1301548, and NSF CAREER grant DMS-1555149. Conlon research supported by a Royal Society University Research Fellowship and ERC Starting Grant 676632. \n\nWe would like to thank Jacques Verstraete for interesting discussions relating to the topic of this paper. We would also like to thank an anonymous referee and Lisa Sauermann for a number of useful comments and corrections.\n\n

Submitted - 1506.06406.pdf

", "abstract": "Given a family of graphs \u210c, the extremal number ex(n, \u210c) is the largest m for which there exists a graph with n vertices and m edges containing no graph from the family \u210c as a subgraph. We show that for every rational number r between 1 and 2, there is a family of graphs \u210c_r such that ex (n, \u210c_r) = \u0398(n^r). This solves a longstanding problem in the area of extremal graph theory.", "date": "2018", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "20", "number": "7", "publisher": "European Mathematical Society", "pagerange": "1747-1757", "id_number": "CaltechAUTHORS:20190812-163000355", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000355", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "DMS-1301548" }, { "agency": "NSF", "grant_number": "DMS-1555149" }, { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/jems/798", "primary_object": { "basename": "1506.06406.pdf", "url": "https://authors.library.caltech.edu/records/fjteg-4ys50/files/1506.06406.pdf" }, "pub_year": "2018", "author_list": "Bukh, Boris and Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/j7rjr-48m27", "eprint_id": 83396, "eprint_status": "archive", "datestamp": "2023-08-21 22:19:00", "lastmod": "2026-04-01 06:33:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "B\u00f6ttcher-A", "name": { "family": "B\u00f6ttcher", "given": "Albrecht" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Spitkovsky-I", "name": { "family": "Spitkovsky", "given": "Ilya" } } ] }, "title": "Similarity Between Two Projections", "ispublished": "pub", "full_text_status": "public", "keywords": "Intertwining operators; Intertwining unitaries; Similar projections; Two projections", "note": "\u00a9 2017 Springer International Publishing AG, part of Springer Nature. \n\nReceived: 29 May 2017; Revised: 01 November 2017; First Online: 20 November 2017. \n\nResearch of the Barry Simon supported in part by NSF Grants DMS-1265592 and DMS-1665526 and in part by Israeli BSF Grant No. 2014337. The Ilya Spitkovsky was supported in part by Faculty Research funding from the Division of Science and Mathematics, New York University Abu Dhabi.\n\n

Submitted - 1705.08937.pdf

", "abstract": "Given two orthogonal projections P and Q, we are interested in all unitary operators U such that UP=QU and UQ=PU. Such unitaries U have previously been constructed by Wang, Du, and Dou and also by one of the authors. One purpose of this note is to compare these constructions. Very recently, Dou, Shi, Cui, and Du described all unitaries U with the required property. Their proof is via the two projections theorem by Halmos. We here give a proof based on the supersymmetric approach by Avron, Seiler, and one of the authors.", "date": "2017-12", "date_type": "published", "publication": "Integral Equations and Operator Theory", "volume": "89", "number": "4", "publisher": "Springer", "pagerange": "507-518", "id_number": "CaltechAUTHORS:20171121-100155399", "issn": "0378-620X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171121-100155399", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "NSF", "grant_number": "DMS-1665526" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" }, { "agency": "New York University Abu Dhabi" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00020-017-2414-6", "primary_object": { "basename": "1705.08937.pdf", "url": "https://authors.library.caltech.edu/records/j7rjr-48m27/files/1705.08937.pdf" }, "pub_year": "2017", "author_list": "B\u00f6ttcher, Albrecht; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/qw0zn-q6082", "eprint_id": 77113, "eprint_status": "archive", "datestamp": "2023-08-19 06:12:08", "lastmod": "2026-04-01 06:35:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Sabin-J", "name": { "family": "Sabin", "given": "Julien" } } ] }, "title": "Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Johns Hopkins University Press.\n\nManuscript received May 18, 2015; revised March 17, 2016.\n\nThe authors are grateful to A. Laptev, M. Lewin and A. Pushnitski for useful discussions. J. S. thanks the Mathematics Department of Caltech for the Research Stay during which this work has been done. Financial support from the U.S. National Science Foundation through grant PHY-1347399 (R. F.), from the ERC MNIQS-258023 and from the ANR \"NoNAP\" (ANR-10-BLAN 0101) of the French ministry of research (J. S.) are acknowledged.\n\n

Submitted - 1404.2817.pdf

", "abstract": "We generalize the theorems of Stein-Tomas and Strichartz about surface restrictions of Fourier transforms to systems of orthonormal functions with an optimal dependence on the number of functions. We deduce the corresponding Strichartz bounds for solutions to Schr\u00f6dinger equations up to the endpoint, thereby solving an open problem of Frank, Lewin, Lieb and Seiringer. We also prove uniform Sobolev estimates in Schatten spaces, extending the results of Kenig, Ruiz, and Sogge. We finally provide applications of these results to a Limiting Absorption Principle in Schatten spaces, to the well-posedness of the Hartree equation in Schatten spaces, to Lieb-Thirring bounds for eigenvalues of Schr\u00f6dinger operators with complex potentials, and to Schatten properties of the scattering matrix.", "date": "2017-12", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "139", "number": "6", "publisher": "Johns Hopkins University Press", "pagerange": "1649-1691", "id_number": "CaltechAUTHORS:20170501-160524071", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-160524071", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "European Research Council (ERC)", "grant_number": "MNIQS-258023" }, { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-10-BLAN 0101" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1353/ajm.2017.0041", "primary_object": { "basename": "1404.2817.pdf", "url": "https://authors.library.caltech.edu/records/qw0zn-q6082/files/1404.2817.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L. and Sabin, Julien" }, { "id": "https://authors.library.caltech.edu/records/204g5-emb23", "eprint_id": 78998, "eprint_status": "archive", "datestamp": "2023-08-19 06:12:48", "lastmod": "2026-04-01 07:13:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fathizadeh-F", "name": { "family": "Fathizadeh", "given": "Farzad" }, "orcid": "0000-0002-7863-4009" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Periods and motives in the spectral action of Robertson-Walker spacetimes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Springer-Verlag GmbH Germany. \n\nReceived: 6 April 2017; Accepted: 21 July 2017; First Online: 20 September 2017. \n\nThe second author acknowledges support from NSF grants DMS-1201512, DMS-1707882, and PHY-919 1205440. Part of this work was done at the Perimeter Institute for Theoretical Physics, supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation.\n\n

Submitted - 1611.01815.pdf

", "abstract": "We show that, when considering the scaling factor as an affine variable, the coefficients of the asymptotic expansion of the spectral action on a (Euclidean) Robertson\u2013Walker spacetime are periods of mixed Tate motives, involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces and divisors given by unions of coordinate hyperplanes.", "date": "2017-12", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "356", "number": "2", "publisher": "Springer", "pagerange": "641-671", "id_number": "CaltechAUTHORS:20170712-091141446", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-091141446", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-017-2991-x", "primary_object": { "basename": "1611.01815.pdf", "url": "https://authors.library.caltech.edu/records/204g5-emb23/files/1611.01815.pdf" }, "pub_year": "2017", "author_list": "Fathizadeh, Farzad and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/qr4fk-vrs74", "eprint_id": 79256, "eprint_status": "archive", "datestamp": "2023-08-19 05:47:05", "lastmod": "2026-04-01 17:05:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Trisecting non-Lagrangian theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Topological Field Theories, Supersymmetry and Duality, D-branes, Topological Strings", "note": "\u00a9 2017 The Author(s). This article is distributed under the terms of the Creative Commons ttribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: October 5, 2017; Accepted: November 6, 2017; Published: November 27, 2017. \n\nIt is pleasure to thank M. Atiyah, M. Dedushenko, T. Dumitrescu, D. Gay, A. Giveon, N. Hitchin, R. Kirby, D. Kutasov, D. L\u00fcst, M. Mari\u00f1o, J. Meier, I. Melnikov, P. Putrov, L. Schaposnik, E. Sharpe, S. Shatashvili, E. Silverstein, J. Song, J. Troost, and K. Ye for useful discussions and comments. This work is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DESC0011632.\n\n

Published - 10.1007_2FJHEP11_2017_178.pdf

Submitted - 1707.01515.pdf

", "abstract": "We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with rather unusual targets, such as compact and non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton theories, \"self-mirror\" geometries, varieties with complex multiplication, etc.", "date": "2017-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 178", "id_number": "CaltechAUTHORS:20170720-171152878", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170720-171152878", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP11(2017)178", "primary_object": { "basename": "10.1007_2FJHEP11_2017_178.pdf", "url": "https://authors.library.caltech.edu/records/qr4fk-vrs74/files/10.1007_2FJHEP11_2017_178.pdf" }, "related_objects": [ { "basename": "1707.01515.pdf", "url": "https://authors.library.caltech.edu/records/qr4fk-vrs74/files/1707.01515.pdf" } ], "pub_year": "2017", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/ds0pp-v5489", "eprint_id": 111023, "eprint_status": "archive", "datestamp": "2023-08-19 05:28:42", "lastmod": "2026-04-01 20:39:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Peres-Yuval", "name": { "family": "Peres", "given": "Yuval" }, "orcid": "0000-0001-5456-6323" } ] }, "title": "Boundaries of planar graphs: a unified approach", "ispublished": "pub", "full_text_status": "public", "keywords": "Circle packing, Harmonic functions, Martin boundary, Planar graphs, Poisson boundary, Random walk, Rough isometry, square tiling", "note": "\u00a9 2017 The Author(s). Creative Commons Attribution 4.0 International License. \n\nSubmitted to EJP on August 13, 2016, final version accepted on October 9, 2017. \n\nThis work was carried out while TH was an intern at Microsoft Research, Redmond. We thank Russ Lyons and Asaf Nachmias for helpful discussions, and thank the anonymous referee for their careful reading of the paper. We thank Itai Benjamini for granting us permission to include the square tiling of Figure 1, which originally appeared in [5]. The circle packing in Figure 1 was created using Ken Stephenson's CirclePack software.\n\n

Published - 17-EJP116.pdf

Submitted - 1508.03923.pdf

", "abstract": "We give a new proof that the Poisson boundary of a planar graph coincides with the boundary of its square tiling and with the boundary of its circle packing, originally proven by Georgakopoulos [9] and Angel, Barlow, Gurel-Gurevich and Nachmias [2] respectively. Our proof is robust, and also allows us to identify the Poisson boundaries of graphs that are rough-isometric to planar graphs. \n\nWe also prove that the boundary of the square tiling of a bounded degree plane triangulation coincides with its Martin boundary. This is done by comparing the square tiling of the triangulation with its circle packing.", "date": "2017-10", "date_type": "published", "publication": "Electronic Journal of Probability", "volume": "22", "publisher": "Institute of Mathematical Statistics", "pagerange": "Art. No. 100", "id_number": "CaltechAUTHORS:20210924-183504452", "issn": "1083-6489", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-183504452", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/17-ejp116", "primary_object": { "basename": "1508.03923.pdf", "url": "https://authors.library.caltech.edu/records/ds0pp-v5489/files/1508.03923.pdf" }, "related_objects": [ { "basename": "17-EJP116.pdf", "url": "https://authors.library.caltech.edu/records/ds0pp-v5489/files/17-EJP116.pdf" } ], "pub_year": "2017", "author_list": "Hutchcroft, Tom and Peres, Yuval" }, { "id": "https://authors.library.caltech.edu/records/2mx9p-hn240", "eprint_id": 78101, "eprint_status": "archive", "datestamp": "2023-08-21 21:49:04", "lastmod": "2026-04-01 20:38:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Thorngren-R", "name": { "family": "Thorngren", "given": "Ryan" }, "orcid": "0000-0001-9433-3399" } ] }, "title": "Fermionic SPT phases in higher dimensions and bosonization", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories; Effective Field Theories; Topological Field Theories; Topological States of Matter", "note": "\u00a9 2017 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: April 12, 2017; Accepted: September 28, 2017; Published: October 11, 2017. \n\nA. K. would like to thank Greg Brumfiel, John Morgan and Anibal Medina for communicating to him some of their unpublished results. R. T. would like to thank Dominic Williamson, Dave Aasen, and Ethan Lake for many enlightening discussions. This paper was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. The work of A. K. was also supported by the Simons Investigator Award. R. T. is supported by an NSF GRFP grant. A. K. and R. T. are grateful to KITP, Santa Barbara, for hospitality during the initial stages of this project.\n\n

Published - 10.1007_JHEP10_2017_080.pdf

Submitted - 1701.08264.pdf

", "abstract": "We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological parameters which label such phases and the connection with higher-form symmetries. We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry G. It generalizes the supercohomology of Gu and Wen. We argue that the most general such phase can be obtained from a bosonic \"shadow\" by condensing both fermionic particles and strings.", "date": "2017-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 080", "id_number": "CaltechAUTHORS:20170612-103422222", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170612-103422222", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "NSF Graduate Research Fellowship" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP10(2017)080", "primary_object": { "basename": "1701.08264.pdf", "url": "https://authors.library.caltech.edu/records/2mx9p-hn240/files/1701.08264.pdf" }, "related_objects": [ { "basename": "10.1007_JHEP10_2017_080.pdf", "url": "https://authors.library.caltech.edu/records/2mx9p-hn240/files/10.1007_JHEP10_2017_080.pdf" } ], "pub_year": "2017", "author_list": "Kapustin, Anton and Thorngren, Ryan" }, { "id": "https://authors.library.caltech.edu/records/7kxbt-v6s41", "eprint_id": 55045, "eprint_status": "archive", "datestamp": "2023-08-19 05:14:26", "lastmod": "2026-04-01 08:01:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Pei-Du", "name": { "family": "Pei", "given": "Du" }, "orcid": "0000-0001-5587-6905" } ] }, "title": "Equivariant Verlinde formula from fivebranes and vortices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Springer-Verlag GmbH Germany. \n\nReceived: 02 June 2016; Accepted: 03 May 2017; First Online: 03 July 2017. \n\nWe wish to thank Anton Alekseev for a wonderful set of notes [67] that we recommend to all the beginners. We also thank S. Shatashvili for discussions of this work in Fall 2013 and Spring 2014, which stimulated [60].We also benefited from discussions with Mina Aganagic, Sir Michael Atiyah, Tudor Dimofte, Abhijit Gadde, Jaume Gomis, Nigel Hitchin, Tadashi Okazaki, Satoshi Okuda, Pavel Putrov, Richard Wentworth and Wenbin Yan. This work is funded by the DOE Grant DE-SC0011632, NSF Grants DMS 1107452, 1107263, 1107367 (the GEAR Network), and the Walter Burke Institute for Theoretical Physics.\n\n

Submitted - 1501.01310v1.pdf

", "abstract": "We study complex Chern\u2013Simons theory on a Seifert manifold M_3 by embedding it into string theory. We show that complex Chern\u2013Simons theory on M_3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in four-dimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern\u2013Simons theory on \u03a3\u00d7S^1 and (4) index of a spin^c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the \"equivariant Verlinde algebra\" for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern\u2013Simons theory on \u03a3\u00d7S^1 and (4) the equivariant index of a spin^c Dirac operator on the moduli space of Higgs bundles.", "date": "2017-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "355", "number": "1", "publisher": "Springer", "pagerange": "1-50", "id_number": "CaltechAUTHORS:20150220-093858198", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150220-093858198", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "NSF", "grant_number": "DMS-1107452" }, { "agency": "NSF", "grant_number": "DMS-107263" }, { "agency": "NSF", "grant_number": "DMS-1107367" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" } ] }, "other_numbering_system": { "items": [ { "id": "2014-171", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-017-2931-9", "primary_object": { "basename": "1501.01310v1.pdf", "url": "https://authors.library.caltech.edu/records/7kxbt-v6s41/files/1501.01310v1.pdf" }, "pub_year": "2017", "author_list": "Gukov, Sergei and Pei, Du" }, { "id": "https://authors.library.caltech.edu/records/2hvrq-qmd73", "eprint_id": 79339, "eprint_status": "archive", "datestamp": "2023-08-19 05:17:07", "lastmod": "2026-04-01 06:33:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ormerod-C-M", "name": { "family": "Ormerod", "given": "Chris M." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "An Elliptic Garnier System", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Springer-Verlag GmbH Germany. \n\nReceived: 21 December 2016; Accepted: 31 March 2017; First Online: 24 July 2017. \n\nThe work of EMR was partially supported by the National Science Foundation under the Grant DMS-1500806.\n\n

Submitted - 1607.07831.pdf

", "abstract": "We present a linear system of difference equations whose entries are expressed in terms of theta functions. This linear system is singular at 4m + 12 points for m \u2265 1, which appear in pairs due to a symmetry condition. We parameterize this linear system in terms of a set of kernels at the singular points. We regard the system of discrete isomonodromic deformations as an elliptic analogue of the Garnier system. We identify the special case in which m = 1 with the elliptic Painlev\u00e9 equation; hence, this work provides an explicit form and Lax pair for the elliptic Painlev\u00e9 equation.", "date": "2017-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "355", "number": "2", "publisher": "Springer", "pagerange": "741-766", "id_number": "CaltechAUTHORS:20170725-124624205", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170725-124624205", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1500806" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-017-2934-6", "primary_object": { "basename": "1607.07831.pdf", "url": "https://authors.library.caltech.edu/records/2hvrq-qmd73/files/1607.07831.pdf" }, "pub_year": "2017", "author_list": "Ormerod, Chris M. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/zprzp-wan75", "eprint_id": 77120, "eprint_status": "archive", "datestamp": "2023-08-19 05:13:22", "lastmod": "2026-04-01 06:35:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Eigenvalue bounds for Schr\u00f6dinger operators with complex potentials. II", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator, complex-valued potential, eigenvalue bounds, embedded eigenvalue", "note": "\u00a9 2017 European Mathematical Society. \n\nReceived April 5, 2015; revised May 26, 2015. Published online: 2017-09-28. \n\nWork partially supported by U.S. National Science Foundation grants PHY-1347399, DMS-1363432 (R. L. Frank), and DMS-1265592 (B. Simon).\n\n

Submitted - 1504.01144.pdf

", "abstract": "Laptev and Safronov conjectured that any non-positive eigenvalue of a Schr\u00f6dinger operator -\u0394+V in L^2 (R^\u03bd) with complex potential has absolute value at most a constant times ||V||^(\u03b3+\u03bd/2)/\u03b3)_(\u03b3+\u03bd/2) for 0 < \u03b3 \u2264 \u03bd/2 in dimension \u03bd \u2265 2. We prove this conjecture for radial potentials if 0 < \u03b3 < \u03bd/2 and we 'almost disprove' it for general potentials if 1/2 < \u03b3 < \u03bd/2. In addition, we prove various bounds that hold, in particular, for positive eigenvalues.", "date": "2017-09-28", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "7", "number": "3", "publisher": "European Mathematical Society", "pagerange": "633-658", "id_number": "CaltechAUTHORS:20170502-082840587", "issn": "1664-039X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1265592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4171/JST/173", "primary_object": { "basename": "1504.01144.pdf", "url": "https://authors.library.caltech.edu/records/zprzp-wan75/files/1504.01144.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/2fwrq-dyq34", "eprint_id": 81516, "eprint_status": "archive", "datestamp": "2023-08-19 05:08:58", "lastmod": "2026-04-01 20:30:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bao-Ning", "name": { "family": "Bao", "given": "Ning" }, "orcid": "0000-0002-3296-1039" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Distinguishability of black hole microstates", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 American Physical Society. \n\nReceived 7 July 2017; published 18 September 2017. \n\nWe would like to thank Aidan Chatwin-Davies, Xi Dong, Netta Engelhardt, Daniel Harlow, Thomas Hartman, Akio Hosoya, Veronika Hubeny, Tomonori Ugajin, and Beni Yoshida for discussions. This research is supported in part by U.S. Department of Energy Grant No. DE-SC0011632. N.\u2009B. is also supported in part by the DuBridge Fellowship of the Walter Burke Institute for Theoretical Physics. H.\u2009O. is also supported in part by Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research C-26400240 and 15H05895. The Kavli Institute for the Physics and Mathematics of the Universe is supported in part by the World Premier International Research Center Initiative, MEXT, Japan.\n\n

Published - PhysRevD.96.066017.pdf

Submitted - 1705.07943.pdf

", "abstract": "We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.", "date": "2017-09-15", "date_type": "published", "publication": "Physical Review D", "volume": "96", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066017", "id_number": "CaltechAUTHORS:20170918-091256373", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170918-091256373", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Lee A. DuBridge Foundation" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.96.066017", "primary_object": { "basename": "1705.07943.pdf", "url": "https://authors.library.caltech.edu/records/2fwrq-dyq34/files/1705.07943.pdf" }, "related_objects": [ { "basename": "PhysRevD.96.066017.pdf", "url": "https://authors.library.caltech.edu/records/2fwrq-dyq34/files/PhysRevD.96.066017.pdf" } ], "pub_year": "2017", "author_list": "Bao, Ning and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/7nbpy-f0214", "eprint_id": 77072, "eprint_status": "archive", "datestamp": "2023-08-21 21:43:58", "lastmod": "2026-04-01 06:44:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Sabin-J", "name": { "family": "Sabin", "given": "Julien" } } ] }, "title": "Spectral cluster bounds for orthonormal systems and oscillatory integral operators in Schatten spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Laplace Beltrami operator; Eigenfunctions; Spectral clusters; Oscillatory integrals; Schatten spaces", "note": "\u00a9 2017 Elsevier Inc. \n\nReceived 30 August 2016, Revised 20 June 2017, Accepted 20 June 2017, Available online 10 July 2017. \n\nPartial support by U.S. National Science Foundation DMS-1363432 (R.L.F.) is acknowledged. J.S. would like to thank Nicolas Burq and Bernard Helffer for useful discussions.\n\n

Submitted - 1608.08299.pdf

", "abstract": "We generalize the L^p spectral cluster bounds of Sogge for the Laplace\u2013Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. The optimality of these new bounds is also discussed. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators.", "date": "2017-09-07", "date_type": "published", "publication": "Advances in Mathematics", "volume": "317", "publisher": "Elsevier", "pagerange": "157-192", "id_number": "CaltechAUTHORS:20170428-155217715", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170428-155217715", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2017.06.023", "primary_object": { "basename": "1608.08299.pdf", "url": "https://authors.library.caltech.edu/records/7nbpy-f0214/files/1608.08299.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L. and Sabin, Julien" }, { "id": "https://authors.library.caltech.edu/records/w002p-sx481", "eprint_id": 77282, "eprint_status": "archive", "datestamp": "2023-08-21 21:42:18", "lastmod": "2026-04-01 15:32:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Unitaries permuting two orthogonal projections", "ispublished": "pub", "full_text_status": "public", "keywords": "Pairs of projections; Index", "note": "\u00a9 2017 Elsevier Inc. \n\nReceived 15 March 2017, Accepted 27 March 2017, Available online 29 March 2017. \n\nSubmitted by P. Semrl. \n\nResearch supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2010348.\n\n

Submitted - 1703.05437.pdf

", "abstract": "Let P and Q be two orthogonal projections on a separable Hilbert space, H. Wang, Du and Dou proved that there exists a unitary, U, with UPU^(\u22121) =Q, UQU^(\u22121) =P if and only if dim\u2061(ker\u2061P\u2229ker\u2061(1\u2212Q))=dim\u2061(ker\u2061Q\u2229ker\u2061(1\u2212P)) (both may be infinite). We provide a new proof using the supersymmetric machinery of Avron, Seiler and Simon.", "date": "2017-09-01", "date_type": "published", "publication": "Linear Algebra and its Applications", "volume": "528", "publisher": "Elsevier", "pagerange": "436-441", "id_number": "CaltechAUTHORS:20170509-073922440", "issn": "0024-3795", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170509-073922440", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010348" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.laa.2017.03.026", "primary_object": { "basename": "1703.05437.pdf", "url": "https://authors.library.caltech.edu/records/w002p-sx481/files/1703.05437.pdf" }, "pub_year": "2017", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/yzec3-5ya52", "eprint_id": 79000, "eprint_status": "archive", "datestamp": "2023-08-19 04:51:35", "lastmod": "2026-04-01 06:34:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Burton-P-J", "name": { "family": "Burton", "given": "Peter J." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Invariant random subgroups and action versus representation maximality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 American Mathematical Society. \n\nReceived by the editors August 25, 2016 and, in revised form, October 12, 2016. Article electronically published on April 7, 2017. \n\nResearch partially supported by NSF Grant DMS-1464475.\n\n

Submitted - 1608.01331.pdf

", "abstract": "We show that weak containment of free ergodic measure-preserving actions of F\u221e is not equivalent to weak containment of the corresponding Koopman representations. This result is based on the construction of an invariant random subgroup of F\u221e which is supported on the maximal actions.", "date": "2017-09", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "145", "number": "9", "publisher": "American Mathematical Society", "pagerange": "3961-3971", "id_number": "CaltechAUTHORS:20170712-091809776", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-091809776", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1464475" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/proc/13591", "primary_object": { "basename": "1608.01331.pdf", "url": "https://authors.library.caltech.edu/records/yzec3-5ya52/files/1608.01331.pdf" }, "pub_year": "2017", "author_list": "Burton, Peter J. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/try6f-rqq87", "eprint_id": 78281, "eprint_status": "archive", "datestamp": "2023-08-19 04:50:01", "lastmod": "2026-04-01 19:51:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori, II", "ispublished": "pub", "full_text_status": "restricted", "keywords": "virtual Betti number, virtual symplecticity, 4-dimensional mapping torus, reducible 3-manifold", "note": "\u00a9 2017 Science China Press and Springer-Verlag Berlin Heidelberg. \n\nReceived December 23, 2016; accepted March 6, 2017. First Online: 07 April 2017. \n\nDedicated to Professor Boju Jiang on the Occasion of His 80th Birthday. \n\nThis work was supported by National Science Foundation of USA (Grant No. DMS-1252992) and an Alfred P. Sloan Research Fellowship. The author thanks a referee for clarifying some arguments in geometric group theory.", "abstract": "We show that if the fiber of a closed 4-dimensional mapping torus X is reducible and not S^2\u00d7S^1 or \u211dP^3#\u211dP^3, then the virtual first Betti number of X is infinite and X is not virtually symplectic. This confirms two conjectures made by Li and Ni (2014) in an earlier paper.", "date": "2017-09", "date_type": "published", "publication": "Science China Mathematics", "volume": "60", "number": "9", "publisher": "Springer", "pagerange": "1591-1598", "id_number": "CaltechAUTHORS:20170616-111024361", "issn": "1674-7283", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170616-111024361", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11425-016-9052-8", "pub_year": "2017", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/t9r63-6sn29", "eprint_id": 71762, "eprint_status": "archive", "datestamp": "2023-08-19 04:39:35", "lastmod": "2026-04-01 16:25:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Turzillo-A", "name": { "family": "Turzillo", "given": "Alex" }, "orcid": "0000-0003-4293-4293" }, { "id": "You-Minyoung", "name": { "family": "You", "given": "Minyoung" } } ] }, "title": "Topological Field Theory and Matrix Product States", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 American Physical Society. \n\nReceived 6 June 2017; published 14 August 2017. \n\nA.K. would like to thank P. Etingof and V. Ostrik for discussions. A.T. is grateful to I. Saberi and D. Williamson for helpful conversations. While this paper was nearing completion, we learned that closely related results have been obtained by K. Shiozaki and S. Ryu. This paper was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.\n\n

Published - PhysRevB.96.075125.pdf

Submitted - 1607.06766v1.pdf

Submitted - 1610.10075v2.pdf

", "abstract": "It is believed that most (perhaps all) gapped phases of matter can be described at long distances by topological quantum field theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped Hamiltonians can be approximated by matrix product states (MPS). We show that the state-sum construction of 2d TQFT naturally leads to MPS in their standard form. In the case of systems with a global symmetry G\n, this leads to a classification of gapped phases in 1+1d in terms of Morita-equivalence classes of G-equivariant algebras. Nonuniqueness of the MPS representation is traced to the freedom of choosing an algebra in a particular Morita class. In the case of short-range entangled phases, we recover the group cohomology classification of SPT phases.", "date": "2017-08-15", "date_type": "published", "publication": "Physical Review B", "volume": "96", "number": "7", "publisher": "American Physical Society", "pagerange": "Art. No. 075125", "id_number": "CaltechAUTHORS:20161107-091619292", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161107-091619292", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.96.075125", "primary_object": { "basename": "1610.10075v2.pdf", "url": "https://authors.library.caltech.edu/records/t9r63-6sn29/files/1610.10075v2.pdf" }, "related_objects": [ { "basename": "PhysRevB.96.075125.pdf", "url": "https://authors.library.caltech.edu/records/t9r63-6sn29/files/PhysRevB.96.075125.pdf" }, { "basename": "1607.06766v1.pdf", "url": "https://authors.library.caltech.edu/records/t9r63-6sn29/files/1607.06766v1.pdf" } ], "pub_year": "2017", "author_list": "Kapustin, Anton; Turzillo, Alex; et al." }, { "id": "https://authors.library.caltech.edu/records/pnnpa-h6826", "eprint_id": 78989, "eprint_status": "archive", "datestamp": "2023-08-19 04:35:14", "lastmod": "2026-04-01 17:10:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Zhi-Ren", "name": { "family": "Zhi", "given": "Ren" } } ] }, "title": "q-deformations of statistical mechanical systems and motives over finite fields", "ispublished": "pub", "full_text_status": "public", "keywords": "Witt rings, q-analogs, zeta functions, Quantum Statistical Mechanics", "note": "\u00a9 2017 Pleiades Publishing, Ltd. \n\nReceived: 05 May 2017; First Online: 03 August 2017. \n\nThe first author was partially supported by NSF grants DMS-1201512, DMS-1707882 and PHY-1205440. The second author was supported by a Summer Undergraduate Research Fellowship at Caltech.\n\n

Submitted - 1704.06367.pdf

", "abstract": "We consider q-deformations of Witt rings, based on geometric operations on zeta functions of motives over finite fields, and we use these deformations to construct q-analogs of the Bost-Connes quantum statistical mechanical system. We show that the q-deformations obtained in this way can be related to Habiro ring constructions of analytic functions over F_1 and to categorifications of Bost-Connes systems.", "date": "2017-08-03", "date_type": "published", "publication": "p-Adic Numbers, Ultrametric Analysis and Applications", "volume": "9", "number": "3", "publisher": "Springer", "pagerange": "204-227", "id_number": "CaltechAUTHORS:20170712-084525536", "issn": "2070-0466", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-084525536", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/S2070046617030049", "primary_object": { "basename": "1704.06367.pdf", "url": "https://authors.library.caltech.edu/records/pnnpa-h6826/files/1704.06367.pdf" }, "pub_year": "2017", "author_list": "Marcolli, Matilde and Zhi, Ren" }, { "id": "https://authors.library.caltech.edu/records/ehfed-mgm13", "eprint_id": 97839, "eprint_status": "archive", "datestamp": "2023-08-21 21:31:53", "lastmod": "2026-04-01 20:52:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aigner-Horev-E", "name": { "family": "Aigner-Horev", "given": "Elad" } }, { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "H\u00e0n-Hi\u1ec7p", "name": { "family": "H\u00e0n", "given": "Hi\u1ec7p" } }, { "id": "Person-Y", "name": { "family": "Person", "given": "Yury" } }, { "id": "Schacht-M", "name": { "family": "Schacht", "given": "Mathias" } } ] }, "title": "Quasirandomness in hypergraphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Hypergraphs; quasirandomness", "note": "\u00a9 2017 Published by Elsevier B.V. \n\nAvailable online 3 August 2017. \n\nThe second author was supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. The third author was supported by the FONDECYT Iniciaci\u00f3n grant 11150913 and by Millenium Nucleus Information and Coordination in Networks. The fourth author was supported by DFG grant PE 2299/1-1. The fifth author was supported by ERC Consolidator Grant 724903. \n\nWe are indebted to the anonymous referee for their careful review.\n\n

Submitted - 1711.04750.pdf

", "abstract": "A graph G is called quasirandom if it possesses typical properties of the corresponding random graph G(n, p) with the same edge density as G. A well-known theorem of Chung, Graham and Wilson states that, in fact, many such 'typical' properties are asymptotically equivalent and, thus, a graph G possessing one property immediately satisfies the others.\n\nIn recent years, more quasirandom graph properties have been found and extensions to hypergraphs have been explored. For the latter, however, there exist several distinct notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. The purpose of this paper is to give short purely combinatorial proofs of most of Towsner's results.", "date": "2017-08", "date_type": "published", "publication": "Electronic Notes in Discrete Mathematics", "volume": "61", "publisher": "Elsevier", "pagerange": "13-19", "id_number": "CaltechAUTHORS:20190812-163000449", "issn": "1571-0653", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000449", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (FONDECYT)", "grant_number": "11150913" }, { "agency": "Millenium Nucleus Information and Coordination in Networks" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "PE 2299/1-1" }, { "agency": "European Research Council (ERC)", "grant_number": "724903" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.endm.2017.06.015", "primary_object": { "basename": "1711.04750.pdf", "url": "https://authors.library.caltech.edu/records/ehfed-mgm13/files/1711.04750.pdf" }, "pub_year": "2017", "author_list": "Aigner-Horev, Elad; Conlon, David; et al." }, { "id": "https://authors.library.caltech.edu/records/85q64-q6758", "eprint_id": 97809, "eprint_status": "archive", "datestamp": "2023-08-21 21:29:18", "lastmod": "2026-04-01 20:39:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Lee-Joonkyung", "name": { "family": "Lee", "given": "Joonkyung" } } ] }, "title": "Finite reflection groups and graph norms", "ispublished": "pub", "full_text_status": "public", "keywords": "Graph norms; Sidorenko's conjecture; Quasirandomness", "note": "\u00a9 2017 Elsevier Inc. All rights reserved.\n\nReceived 1 December 2016; accepted 16 May 2017; available online 13 June 2017. \n\nConlon research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. Lee supported by the ILJU Foundation of Education and Culture. \n\nPart of this work was carried out while the authors participated in the LMS-CMI Research School on Regularity and Analytic Methods in Combinatorics at the University of Warwick and also while the second author was visiting KIAS. The second author would like to thank Seung Jin Lee for suggestions of references and helpful discussions on algebraic combinatorics. We would also like to thank Alexander Sidorenko for some helpful remarks on an earlier version of this paper.\n\n

Submitted - 1611.05784.pdf

", "abstract": "Given a graph H on vertex set {1, 2, \u2022 \u2022 \u2022, n} and a function f : [0, 1]^2 \u2192 \u211d, define [equation; see abstract in PDF for details], where \u03bc is the Lebesgue measure on [0, 1]. We say that H is norming if \u2225\u2022\u2225_H is a semi-norm. A similar notion \u2225\u2022\u2225_r(H) is defined by \u2225f\u2225_r(H) := \u2225|f|\u2225_H and H is said to be weakly norming if \u2225\u2022\u2225_r(H) is a norm. Classical results show that weakly norming graphs are necessarily bipartite. In the other direction, Hatami showed that even cycles, complete bipartite graphs, and hypercubes are all weakly norming. We demonstrate that any graph whose edges percolate in an appropriate way under the action of a certain natural family of automorphisms is weakly norming. This result includes all previously known examples of weakly norming graphs, but also allows us to identify a much broader class arising from finite reflection groups. We include several applications of our results. In particular, we define and compare a number of generalisations of Gowers' octahedral norms and we prove some new instances of Sidorenko's conjecture.", "date": "2017-07-31", "date_type": "published", "publication": "Advances in Mathematics", "volume": "315", "publisher": "Elsevier", "pagerange": "130-165", "id_number": "CaltechAUTHORS:20190812-162957357", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957357", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "ILJU Foundation of Education and Culture" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2017.05.009", "primary_object": { "basename": "1611.05784.pdf", "url": "https://authors.library.caltech.edu/records/85q64-q6758/files/1611.05784.pdf" }, "pub_year": "2017", "author_list": "Conlon, David and Lee, Joonkyung" }, { "id": "https://authors.library.caltech.edu/records/2vex0-yd257", "eprint_id": 75103, "eprint_status": "archive", "datestamp": "2023-08-19 04:09:06", "lastmod": "2026-04-01 20:01:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Spodyneiko-L", "name": { "family": "Spodyneiko", "given": "Lev" }, "orcid": "0000-0002-6099-7717" } ] }, "title": "New Kaluza-Klein Instantons and Decay of AdS Vacua", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 American Physical Society. \n\nReceived 17 April 2017; published 19 July 2017. \n\nThe authors would like to thank G. Horowitz, S. Gukov, I. Klebanov, and H. Reall for discussions. This research is supported in part by the U.S. Department of Energy Grant No. DE-SC0011632. H.\u2009O. is also supported in part by the Simons Investigator Award, by the World Premier International Research Center Initiative, Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research No. C-26400240, and by the JSPS Grant-in-Aid for Scientific Research on Innovative Areas No. 15H05895.\n\n

Published - PhysRevD.96.026016.pdf

Submitted - 1703.03105.pdf

", "abstract": "We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit the instability of nonsupersymmetric AdS_5 vacua in M theory compactified on positive K\u00e4hler-Einstein spaces, providing further evidence for the recent conjecture that any nonsupersymmetric anti\u2013de Sitter vacuum supported by fluxes must be unstable.", "date": "2017-07-15", "date_type": "published", "publication": "Physical Review D", "volume": "96", "number": "2", "publisher": "American Physical Society", "pagerange": "Art. No. 026016", "id_number": "CaltechAUTHORS:20170314-133249092", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170314-133249092", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" } ] }, "other_numbering_system": { "items": [ { "id": "2017-014", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.96.026016", "primary_object": { "basename": "1703.03105.pdf", "url": "https://authors.library.caltech.edu/records/2vex0-yd257/files/1703.03105.pdf" }, "related_objects": [ { "basename": "PhysRevD.96.026016.pdf", "url": "https://authors.library.caltech.edu/records/2vex0-yd257/files/PhysRevD.96.026016.pdf" } ], "pub_year": "2017", "author_list": "Ooguri, Hirosi and Spodyneiko, Lev" }, { "id": "https://authors.library.caltech.edu/records/2h0p1-vme48", "eprint_id": 77119, "eprint_status": "archive", "datestamp": "2023-08-19 04:07:45", "lastmod": "2026-04-01 19:34:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Eigenvalue bounds for Schr\u00f6dinger operators with complex potentials. III", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 by the Author. \n\nReceived by the editors October 12, 2015 and, in revised form, March 14, 2016. Published electronically: July 13, 2017. \n\nThe author was supported by NSF grant DMS-1363432. \n\nFundamental for several of the new theorems here are results from [13], which were obtained jointly with J. Sabin to whom the author is most grateful. He would also like to thank M. Demuth and M. Hansmann for fruitful discussions and M. Demuth, L. Golinskii and F. Hanauska for helpful remarks on a previous version of this manuscript. This paper has its origin at the conference \"Mathematical aspects of physics with non-self-adjoint operators\" in June 2015 and the author is grateful to the organizers and the American Institute of Mathematics for the invitation. This paper was finished at the Mittag\u2013Leffler Institute and the author is grateful to A. Laptev for the hospitality.\n\n

Submitted - 1510.03411.pdf

", "abstract": "We discuss the eigenvalues E_j of Schr\u00f6dinger operators \u2212\u0394+V in L^2(R^d) with complex potentials V \u2208 L^p, p < \u221e. We show that (A) Re E_j \u2192 \u221e implies Im E_j \u2192 0, and (B) Re E_j \u2192 E \u2208 [0,\u221e) implies (Im E_j) \u2208 \u2113^q for some q depending on p. We prove quantitative versions of (A) and (B) in terms of the L^p-norm of V.", "date": "2017-07-13", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "370", "publisher": "American Mathematical Society", "pagerange": "219-240", "id_number": "CaltechAUTHORS:20170502-081943954", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170502-081943954", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/6936", "primary_object": { "basename": "1510.03411.pdf", "url": "https://authors.library.caltech.edu/records/2h0p1-vme48/files/1510.03411.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/kbxh0-6mm44", "eprint_id": 65404, "eprint_status": "archive", "datestamp": "2023-08-21 21:19:00", "lastmod": "2026-04-01 21:07:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Fivebranes and 3-manifold homology", "ispublished": "pub", "full_text_status": "public", "keywords": "Chern-Simons Theories; Topological Field Theories; M-Theory Topological Strings", "note": "\u00a9 2017 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 20 October 2016; Revised: 21 April 2017; Accepted: 05 June 2017; First Online: 14 July 2017. \n\nArticle funded by SCOAP3. \n\nWe would like to thank M. Aganagic, A. Gadde, M. Khovanov, C. Manolescu, S. Nawata, P. Ozsvath, J. Rasmussen, M. Romo, L. Rozansky, and E. Witten for useful comments and\ndiscussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics. P.P. gratefully acknowledges support from the Institute for Advanced Study and also would like to thank Caltech and UT Austin theory groups for hospitality during the final stage of the project. The work of C.V. is supported in part by NSF grant PHY-1067976. C.V. would like to thank KITP for hospitality. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - 10.1007_2FJHEP07_2017_071.pdf

Submitted - 1602.05302v1.pdf

", "abstract": "Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.", "date": "2017-07", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "07", "publisher": "Springer", "pagerange": "Art. No. 071", "id_number": "CaltechAUTHORS:20160316-162103450", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160316-162103450", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Institute for Advanced Study" }, { "agency": "NSF", "grant_number": "PHY-1067976" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2016-004", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP07(2017)071", "primary_object": { "basename": "10.1007_2FJHEP07_2017_071.pdf", "url": "https://authors.library.caltech.edu/records/kbxh0-6mm44/files/10.1007_2FJHEP07_2017_071.pdf" }, "related_objects": [ { "basename": "1602.05302v1.pdf", "url": "https://authors.library.caltech.edu/records/kbxh0-6mm44/files/1602.05302v1.pdf" } ], "pub_year": "2017", "author_list": "Gukov, Sergei; Putrov, Pavel; et al." }, { "id": "https://authors.library.caltech.edu/records/ecwe3-ykz45", "eprint_id": 87406, "eprint_status": "archive", "datestamp": "2023-08-19 03:59:40", "lastmod": "2026-04-01 16:45:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Liu-Chiu-Chu-Melissa", "name": { "family": "Liu", "given": "Chiu-Chu Melissa" } }, { "id": "Sheshmani-A", "name": { "family": "Sheshmani", "given": "Artan" } }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" } } ] }, "title": "On topological approach to local theory of surfaces in Calabi\u2013Yau threefolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2018 International Press of Boston. \n\nSpecial Issue: Proceedings of the Strings 2016 Conference in Beijing\nGuest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University) \n\nWe would like to thank Jun Li, Davesh Maulik, and Richard Thomas for helpful conversations. The work of S. Gukov is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 and in part by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\" funded by the European Research Council under the European Union Seventh Framework Programme. The work of C.-C. Liu is partially supported by NSF grants DMS-1206667 and DMS-1159416. A. Sheshmani would like to thank Kavli IPMU, MIT, Harvard and the Institute Henri Poincar\u00e9 (IHP) for creating the opportunity of initiating the discussions about the current article. The work of A. Sheshmani was partially supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan and Laboratory of Mirror Symmetry NRU HSE, RF Government grant, ag. No 14.641.31.0001. S.-T. Y. was partially supported by NSF DMS-0804454, NSF PHY-1306313, and Simons 38558. The work of S.-T. Yau is partially supported by NSF grants DMS 1308244, DMS-159412, PHY-1306313, and PHY-0937443.\n\n

Accepted Version - 1609.04363

", "abstract": "We study the web of dualities relating various enumerative invariants, notably Gromov\u2013Witten invariants and invariants that arise in topological gauge theory. In particular, we study Donaldson\u2013Thomas gauge theory and its reductions to D=4D=4 and D=2D=2 which are relevant to the local theory of surfaces in Calabi\u2013Yau threefolds.", "date": "2017-07", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "21", "number": "7", "publisher": "International Press", "pagerange": "1679-1728", "id_number": "CaltechAUTHORS:20180627-133558358", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180627-133558358", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "NSF", "grant_number": "DMS-1206667" }, { "agency": "NSF", "grant_number": "DMS-1159416" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "14.641.31.0001" }, { "agency": "NSF", "grant_number": "DMS-0804454" }, { "agency": "NSF", "grant_number": "PHY-1306313" }, { "agency": "Simons Foundation", "grant_number": "38558" }, { "agency": "NSF", "grant_number": "DMS 1308244" }, { "agency": "NSF", "grant_number": "DMS-159412" }, { "agency": "NSF", "grant_number": "PHY-0937443" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2017.v21.n7.a4", "primary_object": { "basename": "1609.04363", "url": "https://authors.library.caltech.edu/records/ecwe3-ykz45/files/1609.04363" }, "pub_year": "2017", "author_list": "Gukov, Sergei; Liu, Chiu-Chu Melissa; et al." }, { "id": "https://authors.library.caltech.edu/records/2wjwa-cq465", "eprint_id": 71981, "eprint_status": "archive", "datestamp": "2023-08-19 03:47:16", "lastmod": "2026-04-01 16:17:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bowen-L", "name": { "family": "Bowen", "given": "Lewis" } }, { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Generic Stationary Measures and Actions", "ispublished": "pub", "full_text_status": "public", "keywords": "stationary action, Poisson boundary", "note": "\u00a9 2017 American Mathematical Society. \n\nReceived by the editors February 17, 2015 and, in revised form, July 2, 2015, August 10, 2015, and August 14, 2015.\nPublished electronically: January 9, 2017. \n\nThe first author was supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274. \n\nThe second author was supported by the European Research Council, grant 239885.\n\n

Submitted - 1405.2260.pdf

", "abstract": "Let G be a countably infinite group, and let \u03bc be a generating probability measure on G. We study the space of \u03bc-stationary Borel probability measures on a topological G space, and in particular on Z^G, where Z is any perfect Polish space. We also study the space of \u03bc-stationary, measurable G-actions on a standard, nonatomic probability space.\nEquip the space of stationary measures with the weak* topology. When \u03bc has finite entropy, we show that a generic measure is an essentially free extension of the Poisson boundary of (G, \u03bc). When Z is compact, this implies that the simplex of \u03bc-stationary \nmeasures on Z^G is a Poulsen simplex. We show that this is also the case for the simplex of stationary measures on {0, 1}^G.\nWe furthermore show that if the action of G on its Poisson boundary is essentially free then a generic measure is isomorphic to the Poisson boundary. \nNext, we consider the space of stationary actions, equipped with a standard topology known as the weak topology. Here we show that when G has property (T), the \nergodic actions are meager. We also construct a group G without property (T) such that the ergodic actions are not dense, for some \u03bc.\nFinally, for a weaker topology on the set of actions, which we call the very weak topology, we show that a dynamical property (e.g., ergodicity) is topologically generic if and only if it is generic in the space of measures. There we also show a Glasner-King type 0-1 law stating that every dynamical property is either meager or residual.", "date": "2017-07", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "369", "number": "7", "publisher": "American Mathematical Society", "pagerange": "4889-4929", "id_number": "CaltechAUTHORS:20161114-092928470", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-092928470", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968762" }, { "agency": "NSF", "grant_number": "DMS-0954606" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2008274" }, { "agency": "European Research Council (ERC)", "grant_number": "239885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/6803", "primary_object": { "basename": "1405.2260.pdf", "url": "https://authors.library.caltech.edu/records/2wjwa-cq465/files/1405.2260.pdf" }, "pub_year": "2017", "author_list": "Bowen, Lewis; Hartman, Yair; et al." }, { "id": "https://authors.library.caltech.edu/records/4dw0r-g6052", "eprint_id": 71434, "eprint_status": "archive", "datestamp": "2023-08-19 03:47:08", "lastmod": "2026-04-01 08:08:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Non-supersymmetric AdS and the Swampland", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 International Press of Boston, Inc. \n\nSpecial Issue: Proceedings of the Strings 2016 Conference in Beijing\nGuest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University) \n\nWe would like to thank N. Arkani-Hamed, T. Dumitrescu, D. Harlow, I. Klebanov, J. Maldacena, G. Remmen, T. Rudelius, A. Sen, S. Shenker, A. Strominger, and E. Witten for discussions. The research of HO is supported in part by U.S. Department of Energy grant DE-SC0011632, by the Simons Investigator Award, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. HO also thanks the hospitality of the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1066293, and of the the Center for Mathematical Sciences and Applications and the Center for the Fundamental Laws of Nature at Harvard University. The research of CV is supported by the NSF grant PHY-1067976.\n\n

Published - ATMP-2017-0021-0007-a008.pdf

Submitted - 1610.01533v2.pdf

", "abstract": "We propose to sharpen the weak gravity conjecture by the statement that, except for BPS states in a supersymmetric theory, the gravitational force is strictly weaker than any electric force and provide a number of evidences for this statement. Our conjecture implies that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable, as is the case for all known attempts at such holographic constructions.", "date": "2017-07", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "21", "number": "7", "publisher": "International Press", "pagerange": "1787-1801", "id_number": "CaltechAUTHORS:20161024-200308753", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161024-200308753", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "NSF", "grant_number": "PHY-1067976" } ] }, "other_numbering_system": { "items": [ { "id": "2016-027", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2017.v21.n7.a8", "primary_object": { "basename": "ATMP-2017-0021-0007-a008.pdf", "url": "https://authors.library.caltech.edu/records/4dw0r-g6052/files/ATMP-2017-0021-0007-a008.pdf" }, "related_objects": [ { "basename": "1610.01533v2.pdf", "url": "https://authors.library.caltech.edu/records/4dw0r-g6052/files/1610.01533v2.pdf" } ], "pub_year": "2017", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/j71yf-a4p48", "eprint_id": 78992, "eprint_status": "archive", "datestamp": "2023-08-21 21:21:19", "lastmod": "2026-04-01 17:40:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Atiyah-M", "name": { "family": "Atiyah", "given": "Michael" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Anyons in Geometric Models of Matter", "ispublished": "pub", "full_text_status": "public", "keywords": "Anyons; Differential and Algebraic Geometry", "note": "\u00a9 2017 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: November 22, 2016; Revised: May 28, 2017; Accepted: July 6, 2017; Published: July 14, 2017. \n\nArticle funded by SCOAP3. \n\nThe first author received support from the Clay Mathematical Institute, Trinity College Cambridge, and the University of Edinburgh. The second author was partially supported by NSF grants DMS-1201512 and 1707882 and PHY-1205440 and the Perimeter Institute for Theoretical Physics. The second author would also like to thank Andrew Ranicki and Ida Thompson for their generous hospitality during her visits to the first author in Edinburgh.\n\n

Published - 10.1007_2FJHEP07_2017_076.pdf

Submitted - 1611.04047.pdf

", "abstract": "We show that the \"geometric models of matter\" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through the braid representation of surface braids wrapped around the orbifold singularities, coming from multisections of the orbifold normal bundle of the embedded surface. We show that the resulting braid representations can give rise to a universal quantum computer.", "date": "2017-07", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "07", "publisher": "Springer", "pagerange": "Art. No. 076", "id_number": "CaltechAUTHORS:20170712-085827096", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-085827096", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematical Institute" }, { "agency": "Trinity College Cambridge" }, { "agency": "University of Edinburgh" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP07(2017)076", "primary_object": { "basename": "10.1007_2FJHEP07_2017_076.pdf", "url": "https://authors.library.caltech.edu/records/j71yf-a4p48/files/10.1007_2FJHEP07_2017_076.pdf" }, "related_objects": [ { "basename": "1611.04047.pdf", "url": "https://authors.library.caltech.edu/records/j71yf-a4p48/files/1611.04047.pdf" } ], "pub_year": "2017", "author_list": "Atiyah, Michael and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/6j17p-vfb40", "eprint_id": 78825, "eprint_status": "archive", "datestamp": "2023-08-21 21:18:44", "lastmod": "2026-04-01 07:05:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gubser-S-S", "name": { "family": "Gubser", "given": "Steven S." } }, { "id": "Heydeman-Matthew", "name": { "family": "Heydeman", "given": "Matthew" }, "orcid": "0000-0001-7033-9075" }, { "id": "Jepsen-C-B", "name": { "family": "Jepsen", "given": "Christian" }, "orcid": "0000-0002-1159-0574" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Parikh-Sarthak", "name": { "family": "Parikh", "given": "Sarthak" }, "orcid": "0000-0002-5831-3873" }, { "id": "Saberi-Ingmar-A", "name": { "family": "Saberi", "given": "Ingmar" } }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } }, { "id": "Trundy-B", "name": { "family": "Trundy", "given": "Brian" } } ] }, "title": "Edge length dynamics on graphs with applications to p-adic AdS/CFT", "ispublished": "pub", "full_text_status": "public", "keywords": "Lattice Models of Gravity; AdS-CFT Correspondence; Classical Theories of Gravity", "note": "\u00a9 The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: May 18, 2017. Accepted: June 18, 2017. Published: June 30, 2017. \n\nArticle funded by SCOAP3. \n\nThe work of S. Gubser, C. Jepsen, S. Parikh, and B. Trundy was supported in part by the Department of Energy under Grant No. DE-FG02-91ER40671. The work of M. Heydeman\nwas supported by the Department of Energy under grant DE-SC0011632, as well as by the Walter Burke Institute for Theoretical Physics at Caltech. M. Marcolli is partially supported by NSF grants DMS-1201512 and PHY-1205440, and by the Perimeter Institute for Theoretical Physics. The work of B. Stoica was supported in part by the Simons\nFoundation, and by the U.S. Department of Energy under grant DE-SC-0009987.\n\n

Published - 10.1007_2FJHEP06_2017_157.pdf

Submitted - 1612.09580.pdf

", "abstract": "We formulate a Euclidean theory of edge length dynamics based on a notion of Ricci curvature on graphs with variable edge lengths. In order to write an explicit form for the discrete analog of the Einstein-Hilbert action, we require that the graph should either be a tree or that all its cycles should be sufficiently long. The infinite regular tree with all edge lengths equal is an example of a graph with constant negative curvature, providing a connection with p-adic AdS/CFT, where such a tree takes the place of anti-de Sitter space. We compute simple correlators of the operator holographically dual to edge length fluctuations. This operator has dimension equal to the dimension of the boundary, and it has some features in common with the stress tensor.", "date": "2017-06-30", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "6", "publisher": "Springer", "pagerange": "1-35", "id_number": "CaltechAUTHORS:20170707-065452085", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170707-065452085", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-91ER40671" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC-0009987" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP06(2017)157", "primary_object": { "basename": "10.1007_2FJHEP06_2017_157.pdf", "url": "https://authors.library.caltech.edu/records/6j17p-vfb40/files/10.1007_2FJHEP06_2017_157.pdf" }, "related_objects": [ { "basename": "1612.09580.pdf", "url": "https://authors.library.caltech.edu/records/6j17p-vfb40/files/1612.09580.pdf" } ], "pub_year": "2017", "author_list": "Gubser, Steven S.; Heydeman, Matthew; et al." }, { "id": "https://authors.library.caltech.edu/records/tw0pb-nsv65", "eprint_id": 71963, "eprint_status": "archive", "datestamp": "2023-08-19 03:44:48", "lastmod": "2026-04-01 15:27:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Opinion Exchange Dynamics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Institute of Mathematical Statistics. Creative Commons Attribution 4.0 International License. \n\nReceived: January 2014. First available in Project Euclid: 27 June 2017. \n\nAllan Sly is our main collaborator in this field. We are grateful to him for allowing us to include some of our joint results, as well as for all that we learned from him. The manuscript was prepared for the 9th Probability Summer School in Cornell, which took place in July 2013.We are grateful to Laurent Saloff-Coste and Lionel Levine for organizing the school and for the participants for helpful comments and discussions. We would like to thank Shachar Kariv for introducing us to this field, and Eilon Solan for encouraging us to continue working in it. The research of Elchanan Mossel is partially supported by NSF grants DMS 1106999 and CCF 1320105, and by ONR grant N000141110140. Omer Tamuz was supported by a Google Europe Fellowship in Social Computing.\n\n

Published - euclid.ps.1498528815.pdf

Submitted - 1401.4770.pdf

", "abstract": "The exchange of opinions between individuals is a fundamental social interaction that plays a role in nearly any social, political and economic process. While it is unlikely that a simple mathematical model can accurately describe the exchange of opinions between two people, one could hope to gain some insights on emergent phenomena that affect large groups of people.", "date": "2017-06-27", "date_type": "published", "publication": "Probability Surveys", "volume": "14", "publisher": "Institute of Mathematical Statistics", "pagerange": "155-204", "id_number": "CaltechAUTHORS:20161111-150254761", "issn": "1549-5787", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-150254761", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1106999" }, { "agency": "NSF", "grant_number": "CCF-1320105" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N000141110140" }, { "agency": "Google Europe Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/14-PS230", "primary_object": { "basename": "1401.4770.pdf", "url": "https://authors.library.caltech.edu/records/tw0pb-nsv65/files/1401.4770.pdf" }, "related_objects": [ { "basename": "euclid.ps.1498528815.pdf", "url": "https://authors.library.caltech.edu/records/tw0pb-nsv65/files/euclid.ps.1498528815.pdf" } ], "pub_year": "2017", "author_list": "Mossel, Elchanan and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/9vs1v-3e586", "eprint_id": 111022, "eprint_status": "archive", "datestamp": "2023-08-19 03:31:56", "lastmod": "2026-04-01 20:13:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Nachmias-Asaf", "name": { "family": "Nachmias", "given": "Asaf" }, "orcid": "0000-0002-4852-5645" } ] }, "title": "Indistinguishability of trees in uniform spanning forests", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag Berlin Heidelberg 2016. \n\nReceived: 22 October 2015 / Revised: 2 April 2016 / Published online: 16 April 2016. \n\nWe are grateful to Russ Lyons for many comments, corrections and improvements to the manuscript, and also to Ander Holroyd and Yuval Peres for useful discussions. TH thanks Tel Aviv University and both authors thank the Issac Newton Institute, where part of this work was carried out, for their hospitality. This Project is supported by NSERC.\n\n

Accepted Version - 1506.00556.pdf

", "abstract": "We prove that in both the free and the wired uniform spanning forest (FUSF and WUSF) of any unimodular random rooted network (in particular, of any Cayley graph), it is impossible to distinguish the connected components of the forest from each other by invariantly defined graph properties almost surely. This confirms a conjecture of Benjamini et al. (Ann Probab 29(1):1\u201365, 2001). We also answer positively two additional questions of Benjamini et al. (Ann Probab 29(1):1\u201365, 2001) under the assumption of unimodularity. We prove that on any unimodular random rooted network, the FUSF is either connected or has infinitely many connected components almost surely, and, if the FUSF and WUSF are distinct, then every component of the FUSF is transient and infinitely-ended almost surely. All of these results are new even for Cayley graphs.", "date": "2017-06", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "168", "number": "1-2", "publisher": "Springer", "pagerange": "113-152", "id_number": "CaltechAUTHORS:20210923-225150172", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210923-225150172", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-016-0707-3", "primary_object": { "basename": "1506.00556.pdf", "url": "https://authors.library.caltech.edu/records/9vs1v-3e586/files/1506.00556.pdf" }, "pub_year": "2017", "author_list": "Hutchcroft, Tom and Nachmias, Asaf" }, { "id": "https://authors.library.caltech.edu/records/b1vkb-7j145", "eprint_id": 79243, "eprint_status": "archive", "datestamp": "2023-08-21 21:10:12", "lastmod": "2026-04-01 15:32:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Norms of quantum Gaussian multi-mode channels", "ispublished": "pub", "full_text_status": "public", "keywords": "Operator theory; Eigenvalues; Entropy; Inequalities; Tensor methods", "note": "\u00a9 2017 AIP Publishing. \n\nReceived 27 April 2017; accepted 12 June 2017; published online 27 June 2017. \n\nWe are grateful to Mark Wilde for references concerning Corollary 5 and to Saikat Guha for discussions about Gaussian channels. Partial support by the U.S. National Science Foundation through Grant Nos. DMS-1363432 (R.L.F.) and PHY-1265118 (E.H.L.) is acknowledged.\n\n

Published - 1.4989809.pdf

Submitted - 1704.08720.pdf

", "abstract": "We compute the S^p\u2192S^p norm of a general Gaussian gauge-covariant multi-mode channel for any 1\u2009\u2264\u2009p\u2009<\u2009\u221e, where S^p is a Schatten space. As a consequence, we verify the Gaussian optimizer conjecture and the multiplicativity conjecture in these cases.", "date": "2017-06", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "58", "number": "6", "publisher": "American Institute of Physics", "pagerange": "Art. No. 062204", "id_number": "CaltechAUTHORS:20170720-090957243", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170720-090957243", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.4989809", "primary_object": { "basename": "1.4989809.pdf", "url": "https://authors.library.caltech.edu/records/b1vkb-7j145/files/1.4989809.pdf" }, "related_objects": [ { "basename": "1704.08720.pdf", "url": "https://authors.library.caltech.edu/records/b1vkb-7j145/files/1704.08720.pdf" } ], "pub_year": "2017", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/fbvpk-8bc42", "eprint_id": 71990, "eprint_status": "archive", "datestamp": "2023-08-19 03:16:10", "lastmod": "2026-04-01 16:33:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "RG Flows and Bifurcations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. \n\nReceived 21 December 2016, Revised 22 March 2017, Accepted 25 March 2017, Available online 29 March 2017. \n\nIt is a pleasure to thank O. Aharony, D. Gross, E. Kiritsis, I. Klebanov, N. Nekrasov, V. Rychkov, N. Seiberg, R. Shrock, D. Sullivan, R. Sundrum, G. Torroba, N. Warner, R. Wijewardhana and E. Witten for useful discussions and comments, and V. Lysov for collaboration during the early stages of this project and for his help with Fig. 6, Fig. 7, Fig. 8 ; Fig. 9. We also thank the anonymous referee for many insightful comments and gratefully acknowledge the warm hospitality of SCGP during the 2016 summer workshop, as well as participants and organizers of the GGI workshop (May 23\u2013July 8) and \"Strings 2016\" conference (August 1\u20135) where preliminary results of this work were presented. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. This work is also supported in part by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\" funded by the European Research Council under the European Union Seventh Framework Programme.\n\n

Published - 1-s2.0-S0550321317301177-main.pdf

Submitted - 1608.06638v1.pdf

", "abstract": "Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases and fixed points, surprisingly, even in familiar theories such as O(N)O(N) model, QED_3, or QCD_4.", "date": "2017-06", "date_type": "published", "publication": "Nuclear Physics B", "volume": "919", "publisher": "Elsevier", "pagerange": "583-638", "id_number": "CaltechAUTHORS:20161114-105557935", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-105557935", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2017.03.025", "primary_object": { "basename": "1608.06638v1.pdf", "url": "https://authors.library.caltech.edu/records/fbvpk-8bc42/files/1608.06638v1.pdf" }, "related_objects": [ { "basename": "1-s2.0-S0550321317301177-main.pdf", "url": "https://authors.library.caltech.edu/records/fbvpk-8bc42/files/1-s2.0-S0550321317301177-main.pdf" } ], "pub_year": "2017", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/b6x55-vf324", "eprint_id": 77389, "eprint_status": "archive", "datestamp": "2023-08-22 01:30:39", "lastmod": "2026-04-01 05:27:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Polynomials; Asymptotics; Jacobi matrices", "note": "\u00a9 2003 Elsevier Inc. \n\nReceived 10 July 2003, Accepted 1 December 2003, Available online 7 February 2004. \n\nCommunicated by Leonid Golinskii \n\nSupported in part by NSF Grant DMS-0140592.", "abstract": "We study ratio asymptotics, that is, existence of the limit of Pn_(+1)(z)/P_n(z) (P_n= monic orthogonal polynomial) and the existence of weak limits of pn^2d\u03bc(p_n=P_n/||P_n||) as n\u2192\u221e for orthogonal polynomials on the real line. We show existence of ratio asymptotics at a single z_0 with Im(z_0)\u22600 implies d\u03bc is in a Nevai class (i.e., a_n\u2192a and bn\u2192b where a_n,b_n are the off-diagonal and diagonal Jacobi parameters). For \u03bc's with bounded support, we prove pn^2d\u03bc has a weak limit if and only if limb_n, lima_(2n), and lima_(2n+1) all exist. In both cases, we write down the limits explicitly.", "date": "2017-05-12", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "126", "number": "2", "publisher": "Elsevier", "pagerange": "198-217", "id_number": "CaltechAUTHORS:20170512-073744838", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744838", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2003.12.002", "pub_year": "2017", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/yp20h-hxa92", "eprint_id": 83331, "eprint_status": "archive", "datestamp": "2023-08-21 21:01:33", "lastmod": "2026-04-01 05:25:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ormerod-C-M", "name": { "family": "Ormerod", "given": "Christopher M." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "A symmetric difference-differential Lax pair for Painlev\u00e9 VI", "ispublished": "pub", "full_text_status": "public", "keywords": "Painlev\u00e9 equations; Lax pair; isomonodromy; difference equations", "note": "\u00a9 2017 The authors. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. \n\nReceived on 24 December 2016; editorial decision on 26 February 2017; accepted on 26 February 2017; Published: 08 May 2017. \n\nWe would like to thank Frank Nijhoff for his correspondence and bringing our attention to [22], ER was supported by a grant from the National Science Foundation, [DMS-1500806]. We would also like to thank the anonymous referees for their diligence.\n\n

Published - xyx003.pdf

Submitted - 1603.04393.pdf

", "abstract": "We present a Lax pair for the sixth Painlev\u00e9 equation arising as a continuous isomonodromic deformation of a system of linear difference equations with an additional symmetry structure. We call this a symmetric difference-differential Lax pair. We show how the discrete isomonodromic deformations of the associated linear problem gives us a discrete version of the fifth Painlev\u00e9 equation. By considering degenerations, we obtain symmetric difference-differential Lax pairs for the fifth Painlev\u00e9 equation and the various degenerate versions of the third Painlev\u00e9 equation.", "date": "2017-05-08", "date_type": "published", "publication": "Journal of Integrable Systems", "volume": "2", "number": "1", "publisher": "Oxford University Press", "pagerange": "1-20", "id_number": "CaltechAUTHORS:20171120-085000823", "issn": "2058-5985", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171120-085000823", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1500806" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/integr/xyx003", "primary_object": { "basename": "1603.04393.pdf", "url": "https://authors.library.caltech.edu/records/yp20h-hxa92/files/1603.04393.pdf" }, "related_objects": [ { "basename": "xyx003.pdf", "url": "https://authors.library.caltech.edu/records/yp20h-hxa92/files/xyx003.pdf" } ], "pub_year": "2017", "author_list": "Ormerod, Christopher M. and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/a7pxt-e5d96", "eprint_id": 77013, "eprint_status": "archive", "datestamp": "2023-08-21 20:59:47", "lastmod": "2026-04-01 17:36:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Schimmer-L", "name": { "family": "Schimmer", "given": "Lukas" } } ] }, "title": "Endpoint resolvent estimates for compact Riemannian manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Resolvent; Laplace\u2013Beltrami operator; Hadamard parametrix; Oscillatory integrals", "note": "\u00a9 2016 Elsevier Inc. \n\nReceived 2 November 2016. Accepted 30 November 2016. Available online 12 December 2016. \n\nCommunicated by Daniel W. Stroock. \n\nThe first author is partially supported by U.S. National Science Foundation grant DMS-1363432.\n\n

Submitted - 1611.00462

", "abstract": "We prove L^p\u2192L^p\u2032 bounds for the resolvent of the Laplace\u2013Beltrami operator on a compact Riemannian manifold of dimension n in the endpoint case p=2(n+1)/(n+3). It has the same behavior with respect to the spectral parameter z as its Euclidean analogue, due to Kenig\u2013Ruiz\u2013Sogge, provided a parabolic neighborhood of the positive half-line is removed. This is region is optimal, for instance, in the case of a sphere.", "date": "2017-05-01", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "272", "number": "9", "publisher": "Elsevier", "pagerange": "3904-3918", "id_number": "CaltechAUTHORS:20170427-140719939", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170427-140719939", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2016.11.012", "primary_object": { "basename": "1611.00462", "url": "https://authors.library.caltech.edu/records/a7pxt-e5d96/files/1611.00462" }, "pub_year": "2017", "author_list": "Frank, Rupert L. and Schimmer, Lukas" }, { "id": "https://authors.library.caltech.edu/records/fd3nb-r4991", "eprint_id": 97840, "eprint_status": "archive", "datestamp": "2023-08-21 20:57:53", "lastmod": "2026-04-01 20:49:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Ferber-Asaf", "name": { "family": "Ferber", "given": "Asaf" } }, { "id": "Nenadov-Rajko", "name": { "family": "Nenadov", "given": "Rajko" } }, { "id": "\u0160kori\u0107-Nemanja", "name": { "family": "\u0160kori\u0107", "given": "Nemanja" } } ] }, "title": "Almost-spanning universality in random graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Bounded degree graphs; random graphs; universality", "note": "\u00a9 2016 Wiley. \n\nIssue online 23 March 2017; version of record online 28 April 2016; manuscript accepted 12 January 2016; manuscript received 19 March 2015. \n\nSupported by Royal Society University Research Fellowship (to D.C.). \n\nWe would like to thank the anonymous referees for their thorough reviews and valuable remarks.\n\n

Submitted - 1503.05612.pdf

", "abstract": "A graph G is said to be \u210b(n, \u0394)-universal if it contains every graph on n vertices with maximum degree at most \u0394. It is known that for any \u03b5 > 0 and any natural number \u0394 there exists c > 0 such that the random graph G(n, p) is asymptotically almost surely \u210b((1 - \u03b5)n, \u0394)-universal for p \u2265 c(log n/n)^(1/\u0394). Bypassing this natural boundary \u0394 \u2265 3, we show that for the same conclusion holds when [equation; see abstract in PDF for details].", "date": "2017-05", "date_type": "published", "publication": "Random Structures & Algorithms", "volume": "50", "number": "3", "publisher": "Wiley", "pagerange": "380-393", "id_number": "CaltechAUTHORS:20190812-163000547", "issn": "1042-9832", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000547", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.20661", "primary_object": { "basename": "1503.05612.pdf", "url": "https://authors.library.caltech.edu/records/fd3nb-r4991/files/1503.05612.pdf" }, "pub_year": "2017", "author_list": "Conlon, David; Ferber, Asaf; et al." }, { "id": "https://authors.library.caltech.edu/records/dk4bg-pw844", "eprint_id": 87362, "eprint_status": "archive", "datestamp": "2023-08-21 20:57:44", "lastmod": "2026-04-01 20:21:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" }, { "id": "Oh-Sung-Jin", "name": { "family": "Oh", "given": "Sung-Jin" } } ] }, "title": "On the kinetic energy profile of H\u00f6lder continuous Euler flows", "ispublished": "pub", "full_text_status": "public", "keywords": "Convex integration; Incompressible Euler equations; Weak solutions; Conservation of energy", "note": "\u00a9 2016 Elsevier Masson SAS. \n\nReceived 22 October 2015, Revised 22 March 2016, Accepted 13 May 2016, Available online 1 June 2016. \n\nThe work of P. Isett is supported by the National Science Foundation under Award No. DMS-1402370. \n\nS.-J. Oh is a Miller Research Fellow, and would like to thank the Miller Institute at UC Berkeley for support. \n\nWe thank Emil Wiedemann and Camillo De Lellis for encouraging our pursuit of Theorem 1.1. We also thank the Institut Henri Poincar\u00e9 for its hospitality, where part of this work was done.\n\n

Submitted - 238965fe25a41fb3969f274c98eaa5aec068.pdf

", "abstract": "In [8], the first author proposed a strengthening of Onsager's conjecture on the failure of energy conservation for incompressible Euler flows with H\u00f6lder regularity not exceeding 1/3. This stronger form of the conjecture implies that anomalous dissipation will fail for a generic Euler flow with regularity below the Onsager critical space L_t^\u221e(B_(3,\u221e)^(1/3) due to low regularity of the energy profile. \n\nThe present paper is the second in a series of two papers whose results may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with H\u00f6lder exponent less than 1/5. The main result of this paper shows that any non-negative function with compact support and H\u00f6lder regularity 1/2 can be prescribed as the energy profile of an Euler flow in the class C_(t,x)^(1/5 \u2212 \u03f5). The exponent 1/2 is sharp in view of a regularity result of Isett [8]. The proof employs an improved greedy algorithm scheme that builds upon that in Buckmaster\u2013De Lellis\u2013Sz\u00e9kelyhidi [1].", "date": "2017-05", "date_type": "published", "publication": "Annales de l'Institut Henri Poincare (C) Non Linear Analysis", "volume": "34", "number": "3", "publisher": "Elsevier", "pagerange": "711-730", "id_number": "CaltechAUTHORS:20180626-154151950", "issn": "0294-1449", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180626-154151950", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1402370" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.anihpc.2016.05.002", "primary_object": { "basename": "238965fe25a41fb3969f274c98eaa5aec068.pdf", "url": "https://authors.library.caltech.edu/records/dk4bg-pw844/files/238965fe25a41fb3969f274c98eaa5aec068.pdf" }, "pub_year": "2017", "author_list": "Isett, Philip and Oh, Sung-Jin" }, { "id": "https://authors.library.caltech.edu/records/3ha7c-65v85", "eprint_id": 77995, "eprint_status": "archive", "datestamp": "2023-08-19 02:55:02", "lastmod": "2026-04-01 20:39:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Komargodski-Z", "name": { "family": "Komargodski", "given": "Zohar" }, "orcid": "0000-0002-8486-0811" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" } ] }, "title": "Theta, time reversal and temperature", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories Confinement Spontaneous Symmetry Breaking Wilson 't Hooft and Polyakov loops", "note": "\u00a9 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in\nany medium, provided the original author(s) and source are credited. \n\nReceived: March 31, 2017. Accepted: May 7, 2017. Published: May 17, 2017. \n\nWe would like to thank O. Aharony, F. Benini, C. Cordova, M. Dine, J. Gomis, M.B. Green, T. Johnson-Freyd, M. Metlitski, A. Schwimmer, S. Shenker, and E. Witten for useful discussions, and especially Y. Tachikawa for collaboration at the early stage of this work. The work of D.G. was supported by the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. A.K. is supported by the Simons Investigator Award and in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 Z.K. is supported in part by an Israel Science Foundation center\nfor excellence grant and by the I-CORE program of the Planning and Budgeting Committee and the Israel Science Foundation (grant number 1937/12). Z.K. is also supported by the ERC STG grant 335182 and by the United States-Israel BSF grant 2010/629. NS was supported in part by DOE grant DE-SC0009988. NS thanks the Hanna Visiting Professor\nProgram and the Stanford Institute for Theoretical Physics for support and hospitality during the completion of this work.\n\n

Published - art_3A10.1007_2FJHEP05_282017_29091.pdf

Submitted - 1703.00501.pdf

", "abstract": "SU(N ) gauge theory is time reversal invariant at \u03b8 = 0 and \u03b8 = \u03c0. We show that at \u03b8 = \u03c0 there is a discrete 't Hooft anomaly involving time reversal and the center symmetry. This anomaly leads to constraints on the vacua of the theory. It follows that at \u03b8 = \u03c0 the vacuum cannot be a trivial non-degenerate gapped state. (By contrast, the vacuum at \u03b8 = 0 is gapped, non-degenerate, and trivial.) Due to the anomaly, the theory admits nontrivial domain walls supporting lower-dimensional theories. Depending on the nature of the vacuum at \u03b8 = \u03c0, several phase diagrams are possible. Assuming area law for space-like loops, one arrives at an inequality involving the temperatures at which CP and the center symmetry are restored. We also analyze alternative scenarios for SU(2) gauge theory. The underlying symmetry at \u03b8 = \u03c0 is the dihedral group of 8 elements. If deconfined loops are allowed, one can have two O(2)-symmetric fixed points. It may also be that the four-dimensional theory around \u03b8 = \u03c0 is gapless, e.g. a Coulomb phase could match the underlying anomalies.", "date": "2017-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 091", "id_number": "CaltechAUTHORS:20170607-094158330", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170607-094158330", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Ontario Ministry of Economic Development and Innovation" }, { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Industry Canada" }, { "agency": "I-CORE Program of the Planning and Budgeting Committee" }, { "agency": "Israel Science Foundation", "grant_number": "1937/12" }, { "agency": "European Research Council (ERC)", "grant_number": "335182" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010/629" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "Stanford Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP05(2017)091", "primary_object": { "basename": "1703.00501.pdf", "url": "https://authors.library.caltech.edu/records/3ha7c-65v85/files/1703.00501.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2FJHEP05_282017_29091.pdf", "url": "https://authors.library.caltech.edu/records/3ha7c-65v85/files/art_3A10.1007_2FJHEP05_282017_29091.pdf" } ], "pub_year": "2017", "author_list": "Gaiotto, Davide; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/0dmm2-xwk63", "eprint_id": 71891, "eprint_status": "archive", "datestamp": "2023-08-19 02:13:55", "lastmod": "2026-04-01 16:35:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "Asymptotics of Chebyshev polynomials, I: subsets of \u211d", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Springer-Verlag Berlin Heidelberg. \n\nReceived: 18 October 2015; Accepted: 30 April 2016; First Online: 19 September 2016. \n\nB. Simon's research was supported in part by NSF Grant DMS-1265592 and in part by Israeli BSF Grant No. 2010348. M. Zinchenko's research was supported in part by Simons Foundation Grant CGM-281971.\n\n

Submitted - 1505.02604v1.pdf

", "abstract": "We consider Chebyshev polynomials, T_n(z), for infinite, compact sets e\u2282\u211d (that is, the monic polynomials minimizing the sup-norm, ||T_n||_e, on e). We resolve a 45+ year old conjecture of Widom that for finite gap subsets of R, his conjectured asymptotics (which we call Szeg\u0151\u2013Widom asymptotics) holds. We also prove the first upper bounds of the form ||T_n||_e\u2264QC(e)^n(where C(e) is the logarithmic capacity of e) for a class of e's with an infinite number of components, explicitly for those e\u2282\u211d that obey a Parreau\u2013Widom condition.", "date": "2017-04", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "208", "number": "1", "publisher": "Springer", "pagerange": "217-245", "id_number": "CaltechAUTHORS:20161109-142515049", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-142515049", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010348" }, { "agency": "Simons Foundation", "grant_number": "CGM-281971" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00222-016-0689-x", "primary_object": { "basename": "1505.02604v1.pdf", "url": "https://authors.library.caltech.edu/records/0dmm2-xwk63/files/1505.02604v1.pdf" }, "pub_year": "2017", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/jwvh4-crb16", "eprint_id": 77074, "eprint_status": "archive", "datestamp": "2023-08-19 02:19:04", "lastmod": "2026-04-01 05:35:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lemm-M", "name": { "family": "Lemm", "given": "Marius" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Condensation of fermion pairs in a domain", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Springer-Verlag Berlin Heidelberg. \n\nReceived: 4 August 2016; Accepted: 20 February 2017; Published online: 3 April 2017. \n\nThe authors would like to thank Christian Hainzl and Robert Seiringer for helpful discussions and the anonymous referee for useful remarks. R.L.F. was supported by the U.S. National Science Foundation through Grants PHY-1347399 and DMS-1363432. B.S. was supported by the U.S. National Science Foundation through Grant DMS-1265592 and by the Israeli Binational Science Foundation through Grant 2014337.\n\n

Submitted - 1608.01088.pdf

", "abstract": "We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two-body potential which admits a bound state. The particles are confined to a domain with Dirichlet boundary conditions. Starting from the microscopic BCS theory, we derive an effective macroscopic Gross\u2013Pitaevskii (GP) theory describing the condensate of fermion pairs. The GP theory also has Dirichlet boundary conditions. Along the way, we prove that the GP energy, defined with Dirichlet boundary conditions on a bounded Lipschitz domain, is continuous under interior and exterior approximations of that domain.", "date": "2017-04", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "56", "publisher": "Springer", "pagerange": "Art. No. 54", "id_number": "CaltechAUTHORS:20170428-160716872", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170428-160716872", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1265592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00526-017-1140-x", "primary_object": { "basename": "1608.01088.pdf", "url": "https://authors.library.caltech.edu/records/jwvh4-crb16/files/1608.01088.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L.; Lemm, Marius; et al." }, { "id": "https://authors.library.caltech.edu/records/5tgcv-gc327", "eprint_id": 76596, "eprint_status": "archive", "datestamp": "2023-08-22 19:56:45", "lastmod": "2026-04-01 17:10:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Xu-Yujie", "name": { "family": "Xu", "given": "Yujie" } } ] }, "title": "Quantum statistical mechanics in arithmetic topology", "ispublished": "pub", "full_text_status": "public", "keywords": "Arithmetic topology; Quantum statistical mechanics; Operator algebra; Knots", "note": "\u00a9 2016 Elsevier B.V. \n\nReceived 21 August 2016, Revised 27 November 2016, Accepted 28 November 2016, Available online 9 December 2016. \n\nThe first author is supported by NSF grants DMS-1201512 and PHY-1205440. The second author is supported by a Summer Undergraduate Research Fellowship at Caltech.\n\n

Submitted - 1602.04890.pdf

", "abstract": "This paper provides a construction of a quantum statistical mechanical system associated to knots in the 33-sphere and cyclic branched coverings of the 33-sphere, which is an analog, in the sense of arithmetic topology, of the Bost\u2013Connes system, with knots replacing primes, and cyclic branched coverings of the 33-sphere replacing abelian extensions of the field of rational numbers. The operator algebraic properties of this system differ significantly from the Bost\u2013Connes case, due to the properties of the action of the semigroup of knots on a direct limit of knot groups. The resulting algebra of observables is a noncommutative Bernoulli product. We describe the main properties of the associated quantum statistical mechanical system and of the relevant partition functions, which are obtained from simple knot invariants like genus and crossing number.", "date": "2017-04", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "114", "publisher": "Elsevier", "pagerange": "153-183", "id_number": "CaltechAUTHORS:20170417-110402207", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170417-110402207", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2016.11.029", "primary_object": { "basename": "1602.04890.pdf", "url": "https://authors.library.caltech.edu/records/5tgcv-gc327/files/1602.04890.pdf" }, "pub_year": "2017", "author_list": "Marcolli, Matilde and Xu, Yujie" }, { "id": "https://authors.library.caltech.edu/records/5fytb-36g11", "eprint_id": 76932, "eprint_status": "archive", "datestamp": "2023-08-22 19:57:17", "lastmod": "2026-04-01 15:29:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bhardwaj-L", "name": { "family": "Bhardwaj", "given": "Lakshya" }, "orcid": "0000-0001-6957-7244" }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories; Discrete Symmetries; Topological Field Theories; Topological States of Matter", "note": "\u00a9 The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in\nany medium, provided the original author(s) and source are credited. \n\nReceived: September 28, 2016. Accepted: February 3, 2017. Published: April 18, 2017. \n\nArticle funded by SCOAP3. \n\nWe thank V. Ostrik for explaining the results of [36] to one of us (A.K.). We are grateful to J. Brundan and A. Ellis for making their results [26] available prior to publication. We also thank A. Karagiozova for helping LB and DG code the figures. A. K. is grateful to J. Morgan for communicating to him the unpublished results of J. Morgan and G. Brumfiel which helped to detect an error in the first version of the paper. The research of LB and DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of A. K. was supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632 Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - art_3A10.1007_2FJHEP04_282017_29096.pdf

Submitted - 1605.01640.pdf

", "abstract": "It is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic \"shadow\" theories, which are obtained from the original theory by \"gauging fermionic parity\". The fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a one-form symmetry generated by quasi-particles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain Turaev-Viro-like and Levin-Wen-like constructions of fermionic phases of matter. We describe the group structure of fermionic SPT phases protected by \u2124_2^f\u2009\u00d7\u2009G. The quaternion group makes a surprise appearance.", "date": "2017-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 096", "id_number": "CaltechAUTHORS:20170426-065601568", "issn": "1029-8479", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170426-065601568", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2017)096", "primary_object": { "basename": "art_3A10.1007_2FJHEP04_282017_29096.pdf", "url": "https://authors.library.caltech.edu/records/5fytb-36g11/files/art_3A10.1007_2FJHEP04_282017_29096.pdf" }, "related_objects": [ { "basename": "1605.01640.pdf", "url": "https://authors.library.caltech.edu/records/5fytb-36g11/files/1605.01640.pdf" } ], "pub_year": "2017", "author_list": "Bhardwaj, Lakshya; Gaiotto, Davide; et al." }, { "id": "https://authors.library.caltech.edu/records/vfd4g-req20", "eprint_id": 76585, "eprint_status": "archive", "datestamp": "2023-09-28 19:36:43", "lastmod": "2026-04-01 16:25:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Behrndt-J", "name": { "family": "Behrndt", "given": "Jussi" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "K\u00fchn-C", "name": { "family": "K\u00fchn", "given": "Christian" } }, { "id": "Lotoreichik-V", "name": { "family": "Lotoreichik", "given": "Vladimir" } }, { "id": "Rohleder-Jonathan", "name": { "family": "Rohleder", "given": "Jonathan" } } ] }, "title": "Spectral Theory for Schr\u00f6dinger Operators with \u03b4-Interactions Supported on Curves in R\u00b3", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nCommunicated by Jan Derezinski. \n\nOpen access funding provided by Graz University of Technology. Jussi Behrndt, Christian K\u00fchn, Vladimir Lotoreichik, and Jonathan Rohleder gratefully acknowledge financial support by the Austrian Science Fund (FWF), Project P 25162-N26. Vladimir Lotoreichik also acknowledges financial support by the Czech Science Foundation, Project 14-06818S. Rupert Frank acknowledges support through NSF Grant DMS-1363432. The authors also wish to thank Johannes Brasche and Andrea Posilicano for helpful discussions and the anonymous referees for their helpful comments which led to various improvements.\n\n

Published - s00023-016-0532-3.pdf

Submitted - 1601_06433.pdf

", "abstract": "The main objective of this paper is to systematically develop a spectral and scattering theory for self-adjoint Schr\u00f6dinger operators with \u03b4-interactions supported on closed curves in R^3. We provide bounds for the number of negative eigenvalues depending on the geometry of the curve, prove an isoperimetric inequality for the principal eigenvalue, derive Schatten\u2013von Neumann properties for the resolvent difference with the free Laplacian, and establish an explicit representation for the scattering matrix.", "date": "2017-04", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "18", "number": "4", "publisher": "Springer", "pagerange": "1305-1347", "id_number": "CaltechAUTHORS:20170417-074808881", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170417-074808881", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Graz University of Technology" }, { "agency": "FWF Der Wissenschaftsfonds", "grant_number": "P 25162-N26" }, { "agency": "Czech Science Foundation", "grant_number": "14-06818S" }, { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-016-0532-3", "primary_object": { "basename": "1601_06433.pdf", "url": "https://authors.library.caltech.edu/records/vfd4g-req20/files/1601_06433.pdf" }, "related_objects": [ { "basename": "s00023-016-0532-3.pdf", "url": "https://authors.library.caltech.edu/records/vfd4g-req20/files/s00023-016-0532-3.pdf" } ], "pub_year": "2017", "author_list": "Behrndt, Jussi; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/t4b2v-c5r37", "eprint_id": 98024, "eprint_status": "archive", "datestamp": "2023-08-19 01:58:50", "lastmod": "2026-04-01 20:22:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" } } ] }, "title": "Quasirandom Cayley graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 David Conlon and Yufei Zhao. Licensed under a Creative Commons Attribution License (CC-BY). \n\nReceived 21 April 2016; revised 28 February 2017; published 8 March 2017. \n\nThe first author was supported by a Royal Society University Research Fellowship and ERC Starting Grant 676632. The second author was supported by an Esm\u00e9e Fairbairn Junior Research Fellowship at New College, Oxford.\n\n

Published - 1603.03025.pdf

", "abstract": "We prove that the properties of having small discrepancy and having small second eigenvalue are equivalent in Cayley graphs, extending a result of Kohayakawa, R\u00f6dl, and Schacht, who treated the abelian case. The proof relies on Grothendieck's inequality. As a corollary, we also prove that a similar result holds in all vertex-transitive graphs.", "date": "2017-03-08", "date_type": "published", "publication": "Discrete Analysis", "publisher": "Diamond Open Access Journals", "pagerange": "Art. No. 6", "id_number": "CaltechAUTHORS:20190819-170904052", "issn": "2397-3129", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-170904052", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" }, { "agency": "New College, Oxford" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.19086/da.1294", "primary_object": { "basename": "1603.03025.pdf", "url": "https://authors.library.caltech.edu/records/t4b2v-c5r37/files/1603.03025.pdf" }, "pub_year": "2017", "author_list": "Conlon, David and Zhao, Yufei" }, { "id": "https://authors.library.caltech.edu/records/g4na6-qn093", "eprint_id": 97842, "eprint_status": "archive", "datestamp": "2023-08-19 01:53:56", "lastmod": "2026-04-01 18:32:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "A Sequence of Triangle-Free Pseudorandom Graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Cambridge University Press 2016. \n\nPublished online by Cambridge University Press: 13 September 2016. \n\nResearch supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. \n\nI would like to thank the anonymous referee for a number of helpful remarks.\n\n

Submitted - 1602.03773.pdf

", "abstract": "A construction of Alon yields a sequence of highly pseudorandom triangle-free graphs with edge density significantly higher than one might expect from comparison with random graphs. We give an alternative construction for such graphs.", "date": "2017-03", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "26", "number": "2", "publisher": "Cambridge University Press", "pagerange": "195-200", "id_number": "CaltechAUTHORS:20190812-163000736", "issn": "0963-5483", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000736", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548316000298", "primary_object": { "basename": "1602.03773.pdf", "url": "https://authors.library.caltech.edu/records/g4na6-qn093/files/1602.03773.pdf" }, "pub_year": "2017", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/rqpp7-81c15", "eprint_id": 97841, "eprint_status": "archive", "datestamp": "2023-08-19 01:53:52", "lastmod": "2026-04-01 07:29:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "D." }, "orcid": "0000-0001-5899-1829" }, { "id": "Gowers-W-T", "name": { "family": "Gowers", "given": "W. T." } } ] }, "title": "Freiman homomorphisms on sparse random sets", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 Oxford University Press. \n\nConlon research supported by a Royal Society University Research Fellowship and by ERC Starting Grant 676632. Gowers research supported by a Royal Society 2010 Anniversary Research Professorship.\n\n

Submitted - 1603.01734.pdf

", "abstract": "A result of Fiz Pontiveros shows that if A is a random subset of \u2124_N where each element is chosen independently with probability N^(\u22121/2+o(1))\u2060, then with high probability every Freiman homomorphism defined on A can be extended to a Freiman homomorphism on the whole of \u2124_N\u2060. In this paper, we improve the bound to CN^(\u22122/3)(logN)^(1/3)\u2060, which is best possible up to the constant factor.", "date": "2017-03", "date_type": "published", "publication": "Quarterly Journal of Mathematics", "volume": "68", "number": "1", "publisher": "Oxford University Press", "pagerange": "275-300", "id_number": "CaltechAUTHORS:20190812-163000651", "issn": "0033-5606", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000651", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "European Research Council (ERC)", "grant_number": "676632" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/qmath/haw058", "primary_object": { "basename": "1603.01734.pdf", "url": "https://authors.library.caltech.edu/records/rqpp7-81c15/files/1603.01734.pdf" }, "pub_year": "2017", "author_list": "Conlon, D. and Gowers, W. T." }, { "id": "https://authors.library.caltech.edu/records/n97fn-5hz17", "eprint_id": 78207, "eprint_status": "archive", "datestamp": "2023-08-22 19:48:10", "lastmod": "2026-04-01 17:16:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Shu-Kevin", "name": { "family": "Shu", "given": "Kevin" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Syntactic Structures and Code Parameters", "ispublished": "pub", "full_text_status": "public", "keywords": "Natural languages; Syntactic parameters; Error-correcting codes; Code parameters; Asymptotic bounds; Spin glass dynamics", "note": "\u00a9 2017 Springer International Publishing. \n\nReceived: 30 November 2016; Revised: 15 February 2017; Accepted: 22 February 2017 First Online: 24 March 2017.\n\n

Submitted - 1610.00311.pdf

", "abstract": "We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters. We show that, while most codes populate the lower region approximating a superposition of Thomae functions, there is a substantial presence of codes above the Gilbert\u2013Varshamov bound and even above the asymptotic bound and the Plotkin bound. We investigate the dynamics induced on the space of code parameters by spin glass models of language change, and show that, in the presence of entailment relations between syntactic parameters the dynamics can sometimes improve the code. For large sets of languages and syntactic data, one can gain information on the spin glass dynamics from the induced dynamics in the space of code parameters.", "date": "2017-03", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "11", "number": "1", "publisher": "Springer Verlag", "pagerange": "79-90", "id_number": "CaltechAUTHORS:20170614-110933652", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170614-110933652", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-017-0298-0", "primary_object": { "basename": "1610.00311.pdf", "url": "https://authors.library.caltech.edu/records/n97fn-5hz17/files/1610.00311.pdf" }, "pub_year": "2017", "author_list": "Shu, Kevin and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/g8752-7y730", "eprint_id": 77852, "eprint_status": "archive", "datestamp": "2023-08-22 19:47:58", "lastmod": "2026-04-01 16:50:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Spectral action gravity and cosmological models", "ispublished": "pub", "full_text_status": "public", "keywords": "Modified gravity; Spectral action; Dirac operator; Cosmic inflation", "note": "\u00a9 2017 Elsevier B.V. \n\nAvailable online 29 May 2017.", "abstract": "This paper surveys recent work of the author and collaborators on cosmological models based on the spectral action functional of gravity. A more detailed presentation of the topics surveyed here will be available in a forthcoming book [1].", "date": "2017-03", "date_type": "published", "publication": "Comptes Rendus Physique", "volume": "18", "number": "3-4", "publisher": "Elsevier Masson SAS", "pagerange": "226-234", "id_number": "CaltechAUTHORS:20170531-104221597", "issn": "1631-0705", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170531-104221597", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.crhy.2017.03.001", "pub_year": "2017", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/vr9q2-gtp94", "eprint_id": 66642, "eprint_status": "archive", "datestamp": "2023-08-22 19:45:46", "lastmod": "2026-04-01 21:54:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Turzillo-A", "name": { "family": "Turzillo", "given": "Alex" }, "orcid": "0000-0003-4293-4293" } ] }, "title": "Equivariant Topological Quantum Field Theory and Symmetry Protected Topological Phases", "ispublished": "pub", "full_text_status": "public", "keywords": "Topological Field Theories; Discrete Symmetries; Topological States of Matter", "note": "\u00a9 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: December 5, 2016; Accepted: February 14, 2017; Published: March 1, 2017. \n\nA.K. would like to thank V. Ostrik for helpful discussions. The work of A.K. was supported by the Simons Foundation. The work of A.T. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632.\n\n

Published - art_3A10.1007_2FJHEP03_282017_29006.pdf

Submitted - 1504.01830.pdf

", "abstract": "Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev's description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.", "date": "2017-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "03", "publisher": "Springer", "pagerange": "Art. No. 006", "id_number": "CaltechAUTHORS:20160504-101448724", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-101448724", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP03(2017)006", "primary_object": { "basename": "1504.01830.pdf", "url": "https://authors.library.caltech.edu/records/vr9q2-gtp94/files/1504.01830.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2FJHEP03_282017_29006.pdf", "url": "https://authors.library.caltech.edu/records/vr9q2-gtp94/files/art_3A10.1007_2FJHEP03_282017_29006.pdf" } ], "pub_year": "2017", "author_list": "Kapustin, Anton and Turzillo, Alex" }, { "id": "https://authors.library.caltech.edu/records/5kpzm-wax49", "eprint_id": 56816, "eprint_status": "archive", "datestamp": "2023-08-19 01:10:50", "lastmod": "2026-04-01 19:40:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Zhang-Xingru", "name": { "family": "Zhang", "given": "Xingru" } } ] }, "title": "Detection of knots and a cabling formula for A-polynomials", "ispublished": "pub", "full_text_status": "public", "keywords": "knot Floer homology, A-polynomial, cabling formula, Eudave-Mu\u00f1oz knots", "note": "\u00a9 2017 Mathematical Sciences Publishers.\n\nReceived: 26 March 2015;\nRevised: 9 May 2016;\nAccepted: 19 May 2016;\nPublished: 26 January 2017.\n\n\nNi was partially supported by NSF grant numbers DMS-1103976\nand DMS-1252992 and an Alfred P Sloan Research Fellowship.\n\n

Submitted - 1411.0353.pdf

", "abstract": "We say that a given knot J \u2282 S^3 is detected by its knot Floer homology and AA\u2013polynomial if whenever a knot K \u2282 S^3 has the same knot Floer homology and the same A\u2013polynomial as J, then K=J. In this paper we show that every torus knot T(p,q) is detected by its knot Floer homology and A\u2013polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in S^3 each of which is detected by its knot Floer homology and AA\u2013polynomial. In addition we give a cabling formula for the AA\u2013polynomials of cabled knots in S^3, which is of independent interest. In particular we give explicitly the AA\u2013polynomials of iterated torus knots.", "date": "2017-01-26", "date_type": "published", "publication": "Algebraic and Geometric Topology", "volume": "17", "number": "1", "publisher": "Geometry & Topology Publications", "pagerange": "65-109", "id_number": "CaltechAUTHORS:20150421-115826798", "issn": "1472-2747", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115826798", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/agt.2017.17.65", "primary_object": { "basename": "1411.0353.pdf", "url": "https://authors.library.caltech.edu/records/5kpzm-wax49/files/1411.0353.pdf" }, "pub_year": "2017", "author_list": "Ni, Yi and Zhang, Xingru" }, { "id": "https://authors.library.caltech.edu/records/b4p7m-8qn09", "eprint_id": 81394, "eprint_status": "archive", "datestamp": "2023-08-19 00:54:12", "lastmod": "2026-03-09 21:38:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Noncommutative geometry and particle physics [Book Review]", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2016 American Mathematical Society. \n\nArticle electronically published on September 6, 2016. \n\nBook review of: Noncommutative geometry and particle physics, by Walter D. van Suijlekom, Mathematical Physics Studies, Springer, Dordrecht, 2015, xvi+237 pp., ISBN 978-94-017-9161-8 (hardcover), 978-94-017-9162-5 (electronic).", "abstract": "The use of noncommutative geometry (NCG) as a tool for constructing particle physics models originated in the 1990s [9, 11]. The main idea can be heuristically\nregarded as similar to the idea of \"extra dimensions\" in String Theory, except for the fact that the nature and scope of these extra dimensions is quite different. In the\nNCG model one considers an \"almost commutative geometry\", which is a product (or locally a product in a more refined and more recent version [4]) of a four-dimensional\nspacetime manifold and a space of inner degrees of freedom, which is a \"finite\" noncommutative space, whose ring of functions is a sum of matrix algebras. According to the choice of this finite geometry, one obtains different\npossible particle contents for the resulting physics model. The physical content is expressed through an action functional, the spectral action [5], which is defined for\nmore general noncommutative spaces, in terms of the spectrum of a Dirac operator.", "date": "2017-01", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "54", "number": "1", "publisher": "American Mathematical Society", "pagerange": "167-169", "id_number": "CaltechAUTHORS:20170913-081309497", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170913-081309497", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/bull/1555", "pub_year": "2017", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/v2sqk-x4v76", "eprint_id": 97843, "eprint_status": "archive", "datestamp": "2023-08-22 19:27:47", "lastmod": "2026-03-08 03:39:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Lee-Choongbum", "name": { "family": "Lee", "given": "Choongbum" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Ordered Ramsey numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey theory; Ordered graphs; Sparse graphs", "note": "\u00a9 2016 Elsevier Inc. \n\nReceived 20 October 2014, available online 16 July 2016. \n\nConlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Packard Fellowship, by NSF Career Award DMS-1352121 and by an Alfred P. Sloan Foundation Fellowship. Lee research supported by NSF Grant DMS-1362326. Sudakov research supported in part by SNSF grant 200021-149111. \n\nWe would like to thank the anonymous referees for a number of helpful remarks.\n\n

Submitted - 1410.5292.pdf

", "abstract": "Given a labeled graph H with vertex set {1, 2 . . ., n}, the ordered Ramsey number r < (H) is the minimum N such that every two-coloring of the edges of the complete graph on {1, 2 . . ., N} contains a copy of H with vertices appearing in the same order as in H. The ordered Ramsey number of a labeled graph H is at least the Ramsey number r(H) and the two coincide for complete graphs. However, we prove that even for matchings there are labelings where the ordered Ramsey number is superpolynomial in the number of vertices. Among other results, we also prove a general upper bound on ordered Ramsey numbers which implies that there exists a constant c such that r < (H) \u2264 r(H)^(c log^(2) n) for any labeled graph H on vertex set {1, 2 . . ., n}.", "date": "2017-01", "date_type": "published", "publication": "Journal of Combinatorial Theory, Series B", "volume": "122", "publisher": "Elsevier", "pagerange": "353-383", "id_number": "CaltechAUTHORS:20190812-163000833", "issn": "0095-8956", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000833", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "DMS-1362326" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jctb.2016.06.007", "primary_object": { "basename": "1410.5292.pdf", "url": "https://authors.library.caltech.edu/records/v2sqk-x4v76/files/1410.5292.pdf" }, "pub_year": "2017", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/y043q-4bd72", "eprint_id": 72006, "eprint_status": "archive", "datestamp": "2023-08-22 19:23:08", "lastmod": "2026-03-09 22:00:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gomis-J", "name": { "family": "Gomis", "given": "Jaume" } }, { "id": "Komargodski-Z", "name": { "family": "Komargodski", "given": "Zohar" }, "orcid": "0000-0002-8486-0811" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" }, { "id": "Wang-Yifan", "name": { "family": "Wang", "given": "Yifan" }, "orcid": "0000-0001-9965-9777" } ] }, "title": "Shortening Anomalies in Supersymmetric Theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Anomalies in Field and String Theories; Conformal Field Theory; Supersymmetric gauge theory", "note": "\u00a9 2017 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: 08 December 2016; Accepted: 17 December 2016;\nFirst Online: 17 January 2017. \n\nWe thank Kevin Costello, David Morrison, Kyriakos Papadodimas, Ronen Plesser, Adam Schwimmer, Stefan Theisen, and Edward Witten for useful discussions. J.G.'s research was supported in part by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. Z.K. is supported in part by an Israel Science Foundation center for excellence grant and by\nthe I-CORE program of the Planning and Budgeting Committee and the Israel Science Foundation (grant number 1937/12). Z.K. is also supported by the ERC STG grant 335182 and by the United States-Israel BSF grant 2010/629. H.O. is supported in part by U.S. Department of Energy grant DE-SC0011632, by the Simons Investigator Award, by the World Premier International Research Center Initiative, MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. N.S. was supported in part by DOE grant DE-SC0009988. Y.W. was supported by the NSF grant PHY-1620059 and by the Simons Foundation Grant #488653. H.O. thanks the hospitality of the Institute for Advanced Study and Harvard University, where he spent his sabbatical in 2015 - 2016, and of the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1066293. N.S. thanks the hospitality of the Weizmann Institute of Science during the completion of this work.\n\n

Published - art_3A10.1007_2FJHEP01_282017_29067.pdf

Submitted - 1611.03101v1.pdf

", "abstract": "We present new anomalies in two-dimensiona N=(2,2) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from N=(2,2) spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond N=(2,2). These anomalies explain why the conformal manifolds of the K3 and T^4 sigma models are not K\u00e4hler and do not factorize into chiral and twisted chiral moduli spaces and why there are no N=(2,2) gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.", "date": "2017-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2017", "number": "01", "publisher": "Springer", "pagerange": "Art. No. 67", "id_number": "CaltechAUTHORS:20161114-154042042", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-154042042", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Research and Innovation" }, { "agency": "Israel Science Foundation", "grant_number": "1937/12" }, { "agency": "I-CORE Program of the Planning and Budgeting Committee" }, { "agency": "European Research Council (ERC)", "grant_number": "335182" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010/629" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "NSF", "grant_number": "PHY-1620059" }, { "agency": "Simons Foundation", "grant_number": "488653" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2016-031", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP01(2017)067", "primary_object": { "basename": "1611.03101v1.pdf", "url": "https://authors.library.caltech.edu/records/y043q-4bd72/files/1611.03101v1.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2FJHEP01_282017_29067.pdf", "url": "https://authors.library.caltech.edu/records/y043q-4bd72/files/art_3A10.1007_2FJHEP01_282017_29067.pdf" } ], "pub_year": "2017", "author_list": "Gomis, Jaume; Komargodski, Zohar; et al." }, { "id": "https://authors.library.caltech.edu/records/k6xmk-fy705", "eprint_id": 74336, "eprint_status": "archive", "datestamp": "2023-08-19 00:49:55", "lastmod": "2026-03-09 21:52:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Fintushel-Stern knot surgery in torus bundles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 London Mathematical Society. \n\nReceived 4 December 2015; revised 15 September 2016; published online 15 February 2017. \n\nThe author was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship.\n\n

Submitted - 1510.07715.pdf

", "abstract": "Suppose that X is a torus bundle over a closed surface with homologically essential fibers. Let X_K be the manifold obtained by Fintushel\u2013Stern knot surgery on a fiber using a knot K\u2282S^3. We prove that X_K has a symplectic structure if and only if K is a fibered knot. The proof uses Seiberg\u2013Witten theory and a result of Friedl\u2013Vidussi on twisted Alexander polynomials.", "date": "2017-01", "date_type": "published", "publication": "Journal of Topology", "volume": "10", "number": "1", "publisher": "Oxford University Press", "pagerange": "164-177", "id_number": "CaltechAUTHORS:20170215-145039098", "issn": "1753-8416", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170215-145039098", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/topo.12002", "primary_object": { "basename": "1510.07715.pdf", "url": "https://authors.library.caltech.edu/records/k6xmk-fy705/files/1510.07715.pdf" }, "pub_year": "2017", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/9nf1n-af924", "eprint_id": 77070, "eprint_status": "archive", "datestamp": "2023-08-19 00:41:04", "lastmod": "2026-03-09 02:14:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "M\u00e9hats-F", "name": { "family": "M\u00e9hats", "given": "Florian" } }, { "id": "Sparber-C", "name": { "family": "Sparber", "given": "Christof" } } ] }, "title": "Averaging of nonlinear Schr\u00f6dinger equations with strong magnetic confinement", "ispublished": "pub", "full_text_status": "public", "keywords": "nonlinear Schr\u00f6dinger equation, magnetic confinement, Landau levels, averaging", "note": "\u00a9 2017 International Press. \n\nPaper received on 15 March 2017; Paper accepted on 30 June 2017. \n\nR.L.F. has been supported by the U.S. National Science Foundation through grant no. DMS-1363432. \n\nF.M. acknowledges support by the ANR project Moonrise ANR-14-CE23-0007-01. \n\nC.S. has been supported by the U.S. National Science Foundation through grant no. DMS-1348092.\n\n

Submitted - 1611.01574.pdf

", "abstract": "We consider the dynamics of nonlinear Schr\u00f6dinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the Landau Hamiltonian. Using an averaging technique we derive an associated effective description via an averaged model of nonlinear Schr\u00f6dinger type. In a special case this also yields a derivation of the LLL equation.", "date": "2017", "date_type": "published", "publication": "Communications in Mathematical Sciences", "volume": "15", "number": "7", "publisher": "International Press", "pagerange": "1933-1945", "id_number": "CaltechAUTHORS:20170428-154120889", "issn": "1539-6746", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170428-154120889", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Agence Nationale de la Recherche (ANR)", "grant_number": "ANR-14-CE23-0007-01" }, { "agency": "NSF", "grant_number": "DMS-1348092" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CMS.2017.v15.n7.a7", "primary_object": { "basename": "1611.01574.pdf", "url": "https://authors.library.caltech.edu/records/9nf1n-af924/files/1611.01574.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L.; M\u00e9hats, Florian; et al." }, { "id": "https://authors.library.caltech.edu/records/p80nw-3tg76", "eprint_id": 79014, "eprint_status": "archive", "datestamp": "2023-08-19 00:42:02", "lastmod": "2026-03-09 21:43:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Seipp-K", "name": { "family": "Seipp", "given": "Kyle" } } ] }, "title": "Twisted index theory on orbifold symmetric products and the fractional quantum Hall effect", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2017 International Press. \n\nThe first author was supported by NSF grants DMS-1007207, DMS-1201512, PHY-1205440, and DMS-1707882. The second author contributed to this project as part of his summer undergraduate research.\n\n

Published - ATMP-2017-0021-0002-a003.pdf

Submitted - 1502.01314.pdf

", "abstract": "We extend the noncommutative geometry model of the fractional quantum Hall effect, previously developed by Mathai and the first author, to orbifold symmetric products. It retains the same properties of quantization of the Hall conductance at integer multiples of the fractional Satake orbifold Euler characteristics. We show that it also allows for interesting composite fermions and anyon representations, and possibly for Laughlin type wave functions.", "date": "2017", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "21", "number": "2", "publisher": "International Press", "pagerange": "451-501", "id_number": "CaltechAUTHORS:20170712-130729557", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-130729557", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "NSF", "grant_number": "DMS-1707882" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2017.v21.n2.a3", "primary_object": { "basename": "1502.01314.pdf", "url": "https://authors.library.caltech.edu/records/p80nw-3tg76/files/1502.01314.pdf" }, "related_objects": [ { "basename": "ATMP-2017-0021-0002-a003.pdf", "url": "https://authors.library.caltech.edu/records/p80nw-3tg76/files/ATMP-2017-0021-0002-a003.pdf" } ], "pub_year": "2017", "author_list": "Marcolli, Matilde and Seipp, Kyle" }, { "id": "https://authors.library.caltech.edu/records/xfdda-wzy15", "eprint_id": 75562, "eprint_status": "archive", "datestamp": "2023-08-19 00:40:50", "lastmod": "2026-03-09 21:38:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Bost\u2013Connes systems, categorification, quantum statistical mechanics, and Weil numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "Quantum statistical mechanical systems, Gibbs states, zeta function, polylogarithms, Tannakian categories, Weil numbers, motives, Weil restriction", "note": "\u00a9 2017 EMS Publishing House. \n\nReceived 20 March, 2015. \n\nM. Marcolli was partially supported by the NSF grants DMS-1007207, DMS-1201512, and PHY-1205440. \n\nG. Tabuada was partially supported by a NSF CAREER Award.\n\n

Submitted - 1411.3223.pdf

", "abstract": "In this article we develop a broad generalization of the classical Bost\u2013Connes system, where roots of unity are replaced by an algebraic datum consisting of an abelian group and a semi-group of endomorphisms. Examples include roots of unity, Weil restriction, algebraic numbers,Weil numbers, CM fields, germs, completion ofWeil numbers, etc. Making use of the Tannakian formalism, we categorify these algebraic data. For example, the categorification of roots of unity is given by a limit of orbit categories of Tate motives while the categorification of Weil numbers is given by Grothendieck's category of numerical motives over a finite field. To some of these algebraic data (e.g. roots of unity, algebraic numbers, Weil numbers, etc), we associate also a quantum statistical mechanical system with several remarkable properties, which generalize those of the classical Bost\u2013Connes system. The associated partition function, low temperature Gibbs states, and Galois action on zero-temperature states are then studied in detail. For example, we show that in the particular case of the Weil numbers the partition function and the low temperature Gibbs states can be described as series of polylogarithms.", "date": "2017", "date_type": "published", "publication": "Journal of Noncommutative Geometry", "volume": "11", "number": "1", "publisher": "European Mathematical Society", "pagerange": "1-49", "id_number": "CaltechAUTHORS:20170330-165516108", "issn": "1661-6952", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170330-165516108", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JNCG/11-1-1", "primary_object": { "basename": "1411.3223.pdf", "url": "https://authors.library.caltech.edu/records/xfdda-wzy15/files/1411.3223.pdf" }, "pub_year": "2017", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/421f2-y3742", "eprint_id": 76974, "eprint_status": "archive", "datestamp": "2023-08-19 00:40:59", "lastmod": "2026-03-09 02:15:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Zhou-Gang", "name": { "family": "Zhou", "given": "Gang" } } ] }, "title": "Derivation of an effective evolution equation for a strongly coupled polaron", "ispublished": "pub", "full_text_status": "public", "keywords": "polaron, dynamics, quantized field", "note": "\u00a9 2017 Mathematical Sciences Publishers. \n\nReceived: 30 June 2016. Accepted: 28 November 2016. Published: 23 February 2017. \n\nThe authors are grateful to J. Fr\u00f6hlich, M. Lewin, B. Schlein and R. Seiringer for their helpful remarks at various stages of this project, as well as to the anonymous referees who helped improve this paper. Support through NSF grants PHY\u20131347399 and DMS\u20131363432 (R.L.F.) and DMS\u20131308985 and DMS\u20131443225 (Z.G.) is acknowledged.\n\n

Published - apde-v10-n2-p06-s.pdf

Submitted - 1505.03059

", "abstract": "Fr\u00f6hlich's polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron are approximated by an effective nonlinear partial differential equation due to Landau and Pekar, in which the phonon field is treated as a classical field.", "date": "2017", "date_type": "published", "publication": "Analysis & PDE", "volume": "10", "number": "2", "publisher": "Mathematical Sciences Publishers", "pagerange": "379-422", "id_number": "CaltechAUTHORS:20170427-075023929", "issn": "2157-5045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170427-075023929", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY\u20131347399" }, { "agency": "NSF", "grant_number": "DMS\u20131363432" }, { "agency": "NSF", "grant_number": "DMS\u20131308985" }, { "agency": "NSF", "grant_number": "DMS\u20131443225" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/apde.2017.10.379", "primary_object": { "basename": "1505.03059", "url": "https://authors.library.caltech.edu/records/421f2-y3742/files/1505.03059" }, "related_objects": [ { "basename": "apde-v10-n2-p06-s.pdf", "url": "https://authors.library.caltech.edu/records/421f2-y3742/files/apde-v10-n2-p06-s.pdf" } ], "pub_year": "2017", "author_list": "Frank, Rupert L. and Zhou, Gang" }, { "id": "https://authors.library.caltech.edu/records/j7bhm-3q764", "eprint_id": 73658, "eprint_status": "archive", "datestamp": "2023-08-22 19:13:14", "lastmod": "2026-04-02 15:59:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Y-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Semantic Spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Semantics; Vector space model; Algebraic geometry", "note": "\u00a9 2016 Springer International Publishing. \n\nReceived: 27 May 2016; Accepted: 4 October 2016; Published online: 27 October 2016.\n\n

Submitted - 1605.04238v1.pdf

", "abstract": "Any natural language can be considered as a tool for producing large databases (consisting of texts, written, or discursive). This tool for its description in turn requires other large databases (dictionaries, grammars etc.). Nowadays, the notion of database is associated with computer processing and computer memory. However, a natural language resides also in human brains and functions in human communication, from interpersonal to intergenerational one. We discuss in this survey/research paper mathematical, in particular geometric, constructions, which help to bridge these two worlds. In particular, in this paper we consider the Vector Space Model of semantics based on frequency matrices, as used in Natural Language Processing. We investigate underlying geometries, formulated in terms of Grassmannians, projective spaces, and flag varieties. We formulate the relation between vector space models and semantic spaces based on semic axes in terms of projectability of subvarieties in Grassmannians and projective spaces. We interpret Latent Semantics as a geometric flow on Grassmannians. We also discuss how to formulate G\u00e4rdenfors' notion of \"meeting of minds\" in our geometric setting.", "date": "2016-12", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "10", "number": "4", "publisher": "Springer Verlag", "pagerange": "459-477", "id_number": "CaltechAUTHORS:20170124-100433482", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170124-100433482", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-016-0278-9", "primary_object": { "basename": "1605.04238v1.pdf", "url": "https://authors.library.caltech.edu/records/j7bhm-3q764/files/1605.04238v1.pdf" }, "pub_year": "2016", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/dvk9d-azm60", "eprint_id": 72966, "eprint_status": "archive", "datestamp": "2023-08-19 00:15:07", "lastmod": "2026-04-02 00:48:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lashkari-N", "name": { "family": "Lashkari", "given": "Nima" }, "orcid": "0000-0003-3446-5933" }, { "id": "Lin-Jennifer", "name": { "family": "Lin", "given": "Jennifer" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } }, { "id": "Van-Raamsdonk-M", "name": { "family": "Van Raamsdonk", "given": "Mark" } } ] }, "title": "Gravitational Positive Energy Theorems from Information Inequalities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2016. Published by Oxford University Press on behalf of the Physical Society of Japan. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. \n\nFunded by SCOAP3. \n\nReceived May 25, 2016; Accepted August 4, 2016; Published December 19, 2016. \n\nWe thank Xi Dong, Thomas Faulkner, Simon Gentle, Daniel Harlow, Ken Intriligator, Lampros Lamprou, Aitor Lewkowycz, Hong Liu, Juan Maldacena, Travis Maxfield, John McGreevy, Rob Myers, Ingmar Saberi, Jaewon Song, and Edward Witten for discussions. The research of MVR is supported in part by the Natural Sciences and Engineering Research Council of Canada, and by grant 376206 from the Simons Foundation. The research of HO and BS is supported in part by U.S. Department of Energy grant DE-SC0011632 and by Caltech's Walter Burke Institute for Theoretical Physics and Moore Center for Theoretical Cosmology and Physics. The research of HO is also supported in part by the Simons Investigator Award, by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for Scientific Research on Innovative Areas 15H05895. NL is supported in part by funds provided by the MIT\u2013Skoltech Initiative. JL acknowledges support from the Schmidt Fellowship and the U.S. Department of Energy. We acknowledge the hospitality of the Institute for Advanced Study, where HO was the Director's Visiting Professor in the fall of 2015. HO also acknowledges the hospitality of the Aspen Center for Physics, the Simons Center for Geometry and Physics, and the Center for Mathematical Sciences and Applications and the Center for the Fundamental Laws of Nature at Harvard University, where he is a visiting scholar in the spring 2016. BS thanks MIT, Stanford University, and the Simons Center for Geometry and Physics for their hospitality.\n\n

Published - ptw139.pdf

Submitted - 1605.01075.pdf

", "abstract": "In this paper we argue that classical asymptotically anti-de Sitter spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region B of the boundary spacetime we can associate a bulk spatial region \u03a3_B between B and the bulk extremal surface \nB \nwith the same boundary as B. We show that there exists a natural notion of a gravitational energy for every such region that is non-negative, and non-increasing as one makes the region smaller. The results follow from identifying this gravitational energy with a quantum relative entropy in the associated dual conformal field theory state. The positivity and monotonicity properties of the gravitational energy are implied by the positivity and monotonicity of relative entropy, which holds universally in all quantum systems.", "date": "2016-12", "date_type": "published", "publication": "Progress of Theoretical and Experimental Physics", "volume": "2016", "number": "12", "publisher": "Oxford University Press", "pagerange": "Art. No. 12C109", "id_number": "CaltechAUTHORS:20161220-092051390", "issn": "2050-3911", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-092051390", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Simons Foundation", "grant_number": "376206" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "MIT-Skoltech Initiative" }, { "agency": "Schmidt Fellowship" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1093/ptep/ptw139", "primary_object": { "basename": "1605.01075.pdf", "url": "https://authors.library.caltech.edu/records/dvk9d-azm60/files/1605.01075.pdf" }, "related_objects": [ { "basename": "ptw139.pdf", "url": "https://authors.library.caltech.edu/records/dvk9d-azm60/files/ptw139.pdf" } ], "pub_year": "2016", "author_list": "Lashkari, Nima; Lin, Jennifer; et al." }, { "id": "https://authors.library.caltech.edu/records/q76sn-q5t92", "eprint_id": 110831, "eprint_status": "archive", "datestamp": "2023-08-19 00:24:55", "lastmod": "2026-04-02 06:08:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Enumeration of holomorphic cylinders in log Calabi\u2013Yau surfaces. I", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 Springer. \n\nReceived 09 May 2015. Revised 19 January 2016. Published 04 February 2016. Issue Date: December 2016. \n\nI am very grateful to Maxim Kontsevich for suggesting this direction of research and sharing with me many fruitful ideas. Special thanks to Antoine Chambert-Loir for continuous support. During revision, Sean Keel suggested me a better way to deal with the curve classes. I am equally grateful to Luis Alvarez-Consul, Denis Auroux, Vladimir Berkovich, Beno\u00eet Bertrand, Philip Boalch, Olivier Debarre, Lie Fu, Mark Gross, Ilia Itenberg, Mattias Jonsson, Fran\u00e7ois Loeser, Ernesto Lupercio, Grigory Mikhalkin, Johannes Nicaise, Johannes Rau, Yan Soibelman, Jake Solomon, Michael Temkin and Bertrand To\u00ebn for their helpful comments, and for providing me opportunities to present this work in various seminars and conferences.\n\n

Accepted Version - 1504.01722.pdf

", "abstract": "We define the counting of holomorphic cylinders in log Calabi\u2013Yau surfaces. Although we start with a complex log Calabi\u2013Yau surface, the counting is achieved by applying methods from non-archimedean geometry. This gives rise to new geometric invariants. Moreover, we prove that the counting satisfies a property of symmetry. Explicit calculations are given for a del Pezzo surface in detail, which verify the conjectured wall-crossing formula for the focus-focus singularity. Our holomorphic cylinders are expected to give a geometric understanding of the combinatorial notion of broken line by Gross, Hacking, Keel and Siebert. Our tools include Berkovich spaces, tropical geometry, Gromov\u2013Witten theory and the GAGA theorem for non-archimedean analytic stacks.", "date": "2016-12", "date_type": "published", "publication": "Mathematische Annalen", "volume": "366", "number": "3-4", "publisher": "Springer Verlag", "pagerange": "1649-1675", "id_number": "CaltechAUTHORS:20210914-164412813", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412813", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-016-1376-3", "primary_object": { "basename": "1504.01722.pdf", "url": "https://authors.library.caltech.edu/records/q76sn-q5t92/files/1504.01722.pdf" }, "pub_year": "2016", "author_list": "Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/ycm5n-yw306", "eprint_id": 72849, "eprint_status": "archive", "datestamp": "2023-08-22 19:04:13", "lastmod": "2026-04-02 07:04:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ormerod-C-M", "name": { "family": "Ormerod", "given": "Christopher M." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Commutation Relations and Discrete Garnier Systems", "ispublished": "pub", "full_text_status": "public", "keywords": "integrable systems; difference equations; Lax pairs; discrete isomonodromy", "note": "The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike License. \n\nReceived March 30, 2016, in final form October 30, 2016; Published online November 08, 2016. \n\nThe work of EMR was partially supported by the National Science Foundation under the grant DMS-1500806.\n\n

Published - sigma16-110.pdf

Submitted - 1601.06179v2.pdf

", "abstract": "We present four classes of nonlinear systems which may be considered discrete analogues of the Garnier system. These systems arise as discrete isomonodromic deformations of systems of linear difference equations in which the associated Lax matrices are presented in a factored form. A system of discrete isomonodromic deformations is completely determined by commutation relations between the factors. We also reparameterize these systems in terms of the image and kernel vectors at singular points to obtain a separate birational form. A distinguishing feature of this study is the presence of a symmetry condition on the associated linear problems that only appears as a necessary feature of the Lax pairs for the least degenerate discrete Painlev\u00e9 equations.", "date": "2016-11-08", "date_type": "published", "publication": "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)", "volume": "12", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 110", "id_number": "CaltechAUTHORS:20161215-111704158", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161215-111704158", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1500806" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2016.110", "primary_object": { "basename": "1601.06179v2.pdf", "url": "https://authors.library.caltech.edu/records/ycm5n-yw306/files/1601.06179v2.pdf" }, "related_objects": [ { "basename": "sigma16-110.pdf", "url": "https://authors.library.caltech.edu/records/ycm5n-yw306/files/sigma16-110.pdf" } ], "pub_year": "2016", "author_list": "Ormerod, Christopher M. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/csf5h-1bf02", "eprint_id": 97844, "eprint_status": "archive", "datestamp": "2023-08-22 19:01:46", "lastmod": "2026-04-02 06:52:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Short proofs of some extremal results II", "ispublished": "pub", "full_text_status": "public", "keywords": "Extremal combinatorics; Ramsey problems", "note": "\u00a9 2016 Elsevier Inc. \n\nReceived 2 July 2015; available online 6 April 2016. \n\nConlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Packard Fellowship, by NSF Career Award DMS-1352121 and by an Alfred P. Sloan Fellowship. Sudakov research supported by SNSF grant 200021-149111. \n\nWe would like to thank the anonymous referees for their helpful remarks and Zoltan F\u00fcredi for bringing the reference [30] to our attention.\n\n

Submitted - 1507.00547.pdf

", "abstract": "We prove several results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are quite short.", "date": "2016-11", "date_type": "published", "publication": "Journal of Combinatorial Theory, Series B", "volume": "121", "publisher": "Elsevier", "pagerange": "173-196", "id_number": "CaltechAUTHORS:20190812-163000938", "issn": "0095-8956", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000938", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jctb.2016.03.005", "primary_object": { "basename": "1507.00547.pdf", "url": "https://authors.library.caltech.edu/records/csf5h-1bf02/files/1507.00547.pdf" }, "pub_year": "2016", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/3eaf4-f6079", "eprint_id": 111026, "eprint_status": "archive", "datestamp": "2023-08-18 23:54:59", "lastmod": "2026-04-02 23:55:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Wired cycle-breaking dynamics for uniform spanning forests", "ispublished": "pub", "full_text_status": "public", "keywords": "Spanning forests, unimodular random graphs, reversible random graphs", "note": "\u00a9 2016 Institute of Mathematical Statistics. \n\nReceived April 2015; revised September 2015. \n\nWe thank Tel Aviv University for its hospitality while this work was completed.We also thank Omer Angel and Asaf Nachmias for many valuable comments on earlier versions of the paper, and thank the referee and Associate Editor for their comments and suggestions.\n\n

Published - 15-AOP1063.pdf

Submitted - 1504.03928.pdf

", "abstract": "We prove that every component of the wired uniform spanning forest (WUSF) is one-ended almost surely in every transient reversible random graph, removing the bounded degree hypothesis required by earlier results. We deduce that every component of the WUSF is one-ended almost surely in every supercritical Galton\u2013Watson tree, answering a question of Benjamini, Lyons, Peres and Schramm [Ann. Probab. 29 (2001) 1\u201365]. \n\nOur proof introduces and exploits a family of Markov chains under which the oriented WUSF is stationary, which we call the wired cycle-breaking dynamics.", "date": "2016-11", "date_type": "published", "publication": "Annals of Probability", "volume": "44", "number": "6", "publisher": "Institute of Mathematical Statistics", "pagerange": "3879-3892", "id_number": "CaltechAUTHORS:20210924-190634976", "issn": "0091-1798", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-190634976", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/15-AOP1063", "primary_object": { "basename": "1504.03928.pdf", "url": "https://authors.library.caltech.edu/records/3eaf4-f6079/files/1504.03928.pdf" }, "related_objects": [ { "basename": "15-AOP1063.pdf", "url": "https://authors.library.caltech.edu/records/3eaf4-f6079/files/15-AOP1063.pdf" } ], "pub_year": "2016", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/2bwkj-kyf78", "eprint_id": 71962, "eprint_status": "archive", "datestamp": "2023-08-20 14:17:26", "lastmod": "2026-04-02 01:02:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Biringer-I", "name": { "family": "Biringer", "given": "Ian" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Unimodularity of Invariant Random Subgroups", "ispublished": "pub", "full_text_status": "public", "keywords": "Invariant random subgroups, invariant measures on homogeneous\nspaces, mass transport principle", "note": "\u00a9 2016 American Mathematical Society. \n\nReceived by the editors February 11, 2014 and, in revised form, June 2, 2015. Article electronically published on October 28, 2016. \n\nThe authors are indebted to Lewis Bowen, who first posed the question that led to Theorem 1.1, suggested the inclusion of the statement of Theorem 1.3, and inspired the discussion in Remark 3.3. The first author was partially supported by NSF grant DMS-1308678, and he would like to thank Miklos Ab\u00e9rt for numerous conversations, in particular those relating to the mass transport principle, as without his input the statement given here might not have been considered or solved. The second author\nwould like to thank Yair Hartman for enlightening discussions. Both authors would also like to thank the referee for greatly improving the readability and accuracy of the paper.\n\n

Submitted - 1402.1042.pdf

", "abstract": "An invariant random subgroup H\u2264G is a random closed subgroup whose law is invariant to conjugation by all elements of G. When G is locally compact and second countable, we show that for every invariant random subgroup H\u2264G there almost surely exists an invariant measure on G/H. Equivalently, the modular function of H is almost surely equal to the modular function of G, restricted to H. \n\nWe use this result to construct invariant measures on orbit equivalence relations of measure preserving actions. Additionally, we prove a mass transport principle for discrete or compact invariant random subgroups.", "date": "2016-10-28", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "369", "publisher": "American Mathematical Society", "pagerange": "4043-4061", "id_number": "CaltechAUTHORS:20161111-145903029", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-145903029", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1308678" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/6755", "primary_object": { "basename": "1402.1042.pdf", "url": "https://authors.library.caltech.edu/records/2bwkj-kyf78/files/1402.1042.pdf" }, "pub_year": "2016", "author_list": "Biringer, Ian and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/028j2-q7a57", "eprint_id": 110832, "eprint_status": "archive", "datestamp": "2023-08-22 18:56:07", "lastmod": "2026-04-02 16:10:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Porta-Mauro", "name": { "family": "Porta", "given": "Mauro" }, "orcid": "0000-0002-1239-3409" }, { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Higher analytic stacks and GAGA theorems", "ispublished": "pub", "full_text_status": "public", "keywords": "Analytic stack; Higher stack; Grauert's theorem; Analytification; GAGA; Rigid analytic geometry; Berkovich space; Infinity category", "note": "\u00a9 2016 Elsevier Under an Elsevier user license. \n\nReceived 18 January 2015, Revised 6 July 2016, Accepted 18 July 2016, Available online 1 August 2016. \n\nWe are grateful to Antoine Chambert-Loir, Antoine Ducros, Maxim Kontsevich, Yves Laszlo, Valerio Melani, Fran\u00e7ois Petit, Marco Robalo, Matthieu Romagny, Pierre Schapira, Michael Temkin and Gabriele Vezzosi for very useful discussions. The authors would also like to thank each other for the joint effort.\n\n

Accepted Version - 1412.5166.pdf

", "abstract": "We develop the foundations of higher geometric stacks in complex analytic geometry and in non-archimedean analytic geometry. We study coherent sheaves and prove the analog of Grauert's theorem for derived direct images under proper morphisms. We define analytification functors and prove the analog of Serre's GAGA theorems for higher stacks. We use the language of infinity category to simplify the theory. In particular, it enables us to circumvent the functoriality problem of the lisse-\u00e9tale sites for sheaves on stacks. Our constructions and theorems cover the classical 1-stacks as a special case.", "date": "2016-10-22", "date_type": "published", "publication": "Advances in Mathematics", "volume": "302", "publisher": "Elsevier", "pagerange": "351-409", "id_number": "CaltechAUTHORS:20210914-164412895", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412895", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2016.07.017", "primary_object": { "basename": "1412.5166.pdf", "url": "https://authors.library.caltech.edu/records/028j2-q7a57/files/1412.5166.pdf" }, "pub_year": "2016", "author_list": "Porta, Mauro and Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/acsjx-bdq55", "eprint_id": 66640, "eprint_status": "archive", "datestamp": "2023-08-20 14:14:32", "lastmod": "2026-04-02 15:02:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Spin TQFTs and fermionic phases of matter", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 World Scientific Publishing Company.\n\nPublished 19 October 2016.\n\nWe thank Z. Gu and D. Freed for helpful discussions and J. Morgan for educating one of us (AK) about spin structures and cobordism. The research of DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and\nInnovation. The work of AK was supported in part by the DOE grant DE-FG02-92ER40701 and by the Simons Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding\nagencies.\n\n

Published - s0217751x16450445.pdf

Submitted - 1505.05856.pdf

", "abstract": "We study lattice constructions of gapped fermionic phases of matter. We show that the construction of fermionic Symmetry Protected Topological orders by Gu and Wen has a hidden dependence on a discrete spin structure on the Euclidean space-time. The spin structure is needed to resolve ambiguities which are otherwise present. An identical ambiguity is shown to arise in the fermionic analog of the string-net construction of 2D topological orders. We argue that the need for a spin structure is a general feature of lattice models with local fermionic degrees of freedom and is a lattice analog of the spin-statistics relation.", "date": "2016-10-20", "date_type": "published", "publication": "International Journal of Modern Physics A", "volume": "31", "number": "28-29", "publisher": "World Scientific", "pagerange": "Art. No. 1645044", "id_number": "CaltechAUTHORS:20160504-095915162", "issn": "0217-751X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-095915162", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0217751X16450445", "primary_object": { "basename": "1505.05856.pdf", "url": "https://authors.library.caltech.edu/records/acsjx-bdq55/files/1505.05856.pdf" }, "related_objects": [ { "basename": "s0217751x16450445.pdf", "url": "https://authors.library.caltech.edu/records/acsjx-bdq55/files/s0217751x16450445.pdf" } ], "pub_year": "2016", "author_list": "Gaiotto, Davide and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/rz367-kkm34", "eprint_id": 66791, "eprint_status": "archive", "datestamp": "2023-08-22 18:46:00", "lastmod": "2026-04-02 23:44:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakayama-Yu", "name": { "family": "Nakayama", "given": "Yu" }, "orcid": "0000-0002-1747-5147" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Bulk Local States and Crosscaps in Holographic CFT", "ispublished": "pub", "full_text_status": "public", "keywords": "AdS-CFT Correspondence; Conformal Field Theory; Space-Time Symmetries", "note": "\u00a9 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: September 5, 2016; Accepted: October 9, 2016; Published: October 17, 2016. \n\nWe thank Alex Maloney, Tadashi Takayanagi, and Herman Verlinde for discussions. Our research is supported in part by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. The research of HO is also supported in part by U.S. DOE grant DE-SC0011632, by the Simons Investigator Award, by Caltech's Walter Burke Institute for Theoretical Physics and Moore Center for Theoretical Cosmology and Physics, by JSPS Grant-in-Aid for Scientific Research C-26400240, and by JSPS Grant-in-Aid for\nScientific Research on Innovative Areas 15H05895. HO thank the hospitality of the Institute for Advanced Study as Director's Visiting Professor in the fall 2015, where this work was initiated, and of the Center for Mathematical Sciences and Applications and the Center for the Fundamental Laws of Nature at Harvard University as a visiting scholar in the spring 2016, where this work was completed.\n\n

Published - art_3A10.1007_2FJHEP10_282016_29085.pdf

Submitted - 1605.00334v1.pdf

", "abstract": "In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some expectation, that these two conditions are not compatible to each other in the weak gravity regime. We also present an evidence to show that bulk local states in three dimensions are not organized by the Virasoro symmetry.", "date": "2016-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 085", "id_number": "CaltechAUTHORS:20160509-164600548", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160509-164600548", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Simons Foundation" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Caltech Moore Center for Theoretical Cosmology and Physics" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "Institute for Advanced Study" }, { "agency": "Harvard University" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2016-010", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Moore-Center-for-Theoretical-Cosmology-and-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP10(2016)085", "primary_object": { "basename": "1605.00334v1.pdf", "url": "https://authors.library.caltech.edu/records/rz367-kkm34/files/1605.00334v1.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2FJHEP10_282016_29085.pdf", "url": "https://authors.library.caltech.edu/records/rz367-kkm34/files/art_3A10.1007_2FJHEP10_282016_29085.pdf" } ], "pub_year": "2016", "author_list": "Nakayama, Yu and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/qpymd-ajt43", "eprint_id": 71889, "eprint_status": "archive", "datestamp": "2023-08-20 14:03:29", "lastmod": "2026-04-02 01:04:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Stabilizer rigidity in irreducible group actions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Hebrew University of Jerusalem. \n\nReceived: 11 July 2014; Revised: 24 November 2015; First Online: 30 October 2016. \n\nWe consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader\u2013Shalom and Nevo\u2013Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader\u2013Shalom and Stuck\u2013Zimmer. \n\nWe would like to thank Uri Bader, Amos Nevo, Jesse Peterson and Benjamin Weiss for useful discussions and motivating conversations. We would also like to thank Yehuda Shalom and Lewis Bowen for helpful comments on an early draft of this article. \n\nY. Hartman is supported by the European Research Council, grant 239885. \n\nO. Tamuz is supported by ISF grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing. This research is supported in part by this Google Fellowship.\n\n

Submitted - 1307.7539v3.pdf

", "abstract": "We consider irreducible actions of locally compact product groups, and of higher rank semi-simple Lie groups. Using the intermediate factor theorems of Bader\u2013Shalom and Nevo\u2013Zimmer, we show that the action stabilizers, and all irreducible invariant random subgroups, are co-amenable in their normal closure. As a consequence, we derive rigidity results on irreducible actions that generalize and strengthen the results of Bader\u2013Shalom and Stuck\u2013Zimmer.", "date": "2016-10", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "216", "number": "2", "publisher": "Springer", "pagerange": "679-705", "id_number": "CaltechAUTHORS:20161109-132848541", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-132848541", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "239885" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-016-1424-4", "primary_object": { "basename": "1307.7539v3.pdf", "url": "https://authors.library.caltech.edu/records/qpymd-ajt43/files/1307.7539v3.pdf" }, "pub_year": "2016", "author_list": "Hartman, Yair and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/a1rdy-13148", "eprint_id": 111018, "eprint_status": "archive", "datestamp": "2023-08-20 14:07:45", "lastmod": "2026-04-02 23:13:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Angel-Omer", "name": { "family": "Angel", "given": "Omer" }, "orcid": "0000-0002-6451-8242" }, { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Nachmias-Asaf", "name": { "family": "Nachmias", "given": "Asaf" }, "orcid": "0000-0002-4852-5645" }, { "id": "Ray-Gourab", "name": { "family": "Ray", "given": "Gourab" } } ] }, "title": "Unimodular hyperbolic triangulations: circle packing and random walk", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag Berlin Heidelberg 2016. \n\nReceived: 4 February 2015 / Accepted: 17 February 2016 / Published online: 11 March 2016. \n\nOA is supported in part by NSERC. AN is supported by the Israel Science Foundation Grant 1207/15 as well as NSERC and NSF grants. GR is supported in part by the Engineering and Physical Sciences Research Council under Grant EP/103372X/1. All circle packings above were generated using Ken Stephenson's CirclePack software [40]. We thank Ken for his assistance using this software and for useful conversations. We also thank the referee for their comments and suggestions.\n\n

Accepted Version - 1501.04677.pdf

", "abstract": "We show that the circle packing type of a unimodular random plane triangulation is parabolic if and only if the expected degree of the root is six, if and only if the triangulation is amenable in the sense of Aldous and Lyons [1]. As a part of this, we obtain an alternative proof of the Benjamini\u2013Schramm Recurrence Theorem [19]. Secondly, in the hyperbolic case, we prove that the random walk almost surely converges to a point in the unit circle, that the law of this limiting point has full support and no atoms, and that the unit circle is a realisation of the Poisson boundary. Finally, we show that the simple random walk has positive speed in the hyperbolic metric.", "date": "2016-10", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "206", "number": "1", "publisher": "Springer", "pagerange": "229-268", "id_number": "CaltechAUTHORS:20210923-184021534", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210923-184021534", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Israel Science Foundation", "grant_number": "1207/15" }, { "agency": "NSF" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/103372X/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-016-0653-9", "primary_object": { "basename": "1501.04677.pdf", "url": "https://authors.library.caltech.edu/records/a1rdy-13148/files/1501.04677.pdf" }, "pub_year": "2016", "author_list": "Angel, Omer; Hutchcroft, Tom; et al." }, { "id": "https://authors.library.caltech.edu/records/799c1-2c473", "eprint_id": 72344, "eprint_status": "archive", "datestamp": "2023-08-20 14:03:48", "lastmod": "2026-04-02 07:04:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } }, { "id": "Safronov-O", "name": { "family": "Safronov", "given": "Oleg" } } ] }, "title": "On the number of eigenvalues of Schr\u00f6dinger operators with complex potentials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 London Mathematical Society. \n\nReceived 13 January 2015; revised 15 March 2016; published online 16 June 2016. \n\nThe first author acknowledges support through NSF grant DMS-1363432. Ari Laptev was supported by the grant of the Russian Federation Government to support scientific research under the supervision of leading scientist at Siberian Federal University, No 14.Y26.31.0006.\n\nThe first and third author would like to thank the Mittag-Leffler Institute for hospitality.\n\n

Submitted - 1601.03122v1.pdf

", "abstract": "We study the eigenvalues of Schr\u00f6dinger operators with complex potentials in odd space dimensions. We obtain bounds on the total number of eigenvalues in the case where V decays exponentially at infinity.", "date": "2016-10", "date_type": "published", "publication": "Journal of the London Mathematical Society", "volume": "94", "number": "2", "publisher": "London Mathematical Society", "pagerange": "377-390", "id_number": "CaltechAUTHORS:20161128-153447509", "issn": "0024-6107", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161128-153447509", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Siberian Federal University", "grant_number": "14.Y26.31.0006" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/jlms/jdw039", "primary_object": { "basename": "1601.03122v1.pdf", "url": "https://authors.library.caltech.edu/records/799c1-2c473/files/1601.03122v1.pdf" }, "pub_year": "2016", "author_list": "Frank, Rupert L.; Laptev, Ari; et al." }, { "id": "https://authors.library.caltech.edu/records/32tpn-cwg93", "eprint_id": 70916, "eprint_status": "archive", "datestamp": "2023-08-20 14:01:43", "lastmod": "2026-04-02 06:59:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "On Cohen\u2013Macaulayness of Algebras Generated by Generalized Power Sums", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Springer-Verlag Berlin Heidelberg. \n\nTo Sasha Veselov on his 60th birthday, with admiration. \n\nReceived: 28 July 2015. Accepted: 15 March 2016. Published online: 26 May 2016. \n\nThe work of P.E. was partially supported by the NSF grant DMS-1000113. M.F. is very grateful to P. Etingof for a number of useful and helpful discussions and comments, to I. Losev for explanations about [EGL], to C. Korff, J. Nimmo, and A.P. Veselov for useful discussions. M.F. would also like to thank V. Lunts for the hospitality at his summer seminar 2013, where a part of this work was done.\n\n

Submitted - 1507.07485v1.pdf

", "abstract": "Generalized power sums are linear combinations of ith powers of coordinates. We consider subalgebras of the polynomial algebra generated by generalized power sums, and study when such algebras are Cohen\u2013Macaulay. It turns out that the Cohen\u2013Macaulay property of such algebras is rare, and tends to be related to quantum integrability and representation theory of Cherednik algebras. Using representation theoretic results and deformation theory, we establish Cohen\u2013Macaulayness of the algebra of q, t-deformed power sums defined by Sergeev and Veselov, and of some generalizations of this algebra, proving a conjecture of Brookner, Corwin, Etingof, and Sam. We also apply representation-theoretic techniques to studying m-quasi-invariants of deformed Calogero\u2013Moser systems. In an appendix to this paper, M. Feigin uses representation theory of Cherednik algebras to compute Hilbert series for such quasi-invariants, and show that in the case of one light particle, the ring of quasi-invariants is Gorenstein.", "date": "2016-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "347", "number": "1", "publisher": "Springer", "pagerange": "163-182", "id_number": "CaltechAUTHORS:20161006-112242015", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161006-112242015", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1000113" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-016-2657-0", "primary_object": { "basename": "1507.07485v1.pdf", "url": "https://authors.library.caltech.edu/records/32tpn-cwg93/files/1507.07485v1.pdf" }, "pub_year": "2016", "author_list": "Etingof, Pavel and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/ka8tg-pvx47", "eprint_id": 69560, "eprint_status": "archive", "datestamp": "2023-08-20 13:34:21", "lastmod": "2026-04-02 07:16:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lenzmann-E", "name": { "family": "Lenzmann", "given": "Enno" } }, { "id": "Silvestre-L", "name": { "family": "Silvestre", "given": "Luis" } } ] }, "title": "Uniqueness of Radial Solutions for the Fractional Laplacian", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Wiley Periodicals, Inc. Issue online: 13 Jul 2016. Version of Record online: 6 Jul 2015. Manuscript Received: Sep 2014.\n\nR. F thanks Elliott Lieb for useful discussions and Iosif Polterovich for pointing out reference [3]. R. F. acknowledges financial support from the NSF grants\nPHY-1068285, PHY-1347399, and DMS-1363432. E. L. expresses his deep gratitude to J\u00fcrg Fr\u00f6hlich for his constant support, interest, and inspirations revolving around (\u2212\u0394)^s.\nMoreover, E. L. acknowledges financial support from the Swiss National Science Foundation (SNF). In addition, R. F. and E. L. thank the Isaac Newton Institute for its kind hospitality in August 2012, where parts of this work were done. L. S. acknowledges financial support from the NSF grants DMS-1001629 and DMS-1065979. Finally, the authors thank the anonymous referees for valuable comments.\n\n

Submitted - 1302.2652v2.pdf

", "abstract": "We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (\u2212\u0394)^s with s\u2009\u220a\u2009(0,1) for any space dimensions N\u2009\u2265\u20091. By extending a monotonicity formula found by Cabr\u00e9 and Sire , we show that the linear equation \n(\u2212\u0394)^s u + Vu=0 in R^N\nhas at most one radial and bounded solution vanishing at infinity, provided that the potential V is radial and nondecreasing. In particular, this result implies that all radial eigenvalues of the corresponding fractional Schr\u00f6dinger operator H = (\u2212\u0394)^s\u2009+\u2009V are simple. Furthermore, by combining these findings on linear equations with topological bounds for a related problem on the upper half-space R^N_+^(+1), we show uniqueness and nondegeneracy of ground state solutions for the nonlinear equation \n(\u2212\u0394)^s Q + Q- \u2502Q\u2502^\u0251 Q=0 in R^N \nfor arbitrary space dimensions N\u2009\u2265\u20091 and all admissible exponents \u03b1\u2009>\u20090. This generalizes the nondegeneracy and uniqueness result for dimension N = 1 recently obtained by the first two authors and, in particular, the uniqueness result for solitary waves of the Benjamin-Ono equation found by Amick and Toland.", "date": "2016-09", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "69", "number": "9", "publisher": "Wiley", "pagerange": "1671-1726", "id_number": "CaltechAUTHORS:20160811-074144777", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160811-074144777", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Swiss National Science Foundation (SNSF)" }, { "agency": "NSF", "grant_number": "DMS-1001629" }, { "agency": "NSF", "grant_number": "DMS-1065979" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/cpa.21591", "primary_object": { "basename": "1302.2652v2.pdf", "url": "https://authors.library.caltech.edu/records/ka8tg-pvx47/files/1302.2652v2.pdf" }, "pub_year": "2016", "author_list": "Frank, Rupert L.; Lenzmann, Enno; et al." }, { "id": "https://authors.library.caltech.edu/records/ahtz2-11b03", "eprint_id": 97813, "eprint_status": "archive", "datestamp": "2023-08-20 13:40:29", "lastmod": "2026-04-03 05:05:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "D." }, "orcid": "0000-0001-5899-1829" }, { "id": "Gowers-W-T", "name": { "family": "Gowers", "given": "W. T." } } ] }, "title": "Combinatorial theorems in sparse random sets", "ispublished": "pub", "full_text_status": "public", "keywords": "Extremal combinatorics, random graphs and sets, sparse analogues", "note": "\u00a9 2016 D. Conlon and W.T. Gowers; this is the published version of arXiv 1011.4310. \n\nReceived 18 November 2010; revised 2 February 2015; accepted 7 April 2016; published online 29 July 2016. \n\nResearch of D.C. supported by a Royal Society University Research Fellowship. Research of W.T.G. supported by a Royal Society 2010 Anniversary Research Professorship.\n\n

Published - 44072019.pdf

Submitted - 1011.4310.pdf

", "abstract": "We develop a new technique that allows us to show in a unified way that many well-known combinatorial theorems, including Tur\u00e1n's theorem, Szemer\u00e9di's theorem and Ramsey's theorem, hold almost surely inside sparse random sets. For instance, we extend Tur\u00e1n's theorem to the random setting by showing that for every \u03f5 > 0 and every positive integer t \u2265 3 there exists a constant C such that, if G is a random graph on n vertices where each edge is chosen independently with probability at least Cn^(\u22122/(t+1)), then, with probability tending to 1 as n tends to infinity, every subgraph of G with at least (1 \u2013 (1/(t\u22121)) + \u03f5)e(G) edges contains a copy of K_t. This is sharp up to the constant C. We also show how to prove sparse analogues of structural results, giving two main applications, a stability version of the random Tur\u00e1n theorem stated above and a sparse hypergraph removal lemma. Many similar results have recently been obtained independently in a different way by Schacht and by Friedgut, R\u00f6dl and Schacht.", "date": "2016-09", "date_type": "published", "publication": "Annals of Mathematics", "volume": "184", "number": "2", "publisher": "Princeton University", "pagerange": "367-454", "id_number": "CaltechAUTHORS:20190812-162957976", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957976", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2016.184.2.2", "primary_object": { "basename": "44072019.pdf", "url": "https://authors.library.caltech.edu/records/ahtz2-11b03/files/44072019.pdf" }, "related_objects": [ { "basename": "1011.4310.pdf", "url": "https://authors.library.caltech.edu/records/ahtz2-11b03/files/1011.4310.pdf" } ], "pub_year": "2016", "author_list": "Conlon, D. and Gowers, W. T." }, { "id": "https://authors.library.caltech.edu/records/yf2xg-byp79", "eprint_id": 87374, "eprint_status": "archive", "datestamp": "2023-08-20 13:40:07", "lastmod": "2026-04-02 16:27:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" }, { "id": "Oh-Sung-Jin", "name": { "family": "Oh", "given": "Sung-Jin" } } ] }, "title": "A heat flow approach to Onsager's conjecture for the Euler equations on manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 American Mathematical Society. \n\nReceived by the editors May 4, 2014 and, in revised form, August 25, 2015. Article electronically published on November 17, 2015. \n\nThe second author is a Miller research fellow, and would like to thank the Miller Institute for support.\n\n

Submitted - 1310.7947.pdf

", "abstract": "We give a simple proof of Onsager's conjecture concerning energy conservation for weak solutions to the Euler equations on any compact Riemannian manifold, extending the results of Constantin-E-Titi and Cheskidov-Constantin-Friedlander-Shvydkoy in the flat case. When restricted to T^d or R^d, our approach yields an alternative proof of the sharp result of the latter authors.\nOur method builds on a systematic use of a smoothing operator defined via a geometric heat flow, which was considered by Milgram-Rosenbloom as a means to establish the Hodge theorem. In particular, we present a simple and geometric way to prove the key nonlinear commutator estimate, whose proof previously relied on a delicate use of convolutions.", "date": "2016-09", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "368", "number": "9", "publisher": "American Mathematical Society", "pagerange": "6519-6537", "id_number": "CaltechAUTHORS:20180627-084240647", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180627-084240647", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/tran/6549", "primary_object": { "basename": "1310.7947.pdf", "url": "https://authors.library.caltech.edu/records/yf2xg-byp79/files/1310.7947.pdf" }, "pub_year": "2016", "author_list": "Isett, Philip and Oh, Sung-Jin" }, { "id": "https://authors.library.caltech.edu/records/cmdmv-hvj13", "eprint_id": 70705, "eprint_status": "archive", "datestamp": "2023-08-20 13:36:42", "lastmod": "2026-04-02 05:41:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lemm-M", "name": { "family": "Lemm", "given": "Marius" } } ] }, "title": "Multi-Component Ginzburg-Landau Theory: Microscopic Derivation and Examples", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Springer International Publishing. \n\nCommunicated by Vieri Mastropietro. \n\nReceived: April 26, 2015. Accepted: November 10, 2015. First Online: 15 March 2016. \n\nThe authors would like to thank Egor Babaev, Christian Hainzl, Edwin Langmann and Robert Seiringer for helpful discussions. R.L.F. was supported by the U.S. National Science Foundation through grants PHY-1347399 and DMS-1363432.\n\n

Submitted - 1504.07306v2.pdf

", "abstract": "This paper consists of three parts. In part I, we microscopically derive Ginzburg\u2013Landau (GL) theory from BCS theory for translation-invariant systems in which multiple types of superconductivity may coexist. Our motivation are unconventional superconductors. We allow the ground state of the effective gap operator K_(Tc) +V to be n-fold degenerate and the resulting GL theory then couples n order parameters. In part II, we study examples of multi-component GL theories which arise from an isotropic BCS theory. We study the cases of (a) pure d-wave order parameters and (b) mixed (s + d)-wave order parameters, in two and three-dimensions. In part III, we present explicit choices of spherically symmetric interactions V which produce the examples in part II. In fact, we find interactions V which produce ground state sectors of K_(Tc) +V of arbitrary angular momentum, for open sets of of parameter values. This is in stark contrast with Schr\u00f6dinger operators \u2212\u2207^2 +V, for which the ground state is always non-degenerate. Along the way, we prove the following fact about Bessel functions: At its first maximum, a half-integer Bessel function is strictly larger than all other half-integer Bessel functions.", "date": "2016-09", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "17", "number": "9", "publisher": "Springer", "pagerange": "2285-2340", "id_number": "CaltechAUTHORS:20160930-133917913", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160930-133917913", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-016-0473-x", "primary_object": { "basename": "1504.07306v2.pdf", "url": "https://authors.library.caltech.edu/records/cmdmv-hvj13/files/1504.07306v2.pdf" }, "pub_year": "2016", "author_list": "Frank, Rupert L. and Lemm, Marius" }, { "id": "https://authors.library.caltech.edu/records/qy3jd-0m146", "eprint_id": 111027, "eprint_status": "archive", "datestamp": "2023-08-20 13:40:54", "lastmod": "2026-04-02 23:14:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" } ] }, "title": "Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Acad\u00e9mie des sciences. Published by Elsevier Masson SAS Under an Elsevier user license. \n\nReceived 3 July 2016, Accepted 27 July 2016, Available online 8 August 2016. \n\nThis work was supported by a Microsoft Research PhD Fellowship and was carried out while the author was an intern at Microsoft Research, Redmond. We thank Ander Holroyd, Gady Kozma, Russ Lyons, Asaf Nachmias, and Tianyi Zheng for helpful comments and suggestions. We also thank Hugo Duminil-Copin and Ben Wallace for the french translation of the title and abstract.\n\n

Submitted - 1605.05301.pdf

", "abstract": "We prove that critical percolation on any quasi-transitive graph of exponential volume growth does not have a unique infinite cluster. This allows us to deduce from earlier results that critical percolation on any graph in this class does not have any infinite clusters. The result is new when the graph in question is either amenable or nonunimodular.", "date": "2016-09", "date_type": "published", "publication": "Comptes Rendus Mathematique", "volume": "354", "number": "9", "publisher": "Elsevier", "pagerange": "944-947", "id_number": "CaltechAUTHORS:20210924-190635043", "issn": "1631-073X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210924-190635043", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.crma.2016.07.013", "primary_object": { "basename": "1605.05301.pdf", "url": "https://authors.library.caltech.edu/records/qy3jd-0m146/files/1605.05301.pdf" }, "pub_year": "2016", "author_list": "Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/cp80m-x8671", "eprint_id": 71548, "eprint_status": "archive", "datestamp": "2023-08-20 13:32:16", "lastmod": "2026-04-02 23:40:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Daigle-J", "name": { "family": "Daigle", "given": "Jay" } }, { "id": "Flach-M", "name": { "family": "Flach", "given": "Matthias" }, "orcid": "0000-0002-4523-9467" } ] }, "title": "On the local Tamagawa number conjecture for Tate motives over tamely ramified fields", "ispublished": "pub", "full_text_status": "public", "keywords": "Tamagawa number conjecture", "note": "\u00a9 2016 Mathematical Sciences Publishers. \n\nReceived: 25 August 2015. Revised: 9 March 2016. Accepted: 18 May 2016. Published: 30 August 2016. Communicated by Kiran S. Kedlaya. \n\nWe would like to thank the referee for a very careful reading of the manuscript, which helped to improve our exposition a lot.\n\n

Submitted - 1508.06031.pdf

", "abstract": "The local Tamagawa number conjecture, which was first formulated by Fontaine and Perrin-Riou, expresses the compatibility of the (global) Tamagawa number conjecture on motivic L-functions with the functional equation. The local conjecture was proven for Tate motives over finite unramified extensions K\u2215\u211a_p by Bloch and Kato. We use the theory of (\u03c6,\u0393)-modules and a reciprocity law due to Cherbonnier and Colmez to provide a new proof in the case of unramified extensions, and to prove the conjecture for \u211a_p(2) over certain tamely ramified extensions.", "date": "2016-08-30", "date_type": "published", "publication": "Algebra and Number Theory", "volume": "10", "number": "6", "publisher": "Mathematical Sciences Publishers", "pagerange": "1221-1275", "id_number": "CaltechAUTHORS:20161027-120750559", "issn": "1937-0652", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161027-120750559", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/ant.2016.10.1221", "primary_object": { "basename": "1508.06031.pdf", "url": "https://authors.library.caltech.edu/records/cp80m-x8671/files/1508.06031.pdf" }, "pub_year": "2016", "author_list": "Daigle, Jay and Flach, Matthias" }, { "id": "https://authors.library.caltech.edu/records/cq1tg-ymd45", "eprint_id": 87363, "eprint_status": "archive", "datestamp": "2023-09-29 01:31:51", "lastmod": "2026-04-02 23:26:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" }, { "id": "Oh-Sung-Jin", "name": { "family": "Oh", "given": "Sung-Jin" } } ] }, "title": "On Nonperiodic Euler Flows with H\u00f6lder Regularity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag Berlin Heidelberg 2016. \n\n(Received April 11, 2015 / Accepted February 2, 2016) \n\nCommunicated by C. De Lellis \n\nThe work of P. Isett is supported by the National Science Foundation under Award No. DMS-1402370. S.-J. Oh is a Miller Research Fellow, and would like to thank the Miller Institute at UC Berkeley for support. \n\nThe authors are grateful to Peter Constantin for conversations related to Theorem 1.1.\n\n

Submitted - 1402-2305.pdf

", "abstract": "In (Isett, Regularity in time along the coarse scale flow for the Euler equations, 2013), the first author proposed a strengthening of Onsager's conjecture on the failure of energy conservation for incompressible Euler flows with H\u00f6lder regularity not exceeding 1/3. This stronger form of the conjecture implies that anomalous dissipation will fail for a generic Euler flow with regularity below the Onsager critical space L^\u221e_t(B^(1/3)_(3,\u221e) due to low regularity of the energy profile. This paper is the first and main paper in a series of two, the results of which may be viewed as first steps towards establishing the conjectured failure of energy regularity for generic solutions with H\u00f6lder exponent less than 1/5 . The main result of the present paper shows that any given smooth Euler flow can be perturbed in C^(1/5 \u2212 \u03f5)_(t,x) on any pre-compact subset of \u211d\u00d7\u211d^3 to violate energy conservation. Furthermore, the perturbed solution is no smoother than C^(1/5 \u2212 \u03f5)_(t,x). As a corollary of this theorem, we show the existence of nonzero C^(1/5 \u2212 \u03f5)_(t,x) solutions to Euler with compact space-time support, generalizing previous work of the first author (Isett, H\u00f6lder continuous Euler flows in three dimensions with compact support in time, 2012) to the nonperiodic setting.", "date": "2016-08", "date_type": "published", "publication": "Archive for Rational Mechanics and Analysis", "volume": "221", "number": "2", "publisher": "Springer", "pagerange": "725-804", "id_number": "CaltechAUTHORS:20180626-155143019", "issn": "0003-9527", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180626-155143019", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1402370" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00205-016-0973-3", "primary_object": { "basename": "1402-2305.pdf", "url": "https://authors.library.caltech.edu/records/cq1tg-ymd45/files/1402-2305.pdf" }, "pub_year": "2016", "author_list": "Isett, Philip and Oh, Sung-Jin" }, { "id": "https://authors.library.caltech.edu/records/8maqs-5f232", "eprint_id": 69466, "eprint_status": "archive", "datestamp": "2023-08-20 13:05:45", "lastmod": "2026-04-02 01:12:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Killip-R", "name": { "family": "Killip", "given": "Rowan" }, "orcid": "0000-0002-4272-7916" }, { "id": "Nam-Phan-Th\u00e0nh", "name": { "family": "Nam", "given": "Phan Th\u00e0nh" } } ] }, "title": "Nonexistence of Large Nuclei in the Liquid Drop Model", "ispublished": "pub", "full_text_status": "public", "keywords": "liquid drop model, minimization problem, nonexistence", "note": "\u00a9 2016 Springer International Publishing. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 18 April 2016; Revised: 7 May 2016; Accepted: 9 May 2016. \n\nOpen access funding provided by Institute of Science and Technology Austria. \n\nPhan Th\u00e0nh Nam would like to thank H. Van Den Bosch for helpful discussions. Partial support by US National Science Foundation DMS-1363432 (R.L.F.), DMS-1265868 (R.K.) and Austrian Science Fund (FWF) Project Nr. P 27533-N27 (P.T.N.) are acknowledged.\n\n

Published - art_3A10.1007_2Fs11005-016-0860-8.pdf

Submitted - 1604.03231v2.pdf

", "abstract": "We give a simplified proof of the nonexistence of large nuclei in the liquid drop model and provide an explicit bound. Our bound is within a factor of 2.3 of the conjectured value and seems to be the first quantitative result.", "date": "2016-08", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "106", "number": "8", "publisher": "Springer", "pagerange": "1033-1036", "id_number": "CaltechAUTHORS:20160805-093315174", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160805-093315174", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Institute of Science and Technology Austria" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "DMS-1265868" }, { "agency": "FWF Der Wissenschaftsfonds", "grant_number": "P 27533-N27" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-016-0860-8", "primary_object": { "basename": "art_3A10.1007_2Fs11005-016-0860-8.pdf", "url": "https://authors.library.caltech.edu/records/8maqs-5f232/files/art_3A10.1007_2Fs11005-016-0860-8.pdf" }, "related_objects": [ { "basename": "1604.03231v2.pdf", "url": "https://authors.library.caltech.edu/records/8maqs-5f232/files/1604.03231v2.pdf" } ], "pub_year": "2016", "author_list": "Frank, Rupert L.; Killip, Rowan; et al." }, { "id": "https://authors.library.caltech.edu/records/m293x-gf131", "eprint_id": 72363, "eprint_status": "archive", "datestamp": "2023-08-20 12:41:21", "lastmod": "2026-04-02 01:11:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Sabin-J", "name": { "family": "Sabin", "given": "Julien" } } ] }, "title": "Maximizers for the Stein\u2013Tomas Inequality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Springer International Publishing. \n\nReceived: March 21, 2016. Accepted: August 3, 2016. Published online October 4, 2016. \n\nR.L.F. and J.S. would like to thank D. Oliveira e Silva and C. Thiele for the summer school 'Sharp inequalities in harmonic analysis' in August 2015 which stimulated our interest in this project. Partial support by U.S. National Science Foundation DMS-1363432 (R.L.F.) and PHY-1265118 (E.H.L.) is acknowledged.\n\n

Submitted - 1603.07658v1.pdf

", "abstract": "We give a necessary and sufficient condition for the precompactness of all optimizing sequences for the Stein\u2013Tomas inequality. In particular, if a well-known conjecture about the optimal constant in the Strichartz inequality is true, we obtain the existence of an optimizer in the Stein\u2013Tomas inequality. Our result is valid in any dimension.", "date": "2016-07", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "26", "number": "4", "publisher": "Springer", "pagerange": "1095-1134", "id_number": "CaltechAUTHORS:20161129-084514277", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161129-084514277", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-016-0380-9", "primary_object": { "basename": "1603.07658v1.pdf", "url": "https://authors.library.caltech.edu/records/m293x-gf131/files/1603.07658v1.pdf" }, "pub_year": "2016", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/agzgj-wxv73", "eprint_id": 69171, "eprint_status": "archive", "datestamp": "2023-08-20 12:34:50", "lastmod": "2026-04-02 07:12:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hainzl-C", "name": { "family": "Hainzl", "given": "Christian" } }, { "id": "Schlein-B", "name": { "family": "Schlein", "given": "Benjamin" } }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Incompatibility of Time-Dependent Bogoliubov\u2013de-Gennes and Ginzburg\u2013Landau Equations", "ispublished": "pub", "full_text_status": "public", "keywords": "superconductivity, quasi-free states, critical temperature, BCS theory", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. \n\nReceived: 6 November 2015; Revised: 15 April 2016; Accepted: 16 April 2016; Published online: 10 May 2016. \n\nOpen access funding provided by Institute of Science and Technology (IST Austria). Financial support from the U.S. National Science Foundation through Grants PHY-1347399 and DMS-1363432 (R.L.F.), SwissMAP and SNF Grant Nr. 200021-153621 (B.S.), and the Austrian Science Fund (FWF) project Nr. P 27533-N27 (R.S.) is acknowledged.\n\n

Published - art_10.1007_s11005-016-0847-5.pdf

Submitted - 1504.05885v2.pdf

", "abstract": "We study the time-dependent Bogoliubov\u2013de-Gennes equations for generic translation-invariant fermionic many-body systems. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a time-dependent Ginzburg\u2013Landau equation, which is often employed as a phenomenological description and predicts a decay of the order parameter in time. The full non-linear structure of the equations is necessary to understand this behavior.", "date": "2016-07", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "106", "number": "7", "publisher": "Springer", "pagerange": "913-923", "id_number": "CaltechAUTHORS:20160722-140945826", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160722-140945826", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Institute of Science and Technology Austria" }, { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "SwissMAP" }, { "agency": "Swiss National Fund (SNF)", "grant_number": "200021-153621" }, { "agency": "FWF Der Wissenschaftsfonds", "grant_number": "P 27533-N27" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-016-0847-5", "primary_object": { "basename": "1504.05885v2.pdf", "url": "https://authors.library.caltech.edu/records/agzgj-wxv73/files/1504.05885v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_s11005-016-0847-5.pdf", "url": "https://authors.library.caltech.edu/records/agzgj-wxv73/files/art_10.1007_s11005-016-0847-5.pdf" } ], "pub_year": "2016", "author_list": "Frank, Rupert L.; Hainzl, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/dfevp-kh744", "eprint_id": 72057, "eprint_status": "archive", "datestamp": "2023-08-20 12:30:30", "lastmod": "2026-04-02 16:18:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Oliver-B", "name": { "family": "Oliver", "given": "Bob" } } ] }, "title": "Fusion systems", "ispublished": "pub", "full_text_status": "public", "keywords": "Fusion, Sylow subgroups, finite simple groups, classifying spaces,\nmodular representation theory", "note": "\u00a9 2016 American Mathematical Society. \n\nReceived by the editors December 27, 2015. Published electronically: June 29, 2016. \n\nThe first author was partially supported by NSF DMS-1265587 and NSF DMS-0969009. \n\nThe second author was partially supported by UMR 7539 of the CNRS.\n\n

Published - S0273-0979-2016-01538-2.pdf

", "abstract": "This is a survey article on the theory of fusion systems, a relatively new area of mathematics with connections to local finite group theory, algebraic topology, and modular representation theory. We first describe the general theory and then look separately at these connections.", "date": "2016-06-29", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "53", "number": "4", "publisher": "American Mathematical Society", "pagerange": "555-615", "id_number": "CaltechAUTHORS:20161116-124215563", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161116-124215563", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-0969009" }, { "agency": "Centre National de la Recherche Scientifique (CNRS)", "grant_number": "UMR 7539" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/bull/1538", "primary_object": { "basename": "S0273-0979-2016-01538-2.pdf", "url": "https://authors.library.caltech.edu/records/dfevp-kh744/files/S0273-0979-2016-01538-2.pdf" }, "pub_year": "2016", "author_list": "Aschbacher, Michael and Oliver, Bob" }, { "id": "https://authors.library.caltech.edu/records/9sngr-rxs67", "eprint_id": 72439, "eprint_status": "archive", "datestamp": "2023-08-20 12:24:39", "lastmod": "2026-03-09 20:39:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Macdonald-H-L", "name": { "family": "Macdonald", "given": "Henry L." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Borel equivalence relations and cardinal algebras", "ispublished": "pub", "full_text_status": "public", "keywords": "countable Borel equivalence relation, Borel reducibility, cardinal algebra", "note": "\u00a9 2016 Instytut Matematyczny PAN. \n\nReceived 21 December 2015; revised 20 April 2016; Published online: 17 June 2016. \n\nResearch partially supported by NSF Grant DMS-1464475. We would like to thank Simon Thomas for his help with Theorem 4.3.\n\n

Submitted - cardinal_algebras.pdf

", "abstract": "We show that Tarski's concept of cardinal algebra appears naturally in the context of the current theory of Borel equivalence relations. As a result one can apply Tarski's theory to discover a number of interesting laws governing the structure of Borel equivalence relations, which, in retrospect rather surprisingly, have not been realized before.", "date": "2016-06-17", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "235", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "183-198", "id_number": "CaltechAUTHORS:20161130-102008360", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161130-102008360", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1464475" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4064/fm242-4-2016", "primary_object": { "basename": "cardinal_algebras.pdf", "url": "https://authors.library.caltech.edu/records/9sngr-rxs67/files/cardinal_algebras.pdf" }, "pub_year": "2016", "author_list": "Macdonald, Henry L. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/zr4ma-33g67", "eprint_id": 68639, "eprint_status": "archive", "datestamp": "2023-08-20 12:23:38", "lastmod": "2026-04-16 01:40:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Burnell-F-J", "name": { "family": "Burnell", "given": "Fiona" } }, { "id": "Chen-Xie", "name": { "family": "Chen", "given": "Xie" }, "orcid": "0000-0003-2215-2497" }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Metlitski-M-A", "name": { "family": "Metlitski", "given": "Max" } }, { "id": "Vishwanath-A", "name": { "family": "Vishwanath", "given": "Ashvin" } } ] }, "title": "Time reversal invariant gapped boundaries of the double semion state", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 American Physical Society. \n\nReceived 30 March 2016; published 30 June 2016. \n\nWe would like to thank Lukasz Fidkowski, Zhenghan Wang, Meng Cheng, and T. Senthil for discussion. X.C. is supported by the Miller Institute for Basic Research in Science at UC Berkeley, the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics. A.V. is supported by the Templeton Foundation. FJB is supported by NSF DMR-1352271 and Sloan FG-2015-65927.\n\n

Published - PhysRevB.93.235161.pdf

Submitted - 1509.00355v1.pdf

", "abstract": "The boundary of a fractionalized topological phase can be gapped by condensing a proper set of bosonic quasiparticles. Interestingly, in the presence of a global symmetry, such a boundary can have different symmetry transformation properties. Here we present an explicit example of this kind, in the double semion state with time reversal symmetry. We find two distinct cases where the semionic excitations on the boundary can transform either as time reversal singlets or as time reversal (Kramers) doublets, depending on the coherent phase factor of the Bose condensate. The existence of these two possibilities are demonstrated using both field-theory argument and exactly solvable lattice models. Furthermore, we study the domain walls between these two types of gapped boundaries and find that the application of time reversal symmetry tunnels a semion between them.", "date": "2016-06-15", "date_type": "published", "publication": "Physical Review B", "volume": "93", "number": "23", "publisher": "American Physical Society", "pagerange": "Art. No. 235161", "id_number": "CaltechAUTHORS:20160623-125613186", "issn": "2469-9950", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160623-125613186", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Miller Institute for Basic Research in Science" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Templeton Foundation" }, { "agency": "NSF", "grant_number": "DMR-1352271" }, { "agency": "Alfred P. Sloan Foundation", "grant_number": "FG-2015-65927" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.93.235161", "primary_object": { "basename": "PhysRevB.93.235161.pdf", "url": "https://authors.library.caltech.edu/records/zr4ma-33g67/files/PhysRevB.93.235161.pdf" }, "related_objects": [ { "basename": "1509.00355v1.pdf", "url": "https://authors.library.caltech.edu/records/zr4ma-33g67/files/1509.00355v1.pdf" } ], "pub_year": "2016", "author_list": "Burnell, Fiona; Chen, Xie; et al." }, { "id": "https://authors.library.caltech.edu/records/sgp63-mg084", "eprint_id": 63374, "eprint_status": "archive", "datestamp": "2023-09-22 22:52:42", "lastmod": "2026-04-02 23:25:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ball-A", "name": { "family": "Ball", "given": "Adam" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology", "ispublished": "pub", "full_text_status": "public", "keywords": "spectral action, modified gravity, Packed swiss cheese cosmology", "note": "\u00a9 2016 IOP Publishing Ltd. \n\nReceived 23 June 2015, revised 23 September 2015, Accepted for publication 15 January 2016, Published 3 May 2016. \n\nWe thank the referees for many extremely useful comments and suggestions that greatly improved the paper. The first author was supported by a Summer Undergraduate Research Fellowship at Caltech. The second author is supported by NSF grants DMS-1007207, DMS-1201512, PHY-1205440, and by the Perimeter Institute for Theoretical Physics.\n\n

Submitted - 1506.01401v1.pdf

", "abstract": "We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the packed swiss cheese cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its expansion on a space obtained as an Apollonian packing of three-dimensional spheres inside a four-dimensional ball. Using information from the zeta function of the Dirac operator of the spectral triple, we compute the leading terms in the asymptotic expansion of the spectral action. They consist of a zeta regularization of the divergent sum of the leading terms of the spectral actions of the individual spheres in the packing. This accounts for the contribution of points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There is an additional term coming from the residue at the additional point in the real dimension spectrum that corresponds to the packing constant, as well as a series of fluctuations coming from log-periodic oscillations, created by the points of the dimension spectrum that are off the real line. These terms detect the fractality of the residue set of the sphere packing. We show that the presence of fractality influences the shape of the slow-roll potential for inflation, obtained from the spectral action. We also discuss the effect of truncating the fractal structure at a certain scale related to the energy scale in the spectral action.", "date": "2016-06-09", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "33", "number": "11", "publisher": "IOP", "pagerange": "Art. No. 115018", "id_number": "CaltechAUTHORS:20160105-102322403", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160105-102322403", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/0264-9381/33/11/115018", "primary_object": { "basename": "1506.01401v1.pdf", "url": "https://authors.library.caltech.edu/records/sgp63-mg084/files/1506.01401v1.pdf" }, "pub_year": "2016", "author_list": "Ball, Adam and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/4ps3z-8tg56", "eprint_id": 67637, "eprint_status": "archive", "datestamp": "2023-08-22 17:52:32", "lastmod": "2026-04-02 15:27:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Babichenko-Y", "name": { "family": "Babichenko", "given": "Yakov" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Graphical potential games", "ispublished": "pub", "full_text_status": "public", "keywords": "Potential games; Graphical games", "note": "\u00a9 2016 Elsevier Inc.\n\nReceived 20 October 2015; final version received 8 February 2016; accepted 18 March 2016; Available online 23 March 2016. \n\nThe authors would like to thank Elchanan Mossel for some enlightening comments.\n\n

Submitted - 1405.1481v2.pdf

", "abstract": "We study the class of potential games that are also graphical games with respect to a given graph G of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of Markov random fields on G. From this characterization, and from the Hammersley\u2013Clifford theorem, it follows that the potentials of such games can be decomposed into local potentials.", "date": "2016-05", "date_type": "published", "publication": "Journal of Economic Theory", "volume": "163", "publisher": "Elsevier", "pagerange": "889-899", "id_number": "CaltechAUTHORS:20160603-083016959", "issn": "0022-0531", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160603-083016959", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jet.2016.03.010", "primary_object": { "basename": "1405.1481v2.pdf", "url": "https://authors.library.caltech.edu/records/4ps3z-8tg56/files/1405.1481v2.pdf" }, "pub_year": "2016", "author_list": "Babichenko, Yakov and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/3xbk1-zwt83", "eprint_id": 71958, "eprint_status": "archive", "datestamp": "2023-08-20 11:31:10", "lastmod": "2026-04-02 01:02:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frisch-J", "name": { "family": "Frisch", "given": "Joshua" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Transitive graphs uniquely determined by their local structure", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 American Mathematical Society. \n\nReceived by the editors June 3, 2015. Article electronically published on October 1, 2015. \n\nThe first author was supported by MIT's Undergraduate Research Opportunities Program. This research was partially conducted at Microsoft Research, New England. \n\nThe authors would like to thank Russell Lyons and Bobby Kleinberg for helpful discussions.\n\n

Submitted - 1411.6534.pdf

", "abstract": "We give an example of an infinite, vertex transitive graph that has the following property: it is the unique completion to a transitive graph of a large enough finite subgraph of itself.", "date": "2016-05", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "144", "number": "5", "publisher": "American Mathematical Society", "pagerange": "1913-1918", "id_number": "CaltechAUTHORS:20161111-141028249", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-141028249", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Massachusetts Institute of Technology (MIT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/proc/12901", "primary_object": { "basename": "1411.6534.pdf", "url": "https://authors.library.caltech.edu/records/3xbk1-zwt83/files/1411.6534.pdf" }, "pub_year": "2016", "author_list": "Frisch, Joshua and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/ajrer-hfd63", "eprint_id": 66344, "eprint_status": "archive", "datestamp": "2023-08-22 17:46:00", "lastmod": "2026-04-02 16:26:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Syntactic Parameters and a Coding Theory Perspective on Entropy and Complexity of Language Families", "ispublished": "pub", "full_text_status": "public", "keywords": "syntax; principles and parameters; error-correcting codes; asymptotic bound; Kolmogorov complexity; Gilbert\u2013Varshamov bound; Shannon entropy", "note": "\u00a9 2016 by the author; licensee MDPI, Basel, Switzerland. This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. \n\nReceived: 14 January 2016; Accepted: 18 March 2016; Published: 7 April 2016. \n\nAcademic Editors: Fr\u00e9d\u00e9ric Barbaresco, Frank Nielsen and Kevin H. Knuth. \n\n(This article belongs to the Special Issue Differential Geometrical Theory of Statistics) \n\nThe author's research is supported by NSF grants DMS-1201512 and PHY-1205440, and by the Perimeter Institute for Theoretical Physics. The author thanks the referees for their useful comments. \n\nThe author declares no conflict of interest.\n\n

Published - entropy-18-00110.pdf

", "abstract": "We present a simple computational approach to assigning a measure of complexity and information/entropy to families of natural languages, based on syntactic parameters and the theory of error correcting codes. We associate to each language a binary string of syntactic parameters and to a language family a binary code, with code words the binary string associated to each language. We then evaluate the code parameters (rate and relative minimum distance) and the position of the parameters with respect to the asymptotic bound of error correcting codes and the Gilbert\u2013Varshamov bound. These bounds are, respectively, related to the Kolmogorov complexity and the Shannon entropy of the code and this gives us a computationally simple way to obtain estimates on the complexity and information, not of individual languages but of language families. This notion of complexity is related, from the linguistic point of view to the degree of variability of syntactic parameter across languages belonging to the same (historical) family.", "date": "2016-04-07", "date_type": "published", "publication": "Entropy", "volume": "18", "number": "4", "publisher": "MDPI", "pagerange": "Art. No. 110", "id_number": "CaltechAUTHORS:20160420-165543640", "issn": "1099-4300", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160420-165543640", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Perimeter Institute for Theoretical Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3390/e18040110", "primary_object": { "basename": "entropy-18-00110.pdf", "url": "https://authors.library.caltech.edu/records/ajrer-hfd63/files/entropy-18-00110.pdf" }, "pub_year": "2016", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/fhxv2-48588", "eprint_id": 61836, "eprint_status": "archive", "datestamp": "2023-08-22 17:39:06", "lastmod": "2026-04-02 23:27:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kim-Hyungrok", "name": { "family": "Kim", "given": "Hyungrok" } }, { "id": "Kravchuk-Petr", "name": { "family": "Kravchuk", "given": "Petr" }, "orcid": "0000-0003-0977-3686" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Reflections on Conformal Spectra", "ispublished": "pub", "full_text_status": "public", "keywords": "Conformal and W Symmetry; Field Theories in Higher Dimensions", "note": "\u00a9 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.\n\nArticle funded by SCOAP3. \n\nReceived: March 20, 2016; Accepted: April 11, 2016; Published: April 29, 2016. \n\nWe thank S. El-Showk, N. Hunter-Jones, C. Keller, Z. Komargodski, Y. Nakayama, S. Rychkov, D. Simmons-Duffin, B. Stoica, and W. Yan for discussion. We also thank S. Rychkov and D. Simmons-Duffin for their comments on the draft of this paper. This work is supported in part by U.S. DOE grant DE-SC0011632, by the WPI Initiative of MEXT, by JSPS KAKENHI Grant Numbers C-26400240 and 15H05895, by the Simons Investigator Award, and by the Walter Burke Institute for Theoretical Physics and the Moore Center for Theoretical Cosmology and Physics at Caltech. We thank the hospitality of the Institute for Advanced Study, where HO is Director's Visiting Professor. HO also thanks the Aspen Center for Physics and the Simons Center for Geometry and Physics, where parts of this work were done.\n\n

Published - Kim2016_Article_ReflectionsOnConformalSpectra.pdf

Submitted - 1510.08772v1.pdf

", "abstract": "We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions \u03940 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite \u03940 as well as for large \u03940. We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function.", "date": "2016-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 184", "id_number": "CaltechAUTHORS:20151104-124350087", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151104-124350087", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15H05895" }, { "agency": "Simons Foundation" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2015-053", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Moore-Center-for-Theoretical-Cosmology-and-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2016)184", "primary_object": { "basename": "1510.08772v1.pdf", "url": "https://authors.library.caltech.edu/records/fhxv2-48588/files/1510.08772v1.pdf" }, "related_objects": [ { "basename": "Kim2016_Article_ReflectionsOnConformalSpectra.pdf", "url": "https://authors.library.caltech.edu/records/fhxv2-48588/files/Kim2016_Article_ReflectionsOnConformalSpectra.pdf" } ], "pub_year": "2016", "author_list": "Kim, Hyungrok; Kravchuk, Petr; et al." }, { "id": "https://authors.library.caltech.edu/records/46gpz-ed792", "eprint_id": 66607, "eprint_status": "archive", "datestamp": "2023-08-20 11:05:33", "lastmod": "2026-04-02 23:50:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chung-Hee-Joong", "name": { "family": "Chung", "given": "Hee-Joong" } }, { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "3d-3d Correspondence Revisited", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Topological Field Theories, Chern-Simons Theories, Supersymmetry and Duality", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: March 4, 2016; Accepted: April 13, 2016; Published: April 21, 2016. \n\nWe would like to thank S. Nawata, S. Razamat, B. Willett, and E. Witten for useful discussions.\nMany ideas in this paper were developed at the 2013 Simons Summer Workshop in\nMathematics and Physics, whose support and hospitality we gratefully acknowledge. The work of H.J.C. and S.G. is supported in part by DOE Grant DE-FG02-92ER40701. The\nwork of T.D. is supported in part by DOE grant DE-SC0009988. This work has also been\nsupported by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\",\nfunded by the European Research Council under the European Union's Seventh Framework\nProgramme.\n\n

Published - art_3A10.1007_2FJHEP04_282016_29140.pdf

Submitted - 1405.3663.pdf

", "abstract": "In fivebrane compactifications on 3-manifolds, we point out the importance of all flat connections in the proper definition of the effective 3d N=2 \ntheory. The Lagrangians of some theories with the desired properties can be constructed with the help of homological knot invariants that categorify colored Jones polynomials. Higgsing the full 3d theories constructed this way recovers theories found previously by Dimofte-Gaiotto-Gukov. We also consider the cutting and gluing of 3-manifolds along smooth boundaries and the role played by all flat connections in this operation.", "date": "2016-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 140", "id_number": "CaltechAUTHORS:20160503-083907514", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-083907514", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2016)140", "primary_object": { "basename": "1405.3663.pdf", "url": "https://authors.library.caltech.edu/records/46gpz-ed792/files/1405.3663.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2FJHEP04_282016_29140.pdf", "url": "https://authors.library.caltech.edu/records/46gpz-ed792/files/art_3A10.1007_2FJHEP04_282016_29140.pdf" } ], "pub_year": "2016", "author_list": "Chung, Hee-Joong; Dimofte, Tudor; et al." }, { "id": "https://authors.library.caltech.edu/records/a4ag2-0qb96", "eprint_id": 63644, "eprint_status": "archive", "datestamp": "2023-08-20 10:48:09", "lastmod": "2026-04-02 15:08:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Nawata-Satoshi", "name": { "family": "Nawata", "given": "Satoshi" } }, { "id": "Saberi-Ingmar-A", "name": { "family": "Saberi", "given": "Ingmar" } }, { "id": "Sto\u0161i\u0107-M", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" } }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Sequencing BPS Spectra", "ispublished": "pub", "full_text_status": "public", "keywords": "Differential and Algebraic Geometry, Supersymmetry and Duality, Topological\nField Theories, Topological Strings", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\n\nArticle funded by SCOAP3. \n\nReceived: January 9, 2016; Accepted: February 15, 2016; Published: March 2, 2016. \n\nS.N. would like to express deep gratitude to the previous institutions, NIKHEF Amsterdam, University of Warsaw and Max Planck Institute for Mathematics at Bonn where most of this work was carried out.\nThis work has been supported by the ERC Starting Grant no. 335739 \"Quantum fields and knot homologies\", funded by the European Research Council under the European Union's Seventh Framework Programme, and by Walter Burke Institute for Theoretical Physics, California Institute of Technology. The work of S.G. is partially supported by the DOE Grant DE-SC0011632. The work of S.N. is partially supported by the ERC Advanced Grant no. 246974, \"Supersymmetry: a window to non-perturbative physics\", and also partially supported by the center of excellence grant \"Center for Quantum Geometry of Moduli Spaces (QGM)\" from the Danish National Research Foundation. M.S. was also partially supported by the Ministry of Education of Serbia, grant no. 174012. P.S. acknowledges the support of the Foundation for Polish Science.\n\n

Published - art_10.1007_JHEP03_2016_004.pdf

Submitted - 1512.07883v2.pdf

", "abstract": "This paper provides both a detailed study of color-dependence of link homologies, as realized in physics as certain spaces of BPS states, and a broad study of the behavior of BPS states in general. We consider how the spectrum of BPS states varies as continuous parameters of a theory are perturbed. This question can be posed in a wide variety of physical contexts, and we answer it by proposing that the relationship between unperturbed and perturbed BPS spectra is described by a spectral sequence. These general considerations unify previous applications of spectral sequence techniques to physics, and explain from a physical standpoint the appearance of many spectral sequences relating various link homology theories to one another. We also study structural properties of colored HOMFLY homology for links and evaluate Poincar\u00e9 polynomials in numerous examples. Among these structural properties is a novel \"sliding\" property, which can be explained by using (refined) modular S-matrix. This leads to the identification of modular transformations in Chern-Simons theory and 3d N=2 theory via the 3d/3d correspondence. Lastly, we introduce the notion of associated varieties as classical limits of recursion relations of colored superpolynomials of links, and study their properties.", "date": "2016-03-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "03", "publisher": "Springer", "pagerange": "Art. No. 004", "id_number": "CaltechAUTHORS:20160113-131017250", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160113-131017250", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "335739" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "European Research Council (ERC)", "grant_number": "246974" }, { "agency": "Danish Research Council" }, { "agency": "Ministry of Education (Serbia)", "grant_number": "174012" }, { "agency": "Foundation for Polish Science" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2015-063", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP03(2016)004", "primary_object": { "basename": "1512.07883v2.pdf", "url": "https://authors.library.caltech.edu/records/a4ag2-0qb96/files/1512.07883v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP03_2016_004.pdf", "url": "https://authors.library.caltech.edu/records/a4ag2-0qb96/files/art_10.1007_JHEP03_2016_004.pdf" } ], "pub_year": "2016", "author_list": "Gukov, Sergei; Nawata, Satoshi; et al." }, { "id": "https://authors.library.caltech.edu/records/twt7w-tq484", "eprint_id": 67426, "eprint_status": "archive", "datestamp": "2023-08-22 17:33:09", "lastmod": "2026-04-02 23:35:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "N-groups and fusion systems", "ispublished": "pub", "full_text_status": "public", "keywords": "Fusion systems; Finite groups", "note": "\u00a9 2015 Elsevier Inc. \n\nThis work was partially supported by NSF grants DMS-1265587 and DMS-0969009.", "abstract": "We classify all saturated 2-fusion systems that are N-systems: that is those systems all of whose local subsystems are solvable, subject to one of the two possible notions of solvability. We also use the result on fusion systems to give a new proof of Thompson's theorem on N-groups; indeed we give a new proof of the theorem determining all finite groups in which all 2-locals are solvable.", "date": "2016-03-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "449", "publisher": "Elsevier", "pagerange": "264-320", "id_number": "CaltechAUTHORS:20160527-090500481", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160527-090500481", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1265587" }, { "agency": "NSF", "grant_number": "DMS-0969009" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2015.10.011", "pub_year": "2016", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/pght2-9va43", "eprint_id": 65428, "eprint_status": "archive", "datestamp": "2023-08-20 10:31:45", "lastmod": "2026-04-02 16:04:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Geisinger-Leander", "name": { "family": "Geisinger", "given": "Leander" } } ] }, "title": "Refined semiclassical asymptotics for fractional powers of the Laplace operator", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 by Walter de Gruyter GmbH.\n\nReceived: 2011-10-20; Revised: 2013-11-03; Published Online: 2014-01-30.\n\n

Submitted - 1105.5181v2.pdf

", "abstract": "We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a two-term formula for the sum of eigenvalues with the leading (Weyl) term given by the volume and the subleading term by the surface area. Our result is valid under very weak assumptions on the regularity of the boundary.", "date": "2016-03", "date_type": "published", "publication": "Journal f\u00fcr die reine und angewandte Mathematik", "volume": "2016", "number": "712", "publisher": "De Gruyter", "pagerange": "1-37", "id_number": "CaltechAUTHORS:20160317-104639269", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160317-104639269", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2013-0120", "primary_object": { "basename": "1105.5181v2.pdf", "url": "https://authors.library.caltech.edu/records/pght2-9va43/files/1105.5181v2.pdf" }, "pub_year": "2016", "author_list": "Frank, Rupert L. and Geisinger, Leander" }, { "id": "https://authors.library.caltech.edu/records/qjp7q-zgn07", "eprint_id": 66440, "eprint_status": "archive", "datestamp": "2023-08-22 17:29:25", "lastmod": "2026-04-02 00:07:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Elliot-R", "name": { "family": "Elliot", "given": "Ross" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Exceptional knot homology", "ispublished": "pub", "full_text_status": "public", "keywords": "BPS states; double affine Hecke algebras; superpolynomials; knot homology; quantum invariants; exceptional Lie algebras; singularity theory; Landau\u2013Ginzburg potential", "note": "\u00a9 2016 World Scientific Publishing Co Pte Ltd. \n\nReceived: 31 July 2015; Accepted: 21 December 2015; Published: 1 February 2016. \n\nOur special thanks go to Ivan Cherednik, who provided the formulas for DAHA-Jones polynomials and participated in the development of many ideas contained herein. Without his contributions, this work would not be possible. \n\nWe would also like to thank J. Adams, M. Aschbacher, D. Bar-Natan, P. Cvitanovi\u0107 , W.A. de Graaf, A. Gabrielov, and S. Morrison for helpful discussions. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics. The work of R.E. is partially supported by a Troesh Family Graduate Fellowship 2014-15.\n\n

Submitted - 1505.01635v1.pdf

", "abstract": "The goal of this paper is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called hyperpolynomials that address the \"problem of negative coefficients\" often encountered in DAHA-based approaches to homological invariants of torus knots and links. Furthermore, from the physics of BPS states and the spectra of singularities associated with Landau\u2013Ginzburg potentials, we also describe a rich structure of differentials that act on homological knot invariants for exceptional groups and uniquely determine the latter for torus knots.", "date": "2016-03", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "25", "number": "3", "publisher": "World Scientific Publishing Co.", "pagerange": "Art. No. 1640003", "id_number": "CaltechAUTHORS:20160425-090534476", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160425-090534476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Troesh Family Graduate Fellowship 2014-15" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0218216516400034", "primary_object": { "basename": "1505.01635v1.pdf", "url": "https://authors.library.caltech.edu/records/qjp7q-zgn07/files/1505.01635v1.pdf" }, "pub_year": "2016", "author_list": "Elliot, Ross and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/n9qm0-c9265", "eprint_id": 64755, "eprint_status": "archive", "datestamp": "2023-08-22 17:20:28", "lastmod": "2026-04-02 06:51:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carlen-E-A", "name": { "family": "Carlen", "given": "Eric A." }, "orcid": "0000-0003-2613-187X" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Some operator and trace function convexity theorems", "ispublished": "pub", "full_text_status": "public", "keywords": "Operator convexity; Operator concavity; Trace inequality; R\u00e9nyi entropy", "note": "\u00a9 2015 Elsevier Inc.\n\nWork partially supported by U.S. National Science Foundation grant DMS-1201354.\n\nWork partially supported by U.S. National Science Foundation grants PHY-1347399 and DMS-1363432.\n\nWork partially supported by U.S. National Science Foundation grant PHY-1265118.\n\nWe thank Marius Lemm and Mark Wilde, as well as the anonymous referee, for useful remarks.\n\n

Submitted - 1409.0564v5.pdf

", "abstract": "We consider trace functions (A,B)\u21a6Tr[(A^(q/2)B^pA^(q/2))^s] where A and B are positive n\u00d7n matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of A^(q/2)B^pA^(q/2) and convexity/concavity of the closely related trace functional Tr[A^(q/2)B^pA^(q/2)C^r]. The concavity questions are completely resolved, thereby settling cases left open by Hiai; the convexity questions are settled in many cases. As a consequence, the Audenaert\u2013Datta R\u00e9nyi entropy conjectures are proved for some cases.", "date": "2016-02-01", "date_type": "published", "publication": "Linear Algebra and its Applications", "volume": "490", "publisher": "Elsevier", "pagerange": "174-185", "id_number": "CaltechAUTHORS:20160225-075610491", "issn": "0024-3795", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160225-075610491", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1201354" }, { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.laa.2015.11.006", "primary_object": { "basename": "1409.0564v5.pdf", "url": "https://authors.library.caltech.edu/records/n9qm0-c9265/files/1409.0564v5.pdf" }, "pub_year": "2016", "author_list": "Carlen, Eric A.; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/q1vhm-qth77", "eprint_id": 97825, "eprint_status": "archive", "datestamp": "2023-08-20 10:09:43", "lastmod": "2026-04-03 00:02:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Lee-Choongbum", "name": { "family": "Lee", "given": "Choongbum" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Ramsey numbers of cubes versus cliques", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 J\u00e1nos Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg. \n\nReceived 08 August 2012; first online 05 November 2014. \n\nConlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Packard Fellowship, a Simons Fellowship, an MIT NEC Corp. award and NSF grant DMS-1069197. Lee research supported in part by a Samsung Scholarship. Sudakov research supported in part by SNSF grant 200021-149111 and by a USA-Israel BSF grant. \n\nWe would like to thank the two anonymous referees for their valuable comments.\n\n

Submitted - 1208.1732.pdf

", "abstract": "The cube graph Q_n is the skeleton of the n-dimensional cube. It is an n-regular graph on 2^n vertices. The Ramsey number r(Q_n, K_s) is the minimum N such that every graph of order N contains the cube graph Q_n or an independent set of order s. In 1983, Burr and Erd\u0151s asked whether the simple lower bound r(Q_n, K_s) \u2265 (s\u22121)(2^(n) \u2212 1) + 1 is tight for s fixed and n sufficiently large. We make progress on this problem, obtaining the first upper bound which is within a constant factor of the lower bound.", "date": "2016-02", "date_type": "published", "publication": "Combinatorica", "volume": "36", "number": "1", "publisher": "Springer", "pagerange": "37-70", "id_number": "CaltechAUTHORS:20190812-162959158", "issn": "0209-9683", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959158", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Samsung" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-014-3010-x", "primary_object": { "basename": "1208.1732.pdf", "url": "https://authors.library.caltech.edu/records/q1vhm-qth77/files/1208.1732.pdf" }, "pub_year": "2016", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/fj57k-akh29", "eprint_id": 65019, "eprint_status": "archive", "datestamp": "2023-08-20 10:07:00", "lastmod": "2026-04-02 06:04:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hainzl-C", "name": { "family": "Hainzl", "given": "Christian" } }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } }, { "id": "Solovej-J-P", "name": { "family": "Solovej", "given": "Jan Philip" } } ] }, "title": "The External Field Dependence of the BCS Critical Temperature", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 1 November 2014; Accepted: 15 September 2015; Published online: 12 December 2015. \n\nThe authors are grateful to I. M. Sigal for useful discussions. Financial support from the US National Science Foundation through Grants PHY-1347399 and DMS-1363432 (R.L.F.), from the Danish council for independent research and from ERC Advanced Grant 321029 (J.P.S.) is acknowledged.\n\n

Published - art_10.1007_s00220-015-2526-2.pdf

Submitted - 1410.2352v1.pdf

", "abstract": "We consider the Bardeen\u2013Cooper\u2013Schrieffer free energy functional for particles interacting via a two-body potential on a microscopic scale and in the presence of weak external fields varying on a macroscopic scale. We study the influence of the external fields on the critical temperature. We show that in the limit where the ratio between the microscopic and macroscopic scale tends to zero, the next to leading order of the critical temperature is determined by the lowest eigenvalue of the linearization of the Ginzburg\u2013Landau equation.", "date": "2016-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "342", "number": "1", "publisher": "Springer", "pagerange": "189-216", "id_number": "CaltechAUTHORS:20160303-112827308", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160303-112827308", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Danish Council for Independent Research" }, { "agency": "European Research Council (ERC)", "grant_number": "321029" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-015-2526-2", "primary_object": { "basename": "1410.2352v1.pdf", "url": "https://authors.library.caltech.edu/records/fj57k-akh29/files/1410.2352v1.pdf" }, "related_objects": [ { "basename": "art_10.1007_s00220-015-2526-2.pdf", "url": "https://authors.library.caltech.edu/records/fj57k-akh29/files/art_10.1007_s00220-015-2526-2.pdf" } ], "pub_year": "2016", "author_list": "Frank, Rupert L.; Hainzl, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/985j8-0fe05", "eprint_id": 97845, "eprint_status": "archive", "datestamp": "2023-08-20 10:09:47", "lastmod": "2026-04-02 23:37:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Stein-Maya", "name": { "family": "Stein", "given": "Maya" } } ] }, "title": "Monochromatic Cycle Partitions in Local Edge Colorings", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 Wiley. \n\nIssue online 08 December 2015; version of record online 14 April 2015; manuscript revised 28 January 2015; manuscript received 24 March 2014. \n\nThe first author is supported by a Royal Society University Research Fellowship and the second author is supported by the Fondecyt grants 11090141 and 1140766.\n\n

Submitted - 1403.5975.pdf

", "abstract": "An edge coloring of a graph is said to be an r\u2010local coloring if the edges incident to any vertex are colored with at most r colors. Generalizing a result of Bessy and Thomass\u00e9, we prove that the vertex set of any 2\u2010locally colored complete graph may be partitioned into two disjoint monochromatic cycles of different colors. Moreover, for any natural number r, we show that the vertex set of any r\u2010locally colored complete graph may be partitioned into O(r^(2) log r) disjoint monochromatic cycles. This generalizes a result of Erd\u0151s, Gy\u00e1rf\u00e1s, and Pyber.", "date": "2016-02", "date_type": "published", "publication": "Journal of Graph Theory", "volume": "81", "number": "2", "publisher": "Wiley", "pagerange": "134-145", "id_number": "CaltechAUTHORS:20190812-163001038", "issn": "0364-9024", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001038", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (FONDECYT)", "grant_number": "11090141" }, { "agency": "Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (FONDECYT)", "grant_number": "1140766" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/jgt.21867", "primary_object": { "basename": "1403.5975.pdf", "url": "https://authors.library.caltech.edu/records/985j8-0fe05/files/1403.5975.pdf" }, "pub_year": "2016", "author_list": "Conlon, David and Stein, Maya" }, { "id": "https://authors.library.caltech.edu/records/msyc3-sq590", "eprint_id": 66672, "eprint_status": "archive", "datestamp": "2023-08-20 09:45:42", "lastmod": "2026-03-09 21:37:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcinek-J", "name": { "family": "Marcinek", "given": "J." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "M." }, "orcid": "0000-0002-2045-2907" } ] }, "title": "KMS weights on higher rank buildings", "ispublished": "pub", "full_text_status": "public", "keywords": "higher rank buildings, KMS states and weights, C*-algebras", "note": "\u00a9 2016 Pleiades Publishing, Ltd. \n\nThe first author was supported by a Summer Undergraduate Research Fellowship at Caltech. The second author is supported by NSF grants DMS-1007207, DMS-1201512, PHY-1205440.\n\n

Submitted - 1506.08906v1.pdf

", "abstract": "We extend some of the results of Carey-Marcolli-Rennie on modular index invariants of Mumford curves to the case of higher rank buildings. We discuss notions of KMS weights on buildings, that generalize the construction of graph weights over graph C*-algebras.", "date": "2016-01", "date_type": "published", "publication": "P-Adic Numbers, Ultrametric Analysis, and Applications", "volume": "8", "number": "1", "publisher": "Springer", "pagerange": "45-67", "id_number": "CaltechAUTHORS:20160505-082023887", "issn": "2070-0466", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-082023887", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/S2070046616010040", "primary_object": { "basename": "1506.08906v1.pdf", "url": "https://authors.library.caltech.edu/records/msyc3-sq590/files/1506.08906v1.pdf" }, "pub_year": "2016", "author_list": "Marcinek, J. and Marcolli, M." }, { "id": "https://authors.library.caltech.edu/records/fg8py-9nx18", "eprint_id": 64419, "eprint_status": "archive", "datestamp": "2023-08-20 09:43:19", "lastmod": "2026-03-10 00:01:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Ryan M." } }, { "id": "Shirley-W-E", "name": { "family": "Shirley", "given": "Wilbur E." } }, { "id": "Natu-S-S", "name": { "family": "Natu", "given": "Stefan S." }, "orcid": "0000-0002-2249-6364" } ] }, "title": "Anomalous supersolidity in a weakly interacting dipolar Bose mixture on a square lattice", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 American Physical Society.\n\nReceived 24 September 2015; published 19 January 2016.\n\nWe acknowledge B. M. Anderson for helpful conversations in the early stages of this work. R.W. acknowledges partial support from the Office of Naval Research under Grant No. N00014115WX01372, and from the National Science Foundation under Grant No. PHY-1516421. W.S. acknowledges support from a JQI-PFC Seed Grant. S.N. thanks the LPS-CMTC, LPS-MPO-CMTC, JQI-NSF-PFC, and ARO-MURI for support.\n\n

Published - PhysRevA.93.011605.pdf

Submitted - 1509.07488v2.pdf

", "abstract": "We calculate the mean-field phase diagram of a zero-temperature, binary Bose mixture on a square optical lattice, where one species possesses a non-negligible dipole moment. Remarkably, this system exhibits supersolidity for anomalously weak dipolar interaction strengths, which are readily accessible with current experimental capabilities. The supersolid phases are robust, in that they occupy large regions in the parameter space. Further, we identify a first-order quantum phase transition between supersolid and superfluid phases. Our results demonstrate the rich features of the dipolar Bose mixture, and suggest that this system is well suited for exploring supersolidity in the experimental setting.", "date": "2016-01", "date_type": "published", "publication": "Physical Review A", "volume": "93", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 011605", "id_number": "CaltechAUTHORS:20160211-105020809", "issn": "2469-9926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160211-105020809", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014115WX01372" }, { "agency": "NSF", "grant_number": "PHY-1516421" }, { "agency": "University of Maryland" }, { "agency": "Army Research Office (ARO)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevA.93.011605", "primary_object": { "basename": "1509.07488v2.pdf", "url": "https://authors.library.caltech.edu/records/fg8py-9nx18/files/1509.07488v2.pdf" }, "related_objects": [ { "basename": "PhysRevA.93.011605.pdf", "url": "https://authors.library.caltech.edu/records/fg8py-9nx18/files/PhysRevA.93.011605.pdf" } ], "pub_year": "2016", "author_list": "Wilson, Ryan M.; Shirley, Wilbur E.; et al." }, { "id": "https://authors.library.caltech.edu/records/f5eey-eyb55", "eprint_id": 64761, "eprint_status": "archive", "datestamp": "2023-08-20 09:44:09", "lastmod": "2026-03-09 02:30:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frenkel-E", "name": { "family": "Frenkel", "given": "Edward" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Teschner-J", "name": { "family": "Teschner", "given": "J\u00f6rg" } } ] }, "title": "Surface operators and separation of variables", "ispublished": "pub", "full_text_status": "public", "keywords": "Brane Dynamics in Gauge Theories, Supersymmetric gauge theory", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: September 19, 2015; Accepted: December 10, 2015; Published: January 29, 2016. \n\nArticle funded by SCOAP3. \n\nWe would like to thank D. Gaiotto, K. Maruyoshi, and N. Nekrasov for useful discussions and comments. The research of E.F. was supported by the NSF grants DMS-1160328 and DMS-1201335. The work of S.G. is funded in part by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.\n\n

Published - art_10.1007_JHEP01_2016_179.pdf

Submitted - 1506.07508v1.pdf

", "abstract": "Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N = 2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one type of surface operators the corresponding 2d theory is the WZW model, and for another type \u2014 the Liouville theory with insertions of extra degenerate fields. We show that these two 4d theories with surface operators exhibit an IR duality, which reflects the known relation (the so-called separation of variables) between the conformal blocks of the WZW model and the Liouville theory. Furthermore, we trace this IR duality to a brane creation construction relating systems of M5 and M2 branes in M-theory. Finally, we show that this duality may be expressed as an explicit relation between the generating functions for the changes of variables between natural sets of Darboux coordinates on the Hitchin moduli space.", "date": "2016-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 179", "id_number": "CaltechAUTHORS:20160225-125012315", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160225-125012315", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "SCOAP3" }, { "agency": "NSF", "grant_number": "DMS-1160328" }, { "agency": "NSF", "grant_number": "DMS-1201335" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP01(2016)179", "primary_object": { "basename": "art_10.1007_JHEP01_2016_179.pdf", "url": "https://authors.library.caltech.edu/records/f5eey-eyb55/files/art_10.1007_JHEP01_2016_179.pdf" }, "related_objects": [ { "basename": "1506.07508v1.pdf", "url": "https://authors.library.caltech.edu/records/f5eey-eyb55/files/1506.07508v1.pdf" } ], "pub_year": "2016", "author_list": "Frenkel, Edward; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/822wv-zxz21", "eprint_id": 55717, "eprint_status": "archive", "datestamp": "2023-08-20 09:39:55", "lastmod": "2026-03-09 02:34:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Counting RG flows", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Renormalization Group", "note": "\u00a9 2016 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: September 2, 2015; Accepted: December 20, 2015; Published: January 5, 2016. \n\nI would like to thank N. Deger, L. Dixon, K. Intriligator, V. Lysov, Yu Nakayama, H. Ooguri, L. Rastelli, D. Roggenkamp, E. Sezgin, A. Shapere, M. Strassler, R. Sundrum, D. Xie, and W. Yan for useful discussions and comments. It is also a pleasure to thank the organizers and participants of the conference \"Progress and Application of Modern QFT\" in Aspen Feb. 16-21, 2015, where I had the opportunity to discuss the results presented here. This work is funded by the DOE Grant DE-SC0011632 and the Walter Burke Institute for Theoretical Physics.\n\n

Published - art_10.1007_JHEP01_2016_020.pdf

Submitted - 1503.01474v1__1_.pdf

", "abstract": "Interpreting renormalization group flows as solitons interpolating between different fixed points, we ask various questions that are normally asked in soliton physics but not in renormalization theory. Can one count RG flows? Are there different \"topological sectors\" for RG flows? What is the moduli space of an RG flow, and how does it compare to familiar moduli spaces of (supersymmetric) dowain walls? Analyzing these questions in a wide variety of contexts \u2014 from counting RG walls to AdS/CFT correspondence \u2014 will not only provide favorable answers, but will also lead us to a unified general framework that is powerful enough to account for peculiar RG flows and predict new physical phenomena. Namely, using Bott's version of Morse theory we relate the topology of conformal manifolds to certain properties of RG flows that can be used as precise diagnostics and \"topological obstructions\" for the strong form of the C-theorem in any dimension. Moreover, this framework suggests a precise mechanism for how the violation of the strong C-theorem happens and predicts \"phase transitions\" along the RG flow when the topological obstruction is non-trivial. Along the way, we also find new conformal manifolds in well-known 4d CFT's and point out connections with the superconformal index and classifying spaces of global symmetry groups.", "date": "2016-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2016", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 020", "id_number": "CaltechAUTHORS:20150311-193040484", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150311-193040484", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2015-10", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP01(2016)020", "primary_object": { "basename": "1503.01474v1__1_.pdf", "url": "https://authors.library.caltech.edu/records/822wv-zxz21/files/1503.01474v1__1_.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP01_2016_020.pdf", "url": "https://authors.library.caltech.edu/records/822wv-zxz21/files/art_10.1007_JHEP01_2016_020.pdf" } ], "pub_year": "2016", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/d3khd-chq05", "eprint_id": 71959, "eprint_status": "archive", "datestamp": "2023-08-20 09:47:48", "lastmod": "2026-03-10 00:00:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bowen-L", "name": { "family": "Bowen", "given": "Lewis" } }, { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Property (T) and the Furstenberg Entropy of Nonsingular Actions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 American Mathematical Society. \n\nReceived by the editors June 30, 2014 and, in revised form, December 1, 2014. Article electronically published on July 24, 2015. \n\nThe first author was supported in part by NSF grant DMS-0968762, NSF CAREER Award DMS-0954606 and BSF grant 2008274. \n\nThe second author was supported by the European Research Council, grant 239885.\n\n

Submitted - 1406.4488.pdf

", "abstract": "We establish a new characterization of property (T) in terms of the Furstenberg entropy of nonsingular actions. Given any generating measure \u03bc on a countable group G, A. Nevo showed that a necessary condition for G to have property (T) is that the Furstenberg \u03bc-entropy values of the ergodic, properly nonsingular G-actions are bounded away from zero. We show that this is also a sufficient condition.", "date": "2016-01", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "144", "number": "1", "publisher": "American Mathematical Society", "pagerange": "31-39", "id_number": "CaltechAUTHORS:20161111-141359999", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-141359999", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968762" }, { "agency": "NSF", "grant_number": "DMS-0954606" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2008274" }, { "agency": "European Research Council (ERC)", "grant_number": "239885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/proc/12685", "primary_object": { "basename": "1406.4488.pdf", "url": "https://authors.library.caltech.edu/records/d3khd-chq05/files/1406.4488.pdf" }, "pub_year": "2016", "author_list": "Bowen, Lewis; Hartman, Yair; et al." }, { "id": "https://authors.library.caltech.edu/records/wbx0k-ht054", "eprint_id": 77071, "eprint_status": "archive", "datestamp": "2023-08-20 09:37:28", "lastmod": "2026-03-09 02:13:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Sabin-J", "name": { "family": "Sabin", "given": "Julien" } } ] }, "title": "The Stein-Tomas inequality in trace ideals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015-2016 Institut des hautes \u00e9tudes scientifiques & Centre de math\u00e9matiques Laurent Schwartz, \u00c9cole polytechnique. Cet article est mis \u00e0 disposition selon les termes de la licence Creative Commons attribution \u2013 pas de modification 3.0 France.\nhttp://creativecommons.org/licenses/by-nd/3.0/fr/ \n\nLemma 2 and Proposition 3 are new results and do not appear anywhere else. They have been obtained in collaboration with Mathieu Lewin.\n\n

Published - SLSEDP_2015-2016____A15_0.pdf

Submitted - 1609.08388.pdf

", "abstract": "The goal of this review is to explain some recent results [5] regarding generalizations of the Stein-Tomas (and Strichartz) inequalities to the context of trace ideals (Schatten spaces).", "date": "2016", "date_type": "published", "publication": "S\u00e9minaire Laurent Schwartz - EDP et applications", "volume": "15", "publisher": "Center for diffusion of academic mathematical journals", "pagerange": "Art. No. 12", "id_number": "CaltechAUTHORS:20170428-154841451", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170428-154841451", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.5802/slsedp.92", "primary_object": { "basename": "1609.08388.pdf", "url": "https://authors.library.caltech.edu/records/wbx0k-ht054/files/1609.08388.pdf" }, "related_objects": [ { "basename": "SLSEDP_2015-2016____A15_0.pdf", "url": "https://authors.library.caltech.edu/records/wbx0k-ht054/files/SLSEDP_2015-2016____A15_0.pdf" } ], "pub_year": "2016", "author_list": "Frank, Rupert L. and Sabin, Julien" }, { "id": "https://authors.library.caltech.edu/records/1dh85-bt711", "eprint_id": 68904, "eprint_status": "archive", "datestamp": "2023-08-20 09:35:28", "lastmod": "2026-03-07 04:15:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Daniel Gorenstein, 1923-1992 - A Biographical Memoir by\n Michael Aschbacher", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 National Academy of Sciences.\n\n

Published - gorenstein-daniel.pdf

", "abstract": "Daniel Gorenstein was one of the most influential figures\nin mathematics during the last few decades of the 20th\ncentury. In particular, he was a primary architect of the\nclassification of the finite simple groups. \n\nDuring his career Gorenstein received many of the honors\nthat the mathematical community reserves for its highest\nachievers. He was awarded the Steele Prize for mathematical\nexposition by the American Mathematical Society in\n1989; he delivered the plenary address at the International\nCongress of Mathematicians in Helsinki, Finland, in 1978;\nand he was the Colloquium Lecturer for the American\nMathematical Society in 1984. He was also a member of\nthe National Academy of Sciences and of the American\nAcademy of Arts and Sciences. \n\nGorenstein was the Jacqueline B. Lewis Professor of\nMathematics at Rutgers University and the founding director of its Center for Discrete\nMathematics and Theoretical Computer Science. He served as chairman of the university's\nmathematics department from 1975 to 1982, and together with his predecessor, Ken\nWolfson, he oversaw a dramatic improvement in the quality of mathematics at Rutgers.", "date": "2016", "date_type": "published", "publication": "Biographical Memoirs", "publisher": "National Academy of Sciences", "pagerange": "1-17", "id_number": "CaltechAUTHORS:20160708-073018195", "issn": "0077-2933", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160708-073018195", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "gorenstein-daniel.pdf", "url": "https://authors.library.caltech.edu/records/1dh85-bt711/files/gorenstein-daniel.pdf" }, "pub_year": "2016", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/sdhnc-fgy26", "eprint_id": 79023, "eprint_status": "archive", "datestamp": "2023-08-20 09:37:49", "lastmod": "2026-03-09 21:44:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Ni-Xiang", "name": { "family": "Ni", "given": "Xiang" } } ] }, "title": "Rota-Baxter algebras, singular hypersurfaces, and renormalization on Kausz compactifications", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2016 Worldwide Center of Mathematics LLC. \n\nReceived: 18 August 2014. Received in revised form: 21 July 2016. \n\nThe authors are very grateful to the anonymous referee for many very detailed and helpful comments and suggestions that greatly improved the paper. The first author was partially supported by NSF grants DMS-1007207, DMS-1201512, and PHY-1205440.\n\n

Submitted - 1408.3754.pdf

", "abstract": "We consider Rota-Baxter algebras of meromorphic forms with poles along a (singular) hypersurface in a smooth projective variety and the associated Birkhoff factorization for algebra homomorphisms from a commutative Hopf algebra. In the case of a normal crossings divisor, the Rota-Baxter structure simplifies considerably and the factorization becomes a simple pole subtraction. We apply this formalism to the unrenormalized momentum space Feynman amplitudes, viewed as (divergent) integrals in the complement of the determinant hypersurface. We lift the integral to the Kausz compactification of the general linear group, whose boundary divisor is normal crossings. We show that the Kausz compactification is a Tate motive and that the boundary divisor and the divisor that contains the boundary of the chain of integration are mixed Tate configurations. The regularization of the integrals that we obtain differs from the usual renormalization of physical Feynman amplitudes, and in particular it may give mixed Tate periods in some cases that have non-mixed Tate contributions when computed with other renormalization methods.", "date": "2016", "date_type": "published", "publication": "Journal of Singularities", "volume": "15", "publisher": "Worldwide Center of Mathematics", "pagerange": "80-117", "id_number": "CaltechAUTHORS:20170712-142940847", "issn": "1949-2006", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-142940847", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.5427/jsing.2016.15e", "primary_object": { "basename": "1408.3754.pdf", "url": "https://authors.library.caltech.edu/records/sdhnc-fgy26/files/1408.3754.pdf" }, "pub_year": "2016", "author_list": "Marcolli, Matilde and Ni, Xiang" }, { "id": "https://authors.library.caltech.edu/records/jtjgb-ezj24", "eprint_id": 66030, "eprint_status": "archive", "datestamp": "2023-08-20 09:34:34", "lastmod": "2026-03-09 21:44:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Noncommutative numerical motives, Tannakian structures, and motivic Galois groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Noncommutative motives, periodic cyclic homology, Tannakian formalism, motivic Galois groups", "note": "\u00a9 2016 EMS Publishing House. \n\nThe first named author was supported by the NSF grants DMS-0901221 and DMS-1007207. \n\nThe second named author was supported by the J.H. and E.V. Wade award.\n\n

Submitted - 1110.2438v1.pdf

", "abstract": "In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum(k)_F of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum(k)_F is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined symmetric monoidal functor HP* on the category of noncommutative Chow motives. This allows us to introduce the correct noncommutative analogues C_(NC) and D_(NC) of Grothendieck's standard conjectures C and D. Assuming C_(NC), we prove that NNum(k)_F can be made into a Tannakian category NNum (k)_F by modifying its symmetry isomorphism constraints. By further assuming D_(NC), we neutralize the Tannakian category Num (k)_F using HP*. Via the (super-)Tannakian formalism, we then obtain well-defined noncommutative motivic Galois (super-)groups. Finally, making use of Deligne-Milne's theory of Tate triples, we construct explicit morphisms relating these noncommutative motivic Galois (super-)groups with the classical ones as suggested by Kontsevich.", "date": "2016", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "18", "number": "3", "publisher": "European Mathematical Society", "pagerange": "623-655", "id_number": "CaltechAUTHORS:20160408-132805755", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160408-132805755", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "J.H. and E.V. Wade Award" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JEMS/598", "primary_object": { "basename": "1110.2438v1.pdf", "url": "https://authors.library.caltech.edu/records/jtjgb-ezj24/files/1110.2438v1.pdf" }, "pub_year": "2016", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/rys2j-awx43", "eprint_id": 110833, "eprint_status": "archive", "datestamp": "2023-08-20 09:23:11", "lastmod": "2026-04-04 20:46:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Tropicalization of the moduli space of stable maps", "ispublished": "pub", "full_text_status": "public", "keywords": "Tropicalization \u00b7 Moduli space \u00b7 Stable map \u00b7 Continuity \u00b7 Polyhedrality \u00b7 Berkovich space \u00b7 Balancing condition \u00b7 Vanishing cycle \u00b7 Quantifier elimination \u00b7 Rigid subanalytic set", "note": "\u00a9 Springer-Verlag Berlin Heidelberg 2015. \n\nReceived 24 March 2015. Accepted 06 July 2015. Published 31 July 2015. Issue Date: December 2015. \n\nI am very grateful to Maxim Kontsevich and Antoine Chambert-Loir for inspirations and support. Special thanks to Antoine Ducros from whom I learned model theory and its applications to tropical geometry. I appreciate valuable discussions with Vladimir Berkovich, Pierrick Bousseau, Ilia Itenberg, Fran\u00e7ois Loeser, Florent Martin, Johannes Nicaise, Sam Payne and Michael Temkin. Comments given by the referees helped greatly improve the paper.\n\n

Accepted Version - 1407.8444.pdf

", "abstract": "Let X be an algebraic variety and let S be a tropical variety associated to X. We study the tropicalization map from the moduli space of stable maps into X to the moduli space of tropical curves in S. We prove that it is a continuous map and that its image is compact and polyhedral. Loosely speaking, when we deform algebraic curves in X, the associated tropical curves in S deform continuously; moreover, the locus of realizable tropical curves inside the space of all tropical curves is compact and polyhedral. Our main tools are Berkovich spaces, formal models, balancing conditions, vanishing cycles and quantifier elimination for rigid subanalytic sets.", "date": "2015-12", "date_type": "published", "publication": "Mathematische Zeitschrift", "volume": "281", "number": "3-4", "publisher": "Springer Verlag", "pagerange": "1035-1059", "id_number": "CaltechAUTHORS:20210914-164412973", "issn": "0025-5874", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164412973", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00209-015-1519-3", "primary_object": { "basename": "1407.8444.pdf", "url": "https://authors.library.caltech.edu/records/rys2j-awx43/files/1407.8444.pdf" }, "pub_year": "2015", "author_list": "Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/4vkp6-yvp72", "eprint_id": 87370, "eprint_status": "archive", "datestamp": "2023-08-22 16:59:01", "lastmod": "2026-04-04 20:24:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" }, { "id": "Vicol-Vlad", "name": { "family": "Vicol", "given": "Vlad" } } ] }, "title": "H\u00f6lder Continuous Solutions of Active Scalar Equations", "ispublished": "pub", "full_text_status": "public", "keywords": "Active scalar equations; h-principle; Convex integration; Onsager conjecture", "note": "\u00a9 2015 Springer International Publishing AG. \n\nReceived: 1 June 2015; Accepted: 3 November 2015; Published online: 14 November 2015. \n\nThe work of P.I. was in part supported by the NSF Postdoctoral Fellowship DMS-1402370, while the work of V.V. was in part supported by the NSF grant DMS-1348193 and an Alfred P. Sloan Fellowship.\n\n

Submitted - 1405.7656.pdf

", "abstract": "We consider active scalar equations \u2202_t\u03b8 + \u2207 \u22c5 (u\u03b8)=0, where u = T[\u03b8] is a divergence-free velocity field, and T is a Fourier multiplier operator with symbol m. We prove that when m is not an odd function of frequency, there are nontrivial, compactly supported solutions weak solutions, with H\u00f6lder regularity C^(1/9\u2212)_(t,x). In fact, every integral conserving scalar field can be approximated in D\u2032 by such solutions, and these weak solutions may be obtained from arbitrary initial data. We also show that when the multiplier m is odd, weak limits of solutions are solutions, so that the h-principle for odd active scalars may not be expected.", "date": "2015-12", "date_type": "published", "publication": "Annals of PDE", "volume": "1", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 2", "id_number": "CaltechAUTHORS:20180627-075939255", "issn": "2524-5317", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180627-075939255", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1402370" }, { "agency": "NSF", "grant_number": "DMS-1348193" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s40818-015-0002-0", "primary_object": { "basename": "1405.7656.pdf", "url": "https://authors.library.caltech.edu/records/4vkp6-yvp72/files/1405.7656.pdf" }, "pub_year": "2015", "author_list": "Isett, Philip and Vicol, Vlad" }, { "id": "https://authors.library.caltech.edu/records/0tsj5-z6170", "eprint_id": 51661, "eprint_status": "archive", "datestamp": "2023-08-20 09:12:14", "lastmod": "2026-04-04 20:13:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Thorngren-R", "name": { "family": "Thorngren", "given": "Ryan" }, "orcid": "0000-0001-9433-3399" }, { "id": "Turzillo-A", "name": { "family": "Turzillo", "given": "Alex" }, "orcid": "0000-0003-4293-4293" }, { "id": "Wang-Zitao", "name": { "family": "Wang", "given": "Zitao" }, "orcid": "0000-0002-2326-2674" } ] }, "title": "Fermionic Symmetry Protected Topological Phases and Cobordisms", "ispublished": "pub", "full_text_status": "public", "keywords": "Topological Field Theories, Effective field theories, Topological States of Matter", "note": "\u00a9 2015 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: August 18, 2015; Accepted: November 25, 2015; Published: December 10, 2015. \n\nR.T. would like to thank Xie Chen for patiently answering his questions and Rob Kirby for an enlightening discussion. A. K. would like to acknowledge conversations with Alexei Kitaev and Zhengcheng Gu. The work of A.K., A.T., and Z.W. was supported in part DOE grant DE-FG02-92ER40701.\n\n

Published - 10.1007_2FJHEP12_2015_052.pdf

Submitted - 1406.7329v1.pdf

", "abstract": "It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with Z_2 symmetry, where Z_2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D \u2264 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.", "date": "2015-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2015", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 052", "id_number": "CaltechAUTHORS:20141112-123606275", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141112-123606275", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2014-163", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP12(2015)052", "primary_object": { "basename": "10.1007_2FJHEP12_2015_052.pdf", "url": "https://authors.library.caltech.edu/records/0tsj5-z6170/files/10.1007_2FJHEP12_2015_052.pdf" }, "related_objects": [ { "basename": "1406.7329v1.pdf", "url": "https://authors.library.caltech.edu/records/0tsj5-z6170/files/1406.7329v1.pdf" } ], "pub_year": "2015", "author_list": "Kapustin, Anton; Thorngren, Ryan; et al." }, { "id": "https://authors.library.caltech.edu/records/8q30x-n0632", "eprint_id": 64898, "eprint_status": "archive", "datestamp": "2023-08-22 16:57:57", "lastmod": "2026-04-04 05:17:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Port-A", "name": { "family": "Port", "given": "Alexander" } } ] }, "title": "Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Lie algebras; pre-Lie operators; Graph Languages; Production rules; Feynman graphs", "note": "\u00a9 2015 Springer Basel. \n\nReceived: 11 March 2015; Accepted: 14 May 2015; Published online: 13 August 2015. \n\nThe first author is supported by NSF Grants DMS-1007207, DMS-1201512, PHY-1205440. The second author was supported by a Summer Undergraduate Research Fellowship at Caltech.\n\n

Submitted - 1502.07796v1.pdf

", "abstract": "Graph grammars extend the theory of formal languages in order to model distributed parallelism in theoretical computer science. We show here that to certain classes of context-free and context-sensitive graph grammars one can associate a Lie algebra, whose structure is reminiscent of the insertion Lie algebras of quantum field theory. We also show that the Feynman graphs of quantum field theories are graph languages generated by a theory dependent graph grammar.", "date": "2015-12", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "9", "number": "4", "publisher": "Springer Verlag", "pagerange": "391-408", "id_number": "CaltechAUTHORS:20160301-093947103", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160301-093947103", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-015-0236-y", "primary_object": { "basename": "1502.07796v1.pdf", "url": "https://authors.library.caltech.edu/records/8q30x-n0632/files/1502.07796v1.pdf" }, "pub_year": "2015", "author_list": "Marcolli, Matilde and Port, Alexander" }, { "id": "https://authors.library.caltech.edu/records/6d62w-ky383", "eprint_id": 63715, "eprint_status": "archive", "datestamp": "2023-08-20 09:08:06", "lastmod": "2026-04-04 21:00:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model", "ispublished": "pub", "full_text_status": "public", "keywords": "liquid drop model, existence of minimizer, compactness", "note": "\u00a9 2015 Rupert L. Frank and Elliott H. Lieb. \n\nReceived by the editors March 2, 2015; accepted for publication (in revised form) September 17, 2015; published electronically November 19, 2015. \n\nThe work of this author was partially supported by U.S. National Science Foundation PHY-1347399 and DMS-1363432. \n\nThe work of this author was partially supported by U.S. National Science Foundation PHY-1265118. \n\nNote added in proof. After our paper was submitted, a preprint by Kn\u00fcpfer, Muratov, and Novaga appeared [KMN] with similar results but with a different methodology. Some of those results had been mentioned by Muratov at the Fields Center meeting in 2014. We are grateful to C. Muratov for helpful remarks on a previous version of this paper.\n\n

Published - 15m1010658.pdf

Submitted - 1503.00192v1.pdf

", "abstract": "The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set \u03a9 \u2282 \u211d^3 with given volume A that minimizes the sum of its surface area and its Coulomb self energy. A ball minimizes the former and maximizes the latter, but the conjecture is that a ball is always a minimizer---when there is a minimizer. Even the existence of minimizers for this interesting geometric problem has not been shown in general. We prove the existence of the absolute minimizer (over all A) of the energy divided by A (the binding energy per particle). A second result of our work is a general method for showing the existence of optimal sets in geometric minimization problems, which we call the \"method of the missing mass.\" A third point is the extension of the pulling back compactness lemma [E. H. Lieb, Invent. Math., 74 (1983), pp. 441--448] from W^1,p to BV.", "date": "2015-11-19", "date_type": "published", "publication": "SIAM Journal on Mathematical Analysis", "volume": "47", "number": "6", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "4436-4450", "id_number": "CaltechAUTHORS:20160115-123530660", "issn": "0036-1410", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160115-123530660", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "NSF", "grant_number": "PHY-1265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/15M1010658", "primary_object": { "basename": "1503.00192v1.pdf", "url": "https://authors.library.caltech.edu/records/6d62w-ky383/files/1503.00192v1.pdf" }, "related_objects": [ { "basename": "15m1010658.pdf", "url": "https://authors.library.caltech.edu/records/6d62w-ky383/files/15m1010658.pdf" } ], "pub_year": "2015", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/r5egw-tmm70", "eprint_id": 97811, "eprint_status": "archive", "datestamp": "2023-08-22 16:47:34", "lastmod": "2026-04-04 22:14:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Ferber-Asaf", "name": { "family": "Ferber", "given": "Asaf" } }, { "id": "Nenadov-Rajko", "name": { "family": "Nenadov", "given": "Rajko" } }, { "id": "\u0160kori\u0107-Nemanja", "name": { "family": "\u0160kori\u0107", "given": "Nemanja" } } ] }, "title": "Almost-spanning universality in random graphs (Extended abstract)", "ispublished": "pub", "full_text_status": "public", "keywords": "Random graphs; Universality; Bounded-degree graphs", "note": "\u00a9 2015 Elsevier. \n\nAvailable online 12 November 2015. \n\nResearch supported by a Royal Society University Research Fellowship.\n\n

Submitted - 1503.05612.pdf

", "abstract": "A graph G is said to be \u210b(n, \u0394)-universal if it contains every graph on n vertices with maximum degree at most \u0394. It is known that for any \u03b5 > 0 and any natural number \u0394 there exists c > 0 such that the random graph G(n, p) is asymptotically almost surely \u210b((1 - \u03b5)n, \u0394)-universal for p \u2265 c(log n/n)^(1/\u0394). Bypassing this natural boundary \u0394 \u2265 3, we show that for the same conclusion holds when [equation; see abstract in PDF for details].", "date": "2015-11", "date_type": "published", "publication": "Electronic Notes in Discrete Mathematics", "volume": "49", "publisher": "Elsevier", "pagerange": "203-211", "id_number": "CaltechAUTHORS:20190812-162957531", "issn": "1571-0653", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957531", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.endm.2015.06.030", "primary_object": { "basename": "1503.05612.pdf", "url": "https://authors.library.caltech.edu/records/r5egw-tmm70/files/1503.05612.pdf" }, "pub_year": "2015", "author_list": "Conlon, David; Ferber, Asaf; et al." }, { "id": "https://authors.library.caltech.edu/records/fcebq-12z86", "eprint_id": 61224, "eprint_status": "archive", "datestamp": "2023-08-22 16:45:01", "lastmod": "2026-04-04 20:31:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tedeschi-N", "name": { "family": "Tedeschi", "given": "Nicolas" } } ] }, "title": "Entropy algebras and Birkhoff factorization", "ispublished": "pub", "full_text_status": "public", "keywords": "Min-plus algebras; Information theoretic entropies; Rota\u2013Baxter algebras; Birkhoff factorization; Witt rings; Zeta functions", "note": "\u00a9 2015 Elsevier B.V. \n\nReceived 23 December 2014; Accepted 14 July 2015; Available online 22 July 2015. \n\nThe first author is supported by NSF grants DMS-1007207, DMS-1201512, PHY-1205440. The second author was supported by a Summer Undergraduate Research Fellowship at Caltech and by the Rose Hills Foundation.\n\n

Submitted - 1412.0247v1.pdf

", "abstract": "We develop notions of Rota\u2013Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.", "date": "2015-11", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "97", "publisher": "Elsevier", "pagerange": "243-265", "id_number": "CaltechAUTHORS:20151016-150705985", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151016-150705985", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Rose Hills Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2015.07.018", "primary_object": { "basename": "1412.0247v1.pdf", "url": "https://authors.library.caltech.edu/records/fcebq-12z86/files/1412.0247v1.pdf" }, "pub_year": "2015", "author_list": "Marcolli, Matilde and Tedeschi, Nicolas" }, { "id": "https://authors.library.caltech.edu/records/kz4x5-wm478", "eprint_id": 61188, "eprint_status": "archive", "datestamp": "2023-08-22 16:44:24", "lastmod": "2026-04-04 05:16:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dasu-S", "name": { "family": "Dasu", "given": "Shival" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Potts models with magnetic field: Arithmetic, geometry, and computation", "ispublished": "pub", "full_text_status": "public", "keywords": "Potts models with magnetic field; Constructible sheaves; Points over finite fields; Grothendieck ring of varieties; Euler characteristic; Computational complexity", "note": "\u00a9 2015 Elsevier B.V. \n\nReceived 13 January 2015; Received in revised form 21 May 2015; Accepted 19 June 2015; Available online 3 July 2015. \n\nThe first author was supported by a \"Summer Undergraduate Research Fellowship at Caltech\". The second author is supported by NSF grants DMS-1007207, DMS-1201512, PHY-1205440. The second author thanks Paolo Aluffi and Spencer Bloch for useful conversations.\n\n

Submitted - 1412.7925v2.pdf

", "abstract": "We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.", "date": "2015-11", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "97", "publisher": "Elsevier", "pagerange": "14-24", "id_number": "CaltechAUTHORS:20151015-160216557", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151015-160216557", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2015.06.018", "primary_object": { "basename": "1412.7925v2.pdf", "url": "https://authors.library.caltech.edu/records/kz4x5-wm478/files/1412.7925v2.pdf" }, "pub_year": "2015", "author_list": "Dasu, Shival and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/xknhb-dfc80", "eprint_id": 59449, "eprint_status": "archive", "datestamp": "2023-08-20 08:41:13", "lastmod": "2026-04-04 20:33:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakayama-Yu", "name": { "family": "Nakayama", "given": "Yu" }, "orcid": "0000-0002-1747-5147" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Bulk Locality and Boundary Creating Operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: August 7, 2015; Accepted: September 18, 2015; Published: October 19, 2015. \n\nWe thank Tadashi Takayanagi for discussion. This work is supported in part by U.S. DOE grant DE-SC0011632, by the Walter Burke Institute for Theoretical Physics, and by the Moore Center for Theoretical Cosmology and Physics at Caltech. The work of H.O. is also supported in part by the Simons Investigator Award, by the WPI Initiative of MEXT of Japan, by MEXT KAKENHI Grant Number 15H05896 and by JSPS Grant-in-Aid for Scientific Research C-26400240. He also thanks the hospitality of the Aspen Center for Physics, where this paper was completed. Y.N. is a Sherman-Fairchild Research Assistant Professor at Caltech. Though we did not attend the KITP programs, \"Quantum Gravity Foundations: UV to IR\" and \"Entanglement in Strongly-Correlated Quantum Matter\", we have been benefited by watching their recorded talks.\n\n

Published - JHEP114.pdf

Submitted - 1507.04130v1.pdf

", "abstract": "We formulate a minimum requirement for CFT operators to be localized in the dual AdS. In any spacetime dimensions, we show that a general solution to the requirement is a linear superposition of operators creating spherical boundaries in CFT, with the dilatation by the imaginary unit from their centers. This generalizes the recent proposal by Miyaji et al. for bulk local operators in the three dimensional AdS. We show that Ishibashi states for the global conformal symmetry in any dimensions and with the imaginary di-latation obey free field equations in AdS and that incorporating bulk interactions require their superpositions. We also comment on the recent proposals by Kabat et al., and by H. Verlinde.", "date": "2015-10-19", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2015", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 114", "id_number": "CaltechAUTHORS:20150812-140634734", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150812-140634734", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Caltech Moore Center for Theoretical Cosmology and Physics" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "15H05896" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "SCOAP3" } ] }, "other_numbering_system": { "items": [ { "id": "2015-037", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Moore-Center-for-Theoretical-Cosmology-and-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP10(2015)114", "primary_object": { "basename": "1507.04130v1.pdf", "url": "https://authors.library.caltech.edu/records/xknhb-dfc80/files/1507.04130v1.pdf" }, "related_objects": [ { "basename": "JHEP114.pdf", "url": "https://authors.library.caltech.edu/records/xknhb-dfc80/files/JHEP114.pdf" } ], "pub_year": "2015", "author_list": "Nakayama, Yu and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/1y3ee-5d087", "eprint_id": 60769, "eprint_status": "archive", "datestamp": "2023-08-20 08:21:29", "lastmod": "2026-04-04 21:35:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fan-Wentao", "name": { "family": "Fan", "given": "Wentao" } }, { "id": "Fathizadeh-F", "name": { "family": "Fathizadeh", "given": "Farzad" }, "orcid": "0000-0002-7863-4009" }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Spectral Action for Bianchi Type-IX Cosmological Models", "ispublished": "pub", "full_text_status": "public", "keywords": "Non-Commutative Geometry, Models of Quantum Gravity", "note": "\u00a9 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: June 30, 2015; Revised: August 21, 2015; Accepted: September 20, 2015; Published: October 13, 2015. \n\nThe first author is supported by a Summer Undergraduate Research Fellowship at Caltech. The third author is partially supported by NSF grants DMS-1201512 and PHY-1205440 and by the Perimeter Institute for Theoretical Physics.\n\n

Published - art_10.1007_JHEP10_2015_085.pdf

Submitted - 1506.06779v1.pdf

", "abstract": "A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors w_1(t), w_2(t), w)3(t), and their higher derivates with respect to time. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients a_0 ,a_2 ,a_4 of the spectral action by using heat kernel methods and parametric pseudodifferential calculus. An efficient method is devised for computing the Seeley-de Witt coefficients of a geometry by making use of Wodzicki's noncommutative residue, and it is confirmed that the method checks out for the cosmological model studied in this article. The advantages of the new method are discussed, which combined with symmetries of the Bianchi type-IX metric, yield an elegant proof of the rationality result.", "date": "2015-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2015", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 085", "id_number": "CaltechAUTHORS:20151005-140911430", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151005-140911430", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "SCOAP3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP10(2015)085", "primary_object": { "basename": "1506.06779v1.pdf", "url": "https://authors.library.caltech.edu/records/1y3ee-5d087/files/1506.06779v1.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP10_2015_085.pdf", "url": "https://authors.library.caltech.edu/records/1y3ee-5d087/files/art_10.1007_JHEP10_2015_085.pdf" } ], "pub_year": "2015", "author_list": "Fan, Wentao; Fathizadeh, Farzad; et al." }, { "id": "https://authors.library.caltech.edu/records/3em69-r7e42", "eprint_id": 56817, "eprint_status": "archive", "datestamp": "2023-08-22 16:24:57", "lastmod": "2026-04-04 21:22:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wu-Zhongtao", "name": { "family": "Wu", "given": "Zhongtao" } } ] }, "title": "Correction terms, Z_2-Thurston norm, and triangulations", "ispublished": "pub", "full_text_status": "public", "keywords": "Heegaard Floer homology; Correction terms; Z_2-Thurston norm; Layered-triangulations", "note": "\u00a9 2015 Elsevier B.V.\n\nReceived 5 December 2014;\nReceived in revised form 1 September 2015;\nAccepted 2 September 2015;\nAvailable online 15 September 2015.\n\nWe wish to thank Ian Agol, Danny Ruberman and Hyam Rubinstein for conversations which motivated this work. The first author was partially supported by NSF grant numbers DMS-1103976, DMS-1252992, and an Alfred P. Sloan Research Fellowship. The second author was partially supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (RGC Project No. CUHK24300714).\n\n

Submitted - 1410.5342v1.pdf

", "abstract": "We explicitly construct layered-triangulations for manifolds admitting a genus-one open book decomposition with connected binding. This construction gives an upper bound to the complexity of these manifolds. In a different direction, we show that the correction terms in Heegaard Floer homology give a lower bound to the genus of one-sided Heegaard splittings and the Z_2-Thurston norm. Using a result of Jaco\u2013Rubinstein\u2013Tillmann, this gives a lower bound to the complexity of certain closed 3-manifolds. We illustrate our theorems with some examples.", "date": "2015-10", "date_type": "published", "publication": "Topology and Its Applications", "volume": "194", "publisher": "Elsevier", "pagerange": "409-426", "id_number": "CaltechAUTHORS:20150421-115830502", "issn": "0166-8641", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115830502", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "NSF", "grant_number": "DMS-1252992" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Research Grants Council of the Hong Kong Special Administrative Region of China", "grant_number": "CUHK24300714" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.topol.2015.09.002", "primary_object": { "basename": "1410.5342v1.pdf", "url": "https://authors.library.caltech.edu/records/3em69-r7e42/files/1410.5342v1.pdf" }, "pub_year": "2015", "author_list": "Ni, Yi and Wu, Zhongtao" }, { "id": "https://authors.library.caltech.edu/records/7rtye-hre15", "eprint_id": 110836, "eprint_status": "archive", "datestamp": "2023-08-20 08:15:43", "lastmod": "2026-03-10 00:02:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "Balancing conditions in global tropical geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "balancing condition, tropical curve, Berkovich space, vanishing cycle", "note": "\u00a9 Association des Annales de l'institut Fourier, 2015. Attribution - Pas de Modification 3.0 France (CC BY-ND 3.0 FR) \n\nManuscrit re\u00e7u le 17 juin 2013, r\u00e9vis\u00e9 le 22 janvier 2015, accept\u00e9 le 24 f\u00e9vrier 2015. \n\nI am very grateful to Maxim Kontsevich for inspiring discussions, from which this article originates. Discussions with Antoine Ducros, Pierrick Bousseau, Jean-Fran\u00e7ois Dat, Ilia Itenberg, Sean Keel, Bernhard Keller, Bruno Klingler and Grigory Mikhalkin are equally very essential and useful. I would also like to thank the referees for valuable comments.\n\n

Published - AIF_2015__65_4_1647_0.pdf

Accepted Version - 1304.2251.pdf

", "abstract": "We study tropical geometry in the global setting using Berkovich's deformation retraction. We state and prove the generalized balancing conditions in this setting. Starting with a strictly semi-stable formal scheme, we calculate certain sheaves of vanishing cycles using analytic \u00e9tale cohomology, then we interpret the tropical weight vectors via these cycles. We obtain the balancing condition for tropical curves on the skeleton associated to the formal scheme in terms of the intersection theory on the special fiber. Our approach works over any complete discrete valuation field.", "date": "2015-09-21", "date_type": "published", "publication": "Annales de l'Institut Fourier", "volume": "65", "number": "4", "publisher": "Association des Annales de l'Institut Fourier", "pagerange": "1647-1667", "id_number": "CaltechAUTHORS:20210914-164413193", "issn": "1777-5310", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164413193", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.5802/aif.2970", "primary_object": { "basename": "1304.2251.pdf", "url": "https://authors.library.caltech.edu/records/7rtye-hre15/files/1304.2251.pdf" }, "related_objects": [ { "basename": "AIF_2015__65_4_1647_0.pdf", "url": "https://authors.library.caltech.edu/records/7rtye-hre15/files/AIF_2015__65_4_1647_0.pdf" } ], "pub_year": "2015", "author_list": "Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/63tqv-sbr95", "eprint_id": 58295, "eprint_status": "archive", "datestamp": "2023-08-20 08:14:48", "lastmod": "2026-04-04 21:08:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bao-Ning", "name": { "family": "Bao", "given": "Ning" }, "orcid": "0000-0002-3296-1039" }, { "id": "Nezami-S", "name": { "family": "Nezami", "given": "Sepehr" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } }, { "id": "Sully-J", "name": { "family": "Sully", "given": "James" } }, { "id": "Walter-M", "name": { "family": "Walter", "given": "Michael" } } ] }, "title": "The Holographic Entropy Cone", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nArticle funded by SCOAP3. \n\nReceived: July 25, 2015; Accepted: August 31, 2015; Published: September 21, 2015. \n\nWe thank Mario Berta, Venkat Chandrasekaran, Bartek Czech, Patrick Hayden, Shaun Maguire, Alexander Maloney, Donald Marolf, Ingmar Saberi, and Adam Sheffer for pleasant discussions. M.W. acknowledges funding provided by the Simons Foundation and FQXi. N.B., H.O., and B.S. are supported in part by U.S. DOE grant DE-SC0011632 and by the Walter Burke Institute for Theoretical Physics (Burke Institute) at Caltech. The work of H.O. is also supported in part by the Simons Investigator Award, by the WPI Initiative of MEXT of Japan, and by JSPS Grant-in-Aid for Scientific Research C-26400240. N.B. is a DuBridge Fellow of the Burke Institute. S.N. is supported by a Stanford Graduate Fellowship. N.B. and B.S. thank the Stanford Institute for Theoretical Physics for hospitality. S.N., J.S., and M.W. thank the Burke Institute at Caltech for hospitality. H.O. thanks the hospitality of the Simons Foundation at the Simons Symposium on Quantum Entanglement.\n\n

Published - art_10.1007_JHEP09_2015_130.pdf

Submitted - 1505.07839v1.pdf

", "abstract": "We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.", "date": "2015-09-21", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2015", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 130", "id_number": "CaltechAUTHORS:20150616-154806338", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150616-154806338", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation" }, { "agency": "Foundational Questions Institute (FQXI)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "Stanford University" }, { "agency": "SCOAP3" }, { "agency": "Lee A. DuBridge Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "2015-020", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "IQIM" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP09(2015)130", "primary_object": { "basename": "art_10.1007_JHEP09_2015_130.pdf", "url": "https://authors.library.caltech.edu/records/63tqv-sbr95/files/art_10.1007_JHEP09_2015_130.pdf" }, "related_objects": [ { "basename": "1505.07839v1.pdf", "url": "https://authors.library.caltech.edu/records/63tqv-sbr95/files/1505.07839v1.pdf" } ], "pub_year": "2015", "author_list": "Bao, Ning; Nezami, Sepehr; et al." }, { "id": "https://authors.library.caltech.edu/records/k5tgz-0m725", "eprint_id": 61191, "eprint_status": "archive", "datestamp": "2023-08-20 08:08:49", "lastmod": "2026-04-04 05:28:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Okounkov-A", "name": { "family": "Okounkov", "given": "Andrei" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Noncommutative geometry and Painlev\u00e9 equations", "ispublished": "pub", "full_text_status": "public", "keywords": "noncommutative geometry, Painlev\u00e9 equations", "note": "\u00a9 2015 Mathematical Sciences Publishers. \n\n\nReceived: 15 May 2014; Revised: 2 April 2015; Accepted: 17 May 2015; Published: 7 September 2015.\n\n\nThe principal results contained in this paper were obtained in September 2008 during our stay at the CRM in Montreal. It is a special pleasure to thank John Harnad and Jacques Hurtubise for making this possible and to acknowledge their fundamental contribution to the subject that is being deformed here in the noncommutative direction. \n\nWe received valuable feedback, in particular, from D. Kaledin and D. Kazhdan during Okounkov's 2009 Zabrodsky Lecture at Hebrew University as well as from many other people on other occasions. \n\nOkounkov thanks the NSF for financial support under FRG DMS-1159416. Rains was supported by NSF grants DMS-0833464 and DMS-1001645.\n\n

Published - ant-v9-n6-p03-s.pdf

Submitted - 1404.5938v1.pdf

", "abstract": "We construct the elliptic Painlev\u00e9 equation and its higher dimensional analogs as the action of line bundles on 1 -dimensional sheaves on noncommutative surfaces.", "date": "2015-09-07", "date_type": "published", "publication": "Algebra and Number Theory", "volume": "9", "number": "6", "publisher": "Mathematical Sciences Publishers", "pagerange": "1363-1400", "id_number": "CaltechAUTHORS:20151016-074552683", "issn": "1937-0652", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151016-074552683", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1159416" }, { "agency": "NSF", "grant_number": "DMS-0833464" }, { "agency": "NSF", "grant_number": "DMS-1001645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/ant.2015.9.1363", "primary_object": { "basename": "1404.5938v1.pdf", "url": "https://authors.library.caltech.edu/records/k5tgz-0m725/files/1404.5938v1.pdf" }, "related_objects": [ { "basename": "ant-v9-n6-p03-s.pdf", "url": "https://authors.library.caltech.edu/records/k5tgz-0m725/files/ant-v9-n6-p03-s.pdf" } ], "pub_year": "2015", "author_list": "Okounkov, Andrei and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/ze2wh-d0577", "eprint_id": 61718, "eprint_status": "archive", "datestamp": "2023-08-20 08:00:03", "lastmod": "2026-04-04 20:36:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Sly-A", "name": { "family": "Sly", "given": "Allan" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Strategic Learning and the Topology of Social Networks", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 The Econometric Society. \n\nManuscript received November, 2013; final revision received May, 2015. \n\nWe would like to thank Shahar Kariv for introducing us to this field. For commenting on drafts of this paper, we would like to thank Nageeb Ali, Ben Golub, Eva Lyubich, Markus Mobius, Ariel Rubinstein, Ran Shorrer, Glen Weyl, and, especially, Scott Kominers. The work of Mossel is supported by NSF award DMS 1106999, by ONR award N000141110140, and by ISF Grant 1300/08. The work of Sly is supported by a Sloan Research Fellowship in mathematics and by NSF award DMS 1208339. The research of Tamuz was supported in part by a Google Europe Fellowship.\n\n

Published - Mossel_et_al-2015-Econometrica.pdf

Submitted - 1209.5527.pdf

Supplemental Material - ecta1540-sup-0001-Supplement.pdf

", "abstract": "We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals and by observing the actions of their neighbors in a social network.", "date": "2015-09", "date_type": "published", "publication": "Econometrica", "volume": "83", "number": "5", "publisher": "Econometric Society", "pagerange": "1755-1794", "id_number": "CaltechAUTHORS:20151029-144956303", "issn": "0012-9682", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151029-144956303", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 1106999" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N000141110140" }, { "agency": "NSF", "grant_number": "1300/08" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "DMS 1208339" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3982/ECTA12058", "primary_object": { "basename": "ecta1540-sup-0001-Supplement.pdf", "url": "https://authors.library.caltech.edu/records/ze2wh-d0577/files/ecta1540-sup-0001-Supplement.pdf" }, "related_objects": [ { "basename": "Mossel_et_al-2015-Econometrica.pdf", "url": "https://authors.library.caltech.edu/records/ze2wh-d0577/files/Mossel_et_al-2015-Econometrica.pdf" }, { "basename": "1209.5527.pdf", "url": "https://authors.library.caltech.edu/records/ze2wh-d0577/files/1209.5527.pdf" } ], "pub_year": "2015", "author_list": "Mossel, Elchanan; Sly, Allan; et al." }, { "id": "https://authors.library.caltech.edu/records/rwyak-pyf27", "eprint_id": 111021, "eprint_status": "archive", "datestamp": "2023-08-22 16:17:19", "lastmod": "2026-04-04 22:13:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hutchcroft-Tom", "name": { "family": "Hutchcroft", "given": "Tom" }, "orcid": "0000-0003-0061-593X" }, { "id": "Peres-Yuval", "name": { "family": "Peres", "given": "Yuval" }, "orcid": "0000-0001-5456-6323" } ] }, "title": "Collisions of random walks in reversible random graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Random Walks; collisions; unimodular random graphs", "note": "\u00a9 2015 The Author(s). Creative Commons Attribution 3.0 License. \n\nSubmitted to ECP on May 26, 2015, final version accepted on September 15, 2015. First available in Project Euclid: 7 June 2016. \n\nThis work was carried out while TH was an intern at Microsoft Research. We thank Itai Benjamini for suggesting this problem, and also thank Lewis Bowen, Perla Sousi and Omer Tamuz for helpful discussions.\n\n

Published - ECP.v20-4330.pdf

Submitted - 1505.02484.pdf

", "abstract": "We prove that in any recurrent reversible random rooted graph, two independent simple random walks started at the same vertex collide infinitely often almost surely. This applies to the Uniform Infinite Planar Triangulation and Quadrangulation and to the Incipient Infinite Cluster in Z\u00b2.", "date": "2015-09", "date_type": "published", "publication": "Electronic Communications in Probability", "volume": "20", "publisher": "Institute of Mathematical Statistics", "pagerange": "Art. No. 4330", "id_number": "CaltechAUTHORS:20210923-215831853", "issn": "1083-589X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210923-215831853", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1214/ecp.v20-4330", "primary_object": { "basename": "1505.02484.pdf", "url": "https://authors.library.caltech.edu/records/rwyak-pyf27/files/1505.02484.pdf" }, "related_objects": [ { "basename": "ECP.v20-4330.pdf", "url": "https://authors.library.caltech.edu/records/rwyak-pyf27/files/ECP.v20-4330.pdf" } ], "pub_year": "2015", "author_list": "Hutchcroft, Tom and Peres, Yuval" }, { "id": "https://authors.library.caltech.edu/records/ywvma-5yd70", "eprint_id": 56822, "eprint_status": "archive", "datestamp": "2023-08-20 07:55:27", "lastmod": "2026-04-04 20:24:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wu-Zhongtao", "name": { "family": "Wu", "given": "Zhongtao" } } ] }, "title": "Cosmetic surgeries on knots in S^3", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 De Gruyter.\n\nReceived March 5th 2012, as revised version July 10, 2013.\n\nThis work was carried out when the first author visited Princeton University. The first author was partially supported by an AIM Five-Year Fellowship and NSF grant number DMS-1021956. The second author was supported by a Simons Postdoctoral Fellowship.\n\n

Published - Ni_2015p1.pdf

Submitted - 1009.4720v2.pdf

", "abstract": "Two Dehn surgeries on a knot are called purely cosmetic, if they yield manifolds\nthat are homeomorphic as oriented manifolds. Suppose there exist purely cosmetic surgeries\non a knot in S^3, we show that the two surgery slopes must be the opposite of each other.\nOne ingredient of our proof is a Dehn surgery formula for correction terms in Heegaard Floer\nhomology.", "date": "2015-09", "date_type": "published", "publication": "Journal F\u00fcr Reine und Angewandte Mathematik", "volume": "2015", "number": "706", "publisher": "Walter de Gruyter", "pagerange": "1-17", "id_number": "CaltechAUTHORS:20150421-115848260", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115848260", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1021956" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2013-0067", "primary_object": { "basename": "1009.4720v2.pdf", "url": "https://authors.library.caltech.edu/records/ywvma-5yd70/files/1009.4720v2.pdf" }, "related_objects": [ { "basename": "Ni_2015p1.pdf", "url": "https://authors.library.caltech.edu/records/ywvma-5yd70/files/Ni_2015p1.pdf" } ], "pub_year": "2015", "author_list": "Ni, Yi and Wu, Zhongtao" }, { "id": "https://authors.library.caltech.edu/records/mrmac-73f25", "eprint_id": 97834, "eprint_status": "archive", "datestamp": "2023-08-20 08:03:49", "lastmod": "2026-04-04 22:18:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Lee-Choongbum", "name": { "family": "Lee", "given": "Choongbum" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "On the Grid Ramsey Problem and Related Questions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2014. Published by Oxford University Press. \n\nPublished 24 October 2014; received 26 May 2014; revision received 25 September 2014; accepted 26 September 2014. \n\nDavid Conlon was supported by a Royal Society University Research Fellowship. Jacob Fox was supported by a Packard Fellowship, a Simons Fellowship, NSF CAREER award DMS-1352121, an Alfred P. Sloan Fellowship and an MIT NEC Corporation Award. Choongbum Lee was supported by NSF Grant DMS-1362326. Benny Sudakov was supported by SNSF grant 200021-149111 and a USA-Israel BSF grant. \n\nWe would like to thank the anonymous referee for several helpful comments.\n\n

Published - rnu190.pdf

Submitted - 1405.6587.pdf

", "abstract": "The Hales-Jewett theorem is one of the pillars of Ramsey theory, from which many other results follow. A celebrated theorem of Shelah says that Hales-Jewett numbers are primitive recursive. A key tool used in his proof, now known as the cube lemma, has become famous in its own right. In its simplest form, this lemma says that if we color the edges of the Cartesian product K_n x K_n in r colors, then, for n sufficiently large, there is a rectangle with both pairs of opposite edges receiving the same color. Shelah's proof shows that [equation; see abstract in PDF for details] suffices. More than 20 years ago, Graham, Rothschild, and Spencer asked whether this bound can be improved to a polynomial in r. We show that this is not possible by providing a superpolynomial lower bound in r. We also discuss a number of related problems.", "date": "2015-09", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2015", "number": "17", "publisher": "Oxford University Press", "pagerange": "8052-8084", "id_number": "CaltechAUTHORS:20190812-162959982", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959982", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "NSF", "grant_number": "DMS-1362326" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnu190", "primary_object": { "basename": "1405.6587.pdf", "url": "https://authors.library.caltech.edu/records/mrmac-73f25/files/1405.6587.pdf" }, "related_objects": [ { "basename": "rnu190.pdf", "url": "https://authors.library.caltech.edu/records/mrmac-73f25/files/rnu190.pdf" } ], "pub_year": "2015", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/qy8xt-0by96", "eprint_id": 58779, "eprint_status": "archive", "datestamp": "2023-08-20 07:26:34", "lastmod": "2026-04-04 21:44:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Geisinger-L", "name": { "family": "Geisinger", "given": "Leander" } } ] }, "title": "The Ground State Energy of a Polaron in a Strong Magnetic Field", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 The Author(s). This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 11 March 2013. Accepted: 28 June 2013. Published online: 1 May 2015. Communicated by H. Spohn.\n\n\nWork partially supported by NSF grants PHY-1068285 (R.L.F.) and PHY-1122309 (L.G.) and DFG grant GE 2369/1-1 (L.G.).\n\n

Submitted - 1303.2382v1.pdf

", "abstract": "We show that the ground state of a polaron in a homogeneous magnetic field B and its energy are described by an effective one-dimensional minimization problem in the limit B \u2192 \u221e . This holds both in the linear Fr\u00f6hlich and in the non-linear Pekar model and makes rigorous an argument of Kochetov, Leschke and Smondyrev.", "date": "2015-08", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "338", "number": "1", "publisher": "Springer", "pagerange": "1-29", "id_number": "CaltechAUTHORS:20150706-132935949", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150706-132935949", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1122309" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "GE 2369/1-1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-015-2367-z", "primary_object": { "basename": "1303.2382v1.pdf", "url": "https://authors.library.caltech.edu/records/qy8xt-0by96/files/1303.2382v1.pdf" }, "pub_year": "2015", "author_list": "Frank, Rupert L. and Geisinger, Leander" }, { "id": "https://authors.library.caltech.edu/records/xcpd9-8rr71", "eprint_id": 62227, "eprint_status": "archive", "datestamp": "2023-08-20 07:16:19", "lastmod": "2026-04-04 21:19:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bhargava-M", "name": { "family": "Bhargava", "given": "Manjul" } }, { "id": "Kane-D-M", "name": { "family": "Kane", "given": "Daniel M." } }, { "id": "Lenstra-H-W", "name": { "family": "Lenstra", "given": "Hendrik W." } }, { "id": "Poonen-B", "name": { "family": "Poonen", "given": "Bjorn" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Modeling the distribution of ranks, Selmer groups, and Shafarevich\u2013Tate groups of elliptic curves", "ispublished": "pub", "full_text_status": "public", "keywords": "Selmer group, Shafarevich-Tate group, rank, maximal isotropic, quadratic space, Weil pairing", "note": "\u00a9 2015 International Press of Boston, Inc. \n\nM.B. was supported by the National Science Foundation grant DMS-1001828. D.K. was supported by a National Science Foundation Graduate Fellowship. B.P. was supported by the Guggenheim Foundation and National Science Foundation grants DMS-0841321 and DMS-1069236. \n\nWe thank the referee for reading our paper carefully and for making many insightful comments. We also thank K\u0119stutis \u010cesnavi\u010dius, Bart de Smit, Christophe Delaunay, and Christopher Skinner for helpful comments. This research was begun during the \"Arithmetic Statistics\" semester at the Mathematical Sciences Research Institute, and continued during the \"Cohen\u2013Lenstra heuristics for class groups\" workshop at the American Institute of Mathematics, the 2012 Canadian Number Theory Association meeting at the University of Lethbridge, the Centre Interfacultaire Bernoulli semester on \"Rational points and algebraic cycles\", the 2013 \"Explicit methods in number theory\" workshop at the Mathematisches Forschungsinstitut Oberwolfach, the \"Rational points 2013\" workshop at Schloss Thurnau, and the \"Counting arithmetic objects\" workshop at the Centre de Recherches Math\u00e9matiques in Montreal.\n\n

Published - CJM-2015-0003-0003-a001.pdf

Submitted - 1304.3971v2.pdf

Updated - rst_distribution.pdf

", "abstract": "Using maximal isotropic submodules in a quadratic module over \u2124_p, we prove the existence of a natural discrete probability distribution on the set of isomorphism classes of short exact sequences of cofinite type \u2124_p-modules, and then conjecture that as E varies over elliptic curves over a fixed global field k, the distribution of\n0 \u2192 E(k)\u2297 \u211a_p/ \u2124_p \u2192 Selp\u221e E \u2192 \u0428[p^\u221e ] \u2192 0 \nis that one. We show that this single conjecture would explain many of the known theorems and conjectures on ranks, Selmer groups, and Shafarevich\u2013Tate groups of elliptic curves. We also prove the existence of a discrete probability distribution on the set of isomorphism classes of finite abelian p-groups equipped with a nondegenerate alternating pairing, defined in terms of the cokernel of a random alternating matrix over \u2124_p, and we prove that the two probability distributions are compatible with each other and with Delaunay's predicted distribution for \u0428. Finally, we prove new theorems on the fppf cohomology of elliptic curves in order to give further evidence for our conjecture.", "date": "2015-07-05", "date_type": "published", "publication": "Cambridge Journal of Mathematics", "volume": "3", "number": "3", "publisher": "International Press", "pagerange": "275-321", "id_number": "CaltechAUTHORS:20151119-085554759", "issn": "2168-0930", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151119-085554759", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1001828" }, { "agency": "NSF Graduate Research Fellowship" }, { "agency": "John Simon Guggenheim Foundation" }, { "agency": "NSF", "grant_number": "DMS-0841321" }, { "agency": "NSF", "grant_number": "DMS-1069236" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CJM.2015.v3.n3.a1", "primary_object": { "basename": "1304.3971v2.pdf", "url": "https://authors.library.caltech.edu/records/xcpd9-8rr71/files/1304.3971v2.pdf" }, "related_objects": [ { "basename": "CJM-2015-0003-0003-a001.pdf", "url": "https://authors.library.caltech.edu/records/xcpd9-8rr71/files/CJM-2015-0003-0003-a001.pdf" }, { "basename": "rst_distribution.pdf", "url": "https://authors.library.caltech.edu/records/xcpd9-8rr71/files/rst_distribution.pdf" } ], "pub_year": "2015", "author_list": "Bhargava, Manjul; Kane, Daniel M.; et al." }, { "id": "https://authors.library.caltech.edu/records/h6fvr-b3k02", "eprint_id": 58000, "eprint_status": "archive", "datestamp": "2023-08-22 15:47:17", "lastmod": "2026-04-04 06:45:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-T", "name": { "family": "Ekholm", "given": "Tomas" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Kova\u0159\u00edk-H", "name": { "family": "Kova\u0159\u00edk", "given": "Hynek" } } ] }, "title": "Weak perturbations of the p-Laplacian", "ispublished": "pub", "full_text_status": "public", "keywords": "p-Laplacian; Weak coupling; Sobolev inequalities", "note": "\u00a9 2014 Springer-Verlag Berlin Heidelberg.\n\nReceived: 18 December 2013; Accepted: 20 July 2014; Published online: 2 September 2014.\n\nFinancial support through Swedish research council grant FS-2009-493 (T. E.), US National Science Foundation grant PHY-1347399 (R. F.) and grant MIUR-PRIN08 grant for the project \"Trasporto ottimo dimassa, disuguaglianze geometriche e funzionali e applicazioni\" (H. K.) is acknowledged.\n\n

Submitted - 1312.5191v2.pdf

", "abstract": "We consider the p-Laplacian in R^d perturbed by a weakly coupled potential. We calculate the asymptotic expansions of the lowest eigenvalue of such an operator in the weak coupling limit separately for p>d and p=d and discuss the connection with Sobolev interpolation inequalities.", "date": "2015-07", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "53", "number": "3-4", "publisher": "Springer", "pagerange": "781-801", "id_number": "CaltechAUTHORS:20150604-085020731", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150604-085020731", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Research Council", "grant_number": "FS-2009-493" }, { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "Ministero dell'Istruzione, dell'Universit\u00e0 e della Ricerca (MIUR)", "grant_number": "PRIN08" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-014-0767-0", "primary_object": { "basename": "1312.5191v2.pdf", "url": "https://authors.library.caltech.edu/records/h6fvr-b3k02/files/1312.5191v2.pdf" }, "pub_year": "2015", "author_list": "Ekholm, Tomas; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/tsfe8-xxa66", "eprint_id": 87372, "eprint_status": "archive", "datestamp": "2023-08-20 07:10:06", "lastmod": "2026-04-04 06:48:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Buckmaster-Tristan", "name": { "family": "Buckmaster", "given": "Tristan" } }, { "id": "De-Lellis-Camillo", "name": { "family": "De Lellis", "given": "Camillo" } }, { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" }, { "id": "Sz\u00e9kelyhidi-L\u00e1szl\u00f3-Jr", "name": { "family": "Sz\u00e9kelyhidi", "given": "L\u00e1szl\u00f3, Jr." } } ] }, "title": "Anomalous dissipation for 1/5-H\u00f6lder Euler flows", "ispublished": "pub", "full_text_status": "public", "keywords": "Kolmogorov's law, Onsager's conjecture, anomalous dissipation, convex integration, h-principle, turbulent flows", "note": "\u00a9 2015 Department of Mathematics, Princeton University. \n\nReceived: 8 August 2013; Revised: 19 August 2014; Accepted: 26 August 2014.\n\n

Published - annals-v182-n1-p03-p.pdf

", "abstract": "Recently the second and fourth authors developed an iterative scheme for obtaining rough solutions of the 3D incompressible Euler equations in H\u00f6lder spaces. The motivation comes from Onsager's conjecture. The construction involves a superposition of weakly interacting perturbed Beltrami flows on infinitely many scales. An obstruction to better regularity arises from the errors in the linear transport of a fast periodic flow by a slow velocity field.\nIn a recent paper the third author has improved upon the methods, introducing some novel ideas on how to deal with this obstruction, thereby reaching a better H\u00f6lder exponent \u2014 albeit weaker than the one conjectured by Onsager. In this paper we give a shorter proof of this final result, adhering more to the original scheme of the second and fourth authors and introducing some new devices. More precisely we show that for any positive \u03b5, there exist periodic solutions of the 3D incompressible Euler equations that dissipate the total kinetic energy and belong to the H\u00f6lder class C^(1/5\u2212\u03b5).", "date": "2015-07", "date_type": "published", "publication": "Annals of Mathematics", "volume": "182", "number": "1", "publisher": "Princeton University", "pagerange": "127-172", "id_number": "CaltechAUTHORS:20180627-082316639", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180627-082316639", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2015.182.1.3", "primary_object": { "basename": "annals-v182-n1-p03-p.pdf", "url": "https://authors.library.caltech.edu/records/tsfe8-xxa66/files/annals-v182-n1-p03-p.pdf" }, "pub_year": "2015", "author_list": "Buckmaster, Tristan; De Lellis, Camillo; et al." }, { "id": "https://authors.library.caltech.edu/records/3apyx-yff34", "eprint_id": 58208, "eprint_status": "archive", "datestamp": "2023-08-22 15:43:31", "lastmod": "2026-04-04 20:25:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Pushnitski-A", "name": { "family": "Pushnitski", "given": "Alexander" } } ] }, "title": "The spectral density of a product of spectral projections", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operators; Anderson orthogonality catastrophy; Spectral asymptotics; Hankel operators", "note": "\u00a9 2015 Elsevier Inc. Received 12 September 2014, Accepted 26 March 2015, Available online 14 April 2015. Communicated by B. Schlein.\n\nFinancial support from the U.S. National Science Foundation through grants PHY-1347399 and DMS-1363432 (R.F.) is acknowledged. The authors are grateful to the anonymous referee for helpful suggestions.\n\n

Submitted - 1409.1206

", "abstract": "We consider the product of spectral projections\n\u03a0_\u03b5(\u03bb)=1_((\u2212\u221e,\u03bb\u2212\u03b5))(H_0)1_((\u03bb+\u03b5,\u221e))(H)1_((\u2212\u221e,\u03bb\u2212\u03b5))(H_0)\nwhere H_0 and H are the free and the perturbed Schr\u00f6dinger operators with a short range potential, \u03bb > 0 is fixed and \u03b5 \u2192 0. We compute the leading term of the asymptotics of Tr\u0192(\u03a0_\u03b5(\u03bb)) as \u03b5 \u2192 0 for continuous functions \u0192 vanishing sufficiently fast near zero. Our construction elucidates calculations that appeared earlier in the theory of \"Anderson's orthogonality catastrophe\" and emphasizes the role of Hankel operators in this phenomenon.", "date": "2015-06-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "268", "number": "12", "publisher": "Elsevier", "pagerange": "3867-3894", "id_number": "CaltechAUTHORS:20150612-085811844", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150612-085811844", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "DMS-1363432" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2015.03.018", "primary_object": { "basename": "1409.1206", "url": "https://authors.library.caltech.edu/records/3apyx-yff34/files/1409.1206" }, "pub_year": "2015", "author_list": "Frank, Rupert L. and Pushnitski, Alexander" }, { "id": "https://authors.library.caltech.edu/records/648b1-q3x68", "eprint_id": 58294, "eprint_status": "archive", "datestamp": "2023-08-20 06:50:27", "lastmod": "2026-04-04 20:37:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lin-Jennifer", "name": { "family": "Lin", "given": "Jennifer" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } } ] }, "title": "Locality of Gravitational Systems from Entanglement of Conformal Field Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 American Physical Society.\n\nReceived 27 December 2014; published 2 June 2015.\n\nWe thank N. Bao, D. Gaiotto, D. Harlow, T. Hartman, P. Hayden, N. Hunter-Jones, C. Keller, D. Kutasov, H. Liu, Y. Nakayama, S. Pufu, P. Sulkowski, T. Takayanagi, M. Van Raamsdonk, and E. Witten for useful discussion. J. L. acknowledges support from the Sidney Bloomenthal fellowship at the University of Chicago. M. M. is currently supported by NSF Grants No. PHY-1205440, No. DMS-1201512, and No. DMS-1007207. H. O. and B. S. are supported in part by the Walter Burke Institute for Theoretical Physics at Caltech, by U.S. DOE Grant No. DE-SC0011632, and by a Simons Investigator award. The work of H. O. is also supported in part by the WPI Initiative of MEXT of Japan and JSPS Grant-in Aid for Scientific Research C-26400240. He also thanks the hospitality of the Aspen Center for Physics and the National Science Foundation, which supports the Center under Grant No. PHY-1066293. B. S. is supported in part by a Dominic Orr Graduate Fellowship. J. L., H. O., and B. S. would like to thank the Institute for Advanced Study, Princeton University, and the Simons Center for Geometry and Physics for hospitality. J. L. also thanks Caltech for hospitality.\n\n

Published - PhysRevLett.114.221601.pdf

", "abstract": "The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of\na minimal surface in its holographic dual. We show that this relation can be inverted for any state in the\nconformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime,\nreconstructing the local data in the bulk from the entanglement on the boundary. We also show that\npositivity, monotonicity, and convexity of the relative entropy for small spherical domains between the\nreduced density matrices of any state and of the ground state of the conformal field theory are guaranteed by\npositivity conditions on the bulk matter energy density. As positivity and monotonicity of the relative\nentropy are general properties of quantum systems, this can be interpreted as a derivation of bulk energy\nconditions in any holographic system for which the Ryu-Takayanagi prescription applies. We discuss an\ninformation theoretical interpretation of the convexity in terms of the Fisher metric.", "date": "2015-06-05", "date_type": "published", "publication": "Physical Review Letters", "volume": "114", "number": "22", "publisher": "American Physical Society", "pagerange": "Art. No. 221601", "id_number": "CaltechAUTHORS:20150616-152928658", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150616-152928658", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "University of Chicago" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0011632" }, { "agency": "Walter Burke Institute for Theoretical Physics, Caltech" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-26400240" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Dominic Orr Graduate Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "2014-162", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.114.221601", "primary_object": { "basename": "PhysRevLett.114.221601.pdf", "url": "https://authors.library.caltech.edu/records/648b1-q3x68/files/PhysRevLett.114.221601.pdf" }, "pub_year": "2015", "author_list": "Lin, Jennifer; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/fecwr-jw093", "eprint_id": 97824, "eprint_status": "archive", "datestamp": "2023-09-22 22:35:00", "lastmod": "2026-04-04 07:41:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" } } ] }, "title": "A relative Szemer\u00e9di theorem", "ispublished": "pub", "full_text_status": "public", "keywords": "Arithmetic Progression; Sparse Graph; Discrepancy Pair; Regularity Lemma; Removal Lemma", "note": "\u00a9 2015 Springer Basel. \n\nReceived 10 September 2014; accepted 20 October 2014; first online 17 March 2015. \n\nThe first author was supported by a Royal Society University Research Fellowship, the second author was supported by a Simons Fellowship, NSF grant DMS-1069197, by an Alfred P. Sloan Fellowship, and by an MIT NEC Corporation Fund Award, and the third author was supported by a Microsoft Research PhD Fellowship. \n\nWe would like to thank Tom Bohman and Ben Green for helpful discussions.\n\n

Submitted - 1305.5440.pdf

", "abstract": "The celebrated Green-Tao theorem states that there are arbitrarily long arithmetic progressions in the primes. One of the main ingredients in their proof is a relative Szemer\u00e9di theorem which says that any subset of a pseudorandom set of integers of positive relative density contains long arithmetic progressions. In this paper, we give a simple proof of a strengthening of the relative Szemer\u00e9di theorem, showing that a much weaker pseudorandomness condition is sufficient. Our strengthened version can be applied to give the first relative Szemer\u00e9di theorem for k-term arithmetic progressions in pseudorandom subsets of \u2124_N of density N^(\u2212ck). The key component in our proof is an extension of the regularity method to sparse pseudorandom hypergraphs, which we believe to be interesting in its own right. From this we derive a relative extension of the hypergraph removal lemma. This is a strengthening of an earlier theorem used by Tao in his proof that the Gaussian primes contain arbitrarily shaped constellations and, by standard arguments, allows us to deduce the relative Szemer\u00e9di theorem.", "date": "2015-06", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "25", "number": "3", "publisher": "Springer", "pagerange": "733-762", "id_number": "CaltechAUTHORS:20190812-162959067", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959067", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-015-0324-9", "primary_object": { "basename": "1305.5440.pdf", "url": "https://authors.library.caltech.edu/records/fecwr-jw093/files/1305.5440.pdf" }, "pub_year": "2015", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/33axv-7sz82", "eprint_id": 57132, "eprint_status": "archive", "datestamp": "2023-08-20 05:59:54", "lastmod": "2026-04-04 21:35:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "van-de-Bult-F-J", "name": { "family": "van de Bult", "given": "Fokko J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Limits of elliptic hypergeometric biorthogonal functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 Elsevier Inc. Received 19 July 2013, Revised 9 June 2014, Accepted 25 June 2014, Available online 2 July 2014. Communicated by Spec. Issue Guest Editor. To Dick Askey on the occasion of his 80th birthday.\n\nWe would like to thank an anonymous reviewer for insightful remarks. Eric M. Rains was partially supported by a grant from the National Science Foundation, DMS-1001645.\n\n

Submitted - 1110.1456v1.pdf

", "abstract": "The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the q-Askey scheme of basic hypergeometric orthogonal polynomials. We aim to achieve this by looking at the limits as p\u21920 of the elliptic hypergeometric biorthogonal functions from Spiridonov (2003), with parameters which depend in varying ways on p. As a result we get 38 systems of biorthogonal functions with for each system at least one explicit measure for the bilinear form. Amongst these we indeed recover the q-Askey scheme. Each system consists of (basic hypergeometric) rational functions or polynomials.", "date": "2015-05", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "193", "publisher": "Elsevier", "pagerange": "128-163", "id_number": "CaltechAUTHORS:20150501-080444288", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150501-080444288", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1001645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jat.2014.06.009", "primary_object": { "basename": "1110.1456v1.pdf", "url": "https://authors.library.caltech.edu/records/33axv-7sz82/files/1110.1456v1.pdf" }, "pub_year": "2015", "author_list": "van de Bult, Fokko J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/yr4pm-hz383", "eprint_id": 71978, "eprint_status": "archive", "datestamp": "2023-08-20 05:42:24", "lastmod": "2026-04-04 20:34:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hartman-Y", "name": { "family": "Hartman", "given": "Yair" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Furstenberg entropy realizations for virtually free groups and lamplighter groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 Hebrew University Magnes Press. \n\nReceived February 21, 2013 and in revised form April 15, 2013. First Online: 01 July 2015. \n\nY. Hartman is supported by the European Research Council, grant 239885. O. Tamuz is supported by ISF grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing. This research is supported in part by this Google Fellowship. \n\nWe are grateful to Yuri Lima for many useful discussions. We also thank Uri Bader and Amos Nevo for motivating conversations, and Lewis Bowen and Vadim Kaimanovich for commenting on the first draft of this paper. Finally, we thank the referee for many insightful comments and suggestions.\n\n

Submitted - 1210.5897.pdf

", "abstract": "Let (G,\u00b5) be a discrete group with a generating probability measure. Nevo showed that if G has Kazhdan's property (T), then there exists \u025b > 0 such that the Furstenberg entropy of any (G,\u00b5)-stationary ergodic space is either 0 or larger than \u025b. Virtually free groups, such as SL_2(\u2124), do not have property (T), and neither do their extensions, such as surface groups. For virtually free groups, we construct stationary actions with arbitrarily small, positive entropy. The construction involves building and lifting spaces of lamplighter groups. For some classical lamplighter gropus, these spaces realize a dense set of entropies between 0 and the Poisson boundary entropy.", "date": "2015-04", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "126", "number": "1", "publisher": "Hebrew University Magnes Press", "pagerange": "227-257", "id_number": "CaltechAUTHORS:20161114-085457028", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-085457028", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "239885" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11854-015-0016-2", "primary_object": { "basename": "1210.5897.pdf", "url": "https://authors.library.caltech.edu/records/yr4pm-hz383/files/1210.5897.pdf" }, "pub_year": "2015", "author_list": "Hartman, Yair and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/mvfjk-9gf09", "eprint_id": 58078, "eprint_status": "archive", "datestamp": "2023-08-20 05:39:10", "lastmod": "2026-04-04 21:07:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "From exceptional collections to motivic decompositions via noncommutative motives", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 De Gruyter. Received: 2012-03-30. Revised: 2012-12-28.\nPublished Online: 2013-05-07.\n\nDedicated to Yuri Manin, on the occasion of his 75th birthday.\n\nM. Marcolli was partially supported by the NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. G. Tabuada was partially supported by the NEC award 2742738 and by the Portuguese Foundation for Science and Technology through the grant PEst-OE/MAT/UI0297/2011 (CMA).\n\n

Published - Marcolli_2015p153.pdf

Submitted - 1202.6297v3.pdf

", "abstract": "Making use of noncommutative motives we relate exceptional collections (and more generally semi-orthogonal decompositions) to motivic decompositions. On one hand we prove that the Chow motive M(X)_Q of every smooth and proper Deligne\u2013Mumford stack X, whose bounded derived category D^b(X) of coherent schemes admits a full exceptional collection, decomposes into a direct sum of tensor powers of the Lefschetz motive. Examples include projective spaces, quadrics, toric varieties, homogeneous spaces, Fano threefolds, and moduli spaces. On the other hand we prove that if M(X)_Q decomposes into a direct sum of tensor powers of the Lefschetz motive and moreover D^b(X) admits a semiorthogonal decomposition, then the noncommutative motive of each one of the pieces of the\nsemi-orthogonal decomposition is a direct sum of \u2297-units. As an application we obtain a simplification of Dubrovin's conjecture.", "date": "2015-04", "date_type": "published", "publication": "Journal F\u00fcr Die Reine und Angewandte Mathematik", "volume": "2015", "number": "701", "publisher": "Walter de Gruyter", "pagerange": "153-167", "id_number": "CaltechAUTHORS:20150608-104133815", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150608-104133815", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "NEC", "grant_number": "2742738" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PEst-OE/MAT/UI0297/2011" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/crelle-2013-0027", "primary_object": { "basename": "1202.6297v3.pdf", "url": "https://authors.library.caltech.edu/records/mvfjk-9gf09/files/1202.6297v3.pdf" }, "related_objects": [ { "basename": "Marcolli_2015p153.pdf", "url": "https://authors.library.caltech.edu/records/mvfjk-9gf09/files/Marcolli_2015p153.pdf" } ], "pub_year": "2015", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/0k09h-gt966", "eprint_id": 56199, "eprint_status": "archive", "datestamp": "2023-08-20 05:35:41", "lastmod": "2026-04-04 20:40:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Pushnitski-A", "name": { "family": "Pushnitski", "given": "Alexander" } } ] }, "title": "Trace Class Conditions for Functions of Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 The Author(s). Copyright \u00a9 2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 4 February 2014. Accepted: 26 May 2014. Published online: 6 November 2014. Communicated by L. Erd\u00f6s.\n\nThe authors are grateful to M. Lewin, J. Sabin and D. Yafaev for useful discussions. Financial support from the U.S. National Science Foundation through Grant PHY-1347399 (R. F.) is acknowledged.\n\n

Published - art_10.1007_s00220-014-2205-8.pdf

Submitted - 1402.0763v1.pdf

", "abstract": "We consider the difference f(\u2212\u0394+V)\u2212f(\u2212\u0394) of functions of Schr\u00f6dinger operators in L^2(R^d) and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions f and in V belonging only to some L^p space. This is motivated by applications in mathematical physics related to Lieb\u2013Thirring inequalities. We show that in the particular case of Schr\u00f6dinger operators the well-known sufficient conditions on f, based on a general operator theoretic result due to V. Peller, can be considerably relaxed. We prove similar theorems for f(\u2212\u0394+V)\u2212f(\u2212\u0394)\u2212^d/_(d\u03b1)f(\u2212\u0394+\u03b1V)|\u03b1=0 . Our key idea is the use of the limiting absorption principle.", "date": "2015-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "335", "number": "1", "publisher": "Springer", "pagerange": "477-496", "id_number": "CaltechAUTHORS:20150330-070612488", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150330-070612488", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-014-2205-8", "primary_object": { "basename": "1402.0763v1.pdf", "url": "https://authors.library.caltech.edu/records/0k09h-gt966/files/1402.0763v1.pdf" }, "related_objects": [ { "basename": "art_10.1007_s00220-014-2205-8.pdf", "url": "https://authors.library.caltech.edu/records/0k09h-gt966/files/art_10.1007_s00220-014-2205-8.pdf" } ], "pub_year": "2015", "author_list": "Frank, Rupert L. and Pushnitski, Alexander" }, { "id": "https://authors.library.caltech.edu/records/p1qtp-rka12", "eprint_id": 97815, "eprint_status": "archive", "datestamp": "2023-08-20 05:23:58", "lastmod": "2026-04-04 05:15:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Gasarch-W", "name": { "family": "Gasarch", "given": "William" } }, { "id": "Harris-D-G", "name": { "family": "Harris", "given": "David G." } }, { "id": "Ulrich-D", "name": { "family": "Ulrich", "given": "Douglas" } }, { "id": "Zbarsky-S", "name": { "family": "Zbarsky", "given": "Samuel" } } ] }, "title": "Distinct Volume Subsets", "ispublished": "pub", "full_text_status": "public", "keywords": "Distinct volumes, canonical Ramsey theorems", "note": "\u00a9 2015 Society for Industrial and Applied Mathematics. \n\nReceived by the editors January 27, 2014; accepted for publication (in revised form) December 16, 2014; published electronically March 11, 2015. \n\nConlon's research was supported by a Royal Society University Research Fellowship. Fox's research was supported by a Packard Fellowship, by a Simons Fellowship, by NSF grant DMS-1069197, by an Alfred P. Sloan Research Fellowship, and by an MIT NEC Corporation Award. \n\nThe authors would like to thank Tucker Bane, Andrew Lohr, Jared Marx-Kuo, Joe Mileti, Jessica Shi, Srinivas Vasudevan, and Yufei Zhao for helpful discussions.\n\n

Published - 140954519.pdf

Submitted - 1401.6734.pdf

", "abstract": "Suppose that a and d are positive integers with a \u2265 2. Let h_(a,d)(n) be the largest integer t such that any set of n points in \u211d^d contains a subset of t points for which all the nonzero volumes of the [equaton; see abstract in PDF for details] subsets of order a are distinct. Beginning with Erd\u0151s in 1957, the function h_(2,d)(n) has been closely studied and is known to be at least a power of n. We improve the best known bound for h_(2,d)(n) and show that h_(a,d)(n) is at least a power of n for all a and d.", "date": "2015-03-11", "date_type": "published", "publication": "SIAM Journal on Discrete Mathematics", "volume": "29", "number": "1", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "472-480", "id_number": "CaltechAUTHORS:20190812-162958151", "issn": "0895-4801", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958151", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/140954519", "primary_object": { "basename": "140954519.pdf", "url": "https://authors.library.caltech.edu/records/p1qtp-rka12/files/140954519.pdf" }, "related_objects": [ { "basename": "1401.6734.pdf", "url": "https://authors.library.caltech.edu/records/p1qtp-rka12/files/1401.6734.pdf" } ], "pub_year": "2015", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/yn98w-t4t25", "eprint_id": 56945, "eprint_status": "archive", "datestamp": "2023-08-22 15:07:45", "lastmod": "2026-04-04 07:32:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lo-Catharine-Wing-Kwan", "name": { "family": "Lo", "given": "Catharine Wing Kwan" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "F_\u03b6-geometry, Tate motives, and the Habiro ring", "ispublished": "pub", "full_text_status": "public", "keywords": "Field with one element; roots of unity; Tate motives; Habiro ring; quantum modular forms", "note": "\u00a9 2015 World Scientific Publishing Company. \n\nReceived 28 October 2013. Accepted 25 May 2014. Published 1 July 2014. \n\nThe first author is supported by a Summer Undergraduate Research Fellowship at Caltech. The second author is supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440.\n\n

Submitted - 1310.2261.pdf

", "abstract": "In this paper, we propose different notions of F_zeta-geometry, for zeta a root of unity, generalizing notions of over finite fields, the Grothendieck class, and the notion of torification. We relate Fzeta-geometry to formal roots of Tate motives, and to functions in the Habiro ring, seen as counting functions of certain ind-varieties. We investigate the existence of Fzeta-structures in examples arising from general linear groups, matrix equations over finite fields, and some quantum modular forms.", "date": "2015-03-02", "date_type": "published", "publication": "International Journal of Number Theory", "volume": "11", "number": "2", "publisher": "World Scientific Publishing", "pagerange": "311-339", "id_number": "CaltechAUTHORS:20150424-091752124", "issn": "1793-0421", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150424-091752124", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S1793042115500189", "primary_object": { "basename": "1310.2261.pdf", "url": "https://authors.library.caltech.edu/records/yn98w-t4t25/files/1310.2261.pdf" }, "pub_year": "2015", "author_list": "Lo, Catharine Wing Kwan and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/gm33c-rsp82", "eprint_id": 62751, "eprint_status": "archive", "datestamp": "2023-08-22 15:05:42", "lastmod": "2026-04-04 20:30:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Napp-J", "name": { "family": "Napp", "given": "John" } } ] }, "title": "Quantum Computation and Real Multiplication", "ispublished": "pub", "full_text_status": "public", "keywords": "Anyons; Topological quantum computing; Noncommutative tori with real multiplication; AF algebras", "note": "\u00a9 2014 Springer Basel. \n\nReceived: 11 January 2014; Revised: 28 March 2014; Accepted: 2 April 2014; Published online: 24 April 2014. \n\nJ. Napp is supported by a Summer Undergraduate Research Fellowship at Caltech. M. Marcolli is supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440.\n\n

Submitted - 1312.3590v1.pdf

", "abstract": "We propose a construction of anyon systems associated to quantum tori with real multiplication and the embedding of quantum tori in AF algebras. These systems generalize the Fibonacci anyons, with weaker categorical properties, and are obtained from the basic modules and the real multiplication structure.", "date": "2015-03", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "9", "number": "1", "publisher": "Springer", "pagerange": "63-84", "id_number": "CaltechAUTHORS:20151209-134217011", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151209-134217011", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-014-0179-8", "primary_object": { "basename": "1312.3590v1.pdf", "url": "https://authors.library.caltech.edu/records/gm33c-rsp82/files/1312.3590v1.pdf" }, "pub_year": "2015", "author_list": "Marcolli, Matilde and Napp, John" }, { "id": "https://authors.library.caltech.edu/records/nkj2h-fmc73", "eprint_id": 56102, "eprint_status": "archive", "datestamp": "2023-08-22 15:02:35", "lastmod": "2026-04-04 22:12:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kr\u00fcger-H", "name": { "family": "Kr\u00fcger", "given": "Helge" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Cantor polynomials and some related classes of OPRL", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials; Cantor set; Almost periodic", "note": "\u00a9 2014 Elsevier Inc.\n\nReceived 30 December 2013; received in revised form 5 March 2014; accepted 7 April 2014; Available online 16 April 2014.\n\nThe first author was supported by the Simons Foundation as a Simons Postodoctal Fellow. The second author was supported in part by National Science Foundation grants DMS-0968856; 1265592.\n\n

Submitted - p334.pdf

", "abstract": "We explore the spectral theory of the orthogonal polynomials associated to the classical Cantor measure and similar singular continuous measures. We prove regularity in the sense of Stahl\u2013Totik with polynomial bounds on the transfer matrix. We present numerical evidence that the Jacobi parameters for this problem are asymptotically almost periodic and discuss the possible meaning of the isospectral torus and the Szeg\u0151 class in this context.", "date": "2015-03", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "191", "publisher": "Elsevier", "pagerange": "71-93", "id_number": "CaltechAUTHORS:20150326-081223615", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150326-081223615", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-0968856" }, { "agency": "NSF", "grant_number": "DMS-1265592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2014.04.003", "primary_object": { "basename": "p334.pdf", "url": "https://authors.library.caltech.edu/records/nkj2h-fmc73/files/p334.pdf" }, "pub_year": "2015", "author_list": "Kr\u00fcger, Helge and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/sehfj-w7m20", "eprint_id": 71972, "eprint_status": "archive", "datestamp": "2023-08-20 04:49:41", "lastmod": "2026-04-04 21:07:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Tessler-R-J", "name": { "family": "Tessler", "given": "Ran J." } } ] }, "title": "Majority Dynamics and the Retention of Information", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 Hebrew University of Jerusalem. \n\nReceived July 18, 2013 and in revised form April 28, 2014. \n\nFirst Online:16 December 2014. \n\nOmer Tamuz is supported by ISF grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing, and this research is supported in part by this Google Fellowship.\n\n

Submitted - 1307.4035.pdf

", "abstract": "We consider a group of agents connected by a social network who participate in majority dynamics: each agent starts with an opinion in {\u22121, +1} and repeatedly updates it to match the opinion of the majority of its neighbors.\n\nWe assume that one of {\u22121, +1} is the \"correct\" opinion S, and consider a setting in which the initial opinions are independent conditioned on S, and biased towards it. They hence contain enough information to reconstruct S with high probability. We ask whether it is still possible to reconstruct S from the agents' opinions after many rounds of updates.\n\nWhile this is not the case in general, we show that indeed, for a large family of bounded degree graphs, information on S is retained by the process of majority dynamics.\n\nOur proof technique yields novel combinatorial results on majority dynamics on both finite and infinite graphs, with applications to zero temperature Ising models.", "date": "2015-02", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "206", "number": "1", "publisher": "Springer", "pagerange": "483-507", "id_number": "CaltechAUTHORS:20161114-074309531", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-074309531", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-014-1148-2", "primary_object": { "basename": "1307.4035.pdf", "url": "https://authors.library.caltech.edu/records/sehfj-w7m20/files/1307.4035.pdf" }, "pub_year": "2015", "author_list": "Tamuz, Omer and Tessler, Ran J." }, { "id": "https://authors.library.caltech.edu/records/kbn12-7ja64", "eprint_id": 56544, "eprint_status": "archive", "datestamp": "2023-08-20 04:47:41", "lastmod": "2026-04-04 20:36:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bengurla-R-D", "name": { "family": "Bengurla", "given": "Rafael D." } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Ground state energy of large polaron systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2015 AIP Publishing LLC. Received 17 December 2014; accepted 3 February 2015; published online 18 February 2015.\n\nThe authors are grateful to Jan Philip Solovej for useful discussions about Theorem 1.1. Work is partially supported by Fondecyt (Chile) project 112\u20130836 and the Iniciativa Cient\u00edfica Milenio (Chile) through the Millenium Nucleus RC\u2013120002 \"F\u00edsica Matem\u00e1tica\" (R.D.B.), and NSF Grant Nos. PHY\u20131347399 and DMS\u20131363432 (R.L.F.); PHY\u20130965859 and PHY\u20131265118 (E.H.L.)\n\n

Published - 1.4908125.pdf

Submitted - 1409.5415v1.pdf

", "abstract": "The last unsolved problem about the many-polaron system, in the Pekar\u2013Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the \"neutral case\"). We prove that the ground state energy, for large N, goes exactly as \u2212N^(7/5), and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 2^(2/5).", "date": "2015-02", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "56", "number": "2", "publisher": "American Institute of Physics", "pagerange": "Art. No. 021901", "id_number": "CaltechAUTHORS:20150409-135549549", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150409-135549549", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico (FONDECYT)", "grant_number": "112\u20130836" }, { "agency": "Iniciativa Cient\u00edfica Milenio", "grant_number": "RC\u2013120002" }, { "agency": "NSF", "grant_number": "PHY\u20131347399" }, { "agency": "NSF", "grant_number": "DMS\u20131363432" }, { "agency": "NSF", "grant_number": "PHY\u20130965859" }, { "agency": "NSF", "grant_number": "PHY\u20131265118" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.4908125", "primary_object": { "basename": "1409.5415v1.pdf", "url": "https://authors.library.caltech.edu/records/kbn12-7ja64/files/1409.5415v1.pdf" }, "related_objects": [ { "basename": "1.4908125.pdf", "url": "https://authors.library.caltech.edu/records/kbn12-7ja64/files/1.4908125.pdf" } ], "pub_year": "2015", "author_list": "Bengurla, Rafael D.; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/7y1cv-mrw60", "eprint_id": 66649, "eprint_status": "archive", "datestamp": "2023-08-20 04:48:54", "lastmod": "2026-04-04 14:06:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" }, { "id": "Willett-B", "name": { "family": "Willett", "given": "Brian" } } ] }, "title": "Generalized global symmetries", "ispublished": "pub", "full_text_status": "public", "keywords": "Global Symmetries, Wilson, 't Hooft and Polyakov loops, Topological States of Matter, Anomalies in Field and String Theories", "note": "\u00a9 2015 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: February 1, 2015. Accepted: February 1, 2015. Published: February 26, 2015. \n\nArticle funded by SCOAP3. \n\nWe are grateful to S. Razamat for collaboration at an early stage of the project and many important discussions. We also thank O. Aharony, N. Arkani-Hamed, J. Maldacena,\nG. Moore, S. Shenker, Y. Tachikawa, and E. Witten for helpful discussions. We also thank Y. Tachikawa for comments on the manuscript. The research of DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported\nby the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of AK was supported in part by the DOE grant DE-FG02-92ER40701 and by Simons Foundation. The work of NS was supported in part by DOE grant DE-SC0009988 and by the United States-Israel Binational Science Foundation (BSF) under grant number 2010/629. The research of BW was supported in part by DOE Grant DE-SC0009988 and the Roger Dashen Membership. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - Gaiotto,_D._et_all_pg172.pdf

Submitted - 1412.5148.pdf

", "abstract": "A q-form global symmetry is a global symmetry for which the charged operators are of space-time dimension q; e.g. Wilson lines, surface defects, etc., and the charged excitations have q spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (q = 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.", "date": "2015-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2015", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 172", "id_number": "CaltechAUTHORS:20160504-105751877", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-105751877", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "SCOAP3" }, { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Simons Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010/629" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "Roger Dashen Membership" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP02(2015)172", "primary_object": { "basename": "Gaiotto,_D._et_all_pg172.pdf", "url": "https://authors.library.caltech.edu/records/7y1cv-mrw60/files/Gaiotto,_D._et_all_pg172.pdf" }, "related_objects": [ { "basename": "1412.5148.pdf", "url": "https://authors.library.caltech.edu/records/7y1cv-mrw60/files/1412.5148.pdf" } ], "pub_year": "2015", "author_list": "Gaiotto, Davide; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/p3703-jjz68", "eprint_id": 55265, "eprint_status": "archive", "datestamp": "2023-08-22 14:47:08", "lastmod": "2026-04-04 21:22:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Gonz\u00e1lez-M-del-M", "name": { "family": "Gonz\u00e1lez", "given": "Mar\u00eda del Mar" } }, { "id": "Monticelli-D-D", "name": { "family": "Monticelli", "given": "Dario D." } }, { "id": "Tan-Jinggang", "name": { "family": "Tan", "given": "Jinggang" } } ] }, "title": "An extension problem for the CR fractional Laplacian", "ispublished": "pub", "full_text_status": "public", "keywords": "Fractional order operators; Fractional order weighted Sobolev spaces; Sublaplacian; CR manifolds; Heisenberg group", "note": "\u00a9 2014 Elsevier Inc. Received 17 December 2013, Accepted 5 September 2014, Available online 13 November 2014. Communicated by Charles Fefferman.\n\nR.F. acknowledges financial support from the NSF grants PHY-1068285 and PHY-1347399. M.G. was supported by Spain Government grant MTM2011-27739-C04-01 and GenCat 2009SGR345. D.M. was supported by GNAMPA project with title \"Equazioni differenziali con invarianze in analisi globale\", by GNAMPA section \"Equazioni differenziali e sistemi dinamici\" and by MIUR project \"Metodi variazionali e topologici nello studio di fenomeni nonlineari\". J.T. was supported by Chile Government grants Fondecyt #1120105, USM 121402, the Spain Government grant MTM2011-27739-C04-01 and Programa Basal, CMM. U. de Chile.\nThe authors wish to thank the referee for many useful comments which helped in the exposition.\n\n

Submitted - 1312.3381v1.pdf

", "abstract": "We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem is different from the one studied, among others, by Caffarelli and Silvestre. We also prove an energy identity that yields a sharp trace Sobolev embedding.", "date": "2015-01-22", "date_type": "published", "publication": "Advances in Mathematics", "volume": "270", "publisher": "Elsevier", "pagerange": "97-137", "id_number": "CaltechAUTHORS:20150226-131020302", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150226-131020302", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "Spain Government", "grant_number": "MTM2011-27739-C04-01" }, { "agency": "Spain Government", "grant_number": "GenCat 2009SGR345" }, { "agency": "GNAMPA project \"Equazioni differenziali con invarianze in analisi globale\"" }, { "agency": "GNAMPA section \"Equazioni differenziali e sistemi dinamici\"" }, { "agency": "MIUR project \"Metodi variazionali e topologici nello studio di fenomeni nonlineari\"" }, { "agency": "Chile Government Fondecyt", "grant_number": "1120105" }, { "agency": "Chile Government Fondecyt", "grant_number": "USM 121402" }, { "agency": "Programa Basal" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2014.09.026", "primary_object": { "basename": "1312.3381v1.pdf", "url": "https://authors.library.caltech.edu/records/p3703-jjz68/files/1312.3381v1.pdf" }, "pub_year": "2015", "author_list": "Frank, Rupert L.; Gonz\u00e1lez, Mar\u00eda del Mar; et al." }, { "id": "https://authors.library.caltech.edu/records/5dchg-1zd18", "eprint_id": 52007, "eprint_status": "archive", "datestamp": "2023-08-22 14:35:43", "lastmod": "2026-03-09 23:11:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "A mild Tchebotarev theorem for GL(n)", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Rallis; Automorphic representation; Tchebotarev; Multiplicity one", "note": "\u00a9 2014 Elsevier Inc.\n\nReceived 31 March 2014;\nReceived in revised form 27 August 2014;\nAccepted 27 August 2014;\nAvailable online 16 September 2014.\n\nWe thank the many people who have shown interest in this work over the past few years, especially to those who have used it and have encouraged, like K. Martin, to have it published. Thanks are also due to the NSF for partial support through the grants DMS-0701089 and DMS-1001916. This article is dedicated to the memory of Steve Rallis from whom this author learnt a lot in conversations over the years.", "abstract": "It is well known that the Tchebotarev density theorem implies that an irreducible \u2113-adic representation \u03c1 of the absolute Galois group of a number field K is determined (up to isomorphism) by the characteristic polynomials of Frobenius elements at any set of primes of density 1. In this Note we make some progress on the automorphic side for GL(n) by showing that, for any cyclic extension K/k of number fields of prime degree p, a cuspidal automorphic representation \u03c0 of GL(n,A_K) is determined up to twist equivalence, even up to isomorphism if p=2, by the knowledge of its local components at the (density one) set S_(K/k) of primes of K of degree 1 over k. The proof uses the Luo\u2013Rudnick\u2013Sarnak bound, certain L-functions of positive type, Kummer theory, and automorphic descent along suitable nested sequences of cyclic p^2-extensions.", "date": "2015-01", "date_type": "published", "publication": "Journal of Number Theory", "volume": "146", "publisher": "Elsevier", "pagerange": "519-533", "id_number": "CaltechAUTHORS:20141120-132636662", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141120-132636662", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0701089" }, { "agency": "NSF", "grant_number": "DMS-1001916" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jnt.2014.08.002", "pub_year": "2015", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/wfkbj-czf19", "eprint_id": 57015, "eprint_status": "archive", "datestamp": "2023-08-20 04:26:27", "lastmod": "2026-03-09 20:29:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Guth-L", "name": { "family": "Guth", "given": "Larry" } }, { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" } ] }, "title": "On the Erd\u0151s distinct distances problem in the plane", "ispublished": "pub", "full_text_status": "public", "keywords": "distinct distances, Incidence geometry, polynomial ham sandwich, polynomial method, ruled surface", "note": "\u00a9 2015 Department of Mathematics, Princeton University. Received: 18 November 2010. Revised: 15 July 2014. Accepted: 14 April 2014.\n\nThe first author is partially supported by NSERC, by NSF grant DMS-0635607, and by the Monell Foundation. The second author is partially supported by NSF grant DMS-1001607. He would like to thank Michael Larsen for some very helpful discussions about algebraic geometry. He would also like to thank the Institute of Advanced Study for the use of its magnificent duck pond during a visit that resulted in this paper. Both authors would like to thank the helpful referee because of whom the exposition in the paper is significantly improved.\n\n

Published - annals-v181-n1-p02-p.pdf

", "abstract": "In this paper, we prove that a set of N points in R^2 has at least c^N_(logN) distinct distances, thus obtaining the sharp exponent in a problem of Erd\u0151s. We follow the setup of Elekes and Sharir which, in the spirit of the Erlangen program, allows us to study the problem in the group of rigid motions of the plane. This converts the problem to one of point-line incidences in space. We introduce two new ideas in our proof. In order to control points where many lines are incident, we create a cell decomposition using the polynomial ham sandwich theorem. This creates a dichotomy: either most of the points are in the interiors of the cells, in which case we immediately get sharp results or, alternatively, the points lie on the walls of the cells, in which case they are in the zero-set of a polynomial of suprisingly low degree, and we may apply the algebraic method. In order to control points incident to only two lines, we use the flecnode polynomial of the Rev. George Salmon to conclude that most of the lines lie on a ruled surface. Then we use the geometry of ruled surfaces to complete the proof.", "date": "2015-01", "date_type": "published", "publication": "Annals of Mathematics", "volume": "181", "number": "1", "publisher": "Princeton University, Department of Mathematics", "pagerange": "155-190", "id_number": "CaltechAUTHORS:20150427-131107573", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150427-131107573", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "Monell Foundation" }, { "agency": "NSF", "grant_number": "DMS-1001607" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2015.181.1.2", "primary_object": { "basename": "annals-v181-n1-p02-p.pdf", "url": "https://authors.library.caltech.edu/records/wfkbj-czf19/files/annals-v181-n1-p02-p.pdf" }, "pub_year": "2015", "author_list": "Guth, Larry and Katz, Nets Hawk" }, { "id": "https://authors.library.caltech.edu/records/mrfhv-pps81", "eprint_id": 97832, "eprint_status": "archive", "datestamp": "2023-08-20 04:29:01", "lastmod": "2026-03-08 03:40:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Lee-Choongbum", "name": { "family": "Lee", "given": "Choongbum" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "The Erd\u0151s-Gy\u00e1rf\u00e1s problem on generalized Ramsey numbers", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 London Mathematical Society. \n\nReceived 2 March 2014; revised 28 April 2014; published online 16 October 2014. \n\nDavid Conlon was supported by a Royal Society University Research Fellowship. Jacob Fox was supported by a Packard Fellowship, by a Simons Fellowship, by NSF grant DMS\u20101069197, by an Alfred P. Sloan Fellowship and by an MIT NEC Corporation Award. Benny Sudakov was supported in part by SNSF grant 200021\u2010149111 and by a USA\u2010Israel BSF grant. \n\nWe thank the anonymous referee for a number of helpful comments on the manuscript.\n\n

Submitted - 1403.0250.pdf

", "abstract": "Fix positive integers p and q with [equation; see abstract in PDF for details]. An edge coloring of the complete graph K_n is said to be a (p,q)-coloring if every K_p receives at least q different colors. The function f(n,p,q) is the minimum number of colors that are needed for K_n to have a (p,q)-coloring. This function was introduced about 40 years ago, but Erd\u0151s and Gy\u00e1rf\u00e1s were the first to study the function in a systematic way. They proved that f(n,p,p) is polynomial in n and asked to determine the maximum q, depending on p, for which f(n,p,q) is subpolynomial in n. We prove that the answer is p - 1.", "date": "2015-01", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "110", "number": "1", "publisher": "London Mathematical Society", "pagerange": "1-18", "id_number": "CaltechAUTHORS:20190812-162959803", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959803", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms/pdu049", "primary_object": { "basename": "1403.0250.pdf", "url": "https://authors.library.caltech.edu/records/mrfhv-pps81/files/1403.0250.pdf" }, "pub_year": "2015", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/fmcwj-k5d18", "eprint_id": 62450, "eprint_status": "archive", "datestamp": "2023-08-20 04:11:48", "lastmod": "2026-03-09 20:29:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets" }, "orcid": "0000-0002-6239-5429" }, { "id": "Tapay-A", "name": { "family": "Tapay", "given": "Andrew" } } ] }, "title": "A model for studying double exponential growth in the two-dimensional Euler equations", "ispublished": "pub", "full_text_status": "public", "keywords": "fluid mechanics, Euler equations, two-dimensional Euler equations", "note": "\u00a9 2015 Mathematical Sciences Publishers. \n\nReceived 16 Oct 2014. Revised 8 May 2015. Accepted 24 Jun 2015. \n\nBoth authors were partially supported by NSF grant DMS 1266104.\n\n

Published - apde-v8-n7-p04-s.pdf

Submitted - 1403.6867v1.pdf

", "abstract": "We introduce a model for the two-dimensional Euler equations which is designed to study whether or not double exponential growth can be achieved for a short time at an interior point of the flow.", "date": "2015", "date_type": "published", "publication": "Analysis & PDE", "volume": "8", "number": "7", "publisher": "Mathematical Sciences Publishers", "pagerange": "1675-1693", "id_number": "CaltechAUTHORS:20151130-132253511", "issn": "2157-5045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151130-132253511", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1266104" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/apde.2015.8.1675", "primary_object": { "basename": "apde-v8-n7-p04-s.pdf", "url": "https://authors.library.caltech.edu/records/fmcwj-k5d18/files/apde-v8-n7-p04-s.pdf" }, "related_objects": [ { "basename": "1403.6867v1.pdf", "url": "https://authors.library.caltech.edu/records/fmcwj-k5d18/files/1403.6867v1.pdf" } ], "pub_year": "2015", "author_list": "Katz, Nets and Tapay, Andrew" }, { "id": "https://authors.library.caltech.edu/records/eycp5-0fg25", "eprint_id": 63485, "eprint_status": "archive", "datestamp": "2023-08-22 14:33:34", "lastmod": "2026-04-23 16:12:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Dimitrov", "given": "Mladen" }, "orcid": "0000-0002-7228-9136" }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Arithmetic Quotients of the Complex Ball and a Conjecture of Lang", "ispublished": "pub", "full_text_status": "public", "keywords": "Rational points; Picard modular surfaces; Albanese varieties; Automorphic representations of unitary groups", "note": "\u00a9 2015 Documenta Mathematica.\n\nReceived: October 10, 2014. Revised: September 28, 2015. \n\nWe would like to thank Don Blasius, Jean-Fran\u00e7ois Dat, Najmuddin Fakhruddin, Dick Gross, Barry Mazur, Matthew Stover and Shing-Tung Yau for helpful conversations. In fact it was Fakhruddin who suggested our use of the Mordell-Lang conjecture for abelian varieties. Needless to say, this Note owes much to the deep results of Faltings. In addition, we thank the referee and Blasius for their corrections and suggestions which led to an improvement of the presentation. Thanks are also due to Serge Lang (posthumously), and to John Tate, for getting one of us interested in the conjectural Mordellic property of hyperbolic varieties. Finally, we are also happy to acknowledge partial support from the following sources: the Agence Nationale de la Recherche grants ANR-10-BLAN-0114 and ANR-11-LABX-0007-01 for the first author, and the NSF grant DMS-1001916 for the second author.", "abstract": "We prove that various arithmetic quotients of the unit ball in C^n are Mordellic, in the sense that they have only finitely many rational points over any finitely generated field extension of Q. In the previously known case of compact hyperbolic complex surfaces, we give a new proof using their Albanese in conjunction with some key results of Faltings, but without appealing to the Shafarevich conjecture. In higher dimension, our methods allow us to solve an alternative of Ullmo and Yafaev. Our strongest result uses in addition Rogawski's theory and establishes the Mordellicity of the Baily-Borel compactifications of Picard modular surfaces of some precise levels related to the discriminant of the imaginary quadratic fields.", "date": "2015", "date_type": "published", "publication": "Documenta Mathematica", "volume": "20", "publisher": "Deutsche Mathematiker-Vereinigung (DMV)", "pagerange": "1185-1205", "id_number": "CaltechAUTHORS:20160108-082533307", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160108-082533307", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Agence Nationale de la Recherche (ANR)", "grant_number": "ANR-10-BLAN-0114" }, { "agency": "Agence Nationale de la Recherche (ANR)", "grant_number": "ANR-11-LABX-0007-01" }, { "agency": "NSF", "grant_number": "DMS-1001916" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Division-of-Physics-Mathematics-and-Astronomy" } ] }, "doi": "10.4171/dm/516", "primary_object": { "basename": "10.4171-dm-516.pdf", "url": "https://authors.library.caltech.edu/records/eycp5-0fg25/files/10.4171-dm-516.pdf" }, "related_objects": [ { "basename": "1401.1628v4.pdf", "url": "https://authors.library.caltech.edu/records/eycp5-0fg25/files/1401.1628v4.pdf" } ], "pub_year": "2015", "author_list": "Dimitrov, Mladen and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/xex3c-8pd94", "eprint_id": 52583, "eprint_status": "archive", "datestamp": "2023-08-22 14:31:28", "lastmod": "2026-04-05 15:41:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wu-Zhongtao", "name": { "family": "Wu", "given": "Zhongtao" } } ] }, "title": "Heegaard Floer correction terms and rational genus bounds", "ispublished": "pub", "full_text_status": "public", "keywords": "Heegaard Floer homology; Correction terms; Rational genus; Lens space; Simple knots", "note": "\u00a9 2014 Elsevier Inc. Received 21 September 2012. Accepted 8 September 2014. Available online 26 September 2014.\nCommunicated by Tomasz S. Mrowka.\n\nThe first author wishes to thank Jacob Rasmussen for asking the question which motivated this work. The first author was partially supported by an AIM Five-Year Fellowship, NSF grant number DMS-1103976 and an Alfred P. Sloan Research Fellowship. The second author was supported by a Simons Postdoctoral Fellowship.\n\n

Submitted - 1205.7053v2.pdf

", "abstract": "Given an element in the first homology of a rational homology 3-sphere Y , one can consider the minimal rational genus of all knots in this homology class. This defines a function \u0398 on _(H1)(Y;Z), which was introduced by Turaev as an analogue of Thurston norm. We will give a lower bound for this function using the correction terms in Heegaard Floer homology. As a corollary, we show that Floer simple knots in L-spaces are genus minimizers in their homology classes, hence answer questions of Turaev and Rasmussen about genus minimizers in lens spaces.", "date": "2014-12-20", "date_type": "published", "publication": "Advances in Mathematics", "volume": "267", "publisher": "Elsevier", "pagerange": "360-380", "id_number": "CaltechAUTHORS:20141211-091257551", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141211-091257551", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2014.09.006", "primary_object": { "basename": "1205.7053v2.pdf", "url": "https://authors.library.caltech.edu/records/xex3c-8pd94/files/1205.7053v2.pdf" }, "pub_year": "2014", "author_list": "Ni, Yi and Wu, Zhongtao" }, { "id": "https://authors.library.caltech.edu/records/2xrg4-tje16", "eprint_id": 97846, "eprint_status": "archive", "datestamp": "2023-08-22 14:24:19", "lastmod": "2026-04-05 14:54:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Cycle packing", "ispublished": "pub", "full_text_status": "public", "keywords": "Graph decompositions; cycles; expanders; Erd\u0151s\u2010Gallai conjecture", "note": "\u00a9 2014 Wiley. \n\nIssue online 06 February 2015; version of record online 06 February 2015; manuscript accepted 13 May 2014; manuscript received 02 October 2013. \n\nSupported by Royal Society University Research Fellowship (to D.C.); Packard Fellowship (to J.F.); Simons Fellowship (to J.F.); NSF Grant (to J.F.) (DMS\u20101069197); Alfred P. Sloan Fellowship (to J.F.); MIT NEC Corporation Award (to J.F.); SNSF Grant (to B.S.) (200021\u2010149111); USA\u2010Israel BSF Grant (to B.S.). \n\nWe would like to thank David Ellis and Daniel Kane for helpful remarks. We would also like to thank the anonymous referees for a number of useful comments.\n\n

Submitted - 1310.0632.pdf

", "abstract": "In the 1960s, Erd\u0151s and Gallai conjectured that the edge set of every graph on n vertices can be partitioned into O(n) cycles and edges. They observed that one can easily get an O(nlogn) upper bound by repeatedly removing the edges of the longest cycle. We make the first progress on this problem, showing that O(nloglogn) cycles and edges suffice. We also prove the Erd\u0151s\u2010Gallai conjecture for random graphs and for graphs with linear minimum degree.", "date": "2014-12", "date_type": "published", "publication": "Random Structures & Algorithms", "volume": "45", "number": "4", "publisher": "Wiley", "pagerange": "608-626", "id_number": "CaltechAUTHORS:20190812-163001129", "issn": "1042-9832", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001129", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-149111" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.20574", "primary_object": { "basename": "1310.0632.pdf", "url": "https://authors.library.caltech.edu/records/2xrg4-tje16/files/1310.0632.pdf" }, "pub_year": "2014", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/adacd-mkj98", "eprint_id": 56820, "eprint_status": "archive", "datestamp": "2023-08-20 03:51:24", "lastmod": "2026-04-05 16:45:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Grigsby-J-E", "name": { "family": "Grigsby", "given": "J. Elisenda" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Sutured Khovanov homology distinguishes braids from other tangles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 International Press. \n\nReceived June 11, 2013. \n\nThe first author was partially supported by NSF grant numbers DMS-0905848 and CAREER DMS-1151671. The second author was partially supported by NSF grant number DMS-1103976 and an Alfred P. Sloan Research Fellowship. We thank the anonymous referee for a number of valuable suggestions.\n\n

Submitted - 1305.2183v2.pdf

", "abstract": "We show that the sutured Khovanov homology of a balanced tangle in the\nproduct sutured manifold D x I has rank 1 if and only if the tangle is isotopic\nto a braid.", "date": "2014-12", "date_type": "published", "publication": "Mathematical Research Letters", "volume": "21", "number": "6", "publisher": "International Press", "pagerange": "1263-1275", "id_number": "CaltechAUTHORS:20150421-115841144", "issn": "1073-2780", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115841144", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0905848" }, { "agency": "NSF", "grant_number": "DMS-1151671" }, { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/MRL.2014.v21.n6.a4", "primary_object": { "basename": "1305.2183v2.pdf", "url": "https://authors.library.caltech.edu/records/adacd-mkj98/files/1305.2183v2.pdf" }, "pub_year": "2014", "author_list": "Grigsby, J. Elisenda and Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/eftgc-sjf73", "eprint_id": 52577, "eprint_status": "archive", "datestamp": "2023-08-20 03:47:37", "lastmod": "2026-04-05 16:40:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bellazzini-J", "name": { "family": "Bellazzini", "given": "Jacopo" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Visciglia-N", "name": { "family": "Visciglia", "given": "Nicola" } } ] }, "title": "Maximizers for Gagliardo\u2013Nirenberg inequalities and related non-local problems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 Springer-Verlag Berlin Heidelberg.\n\nReceived: 28 August 2013; Revised: 9 April 2014; Published online: 9 May 2014.\n\nFIRB2012 'Dinamiche dispersive: analisi di Fourier e metodi variazionali' (J.B.,\nN.V.) and PRIN2009 'Metodi Variazionali e Topologici nello Studio di Fenomeni non Lineari' (J.B.) and\nU.S. National Science Foundation grants PHY-1068285 and PHY-1347399 (R.F.) are acknowledged. The\nauthors would like to thank E. Lieb and G. Ponce for useful discussions.\n\n

Submitted - 1308.5612v1.pdf

", "abstract": "In this paper we study the existence of maximizers for two families of interpolation inequalities, namely a generalized Gagliardo\u2013Nirenberg inequality and a new inequality involving the Riesz energy. Two basic tools in our argument are a generalization of Lieb's Translation Lemma and a Riesz energy version of the Br\u00e9zis\u2013Lieb lemma.", "date": "2014-12", "date_type": "published", "publication": "Mathematische Annalen", "volume": "360", "number": "3-4", "publisher": "Springer Verlag", "pagerange": "653-673", "id_number": "CaltechAUTHORS:20141211-085533969", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141211-085533969", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministero dell'Istruzione, dell'Universit\u00e0 della Ricerca (MIUR)", "grant_number": "FIRB2012" }, { "agency": "Ministero dell'Istruzione, dell'Universit\u00e0 della Ricerca (MIUR)", "grant_number": "PRIN2009" }, { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1347399" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-014-1046-2", "primary_object": { "basename": "1308.5612v1.pdf", "url": "https://authors.library.caltech.edu/records/eftgc-sjf73/files/1308.5612v1.pdf" }, "pub_year": "2014", "author_list": "Bellazzini, Jacopo; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/34fe1-s8t35", "eprint_id": 72932, "eprint_status": "archive", "datestamp": "2023-08-20 03:22:01", "lastmod": "2026-04-05 22:46:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Liu-Hong", "name": { "family": "Liu", "given": "Hong" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } } ] }, "title": "Hall Viscosity and Angular Momentum in Gapless Holographic Models", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 American Physical Society. \n\nReceived 30 August 2014; published 20 October 2014. \n\nWe thank N. Read, O. Saremi, D.\u2009T. Son, and C. Wu for useful discussion. H.\u2009O. and B.\u2009S. are supported in part by U.S. Department of Energy Grant No. DE-FG03-92-ER40701. The work of H.\u2009O. is also supported in part by a Simons Investigator award from the Simons Foundation, the WPI Initiative of MEXT of Japan, and JSPS Grant-in-Aid for Scientific Research No. C-23540285. He also thanks the hospitality of the Aspen Center for Physics and the National Science Foundation, which supports the Center under Grant No. PHY-1066293, and of the Simons Center for Geometry and Physics. The work of B.\u2009S. is supported in part by a Dominic Orr Graduate Fellowship. B.\u2009S. would like to thank the hospitality of the Kavli Institute for the Physics and Mathematics of the Universe and of the Yukawa Institute for Theoretical Physics. H.\u2009L. is supported in part by funds provided by the U.S. Department of Energy under cooperative research agreement No. DE-FG0205ER41360 and thanks the hospitality of the Isaac Newton Institute for Mathematical Sciences.\n\n

Published - PhysRevD.90.086007.pdf

Submitted - 1403.6047.pdf

", "abstract": "We use the holographic approach to compare the Hall viscosity \u03b7_H and the angular momentum density J in gapless systems in 2+1 dimensions at finite temperature. We start with a conformal fixed point and turn on a perturbation which breaks the parity and time-reversal symmetries via gauge and gravitational Chern-Simons couplings in the bulk. While the ratio of \u03b7_H and J shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, \u03b7_H depends only on infrared physics, while J receives contributions from degrees of freedom at all scales.", "date": "2014-10-15", "date_type": "published", "publication": "Physical Review D", "volume": "90", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 086007", "id_number": "CaltechAUTHORS:20161219-092554100", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161219-092554100", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Dominic Orr Graduate Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-05ER41360" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.90.086007", "primary_object": { "basename": "1403.6047.pdf", "url": "https://authors.library.caltech.edu/records/34fe1-s8t35/files/1403.6047.pdf" }, "related_objects": [ { "basename": "PhysRevD.90.086007.pdf", "url": "https://authors.library.caltech.edu/records/34fe1-s8t35/files/PhysRevD.90.086007.pdf" } ], "pub_year": "2014", "author_list": "Liu, Hong; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/rqm2g-s3m13", "eprint_id": 54329, "eprint_status": "archive", "datestamp": "2023-08-20 03:11:02", "lastmod": "2026-04-05 23:52:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Thorngren-R", "name": { "family": "Thorngren", "given": "Ryan" }, "orcid": "0000-0001-9433-3399" } ] }, "title": "Topological field theory on a lattice, discrete theta-angles and confinement", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 International Press of Boston, Inc.\n\nA.K. would like to thank Dan Freed, Sergei Gukov, Michael Hopkins, Nathan Seiberg, Yuji Tachikawa, and Constantin Teleman for discussions. R.T. would also like to thank Scott Carnahan, Evan Jenkins, Alex Rasmussen, David Roberts, and Urs Schreiber for discussions. This work was supported in part by the DOE grant DE-FG02-92ER40701 and by the National Science Foundation under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics.\n\n

Published - ATMP-2014-0018-0005-a004.pdf

Submitted - 1308.2926v2.pdf

", "abstract": "We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We show that possible theta-angles in such a theory are quantized and labeled by quadratic functions on the magnetic gauge group. When the theta-angles vanish, the theory is dual to an ordinary topological gauge theory, but in general it is not isomorphic to it. We also explain how to couple a lattice Yang-Mills theory to a TQFT of this kind so that the 't Hooft flux is well-defined, and quantized values of the theta-angles are allowed. The quantized theta-angles include the discrete theta-angles recently identified by Aharony, Seiberg and Tachikawa.", "date": "2014-10", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "18", "number": "5", "publisher": "International Press", "pagerange": "1233-1247", "id_number": "CaltechAUTHORS:20150203-134056790", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150203-134056790", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "NSF", "grant_number": "PHY-1066293" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2014.v18.n5.a4", "primary_object": { "basename": "1308.2926v2.pdf", "url": "https://authors.library.caltech.edu/records/rqm2g-s3m13/files/1308.2926v2.pdf" }, "related_objects": [ { "basename": "ATMP-2014-0018-0005-a004.pdf", "url": "https://authors.library.caltech.edu/records/rqm2g-s3m13/files/ATMP-2014-0018-0005-a004.pdf" } ], "pub_year": "2014", "author_list": "Kapustin, Anton and Thorngren, Ryan" }, { "id": "https://authors.library.caltech.edu/records/pfh4w-3qv46", "eprint_id": 97823, "eprint_status": "archive", "datestamp": "2023-08-22 13:50:38", "lastmod": "2026-04-05 14:32:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "D." }, "orcid": "0000-0001-5899-1829" }, { "id": "Gowers-W-T", "name": { "family": "Gowers", "given": "W. T." } }, { "id": "Samotij-W", "name": { "family": "Samotij", "given": "W." } }, { "id": "Schacht-M", "name": { "family": "Schacht", "given": "M." } } ] }, "title": "On the K\u0141R conjecture in random graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Bipartite Graph; Random Graph; Sparse Graph; Regularity Lemma; Regular Partition", "note": "\u00a9 Hebrew University of Jerusalem 2014. \n\nReceived 11 May 2013; revised 24 January 2014; first online 21 March 2015. \n\nConlon research supported by a Royal Society University Research Fellowship. Gowers research supported by a Royal Society 2010 Anniversary Research Professorship. Samotij research supported in part by a Trinity College JRF. Schacht research supported by the Heisenberg programme of the DFG.\n\n

Submitted - 1305.2516.pdf

", "abstract": "The K\u0141R conjecture of Kohayakawa, \u0141uczak, and R\u00f6dl is a statement that allows one to prove that asymptotically almost surely all subgraphs of the random graph G_(n, p), for sufficiently large p := p(n), satisfy an embedding lemma which complements the sparse regularity lemma of Kohayakawa and R\u00f6dl. We prove a variant of this conjecture which is sufficient for most known applications to random graphs. In particular, our result implies a number of recent probabilistic versions, due to Conlon, Gowers, and Schacht, of classical extremal combinatorial theorems. We also discuss several further applications.", "date": "2014-10", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "203", "number": "1", "publisher": "Springer", "pagerange": "535-580", "id_number": "CaltechAUTHORS:20190812-162958948", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958948", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Trinity College" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-014-1120-1", "primary_object": { "basename": "1305.2516.pdf", "url": "https://authors.library.caltech.edu/records/pfh4w-3qv46/files/1305.2516.pdf" }, "pub_year": "2014", "author_list": "Conlon, D.; Gowers, W. T.; et al." }, { "id": "https://authors.library.caltech.edu/records/hb194-ptk12", "eprint_id": 54305, "eprint_status": "archive", "datestamp": "2023-08-22 13:50:06", "lastmod": "2026-03-09 23:13:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "An exercise concerning the selfdual cusp forms on GL(3)", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Selfdual representations; automorphic forms; symmetric square; adjoint", "note": "\u00a9 2014 Indian National Science Academy. \n\nReceived 1 September 2013; after final revision 1 September 2014; accepted 7 September 2014.", "abstract": "Using L-functions and various known results, we provide a proof of the following\n\nLet F be a number field and II a cuspidal automorphic form on GL(3)/F which is selfdual. Then, up to replacing II by a quadratic twist, it can be realized as the adjoint of a cusp form \u03c0 on GL(2)/F, with \u03c0 unramified at any prime where II is. We also investigate the properties of \u03c0 when II is regular and algebraic.", "date": "2014-10", "date_type": "published", "publication": "Indian Journal of Pure and Applied Mathematics", "volume": "45", "number": "5", "publisher": "Indian National Science Academy", "pagerange": "777-785", "id_number": "CaltechAUTHORS:20150202-140155905", "issn": "0019-5588", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150202-140155905", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s13226-014-0088-1", "pub_year": "2014", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/rc5z5-bf975", "eprint_id": 48560, "eprint_status": "archive", "datestamp": "2023-08-20 02:42:32", "lastmod": "2026-04-05 17:08:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Stability of Asymptotics of Christoffel\u2013Darboux Kernels", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 Springer-Verlag Berlin Heidelberg.\n\nReceived: 20 April 2013; Accepted: 30 May 2013;Published online: 21 March 2014.\n\nJ. Breuer, Y. Last: Supported in part by The Israel Science Foundation (Grant No. 1105/10). B. Simon: Supported in part by NSF Grant No. DMS-0968856. J. Breuer, Y. Last, B. Simon: Research supported in part by Grant No. 2010348 from the United States- Israel Binational Science Foundation (BSF), Jerusalem, Israel.\n\n

Submitted - 1302.7237

", "abstract": "We study the stability of convergence of the Christoffel\u2013Darboux kernel, associated with a compactly supported measure, to the sine kernel, under perturbations of the Jacobi coefficients of the measure. We prove stability under variations of the boundary conditions and stability in a weak sense under \u2113^(1) and random \u2113^(2) diagonal perturbations. We also show that convergence to the sine kernel at x implies that \u03bc({x}) = 0.", "date": "2014-09", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "330", "number": "3", "publisher": "Springer", "pagerange": "1155-1178", "id_number": "CaltechAUTHORS:20140814-112606518", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140814-112606518", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "1105/10" }, { "agency": "NSF", "grant_number": "DMS-0968856" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010348" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-014-1913-4", "primary_object": { "basename": "1302.7237", "url": "https://authors.library.caltech.edu/records/rc5z5-bf975/files/1302.7237" }, "pub_year": "2014", "author_list": "Breuer, Jonathan; Last, Yoram; et al." }, { "id": "https://authors.library.caltech.edu/records/0hxg6-rgb55", "eprint_id": 97835, "eprint_status": "archive", "datestamp": "2023-08-20 02:49:51", "lastmod": "2026-04-05 15:00:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Pach-J", "name": { "family": "Pach", "given": "J\u00e1nos" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } }, { "id": "Suk-Andrew", "name": { "family": "Suk", "given": "Andrew" } } ] }, "title": "Ramsey-type results for semi-algebraic relations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Copyright 2014 American Mathematical Society. The copyright for this article reverts to public domain 28 years after publication. \n\nReceived by the editors January 1, 2013 and, in revised form, May 7, 2013. Article electronically published on March 5, 2014. \n\nThe first author was supported by a Royal Society University Research Fellowship. The second author was supported by a Packard Fellowship, by a Simons Fellowship, by an Alfred P. Sloan Fellowship, by NSF grant DMS-1069197, and by an MIT NEC Corporation Award. The third author was supported by Swiss National Science Foundation Grants 200021-137574 and 200020-144531, by Hungarian Science Foundation Grant OTKA NN 102029 under the EuroGIGA programs ComPoSe and GraDR, and by NSF grant CCF-08-30272. The fourth author's research was supported in part by NSF grant DMS-1101185 and by a USA-Israel BSF grant. The fifth author was supported by an NSF Postdoctoral Fellowship and by Swiss National Science Foundation Grant 200021-125287/1\n\n

Submitted - 1301.0074.pdf

", "abstract": "A k-ary semi-algebraic relation E on \u211d_d is a subset of \u211d_(kd), the set of k-tuples of points in \u211d_(d), which is determined by a finite number of polynomial inequalities in kd real variables. The description complexity of such a relation is at most t if d, k \u2264 t and the number of polynomials and their degrees are all bounded by t. A set A \u2282 \u211d_d is called homogeneous if all or none of the k-tuples from A satisfy E. A large number of geometric Ramsey-type problems and results can be formulated as questions about finding large homogeneous subsets of sets in \u211d_d equipped with semi-algebraic relations.\n\nIn this paper, we study Ramsey numbers for k-ary semi-algebraic relations of bounded complexity and give matching upper and lower bounds, showing that they grow as a tower of height k \u2212 1. This improves upon a direct application of Ramsey's theorem by one exponential and extends a result of Alon, Pach, Pinchasi, Radoi\u010di\u0107, and Sharir, who proved this for k = 2. We apply our results to obtain new estimates for some geometric Ramsey-type problems relating to order types and one-sided sets of hyperplanes. We also study the off-diagonal case, achieving some partial results.", "date": "2014-09", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "366", "number": "9", "publisher": "American Mathematical Society", "pagerange": "5043-5065", "id_number": "CaltechAUTHORS:20190812-163000075", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000075", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Simons Foundation" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "MIT NEC Corporation" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-137574" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200020-144531" }, { "agency": "Hungarian Scientific Research Fund (OTKA)", "grant_number": "NN 102029" }, { "agency": "NSF", "grant_number": "CCF-08-30272" }, { "agency": "NSF", "grant_number": "DMS-1101185" }, { "agency": "Binational Science Foundation (USA-Israel)" }, { "agency": "NSF" }, { "agency": "Swiss National Science Foundation (SNSF)", "grant_number": "200021-125287/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/s0002-9947-2014-06179-5", "primary_object": { "basename": "1301.0074.pdf", "url": "https://authors.library.caltech.edu/records/0hxg6-rgb55/files/1301.0074.pdf" }, "pub_year": "2014", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/g3mvt-q2747", "eprint_id": 71913, "eprint_status": "archive", "datestamp": "2023-08-22 13:20:23", "lastmod": "2026-04-05 15:44:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Finucane-H", "name": { "family": "Finucane", "given": "Hilary" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Yaari-Y", "name": { "family": "Yaari", "given": "Yariv" } } ] }, "title": "Scenery Reconstruction on Finite Abelian Groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Scenery reconstruction; Random walks; Finite abelian groups", "note": "\u00a9 2014 Elsevier B.V. \n\nReceived 22 May 2012, Revised 22 October 2013, Accepted 30 March 2014, Available online 3 April 2014. \n\nSupported by an ERC grant. Supported by ISF grant 1300/08. Omer Tamuz is a recipient of the Google Europe Fellowship in Social Computing, and this research is supported in part by this Google Fellowship.\n\n

Submitted - 1105.5569.pdf

", "abstract": "We consider the question of when a random walk on a finite abelian group with a given step distribution can be used to reconstruct a binary labeling of the elements of the group, up to a shift. Matzinger and Lember (2006) give a sufficient condition for reconstructability on cycles. While, as we show, this condition is not in general necessary, our main result is that it is necessary when the length of the cycle is prime and larger than 5, and the step distribution has only rational probabilities. We extend this result to other abelian groups.", "date": "2014-08", "date_type": "published", "publication": "Stochastic Processes and their Applications", "volume": "124", "number": "8", "publisher": "Elsevier B.V.", "pagerange": "2754-2770", "id_number": "CaltechAUTHORS:20161110-120309955", "issn": "0304-4149", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-120309955", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.spa.2014.03.012", "primary_object": { "basename": "1105.5569.pdf", "url": "https://authors.library.caltech.edu/records/g3mvt-q2747/files/1105.5569.pdf" }, "pub_year": "2014", "author_list": "Finucane, Hilary; Tamuz, Omer; et al." }, { "id": "https://authors.library.caltech.edu/records/qvxet-adc98", "eprint_id": 47080, "eprint_status": "archive", "datestamp": "2023-08-20 02:03:52", "lastmod": "2026-04-05 16:48:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Schlein-B", "name": { "family": "Schlein", "given": "Benjamin" } } ] }, "title": "Dynamics of a Strongly Coupled Polaron", "ispublished": "pub", "full_text_status": "public", "keywords": "polaron, dynamics, Schr\u00f6dinger operator, quantized field", "note": "\u00a9 2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 23 November 2013; Revised: 24 March 2014; Accepted: 15 April 2014. \n\nU.S. National Science Foundation grant PHY-1347399 (R.F.) and ERC Starting Grant MAQD-240518 (B.S.) are acknowledged.\n\n

Published - art_3A10.1007_2Fs11005-014-0700-7.pdf

Submitted - 1311.5814v1.pdf

", "abstract": "We study the dynamics of large polarons described by the Fr\u00f6hlich Hamiltonian in the limit of strong coupling. The initial conditions are (perturbations of) product states of an electron wave function and a phonon coherent state, as suggested by Pekar. We show that, to leading order on the natural time scale of the problem, the phonon field is stationary and the electron moves according to an effective linear Schr\u00f6dinger equation.", "date": "2014-08", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "104", "number": "8", "publisher": "Springer", "pagerange": "911-929", "id_number": "CaltechAUTHORS:20140708-142118299", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140708-142118299", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "European Research Council (ERC)", "grant_number": "MAQD-240518" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-014-0700-7", "primary_object": { "basename": "1311.5814v1.pdf", "url": "https://authors.library.caltech.edu/records/qvxet-adc98/files/1311.5814v1.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs11005-014-0700-7.pdf", "url": "https://authors.library.caltech.edu/records/qvxet-adc98/files/art_3A10.1007_2Fs11005-014-0700-7.pdf" } ], "pub_year": "2014", "author_list": "Frank, Rupert L. and Schlein, Benjamin" }, { "id": "https://authors.library.caltech.edu/records/4n5fa-mq666", "eprint_id": 48624, "eprint_status": "archive", "datestamp": "2023-08-22 13:10:28", "lastmod": "2026-03-09 21:43:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Y-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology?", "ispublished": "pub", "full_text_status": "public", "keywords": "Big Bang cosmology; algebro-geometric blow-ups; cyclic cosmology; Mixmaster cosmologies; modular curves", "note": "\u00a9 2014. The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. \n\nReceived March 01, 2014, in final form June 27, 2014; Published online July 09, 2014. This paper was conceived after the lecture in Bonn (November 2013), in which Sir Roger Penrose explained his fascinating ideas about cyclic cosmology. Ya. Sinai and O. Bogoyavlenskii made helpful remarks about BKLL treatment of the Bianchi IX model. We are grateful to them. \n\nSpecial Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel\nhttp://www.emis.de/journals/SIGMA/Rieffel.html\n\n

Published - sigma14-073.pdf

", "abstract": "We introduce some algebraic geometric models in cosmology related to the ''boundaries'' of space-time: Big Bang, Mixmaster Universe, Penrose's crossovers between aeons. We suggest to model the kinematics of Big Bang using the algebraic geometric (or analytic) blow up of a point x. This creates a boundary which consists of the projective space of tangent directions to x and possibly of the light cone of x. We argue that time on the boundary undergoes the Wick rotation and becomes purely imaginary. The Mixmaster (Bianchi IX) model of the early history of the universe is neatly explained in this picture by postulating that the reverse Wick rotation follows a hyperbolic geodesic connecting imaginary time axis to the real one. Penrose's idea to see the Big Bang as a sign of crossover from \"the end of previous aeon'' of the expanding and cooling Universe to the ''beginning of the next aeon\" is interpreted as an identification of a natural boundary of Minkowski space at infinity with the Big Bang boundary.", "date": "2014-07-09", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "10", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 73", "id_number": "CaltechAUTHORS:20140815-135716277", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140815-135716277", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2014.073", "primary_object": { "basename": "sigma14-073.pdf", "url": "https://authors.library.caltech.edu/records/4n5fa-mq666/files/sigma14-073.pdf" }, "pub_year": "2014", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/e92vh-36d79", "eprint_id": 50714, "eprint_status": "archive", "datestamp": "2023-08-20 01:40:55", "lastmod": "2026-04-05 17:11:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lewin-M", "name": { "family": "Lewin", "given": "Mathieu" } }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Strichartz inequality for orthonormal functions", "ispublished": "pub", "full_text_status": "public", "keywords": "Strichartz inequality for orthonormal functions, dispersive estimates, wave operators,\ntrace ideals", "note": "\u00a9 2014 European Mathematical Society.\n\nReceived June 12, 2013.\n\nM.L. would like to thank Philippe Gravejat and Julien Sabin for stimulating\ndiscussions. Grants from the U.S. NSF PHY-1068285, PHY-1347399 (R.F.), PHY-0965859 (E.L.),\nNSERC (R.S.), from the Simons Foundation #230207 (E.L.), and from the ERC MNIQS-258023\n(M.L.) are gratefully acknowledged.\n\n

Submitted - 1306.1309v2.pdf

", "abstract": "We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schr\u00f6dinger equation in a time-dependent potential and we show the existence of the wave operator in Schatten spaces.", "date": "2014-07", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "16", "number": "7", "publisher": "European Mathematical Society", "pagerange": "1507-1526", "id_number": "CaltechAUTHORS:20141023-082135692", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141023-082135692", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Simons Foundation", "grant_number": "230207" }, { "agency": "European Research Council (European Union)", "grant_number": "MNIQS-258023" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JEMS/467", "primary_object": { "basename": "1306.1309v2.pdf", "url": "https://authors.library.caltech.edu/records/e92vh-36d79/files/1306.1309v2.pdf" }, "pub_year": "2014", "author_list": "Frank, Rupert L.; Lewin, Mathieu; et al." }, { "id": "https://authors.library.caltech.edu/records/2kn47-3pe52", "eprint_id": 51543, "eprint_status": "archive", "datestamp": "2023-08-20 01:41:01", "lastmod": "2026-04-05 17:02:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Jacobians of noncommutative motives", "ispublished": "pub", "full_text_status": "public", "keywords": "Jacobians, abelian varieties, isogeny, noncommutative motives", "note": "\u00a9 2014 Independent University of Moscow. Received February 07, 2013; in revised form: January 15, 2014.\n\nM. Marcolli was supported by the NSF grants DMS-0901221, DMS-1007207, DMS-1201512 and PHY-1205440. G. Tabuada was supported by the NEC Award-2742738 and by the Portuguese\nFoundation for Science and Technology through the grant PEst-OE/MAT/UI0297/2011 (CMA).\n\n

Published - 2014-014-003-006.pdf

Submitted - 1212.1118v1.pdf

", "abstract": "In this article one extends the classical theory of (intermediate) Jacobians to the \"noncommutative world\". Concretely, one constructs a \u211a-linear additive Jacobian functor N \u2192 J(N) from the category of noncommutative Chow motives to the category of abelian varieties up to isogeny, with the following properties: (i) the first de Rham cohomology group of J(N) agrees with the subspace of the odd periodic cyclic homology of N which is generated by algebraic curves; (ii) the abelian variety J(perf_(dg)(X)) (associated to the derived dg category perf_(dg)(X) of a smooth projective k-scheme X) identifies with the product of all the intermediate algebraic Jacobians of X. As an application, every semi-orthogonal decomposition of the derived category perf(X) gives rise to a decomposition of the intermediate algebraic Jacobians of X.", "date": "2014-07", "date_type": "published", "publication": "Moscow Mathematical Journal", "volume": "14", "number": "3", "publisher": "American Mathematical Society", "pagerange": "577-594", "id_number": "CaltechAUTHORS:20141111-073436103", "issn": "1609-3321", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141111-073436103", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "NEC", "grant_number": "2742738" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PEst-OE/MAT/UI0297/2011" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1212.1118", "primary_object": { "basename": "1212.1118v1.pdf", "url": "https://authors.library.caltech.edu/records/2kn47-3pe52/files/1212.1118v1.pdf" }, "related_objects": [ { "basename": "2014-014-003-006.pdf", "url": "https://authors.library.caltech.edu/records/2kn47-3pe52/files/2014-014-003-006.pdf" } ], "pub_year": "2014", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/mstvp-n3g59", "eprint_id": 47148, "eprint_status": "archive", "datestamp": "2023-08-20 01:25:21", "lastmod": "2026-04-06 00:07:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Thorngren-R", "name": { "family": "Thorngren", "given": "Ryan" }, "orcid": "0000-0001-9433-3399" } ] }, "title": "Anomalous Discrete Symmetries in Three Dimensions and Group Cohomology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 American Physical Society.\n\nReceived 11 March 2014; published 13 June 2014.\n\nWe are grateful to T. Senthil, E. Witten, N. Seiberg, V.\nOstrik, and P. Etingof for discussions. The work of A. K.\nwas supported in part by the DOE Grant No. DE-FG02-\n92ER40701.\n\nNote added.\u2014After this paper appeared on the electronic\npreprint archive, we learned that related results have been\nobtained by Cho et al. [16].\n\n

Published - PhysRevLett.112.231602.pdf

Submitted - 1403.0617v1.pdf

", "abstract": "We study 't Hooft anomalies for a global discrete internal symmetry G . We construct examples of bosonic field theories in three dimensions with a nonvanishing 't Hooft anomaly for a discrete global symmetry. We also construct field theories in three dimensions with a global discrete internal symmetry G_1\u00d7G_2 such that gauging G_1 necessarily breaks G_2 and vice versa. This is analogous to the Adler-Bell-Jackiw axial anomaly in four dimensions and parity anomaly in three dimensions.", "date": "2014-06-13", "date_type": "published", "publication": "Physical Review Letters", "volume": "112", "number": "23", "publisher": "American Physical Society", "pagerange": "Art. No. 231602", "id_number": "CaltechAUTHORS:20140710-133720286", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140710-133720286", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.112.231602", "primary_object": { "basename": "1403.0617v1.pdf", "url": "https://authors.library.caltech.edu/records/mstvp-n3g59/files/1403.0617v1.pdf" }, "related_objects": [ { "basename": "PhysRevLett.112.231602.pdf", "url": "https://authors.library.caltech.edu/records/mstvp-n3g59/files/PhysRevLett.112.231602.pdf" } ], "pub_year": "2014", "author_list": "Kapustin, Anton and Thorngren, Ryan" }, { "id": "https://authors.library.caltech.edu/records/dnpa2-eq143", "eprint_id": 46232, "eprint_status": "archive", "datestamp": "2023-08-20 01:07:01", "lastmod": "2026-04-05 16:32:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Li-Tian-Jun", "name": { "family": "Li", "given": "Tian-Jun" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Virtual Betti numbers and virtual symplecticity of 4-dimensional mapping tori", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Springer-Verlag Berlin Heidelberg. \n\nReceived: 21 November 2012; Accepted: 18 October 2013; Published online: 30 November 2013. \n\nThe proof of Theorem 1.6 was written in 2010. Inspired by recent progress on related topics [5, 6, 15], we expanded this note to the current version. We wish to thank Chung-I Ho, Yi Liu and Stefano Vidussi for interesting discussion. We are also grateful to Anar Akhmedov, Inanc Baykur, Nikolai Saveliev and Stefano Vidussi for comments on earlier versions of this paper. The first author was supported by NSF grant numbers DMS-1065927, DMS-1207037. The second author was supported by an AIM Five-Year Fellowship, NSF grant numbers DMS-1021956, DMS-1103976, and an Alfred P. Sloan Research Fellowship.\n\n

Submitted - 1211.4245v1.pdf

", "abstract": "In this note, we compute the virtual first Betti numbers of 4-manifolds fibering over S^1 with prime fiber. As an application, we show that if such a manifold is symplectic with nonpositive Kodaira dimension, then the fiber itself is a sphere or torus bundle over S^1. In a different direction, we prove that if the 3-dimensional fiber of such a 4-manifold is virtually fibered then the 4-manifold is virtually symplectic unless its virtual first Betti number is 1.", "date": "2014-06", "date_type": "published", "publication": "Mathematische Zeitschrift", "volume": "277", "number": "1-2", "publisher": "Springer Verlag", "pagerange": "195-208", "id_number": "CaltechAUTHORS:20140612-095146369", "issn": "0025-5874", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140612-095146369", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1065927" }, { "agency": "NSF", "grant_number": "DMS-1207037" }, { "agency": "American Institute of Mathematics" }, { "agency": "NSF", "grant_number": "DMS-1021956" }, { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00209-013-1250-x", "primary_object": { "basename": "1211.4245v1.pdf", "url": "https://authors.library.caltech.edu/records/dnpa2-eq143/files/1211.4245v1.pdf" }, "pub_year": "2014", "author_list": "Li, Tian-Jun and Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/45912-mk344", "eprint_id": 48550, "eprint_status": "archive", "datestamp": "2023-08-20 00:57:51", "lastmod": "2026-04-05 17:02:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Liu-Hong", "name": { "family": "Liu", "given": "Hong" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } } ] }, "title": "Angular momentum generation by parity violation", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 American Physical Society. \n\nReceived 23 December 2013; Published 19 May 2014. \n\nNote added.\u2014When this paper was almost complete, we received the paper [37], in which holographic models with nonzero angular momentum and Hall viscosity are discussed. Their models are different from those discussed in this paper. \n\nWe thank S. S. Gubser, O. Saremi and D. T. Son for useful discussion, and we are grateful to N. Yunes for collaboration on the early stages of this project. We would like to thank K. Landsteiner and the referee for their useful comments on the paper. H. O. and B. S. are supported in part by U.S. DOE Grant No. DE-FG03-92-ER40701. The work of H. O. is also supported in part by a Simons Investigator award from the Simons Foundation, the WPI Initiative of MEXT of Japan, and JSPS Grant-in-Aid for Scientific Research No. C-23540285. He also thanks the hospitality of the Aspen Center for Physics and the National Science Foundation, which supports the Center under Grant No. PHY-1066293, and of the Simons Center for Geometry and Physics. The work of B. S. is supported in part by a Dominic Orr Graduate Fellowship. B. S. would like to thank the hospitality of the Kavli Institute for the Physics and Mathematics of the Universe and of the Yukawa Institute for Theoretical Physics. H. L. is supported in part by funds provided by the U.S. DOE under cooperative research agreement Grant No. DEFG0205ER41360 and thanks the hospitality of Isaac Newton Institute for Mathematical Sciences.\n\n

Published - PhysRevD.89.106007.pdf

Submitted - 1311.5879v2.pdf

", "abstract": "We generalize our holographic derivation of spontaneous angular momentum generation in 2+1 dimensions in several directions. We consider cases when a parity-violating perturbation responsible for the angular momentum generation can be nonmarginal (while in our previous paper we restricted to a marginal perturbation), including all possible two-derivative interactions, with parity violations triggered both by gauge and gravitational Chern-Simons terms in the bulk. We make only a minimal assumption about the bulk geometry that it is asymptotically AdS, respects the Poincar\u00e9 symmetry in 2+1 dimensions, and has a horizon. In this generic setup, we find a remarkably concise and universal formula for the expectation value of the angular momentum density, to all orders in the parity violating perturbation.", "date": "2014-05-15", "date_type": "published", "publication": "Physical Review D", "volume": "89", "number": "10", "publisher": "American Physical Society", "pagerange": "Art. No. 106007", "id_number": "CaltechAUTHORS:20140814-092632811", "issn": "1550-7998", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140814-092632811", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Simons Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Dominic Orr Graduate Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-05ER41360" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.89.106007", "primary_object": { "basename": "1311.5879v2.pdf", "url": "https://authors.library.caltech.edu/records/45912-mk344/files/1311.5879v2.pdf" }, "related_objects": [ { "basename": "PhysRevD.89.106007.pdf", "url": "https://authors.library.caltech.edu/records/45912-mk344/files/PhysRevD.89.106007.pdf" } ], "pub_year": "2014", "author_list": "Liu, Hong; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/2a4a3-ndy66", "eprint_id": 97808, "eprint_status": "archive", "datestamp": "2023-08-22 12:40:32", "lastmod": "2026-04-06 00:14:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" } } ] }, "title": "Extremal results in sparse pseudorandom graphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Szemer\u00e9di's regularity lemma; Sparse regularity lemma; Counting lemma; Graph removal lemma; Extremal combinatorics; Sparse graphs", "note": "\u00a9 2014 Elsevier. Under an Elsevier user license. \n\nReceived 4 June 2012; accepted 14 December 2013; available online 25 February 2014. \n\nConlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Simons Fellowship, a Packard Fellowship, an Alfred P. Sloan Fellowship, an MIT NEC Corporation Award, and NSF grant DMS-1069197. Zhao research supported by an Akamai Presidential Fellowship and a Microsoft Research PhD Fellowship. \n\nWe thank the referees for a number of helpful comments which improved the manuscript.\n\n

Submitted - 1204.6645.pdf

", "abstract": "Szemer\u00e9di's regularity lemma is a fundamental tool in extremal combinatorics. However, the original version is only helpful in studying dense graphs. In the 1990s, Kohayakawa and R\u00f6dl proved an analogue of Szemer\u00e9di's regularity lemma for sparse graphs as part of a general program toward extending extremal results to sparse graphs. Many of the key applications of Szemer\u00e9di's regularity lemma use an associated counting lemma. In order to prove extensions of these results which also apply to sparse graphs, it remained a well-known open problem to prove a counting lemma in sparse graphs.\n\nThe main advance of this paper lies in a new counting lemma, proved following the functional approach of Gowers, which complements the sparse regularity lemma of Kohayakawa and R\u00f6dl, allowing us to count small graphs in regular subgraphs of a sufficiently pseudorandom graph. We use this to prove sparse extensions of several well-known combinatorial theorems, including the removal lemmas for graphs and groups, the Erd\u0151s\u2013Stone\u2013Simonovits theorem and Ramsey's theorem. These results extend and improve upon a substantial body of previous work.", "date": "2014-05-01", "date_type": "published", "publication": "Advances in Mathematics", "volume": "256", "publisher": "Elsevier", "pagerange": "206-290", "id_number": "CaltechAUTHORS:20190812-162957263", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957263", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Simons Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Akamai Presidential Graduate Fellowship" }, { "agency": "Microsoft Research Graduate Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2013.12.004", "primary_object": { "basename": "1204.6645.pdf", "url": "https://authors.library.caltech.edu/records/2a4a3-ndy66/files/1204.6645.pdf" }, "pub_year": "2014", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/jkcz6-yba75", "eprint_id": 47267, "eprint_status": "archive", "datestamp": "2023-08-20 00:48:20", "lastmod": "2026-04-05 23:14:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "Walls, lines, and spectral dualities in 3d gauge theories", "ispublished": "pub", "full_text_status": "public", "note": "Open Access \u00a9 The Authors. Article funded by SCOAP3.\n\nReceived: February 15, 2014\nAccepted: April 12, 2014\nPublished: May 12, 2014.\n\nWe thank C. Beem, A. Bytsko, T. Dimofte, A. Gorsky, S. Nawata, N. Nekrasov,\nS. Shatashvili, P. Su lkowski, R. van der Veen for useful discussions on related topics. The\nwork of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of P.P. is supported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the\nviews of funding agencies.\n\n

Published - scoap3-fulltext.pdf

", "abstract": "In this paper we analyze various half-BPS defects in a general three dimensional N = 2 supersymmetric gauge theory T. They correspond to closed paths in SUSY parameter space and their tension is computed by evaluating period integrals along these paths. In addition to such defects, we also study wall defects that interpolate between\nT and its SL(2,Z) transform by coupling the 3d theory to a 4d theory with S-duality wall. We propose a novel spectral duality between 3d gauge theories and integrable systems. This duality complements a similar duality discovered by Nekrasov and Shatashvili. As\nanother application, for 3d N = 2 theories associated with knots and 3-manifolds we compute periods of (super)A-polynomial curves and relate the results with the spectrum of\ndomain walls and line operators.", "date": "2014-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 47", "id_number": "CaltechAUTHORS:20140716-113255164", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140716-113255164", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "PHY-1050729" }, { "agency": "John A. McCone Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2905", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP05(2014)047", "primary_object": { "basename": "scoap3-fulltext.pdf", "url": "https://authors.library.caltech.edu/records/jkcz6-yba75/files/scoap3-fulltext.pdf" }, "pub_year": "2014", "author_list": "Gadde, Abhijit; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/1xdge-aph37", "eprint_id": 71970, "eprint_status": "archive", "datestamp": "2023-08-20 00:50:25", "lastmod": "2026-04-05 17:16:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Neeman-J", "name": { "family": "Neeman", "given": "Joe" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Majority Dynamics and Aggregation of Information in Social Networks", "ispublished": "pub", "full_text_status": "public", "keywords": "Social networks Aggregation of information Majority dynamics Discrete Fourier analysis", "note": "\u00a9 2013 The Author(s). Published online: 11 June 2013. \n\nWe would like to thank Miklos Racz for his careful reading of the manuscript and his suggestions. Elchanan Mossel is supported by a Sloan fellowship in Mathematics, by BSF Grant 2004105, by NSF Career Award (DMS 054829), by ONR Award N00014-07-1-0506 and by ISF Grant 1300/08. Omer Tamuz is supported by ISF Grant 1300/08. Omer Tamuz is a recipient of the Google Europe Fellowship in Social Computing, and this research is supported in part by this Google Fellowship.\n\n

Published - art_3A10.1007_2Fs10458-013-9230-4.pdf

Submitted - 1207.0893.pdf

", "abstract": "Consider n individuals who, by popular vote, choose among q \u2265 2 alternatives, one of which is \"better\" than the others. Assume that each individual votes independently at random, and that the probability of voting for the better alternative is larger than the probability of voting for any other. It follows from the law of large numbers that a plurality vote among the n individuals would result in the correct outcome, with probability approaching one exponentially quickly as n \u2192 \u221e.\nOur interest in this paper is in a variant of the process above where, after forming their initial opinions, the voters update their decisions based on some interaction with their neighbors in a social network. Our main example is \"majority dynamics\", in which each voter adopts the most\npopular opinion among its friends. The interaction repeats for some number of rounds and is then followed by a population-wide plurality vote. The question we tackle is that of \"efficient aggregation of information\": in which cases is the better alternative chosen with probability approaching one as n \u2192 \u221e? Conversely, for which sequences of growing graphs does aggregation fail, so that the wrong alternative gets chosen with probability bounded away from zero? We construct a family of examples in which interaction prevents efficient aggregation of information, and give a condition on the social network which ensures that aggregation occurs. For the case of majority dynamics we also investigate the question of unanimity in the\nlimit. In particular, if the voters' social network is an expander graph, we show that if the initial population is sufficiently biased towards a particular alternative then that alternative will eventually become the unanimous preference of the entire population.", "date": "2014-05", "date_type": "published", "publication": "Autonomous Agents and Mutli-Agent Systems", "volume": "28", "number": "3", "publisher": "Kluwer Academic Publishers", "pagerange": "408-429", "id_number": "CaltechAUTHORS:20161114-070336278", "issn": "1387-2532", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-070336278", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2004105" }, { "agency": "NSF", "grant_number": "DMS 054829" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-07-1-0506" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10458-013-9230-4", "primary_object": { "basename": "1207.0893.pdf", "url": "https://authors.library.caltech.edu/records/1xdge-aph37/files/1207.0893.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs10458-013-9230-4.pdf", "url": "https://authors.library.caltech.edu/records/1xdge-aph37/files/art_3A10.1007_2Fs10458-013-9230-4.pdf" } ], "pub_year": "2014", "author_list": "Mossel, Elchanan; Neeman, Joe; et al." }, { "id": "https://authors.library.caltech.edu/records/n1pmm-2jr02", "eprint_id": 48774, "eprint_status": "archive", "datestamp": "2023-08-20 00:49:00", "lastmod": "2026-04-05 16:40:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Y-I", "name": { "family": "Manin", "given": "Yuri" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Kolmogorov complexity and the asymptotic bound for error-correcting codes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 International Press of Boston, Inc. \n\nReceived 12/10/2012. First available: 9 July 2014.\n\n

Published - euclid.jdg.1404912104.pdf

Submitted - 1203.0653v2.pdf

", "abstract": "The set of all error-correcting block codes over a fixed alphabet with q letters determines a recursively enumerable set of rational points in the unit square with coordinates (R,\u03b4):= (relative transmission rate, relative minimal distance). Limit points of this set form a closed subset, defined by R\u2264\u03b1q(\u03b4), where \u03b1q(\u03b4) is a continuous decreasing function called the asymptotic bound. Its existence was proved by the first-named author in 1981, but no approaches to the computation of this function are known, and in it was even suggested that this function might be uncomputable in the sense of constructive analysis.\nIn this note we show that the asymptotic bound becomes computable with the assistance of an oracle producing codes in the order of their growing Kolmogorov complexity. Moreover, a natural partition function involving complexity allows us to interpret the asymptotic bound as a curve dividing two different thermodynamic phases of codes.", "date": "2014-05", "date_type": "published", "publication": "Journal of Differential Geometry", "volume": "97", "number": "1", "publisher": "International Press", "pagerange": "91-108", "id_number": "CaltechAUTHORS:20140821-111916358", "issn": "0022-040X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140821-111916358", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR3229051", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1203.0653", "primary_object": { "basename": "1203.0653v2.pdf", "url": "https://authors.library.caltech.edu/records/n1pmm-2jr02/files/1203.0653v2.pdf" }, "related_objects": [ { "basename": "euclid.jdg.1404912104.pdf", "url": "https://authors.library.caltech.edu/records/n1pmm-2jr02/files/euclid.jdg.1404912104.pdf" } ], "pub_year": "2014", "author_list": "Manin, Yuri and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/5ke56-ymh17", "eprint_id": 77087, "eprint_status": "archive", "datestamp": "2023-08-22 12:30:08", "lastmod": "2026-04-05 23:44:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lenz-D", "name": { "family": "Lenz", "given": "Daniel" }, "orcid": "0000-0001-5820-475X" }, { "id": "Wingert-D", "name": { "family": "Wingert", "given": "Daniel" } } ] }, "title": "Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Dirichlet form; Intrinsic metric; Spectral theory", "note": "\u00a9 2014 Elsevier Inc. \n\nReceived 5 January 2011, Accepted 5 February 2014, Available online 4 March 2014. \n\nThe second named author would like to express his gratitude to Peter Stollmann, Matthias Keller and Sebastian Haeseler for most stimulating discussions. The third named author thanks Peter Stollmann for his support and encouragement on this work. U.S. National Science Foundation grant PHY-1347399 (R.F.) is acknowledged. The authors would like to thank the referee for his extraordinary careful reading of the manuscript leading to various improvements.\n\n

Submitted - 1012.5050.pdf

", "abstract": "We present a study of what may be called an intrinsic metric for a general regular Dirichlet form. For such forms we then prove a Rademacher type theorem. For strongly local forms we show existence of a maximal intrinsic metric (under a weak continuity condition) and for Dirichlet forms with an absolutely continuous jump kernel we characterize intrinsic metrics by bounds on certain integrals. We then turn to applications on spectral theory and provide for (measure perturbation of) general regular Dirichlet forms an Allegretto-Piepenbrinck type theorem, which is based on a ground state transform, and a Shnol type theorem. Our setting includes Laplacian on manifolds, on graphs and \u03b1-stable processes.", "date": "2014-04-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "266", "number": "8", "publisher": "Elsevier", "pagerange": "4765-4808", "id_number": "CaltechAUTHORS:20170501-080259012", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-080259012", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2014.02.008", "primary_object": { "basename": "1012.5050.pdf", "url": "https://authors.library.caltech.edu/records/5ke56-ymh17/files/1012.5050.pdf" }, "pub_year": "2014", "author_list": "Frank, Rupert L.; Lenz, Daniel; et al." }, { "id": "https://authors.library.caltech.edu/records/feqq5-5pd23", "eprint_id": 45794, "eprint_status": "archive", "datestamp": "2023-08-22 12:25:03", "lastmod": "2026-04-05 23:13:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" } ] }, "title": "Coupling a QFT to a TQFT and duality", "ispublished": "pub", "full_text_status": "public", "keywords": "Wilson; 't Hooft and Polyakov loops; Duality in Gauge Field Theories; Lattice Gauge Field Theories; Topological Field Theories", "note": "\u00a9 2014 The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nPublished for SISSA by Springer. Article funded by SCOAP3.\n\nReceived: February 21, 2014; Accepted: February 24, 2014; Published: April 1, 2014.\n\nWe would like to thank O. Aharony, T. Banks, E. Fradkin, S. Kivelson, A. Kitaev, J. Maldacena, S. Minwalla, G. Moore, S. Razamat, S. Shenker, Y. Tachikawa, B. Willett, and\nE. Witten for useful discussions. The work of AK was supported in part by DOE grant\nDE-FG02-92ER40701 and by the National Science Foundation under Grant No. PHYS-1066293. The work of NS was supported in part by DOE grant DE-SC0009988 and by the\nUnited States-Israel Binational Science Foundation (BSF) under grant number 2010/629.\n\n

Published - art_10.1007_JHEP04_2014_001.pdf

Submitted - 1401.0740v2.pdf

", "abstract": "We consider coupling an ordinary quantum field theory with an infinite number\nof degrees of freedom to a topological field theory. On \u211d^d the new theory differs from the\noriginal one by the spectrum of operators. Sometimes the local operators are the same but\nthere are different line operators, surface operators, etc. The effects of the added topological\ndegrees of freedom are more dramatic when we compactify \u211d^d, and they are crucial in the\ncontext of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and on the lattice. When\nwe couple them to ordinary quantum field theories the topological degrees of freedom allow\nus to express certain characteristic classes of gauge fields as integrals of local densities, thus\nsimplifying the analysis of their physical consequences.", "date": "2014-04-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 001", "id_number": "CaltechAUTHORS:20140516-101255732", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140516-101255732", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010/629" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP04(2014)001", "primary_object": { "basename": "1401.0740v2.pdf", "url": "https://authors.library.caltech.edu/records/feqq5-5pd23/files/1401.0740v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP04_2014_001.pdf", "url": "https://authors.library.caltech.edu/records/feqq5-5pd23/files/art_10.1007_JHEP04_2014_001.pdf" } ], "pub_year": "2014", "author_list": "Kapustin, Anton and Seiberg, Nathan" }, { "id": "https://authors.library.caltech.edu/records/kx14s-qgy91", "eprint_id": 47308, "eprint_status": "archive", "datestamp": "2023-08-20 00:12:10", "lastmod": "2026-04-06 01:25:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "M." }, "orcid": "0000-0002-2045-2907" }, { "id": "Tedeschi-N", "name": { "family": "Tedeschi", "given": "N." } } ] }, "title": "Multifractals, Mumford Curves and Eternal Inflation", "ispublished": "pub", "full_text_status": "public", "keywords": "cosmology, eternal inflation, stochastic processes, Bruhat-Tits tree, p-adic Mumford curves.", "note": "\u00a9 2014 Pleiades Publishing, Ltd. Received December 14, 2013. The second author is supported by a Summer Undergraduate Research Fellowship at Caltech and by the Rose Hills Foundation. The first author is supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440.\n\n

Submitted - 1311.5458v1.pdf

", "abstract": "We relate the Eternal Symmetree model of Harlow, Shenker, Stanford, and Susskind to constructions of stochastic processes related to quantum statistical mechanical systems on Cuntz-Krieger algebras. We extend the eternal inflation model from the Bruhat-Tits tree to quotients by p-adic Schottky groups, again using quantum statistical mechanics on graph algebras.", "date": "2014-04", "date_type": "published", "publication": "P-Adic Numbers, Ultrametric Analysis, and Applications", "volume": "6", "number": "2", "publisher": "Springer", "pagerange": "135-154", "id_number": "CaltechAUTHORS:20140717-154554320", "issn": "2070-0474", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140717-154554320", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Rose Hills Foundation" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/S2070046614020034", "primary_object": { "basename": "1311.5458v1.pdf", "url": "https://authors.library.caltech.edu/records/kx14s-qgy91/files/1311.5458v1.pdf" }, "pub_year": "2014", "author_list": "Marcolli, M. and Tedeschi, N." }, { "id": "https://authors.library.caltech.edu/records/mft2z-b4a35", "eprint_id": 47315, "eprint_status": "archive", "datestamp": "2023-08-20 00:12:17", "lastmod": "2026-04-05 16:40:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Greenfield-M", "name": { "family": "Greenfield", "given": "M." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "M." }, "orcid": "0000-0002-2045-2907" }, { "id": "Teh-Kevin", "name": { "family": "Teh", "given": "K." } } ] }, "title": "Twisted Spectral Triples and Quantum Statistical Mechanical Systems", "ispublished": "pub", "full_text_status": "restricted", "keywords": "quantum statistical mechanics, twisted spectral triples, Riemann gas, Schottky uniformization.", "note": "\u00a9 2014 Pleiades Publishing, Ltd. \n\nReceived April 5, 2014. \n\nThe text was submitted by the authors in English. The first author was supported for this work by a Summer Undergraduate Research Fellowship at Caltech. The second author is partially supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The second author thanks MSRI for hospitality and support.", "abstract": "Spectral triples and quantum statistical mechanical systems are two important constructions in noncommutative geometry. In particular, both lead to interesting reconstruction theorems for a broad range of geometric objects, including number fields, spin manifolds, graphs. There are similarities between the two structures, and we show that the notion of twisted spectral triple, introduced recently by Connes and Moscovici, provides a natural bridge between them. We investigate explicit examples, related to the Bost-Connes quantum statistical mechanical system and to Riemann surfaces and graphs.", "date": "2014-04", "date_type": "published", "publication": "P-Adic Numbers, Ultrametric Analysis, and Applications", "volume": "6", "number": "2", "publisher": "Springer", "pagerange": "81-104", "id_number": "CaltechAUTHORS:20140718-073647086", "issn": "2070-0474", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140718-073647086", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Mathematical Sciences Research Institute (MSRI)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/S2070046614020010", "pub_year": "2014", "author_list": "Greenfield, M.; Marcolli, M.; et al." }, { "id": "https://authors.library.caltech.edu/records/pt9hm-jxk14", "eprint_id": 52619, "eprint_status": "archive", "datestamp": "2023-08-20 00:15:27", "lastmod": "2026-04-05 22:47:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ceyhan-\u00d6", "name": { "family": "Ceyhan", "given": "\u00d6zg\u00fcr" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Algebraic renormalization and Feynman integrals in configuration spaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 International Press.\n\nThe first author is partially supported by PCIG11-GA-2012-322154. The second author acknowledges support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440 and the hospitality and support of the Mathematical Sciences Research Institute in Berkeley and of the Kavli Institute for Theoretical Physics China and the Morningside Center for Mathematics in Beijing. The second author also thanks Li Guo for useful conversations.\n\n

Published - ATMP-2014-0018-0002-a005.pdf

Submitted - 1308.5687v1.pdf

", "abstract": "This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory. We consider a variant of the wonderful compactification of configuration spaces that works simultaneously for all graphs with a given number of vertices and that also accounts for the external structure of Feynman graph. As in our previous work, we consider two version of the Feynman amplitude in configuration space, which we refer to as the real and complex versions. In the real version, we show that we can extend to the massive case a method of evaluating Feynman integrals, based on expansion in Gegenbauer polynomials, that we investigated previously in the massless case. In the complex setting, we show that we can use algebro-geometric methods to renormalize the Feynman amplitudes, so that the renormalized values of the Feynman integrals are given by periods of a mixed Tate motive. The regularization and renormalization procedure is based on pulling back the form to the wonderful compactification and replace it with a cohomologous one with logarithmic poles. A complex of forms with logarithmic poles, endowed with an operator of pole subtraction, determine a Rota-Baxter algebra on the wonderful compactifications. We can then apply the renormalization procedure via Birkhoff factorization, after interpreting the regularization as an algebra homomorphism from the Connes-Kreimer Hopf algebra of Feynman graphs to the Rota-Baxter algebra. We obtain in this setting a description of the renormalization group.We also extend the period interpretation to the case of Dirac fermions and gauge bosons.", "date": "2014-04", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "18", "number": "2", "publisher": "International Press", "pagerange": "469-511", "id_number": "CaltechAUTHORS:20141212-091347163", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141212-091347163", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "PCIG11-GA-2012-322154" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "Mathematical Sciences Research Institute (MSRI)" }, { "agency": "Kavli Institute for Theoretical Physics" }, { "agency": "Morningside Center for Mathematics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2014.v18.n2.a5", "primary_object": { "basename": "1308.5687v1.pdf", "url": "https://authors.library.caltech.edu/records/pt9hm-jxk14/files/1308.5687v1.pdf" }, "related_objects": [ { "basename": "ATMP-2014-0018-0002-a005.pdf", "url": "https://authors.library.caltech.edu/records/pt9hm-jxk14/files/ATMP-2014-0018-0002-a005.pdf" } ], "pub_year": "2014", "author_list": "Ceyhan, \u00d6zg\u00fcr and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/5nkxm-abj06", "eprint_id": 45783, "eprint_status": "archive", "datestamp": "2023-08-20 00:01:33", "lastmod": "2026-04-06 01:24:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Putrov-P", "name": { "family": "Putrov", "given": "Pavel" } } ] }, "title": "(0, 2) trialities", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Supersymmetry and Duality, Supersymmetry\nBreaking", "note": "\u00a9 2014 The Authors.\n\nThis article is distributed under the terms of the Creative Commons\nAttribution License (CC-BY 4.0), which permits any use, distribution and reproduction in\nany medium, provided the original author(s) and source are credited.\n\nArticle funded by SCOAP3.\nPublished for SISSA by Springer.\n\nReceived: December 25, 2013;\nAccepted: February 23, 2014;\nPublished: March 17, 2014.\n\nWe would like to thank F. Benini, N. Bobev, N. Seiberg, E. Sharpe, M. Shifman, A. Vain\nshtein and E. Witten for useful discussions. The work of A.G. is supported in part by\nthe John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of\nS.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02. The work of P.P. is\nsupported in part by the Sherman Fairchild scholarship and by NSF Grant PHY-1050729.\nWe would like to thank the Aspen Center for Physics and the 2013 Simons Workshop in\nMathematics and Physics for hospitality during various states of this work. The Aspen\nCenter for Physics is supported in part by the National Science Foundation under Grant\nNo. PHYS-1066293. Opinions and conclusions expressed here are those of the authors and\ndo not necessarily reflect the views of funding agencies.\n\n

Published - art_10.1007_JHEP03_2014_076.pdf

Submitted - 1310.0818v2.pdf

", "abstract": "Motivated by the connection between 4-manifolds and 2d N = (0, 2) theories,\nwe study the dynamics of a fairly large class of 2d N = (0, 2) gauge theories. We see that\nphysics of such theories is very rich, much as the physics of 4d N = 1 theories. We discover\na new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the\nnew 2d duality is an operation of order three: it is IR equivalence of three different theories\nand, as such, is actually a triality. We also consider quiver theories and study their triality\nwebs. Given a quiver graph, we find that supersymmetry is dynamically broken unless the\nranks of the gauge groups and flavor groups satisfy stringent inequalities. In fact, for most\nof the graphs these inequalities have no solutions. This supports the folklore theorem that\ngeneric 2d N = (0, 2) theories break supersymmetry dynamically.", "date": "2014-03-17", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 76", "id_number": "CaltechAUTHORS:20140516-074913803", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140516-074913803", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "John A. McCone Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "PHY-1050729" }, { "agency": "NSF", "grant_number": "PHYS-1066293" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP03(2014)076", "primary_object": { "basename": "1310.0818v2.pdf", "url": "https://authors.library.caltech.edu/records/5nkxm-abj06/files/1310.0818v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP03_2014_076.pdf", "url": "https://authors.library.caltech.edu/records/5nkxm-abj06/files/art_10.1007_JHEP03_2014_076.pdf" } ], "pub_year": "2014", "author_list": "Gadde, Abhijit; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/78zmy-jdm57", "eprint_id": 45181, "eprint_status": "archive", "datestamp": "2023-08-20 00:01:26", "lastmod": "2026-04-05 23:18:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gadde-A", "name": { "family": "Gadde", "given": "Abhijit" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "2d index and surface operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Brane Dynamics in Gauge Theories", "note": "\u00a9 2014 The Authors. \n\nThis article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in\nany medium, provided the original author(s) and source are credited. Article funded by SCOAP^3.\n\nReceived: December 25, 2013. Accepted: February 20, 2014. Published: March 17, 2014. Available under Open Access. \n\nThe authors would like to thank Yu Nakayama, Hirosi Ooguri, Pavel Putrov and Shlomo Razamat for interesting discussions. Authors are especially grateful to Anton Kapustin for his valuable comments. The work of A.G. is supported in part by the John A. McCone fellowship and by DOE Grant DE-FG02-92-ER40701. The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - art_10.1007_JHEP03_2014_080.pdf

Submitted - 1305.0266v2.pdf

", "abstract": "In this paper we compute the superconformal index of 2d (2, 2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes the 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and under CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong.\n\nIn the later half of the paper, we study half-BPS surface operators in N = 2 super-conformal gauge theories. They are engineered by coupling the 2d (2, 2) supersymmetric gauge theory living on the support of the surface operator to the 4d N = 2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.", "date": "2014-03-17", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2014", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 80", "id_number": "CaltechAUTHORS:20140424-092625660", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140424-092625660", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "John A. McCone Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP03(2014)080", "primary_object": { "basename": "1305.0266v2.pdf", "url": "https://authors.library.caltech.edu/records/78zmy-jdm57/files/1305.0266v2.pdf" }, "related_objects": [ { "basename": "art_10.1007_JHEP03_2014_080.pdf", "url": "https://authors.library.caltech.edu/records/78zmy-jdm57/files/art_10.1007_JHEP03_2014_080.pdf" } ], "pub_year": "2014", "author_list": "Gadde, Abhijit and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/4mtpn-41f04", "eprint_id": 45208, "eprint_status": "archive", "datestamp": "2023-08-19 23:58:35", "lastmod": "2026-04-06 01:10:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Ground-state degeneracy for Abelian anyons in the presence of gapped boundaries", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 American Physical Society.\n\nReceived 24 July 2013; revised manuscript received 21 February 2014; published 19 March 2014.\n\nI would like to thank M. Barkeshli, C. M. Jian, and X. L.\nQi for a discussion. This work was supported in part by DOE\nGrant No. DE-FG02-92ER40701.\n\n

Published - PhysRevB.89.125307.pdf

Submitted - 1306.4254v1.pdf

", "abstract": "Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well defined and can be computed using methods of topological quantum field theory. We derive a general formula for the ground-state degeneracy for Abelian fractional quantum Hall phases, including the cases when connected components of the boundary are subdivided into an arbitrary number of segments, with a different boundary condition on each segment, and in the presence of an arbitrary number of boundary domain walls.", "date": "2014-03-15", "date_type": "published", "publication": "Physical Review B", "volume": "89", "number": "12", "publisher": "American Physical Society", "pagerange": "Art. No. 125307", "id_number": "CaltechAUTHORS:20140425-081308382", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140425-081308382", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevB.89.125307", "primary_object": { "basename": "PhysRevB.89.125307.pdf", "url": "https://authors.library.caltech.edu/records/4mtpn-41f04/files/PhysRevB.89.125307.pdf" }, "related_objects": [ { "basename": "1306.4254v1.pdf", "url": "https://authors.library.caltech.edu/records/4mtpn-41f04/files/1306.4254v1.pdf" } ], "pub_year": "2014", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/t5bwy-kv823", "eprint_id": 44582, "eprint_status": "archive", "datestamp": "2023-08-22 11:49:33", "lastmod": "2026-04-05 16:26:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jin-Zhaorong", "name": { "family": "Jin", "given": "Zhaorong" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Endomotives of toric varieties", "ispublished": "pub", "full_text_status": "public", "keywords": "Noncommutative geometry; Endomotives; Quantum statistical mechanical systems; Toric varieties; Height functions", "note": "\u00a9 2014 Elsevier B.V. \n\nReceived 4 October 2013. Received in revised form 10 December 2013. Accepted 14 December 2013. Available online 21 December 2013. \n\nThis paper is based on the results of the first author's summer research project, supported by a Summer Undergraduate Research Fellowship at Caltech. The second author acknowledges support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440.\n\n

Submitted - 1309.4101v1.pdf

", "abstract": "We construct endomotives associated to toric varieties, in terms of the decomposition of a toric variety into torus orbits and the action of a semigroup of toric morphisms. We show that the endomotives can be endowed with time evolutions and we discuss the resulting quantum statistical mechanical systems. We show that in particular, one can construct a time evolution related to the logarithmic height function. We discuss relations to F_1-geometry.", "date": "2014-03", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "77", "publisher": "Elsevier", "pagerange": "48-71", "id_number": "CaltechAUTHORS:20140401-134330780", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140401-134330780", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2013.12.006", "primary_object": { "basename": "1309.4101v1.pdf", "url": "https://authors.library.caltech.edu/records/t5bwy-kv823/files/1309.4101v1.pdf" }, "pub_year": "2014", "author_list": "Jin, Zhaorong and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/5zd1m-jgn27", "eprint_id": 56179, "eprint_status": "archive", "datestamp": "2023-08-19 23:33:39", "lastmod": "2026-03-08 18:14:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fan-E-S-T", "name": { "family": "Fan", "given": "Edward S. T." } }, { "id": "Flach-M", "name": { "family": "Flach", "given": "M." }, "orcid": "0000-0002-4523-9467" } ] }, "title": "A note on the cohomology of the Langlands group", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Cohomology, topological groups, Langlands group", "note": "\u00a9 2014 American Mathematical Society. The copyright for this article reverts to public domain 28 years after publication. \n\nReceived by editor(s): September 3, 2012. Received by editor(s) in revised form: June 12, 2013. Published electronically: February 25, 2014.", "abstract": "We begin with a comparison of various cohomology theories for topological groups. Using the continuity result for Moore cohomology, we establish a Hochschild-Serre spectral sequence for a slightly larger class of groups. We use these properties to compute the cohomology of the Langlands group of a totally imaginary field. The appendix answers a question raised by Flach concerning the cohomological dimension of the group \u211d.", "date": "2014-02-25", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "367", "number": "4", "publisher": "American Mathematical Society", "pagerange": "2905-2920", "id_number": "CaltechAUTHORS:20150327-104226273", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150327-104226273", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9947-2014-06230-2", "pub_year": "2014", "author_list": "Fan, Edward S. T. and Flach, M." }, { "id": "https://authors.library.caltech.edu/records/qyc5h-rtg18", "eprint_id": 44456, "eprint_status": "archive", "datestamp": "2023-08-19 23:22:43", "lastmod": "2026-04-05 15:58:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Noncommutative motives, numerical equivalence, and semi-simplicity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 The Johns Hopkins University Press. \n\nManuscript received May 25, 2011. \n\nResearch of the first author supported in part by the NSF grants DMS-0651925, DMS-0901221 and DMS-1007207; research of the second author supported in part by the NEC Award 2742738 and by the Portuguese Foundation for Science and Technology through the grants PTDC/MAT/098317/2008 and PEst-OE/MAT/UI0297/2011 (CMA).\n\n

Published - 136.1.marcolli.pdf

Submitted - 1105.2950v1.pdf

", "abstract": "Making use of Hochschild homology, we introduce the correct category NNum(k)_F of noncommutative numerical motives (over a base ring k and with coefficients in a field F). We prove that NNum(k)_F is abelian semi-simple and that Grothendieck's category Num(k)_Q of numerical motives embeds into NNum(k)_Q after being factored out by the action of the Tate object. As an application we obtain an alternative proof of Jannsen's celebrate semi-simplicity result, which uses the noncommutative world instead of a classical Weil cohomology.", "date": "2014-02", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "136", "number": "1", "publisher": "Johns Hopkins University Press", "pagerange": "59-75", "id_number": "CaltechAUTHORS:20140324-104258394", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140324-104258394", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0651925" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NEC", "grant_number": "2742738" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT/098317/2008" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PEst-OE/MAT/UI0297/2011" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1353/ajm.2014.0004", "primary_object": { "basename": "1105.2950v1.pdf", "url": "https://authors.library.caltech.edu/records/qyc5h-rtg18/files/1105.2950v1.pdf" }, "related_objects": [ { "basename": "136.1.marcolli.pdf", "url": "https://authors.library.caltech.edu/records/qyc5h-rtg18/files/136.1.marcolli.pdf" } ], "pub_year": "2014", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/ajxe9-qmg53", "eprint_id": 77195, "eprint_status": "archive", "datestamp": "2023-08-19 23:26:30", "lastmod": "2026-04-05 23:26:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bellazzini-J", "name": { "family": "Bellazzini", "given": "Jacopo" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Existence of ground states for negative ions at the binding threshold", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nPartial financial support from PRIN 2009 'Metodi Variazionali e Topologici nello Studio di Fenomeni non Lineari' (J.B.), the U.S. National Science Foundation through grants PHY-1068285 (R.F.), PHY-0965859 (E.L.), the Simons Foundation (# 230207, E.L.) and the NSERC (R.S.) is acknowledged.\n\n

Submitted - 1301.5370.pdf

", "abstract": "As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition at some critical Z_c. We investigate whether the electrons remain bound when Z=Z_c and whether the radius of the system stays finite as Z_c is approached. Existence of a ground state at Z_c is shown under the condition Z_c", "date": "2014-02", "date_type": "published", "publication": "Reviews in Mathematical Physics", "volume": "26", "number": "01", "publisher": "World Scientific", "pagerange": "Art. No. 1350021", "id_number": "CaltechAUTHORS:20170504-103757590", "issn": "0129-055X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170504-103757590", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministero dell'Istruzione, dell'Universit\u00e0 e della Ricerca (MIUR)" }, { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "Simons Foundation", "grant_number": "230207" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0129055X13500219", "primary_object": { "basename": "1301.5370.pdf", "url": "https://authors.library.caltech.edu/records/ajxe9-qmg53/files/1301.5370.pdf" }, "pub_year": "2014", "author_list": "Bellazzini, Jacopo; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/mftzy-6bb79", "eprint_id": 71971, "eprint_status": "archive", "datestamp": "2023-08-19 23:26:26", "lastmod": "2026-04-05 16:32:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Sly-A", "name": { "family": "Sly", "given": "Allan" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Asymptotic learning on Bayesian social networks", "ispublished": "pub", "full_text_status": "public", "keywords": "Bayesian learning Social networks Aggregation of information Rational expectations", "note": "\u00a9 2013 Springer-Verlag Berlin Heidelberg. \n\nReceived: 29 May 2012. Revised: 1 January 2013. Published online: 13 February 2013. \n\nThe authors would like to thank Shachar Kariv for an enthusiastic introduction to his work with Douglas Gale, and for suggesting the significance of asymptotic learning in this model. Elchanan Mossel is supported by NSF award DMS 1106999, by ONR award N000141110140 and by ISF Grant 1300/08. Allan Sly is supported in part by an Alfred Sloan Fellowship in Mathematics. Omer Tamuz is supported by ISF Grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing. This research is supported in part by this Google Fellowship.\n\n

Submitted - 1207.5893.pdf

", "abstract": "We study a standard model of economic agents on the nodes of a social network graph who learn a binary \"state of the world\" S, from initial signals, by repeatedly observing each other's best guesses. Asymptotic learning is said to occur on a family of graphs G_n=(V_n,E_n) with |V_n|\u2192\u221e if with probability tending to 1 as n\u2192\u221e all agents in G_n eventually estimate S correctly. We identify sufficient conditions for asymptotic learning and contruct examples where learning does not occur when the conditions do not hold.", "date": "2014-02", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "158", "number": "1-2", "publisher": "Springer", "pagerange": "127-157", "id_number": "CaltechAUTHORS:20161114-072802716", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-072802716", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1106999" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N000141110140" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-013-0479-y", "primary_object": { "basename": "1207.5893.pdf", "url": "https://authors.library.caltech.edu/records/mftzy-6bb79/files/1207.5893.pdf" }, "pub_year": "2014", "author_list": "Mossel, Elchanan; Sly, Allan; et al." }, { "id": "https://authors.library.caltech.edu/records/3cn17-xg827", "eprint_id": 45118, "eprint_status": "archive", "datestamp": "2023-08-19 23:24:00", "lastmod": "2026-04-05 16:41:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carlen-E-A", "name": { "family": "Carlen", "given": "Eric A." }, "orcid": "0000-0003-2613-187X" }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Stability Estimates for the Lowest Eigenvalue of a Schr\u00f6dinger Operator", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 Springer Basel. Received: January 22, 2013. Accepted: July 1, 2013. \nPublished online February 14, 2014.\nWork partially supported by NSF grants DMS 0901632, DMS 1201354 (E.A.C.), PHY 1068285, PHY 1347399 (R.L.F.), PHY 0965859, PHY 1265118 (E.H.L.) and the Simons Foundation grant #230207 (E.H.L.).\n\n

Submitted - 1301.5032v2.pdf

", "abstract": "There is a family of potentials that minimize the lowest eigenvalue of a Schr\u00f6dinger operator under the constraint of a given L^p norm of the potential. We give effective estimates for the amount by which the eigenvalue increases when the potential is not one of these optimal potentials. Our results are analogous to those for the isoperimetric problem and the Sobolev inequality. We also prove a stability estimate for H\u00f6lder's inequality, which we believe to be new.", "date": "2014-02", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "24", "number": "1", "publisher": "Springer", "pagerange": "63-84", "id_number": "CaltechAUTHORS:20140422-141713585", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140422-141713585", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 0901632" }, { "agency": "NSF", "grant_number": "DMS 1201354" }, { "agency": "NSF", "grant_number": "PHY 1068285" }, { "agency": "NSF", "grant_number": "PHY 1347399" }, { "agency": "NSF", "grant_number": "PHY 0965859" }, { "agency": "NSF", "grant_number": "PHY 1265118" }, { "agency": "Simons Foundation", "grant_number": "230207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-014-0253-z", "primary_object": { "basename": "1301.5032v2.pdf", "url": "https://authors.library.caltech.edu/records/3cn17-xg827/files/1301.5032v2.pdf" }, "pub_year": "2014", "author_list": "Carlen, Eric A.; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/462v4-3ad27", "eprint_id": 43728, "eprint_status": "archive", "datestamp": "2023-08-22 11:29:12", "lastmod": "2026-04-05 17:13:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Some applications of Gabai's internal hierarchy", "ispublished": "pub", "full_text_status": "public", "keywords": "Heegaard Floer homology; Sutured manifold decomposition; Internal hierarchy; Floer simple knots", "note": "\u00a9 2013 Elsevier Inc. \n\nReceived 4 November 2011; accepted 4 October 2013; Available online 25 October 2013. \n\nCommunicated by Tomasz S. Mrowka. \n\nThis work was started when the author visited Simons Center for Geometry and Physics. The author is grateful to Zolt\u00e1n Szab\u00f3 for asking the question which motivated this work, and to Mirela \u00c7iperiani and David Gabai for helpful conversations. The author thanks Liling Gu for pointing out a mistake in an earlier version of this paper, and the referee for the comments which helped to improve the exposition. The author was partially supported by an AIM Five-Year Fellowship and NSF grant numbers DMS-1021956 and DMS-1103976.\n\n

Submitted - 1111.0914v2.pdf

", "abstract": "Any Haken 3-manifold (possibly with boundary consisting of tori) can be transformed into a surface \u00d7 S^1 by a series of splitting and regluing along incompressible surfaces. This fact was proved by Gabai as an application of his sutured manifold theory. The first half of this paper provides a few technical details in the proof. In the second half of this paper, some applications of Gabai's theorem to Heegaard Floer homology are given. We refine the known results about the Thurson norm and fibrations. We also give some classification results for Floer simple knots in manifolds with positive b_1.", "date": "2014-01-15", "date_type": "published", "publication": "Advances in Mathematics", "volume": "250", "publisher": "Elsevier", "pagerange": "467-495", "id_number": "CaltechAUTHORS:20140207-133156477", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140207-133156477", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "American Institute of Mathematics" }, { "agency": "NSF", "grant_number": "DMS-1021956" }, { "agency": "NSF", "grant_number": "DMS-1103976" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2013.10.001", "primary_object": { "basename": "1111.0914v2.pdf", "url": "https://authors.library.caltech.edu/records/462v4-3ad27/files/1111.0914v2.pdf" }, "pub_year": "2014", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/bzrfb-asr73", "eprint_id": 42511, "eprint_status": "archive", "datestamp": "2023-08-22 11:23:32", "lastmod": "2026-04-05 17:14:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Gijsbers-D-A-H", "name": { "family": "Gijsbers", "given": "Di\u00e9 A. H." } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "The Birman\u2013Murakami\u2013Wenzl Algebras of Type D_n", "ispublished": "pub", "full_text_status": "public", "keywords": "Associative algebra; Birman-Murakami-Wenzl algebra; BMW algebra: Brauer algebra; Cellular algebra; Coxeter group; Generalized Temperley-Lieb algebra; Root system; Semisimple\nalgebra; Word problem in semigroups.", "note": "\u00a9 2014 Taylor & Francis Group, LLC. Received July 19, 2011. Communicated by P. Tiep. Published online: 18 Oct 2013.\n\n

Submitted - 0704.2743v3.pdf

", "abstract": "The Birman\u2013Murakami\u2013Wenzl algebra (BMW algebra) of type D_n is shown to be semisimple and free of rank (2^n + 1)n!! \u2212 (2^n\u22121 + 1)n! over a specified commutative ring R, where n!! =1\u00b73\u2026(2n \u2212 1). We also show it is a cellular algebra over suitable ring extensions of R. The Brauer algebra of type D_n is the image of an R-equivariant homomorphism and is also semisimple and free of the same rank, but over the ring \u2124[\u03b4^(\u00b11)]. A rewrite system for the Brauer algebra is used in bounding the rank of the BMW algebra above. As a consequence of our results, the generalized Temperley\u2013Lieb algebra of type D_n is a subalgebra of the BMW algebra of the same type.", "date": "2014-01-02", "date_type": "published", "publication": "Communications in Algebra", "volume": "42", "number": "1", "publisher": "Taylor & Francis", "pagerange": "22-55", "id_number": "CaltechAUTHORS:20131118-073559089", "issn": "0092-7872", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131118-073559089", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1080/00927872.2012.678955", "primary_object": { "basename": "0704.2743v3.pdf", "url": "https://authors.library.caltech.edu/records/bzrfb-asr73/files/0704.2743v3.pdf" }, "pub_year": "2014", "author_list": "Cohen, Arjeh M.; Gijsbers, Di\u00e9 A. H.; et al." }, { "id": "https://authors.library.caltech.edu/records/ew3yz-n7p38", "eprint_id": 97805, "eprint_status": "archive", "datestamp": "2023-08-19 22:58:42", "lastmod": "2026-03-08 17:35:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Short Proofs of Some Extremal Results", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Cambridge University Press 2013. \n\nReceived 6 December 2012; revised 9 September 2013; first published online 4 November 2013. \n\nConlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Simons Fellowship and NSF grant DMS-1069197. Sudakov research supported in part by NSF grant DMS-1101185, by AFOSR MURI grant FA9550-10-1-0569 and by a USA\u2013Israel BSF grant.\n\n

Published - short_proofs_of_some_extremal_results.pdf

Submitted - 1212.1300.pdf

", "abstract": "We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because in each case the relevant proofs are quite short.", "date": "2014-01", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "23", "number": "1", "publisher": "Cambridge University Press", "pagerange": "8-28", "id_number": "CaltechAUTHORS:20190812-162956937", "issn": "0963-5483", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162956937", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "NSF", "grant_number": "DMS-1101185" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-10-1-0569" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548313000448", "primary_object": { "basename": "1212.1300.pdf", "url": "https://authors.library.caltech.edu/records/ew3yz-n7p38/files/1212.1300.pdf" }, "related_objects": [ { "basename": "short_proofs_of_some_extremal_results.pdf", "url": "https://authors.library.caltech.edu/records/ew3yz-n7p38/files/short_proofs_of_some_extremal_results.pdf" } ], "pub_year": "2014", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/8a08f-xpz22", "eprint_id": 42039, "eprint_status": "archive", "datestamp": "2023-08-19 22:50:29", "lastmod": "2026-03-10 00:01:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } }, { "id": "Wong-T-W-H", "name": { "family": "Wong", "given": "Tony W. H." } } ] }, "title": "Diagonal forms of incidence matrices associated with t-uniform hypergraphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Elsevier Ltd.\nAvailable online 5 July 2013.\nThe research of the first author was supported in part by NSF Grant DMS-0555755.\n\n

Submitted - DiagFormHyper.pdf

", "abstract": "We consider integer matrices N_t(h) whose rows are indexed by the\nt-subsets of an n-set and whose columns are all images of a particular\ncolumn h under the symmetric group S_n. Earlier work has determined\na diagonal form for N_t(h) when h has at least t 'isolated\nvertices' and the results were applied to the binary case of a zerosum\nRamsey-type problem of Alon and Caro involving t-uniform\nhypergraphs. This paper deals with the case that h does not have\nas many as t isolated vertices.", "date": "2014-01", "date_type": "published", "publication": "European Journal of Combinatorics", "volume": "35", "publisher": "Elsevier", "pagerange": "490-508", "id_number": "CaltechAUTHORS:20131024-100335878", "issn": "0195-6698", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131024-100335878", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0555755" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.ejc.2013.06.032", "primary_object": { "basename": "DiagFormHyper.pdf", "url": "https://authors.library.caltech.edu/records/8a08f-xpz22/files/DiagFormHyper.pdf" }, "pub_year": "2014", "author_list": "Wilson, Richard M. and Wong, Tony W. H." }, { "id": "https://authors.library.caltech.edu/records/h2xnt-12531", "eprint_id": 43288, "eprint_status": "archive", "datestamp": "2023-08-22 11:14:37", "lastmod": "2026-03-09 21:36:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "van-Suijlekom-W-D", "name": { "family": "van Suijlekom", "given": "Walter D." } } ] }, "title": "Gauge networks in noncommutative geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "Noncommutative geometry; Spin networks; Lattice gauge theory", "note": "\u00a9 2013 Elsevier B.V. \n\nReceived 26 March 2013. Accepted 1 September 2013. Available online 13 September 2013. \n\nThe first author is partially supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The second author is supported in part by the ESF Research Networking Programme \"Low-Dimensional Topology and Geometry with Mathematical Physics (ITGP)\". Carlos Perez is acknowledged for a careful reading of the manuscript.\n\n

Submitted - 1301.3480v1.pdf

", "abstract": "We introduce gauge networks as generalizations of spin networks and lattice gauge fields to almost-commutative manifolds. The configuration space of quiver representations (modulo equivalence) in the category of finite spectral triples is studied; gauge networks appear as an orthonormal basis in a corresponding Hilbert space. We give many examples of gauge networks, also beyond the well-known spin network examples. We find a Hamiltonian operator on this Hilbert space, inducing a time evolution on the C^\u2217-algebra of gauge network correspondences.\n\nGiven a representation in the category of spectral triples of a quiver embedded in a spin manifold, we define a discretized Dirac operator on the quiver. We compute the spectral action of this Dirac operator on a four-dimensional lattice, and find that it reduces to the Wilson action for lattice gauge theories and a Higgs field lattice system. As such, in the continuum limit it reduces to the Yang\u2013Mills\u2013Higgs system. For the three-dimensional case, we relate the spectral action functional to the Kogut\u2013Susskind Hamiltonian.", "date": "2014-01", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "75", "publisher": "Elsevier", "pagerange": "71-91", "id_number": "CaltechAUTHORS:20140109-093610920", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140109-093610920", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "ESF Research Networking Programme" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2013.09.002", "primary_object": { "basename": "1301.3480v1.pdf", "url": "https://authors.library.caltech.edu/records/h2xnt-12531/files/1301.3480v1.pdf" }, "pub_year": "2014", "author_list": "Marcolli, Matilde and van Suijlekom, Walter D." }, { "id": "https://authors.library.caltech.edu/records/5af6y-91a67", "eprint_id": 42897, "eprint_status": "archive", "datestamp": "2023-08-19 22:50:52", "lastmod": "2026-03-07 04:15:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Finite Groups of Seitz Type", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 American Mathematical Society \nThe copyright for this article reverts to public domain 28 years after publication.\n\nReceived by editor(s): February 23, 2012;\nReceived by editor(s) in revised form: March 7, 2012, and March 9, 2012; \nPosted: October 4, 2013.\n\n\nThis work was partially supported by NSF grants DMS-0504852 and DMS-0969009.\n\n

Published - S0002-9939-2013-11752-1.pdf

", "abstract": "We show that a useful condition of Seitz on finite groups of Lie\ntype over fields of order q > 4 is often satisfied when q is 2 or 3. We also\nobserve that various consequences of the Seitz condition, established by Seitz\nand Cline, Parshall, and Scott when q > 4, also hold when q is 3 or 4.", "date": "2014-01", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "142", "number": "1", "publisher": "American Mathematical Society", "pagerange": "113-120", "id_number": "CaltechAUTHORS:20131209-104216789", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131209-104216789", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" }, { "agency": "NSF", "grant_number": "DMS-0969009" } ] }, "other_numbering_system": { "items": [ { "id": "MR3119186", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9939-2013-11752-1", "primary_object": { "basename": "S0002-9939-2013-11752-1.pdf", "url": "https://authors.library.caltech.edu/records/5af6y-91a67/files/S0002-9939-2013-11752-1.pdf" }, "pub_year": "2014", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/tnnkj-r6c80", "eprint_id": 43527, "eprint_status": "archive", "datestamp": "2023-08-22 11:15:46", "lastmod": "2026-03-09 21:44:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Noncommutative Artin motives", "ispublished": "pub", "full_text_status": "public", "keywords": "Artin motives; Motivic Galois groups; Noncommutative motives", "note": "\u00a9 2013 Springer Basel. \n\nPublished online: 22 June 2013. \n\nThe authors are very grateful to Michael Artin and Yuri Manin for motivating questions, to Joseph Ayoub, Dmitry Kaledin and Burt Totaro for fruitful discussions, to Bernhard Keller for precise comments on a previous draft, and to Yves Andr\u00e9 and Bruno Kahn for useful e-mail exchanges. They are also grateful to the anonymous referee for his/her comments. The first named author was supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The second named author was supported by the NEC Award-2742738 and by the Portuguese Foundation for Science and Technology through PEst-OE/MAT/UI02297/2011 (CMA).\n\n

Submitted - 1205.1732v3.pdf

", "abstract": "In this article, we introduce the category of noncommutative Artin motives as well as the category of noncommutative mixed Artin motives. In the pure world, we start by proving that the classical category AM(k)_Q of Artin motives (over a base field k) can be characterized as the largest category inside Chow motives which fully embeds into noncommutative Chow motives. Making use of a refined bridge between pure motives and noncommutative pure motives, we then show that the image of this full embedding, which we call the category NAM(k)_Q of noncommutative Artin motives, is invariant under the different equivalence relations and modification of the symmetry isomorphism constraints. As an application, we recover the absolute Galois group Gal(k\u00af/k) from the Tannakian formalism applied to NAM(k)_Q . Then, we develop the base-change formalism in the world of noncommutative pure motives. As an application, we obtain new tools for the study of motivic decompositions and Schur/Kimura finiteness. Making use of this theory of base-change, we then construct a short exact sequence relating Gal(k\u00af/k) with the noncommutative motivic Galois groups of k and k\u00af . Finally, we describe a precise relationship between this short exact sequence and the one constructed by Deligne\u2013Milne. In the mixed world, we introduce the triangulated category NMAM(k)_Q of noncommutative mixed Artin motives and construct a faithful functor from the classical category MAM(k)_Q of mixed Artin motives to it. When k is a finite field, this functor is an equivalence. On the other hand, when k is of characteristic zero NMAM(k)_Q is much richer than MAM(k)_Q since its higher Ext-groups encode all the (rationalized) higher algebraic K -theory of finite \u00e9tale k-schemes. In the appendix, we establish a general result about short exact sequences of Galois groups which is of independent interest. As an application, we obtain a new proof of Deligne\u2013Milne's short exact sequence.", "date": "2014-01", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "20", "number": "1", "publisher": "Springer", "pagerange": "315-358", "id_number": "CaltechAUTHORS:20140127-152321287", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140127-152321287", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" }, { "agency": "NEC", "grant_number": "2742738" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PEst-OE/MAT/UI02297/2011" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-013-0131-9", "primary_object": { "basename": "1205.1732v3.pdf", "url": "https://authors.library.caltech.edu/records/tnnkj-r6c80/files/1205.1732v3.pdf" }, "pub_year": "2014", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/748zw-qnd04", "eprint_id": 43760, "eprint_status": "archive", "datestamp": "2023-08-19 22:53:00", "lastmod": "2026-03-09 02:29:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Gauge Theories Labelled by Three-Manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Springer-Verlag Berlin Heidelberg. \n\nReceived: 15 May 2012. Accepted: 6 July 2013. Published online: 15 December 2013. \n\nWe wish to thank A. Kapustin, N. Seiberg, C. Vafa, R. van der Veen, and E. Witten for many helpful and enlightening discussions. The work of TD is supported in part by NSF Grant PHY-0969448. The work of DG is supported in part by NSF grant PHY-0503584 and in part by the Roger Dashen membership in the Institute for Advanced Study. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. TD and SG thank the Kavli Institute for Theoretical Physics (research\nsupported by DARPA under Grant No. HR0011-09-1-0015 and by the National Science Foundation under Grant No. PHY05-51164 and the Simons Center for Geometry and Physics for their hospitality in the summer of 2011. TD also acknowledges the Max Planck Institut f\u00fcr Mathematik for its hospitality and support during June, 2011. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies. Communicated by N. A. Nekrasov\n\n

Submitted - 1108.4389v1.pdf

", "abstract": "We propose a dictionary between geometry of triangulated 3-manifolds and physics of three-dimensional N=2 gauge theories. Under this duality, standard operations on triangulated 3-manifolds and various invariants thereof (classical as well as quantum) find a natural interpretation in field theory. For example, independence of the SL(2) Chern-Simons partition function on the choice of triangulation translates to a statement that S^3_b partition functions of two mirror 3d N=2 gauge theories are equal. Three-dimensional N=2 field theories associated to 3-manifolds can be thought of as theories that describe boundary conditions and duality walls in four-dimensional N=2 SCFTs, thus making the whole construction functorial with respect to cobordisms and gluing.", "date": "2014-01", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "325", "number": "2", "publisher": "Springer", "pagerange": "367-419", "id_number": "CaltechAUTHORS:20140210-154717900", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140210-154717900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0969448" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "Institute for Advanced Study" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0015" }, { "agency": "NSF", "grant_number": "PHY05-51164" }, { "agency": "Simons Center for Geometry and Physics" }, { "agency": "Max Planck Institut f\u00fcr Mathematik" } ] }, "other_numbering_system": { "items": [ { "id": "68-2847", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-013-1863-2", "primary_object": { "basename": "1108.4389v1.pdf", "url": "https://authors.library.caltech.edu/records/748zw-qnd04/files/1108.4389v1.pdf" }, "pub_year": "2014", "author_list": "Dimofte, Tudor; Gaiotto, Davide; et al." }, { "id": "https://authors.library.caltech.edu/records/b18q9-1tp86", "eprint_id": 110835, "eprint_status": "archive", "datestamp": "2023-08-19 22:49:59", "lastmod": "2026-03-10 00:02:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Yu-Tony-Yue", "name": { "family": "Yu", "given": "Tony Yue" }, "orcid": "0000-0002-6019-8552" } ] }, "title": "The number of vertices of a tropical curve is bounded by its area", "ispublished": "pub", "full_text_status": "public", "keywords": "Tropical curves, tropical area, moduli space, finite type", "note": "\u00a9 2014 EMS Publishing House. \n\nI am very grateful to Maxim Kontsevich, Bernhard Keller and Antoine Chambert-Loir for discussions and comments.\n\n

Accepted Version - 1306.3497.pdf

", "abstract": "We introduce the notion of tropical area of a tropical curve defined in an open subset of R^n . We prove that the number of vertices of a tropical curve is bounded by the area of the curve. The approach is totally elementary yet tricky. Our proof employs ideas from intersection theory in algebraic geometry. The result can be interpreted as the fact that the moduli space of tropical curves with bounded area is of finite type.", "date": "2014", "date_type": "published", "publication": "L'Enseignement Math\u00e9matique", "volume": "60", "number": "3/4", "publisher": "European Mathematical Society", "pagerange": "257-271", "id_number": "CaltechAUTHORS:20210914-164413123", "issn": "0013-8584", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210914-164413123", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/lem/60-3/4-3", "primary_object": { "basename": "1306.3497.pdf", "url": "https://authors.library.caltech.edu/records/b18q9-1tp86/files/1306.3497.pdf" }, "pub_year": "2014", "author_list": "Yu, Tony Yue" }, { "id": "https://authors.library.caltech.edu/records/51fj0-sq365", "eprint_id": 51696, "eprint_status": "archive", "datestamp": "2023-08-19 22:43:24", "lastmod": "2026-03-09 21:50:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Thorngren-R", "name": { "family": "Thorngren", "given": "Ryan" }, "orcid": "0000-0001-9433-3399" } ] }, "title": "Thermodynamic semirings", "ispublished": "pub", "full_text_status": "public", "keywords": "Entropy (Shannon, Renyi, Tsallis, Kullback\u2013Leibler divergence), semiring, Witt construction, multifractals, operads, binary guessing games, entropy algebras", "note": "\u00a9 2014 European Mathematical Society. \n\nReceived October 5, 2011; revised May 4, 2012. \n\nThis paper is based on the results of the second author's summer research project, supported by the Summer Undergraduate Research Fellowship program at Caltech. The first author is partly supported by NSF grants DMS-0901221 and DMS-1007207.\n\n

Submitted - 1108.2874v2.pdf

", "abstract": "The Witt construction describes a functor from the category of Rings to the category\nof characteristic 0 rings. It is uniquely determined by a few associativity constraints which do\nnot depend on the types of the variables considered, in other words, by integer polynomials.\nThis universality allowed Alain Connes and Caterina Consani to devise an analogue of the Witt\nring for characteristic one, an attractive endeavour since we know very little about the arithmetic\nin this exotic characteristic and its corresponding field with one element. Interestingly, they\nfound that in characteristic one, the Witt construction depends critically on the Shannon entropy.\nIn the current work, we examine this surprising occurrence, defining a Witt operad for an\narbitrary information measure and a corresponding algebra we call a thermodynamic semiring.\nThis object exhibits algebraically many of the familiar properties of information measures,\nand we examine in particular the Tsallis and Renyi entropy functions and applications to nonextensive\nthermodynamics and multifractals. We find that the arithmetic of the thermodynamic\nsemiring is exactly that of a certain guessing game played using the given information measure.", "date": "2014", "date_type": "published", "publication": "Journal of Noncommutative Geometry", "volume": "8", "number": "2", "publisher": "European Mathematical Society", "pagerange": "337-392", "id_number": "CaltechAUTHORS:20141113-080729733", "issn": "1661-6952", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141113-080729733", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JNCG/159", "primary_object": { "basename": "1108.2874v2.pdf", "url": "https://authors.library.caltech.edu/records/51fj0-sq365/files/1108.2874v2.pdf" }, "pub_year": "2014", "author_list": "Marcolli, Matilde and Thorngren, Ryan" }, { "id": "https://authors.library.caltech.edu/records/afb2p-7tz27", "eprint_id": 55051, "eprint_status": "archive", "datestamp": "2023-08-19 22:45:48", "lastmod": "2026-03-09 21:53:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Homological actions on sutured Floer homology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 International Press of Boston, Inc. Received May 4, 2013.\n\nThis work was carried out when the author participated the \"Homology Theories of Knots and Links\" program at MSRI and when the author visited Princeton University. The author wishes to thank MSRI and David Gabai for their hospitality. The author was partially supported by an AIM Five-Year Fellowship and NSF grant number DMS-1021956.\n\n

Published - MRL-2014-0021-0005-a012.pdf

Submitted - 1010.2808v1.pdf

", "abstract": "We define the action of the homology group H_1(M,\u2202M) on the sutured Floer homology SFH(M,\u03b3). It turns out that the contact invariant EH(M,\u03b3,\u03be) is usually sent to zero by this action. This fact allows us to refine an earlier result proved by Ghiggini and the author. As a corollary, we classify knots in #^n(S^1\u00d7S^2) which have simple knot Floer homology groups: They are essentially the Borromean knots. This answers a question of Ozsv\u00e1th.\n\nIn a different direction, we show that the only links in S^3 with simple knot Floer homology groups are the unlinks.", "date": "2014", "date_type": "published", "publication": "Mathematical Research Letters", "volume": "21", "number": "5", "publisher": "International Press", "pagerange": "1177-1197", "id_number": "CaltechAUTHORS:20150220-113128978", "issn": "1073-2780", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150220-113128978", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1021956" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/MRL.2014.v21.n5.a12", "primary_object": { "basename": "1010.2808v1.pdf", "url": "https://authors.library.caltech.edu/records/afb2p-7tz27/files/1010.2808v1.pdf" }, "related_objects": [ { "basename": "MRL-2014-0021-0005-a012.pdf", "url": "https://authors.library.caltech.edu/records/afb2p-7tz27/files/MRL-2014-0021-0005-a012.pdf" } ], "pub_year": "2014", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/8zjkv-zvw34", "eprint_id": 97849, "eprint_status": "archive", "datestamp": "2023-08-19 22:49:41", "lastmod": "2026-03-08 18:14:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Zhao-Yufei", "name": { "family": "Zhao", "given": "Yufei" } } ] }, "title": "The Green-Tao theorem: an exposition", "ispublished": "pub", "full_text_status": "public", "keywords": "Green-Tao theorem, primes in arithmetic progression", "note": "\u00a9 2014 European Mathematical Society. \n\nPublished online 2014-11-28. \n\nThe first author was supported by a Royal Society University Research Fellowship. The second author was supported by a Packard Fellowship, NSF Career Award DMS-1352121, an Alfred P. Sloan Fellowship, and an MIT NEC Corporation Award. The third author was supported by a Microsoft Research PhD Fellowship. \n\nWe thank Yuval Filmus, Mohammad Bavarian, and the anonymous referee for helpful comments on the manuscript.\n\n

Submitted - 1403.2957.pdf

", "abstract": "The celebrated Green-Tao theorem states that the prime numbers contain arbitrarily long arithmetic progressions. We give an exposition of the proof, incorporating several simplifications that have been discovered since the original paper.", "date": "2014", "date_type": "published", "publication": "EMS Surveys in Mathematical Sciences", "volume": "1", "number": "2", "publisher": "European Mathematical Society", "pagerange": "249-282", "id_number": "CaltechAUTHORS:20190812-163001431", "issn": "2308-2151", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001431", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "DMS-1352121" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/emss/6", "primary_object": { "basename": "1403.2957.pdf", "url": "https://authors.library.caltech.edu/records/8zjkv-zvw34/files/1403.2957.pdf" }, "pub_year": "2014", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/7vfyh-mbc97", "eprint_id": 45989, "eprint_status": "archive", "datestamp": "2023-08-19 22:41:57", "lastmod": "2026-03-09 02:15:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Cwikel's theorem and the CLR inequality", "ispublished": "pub", "full_text_status": "public", "keywords": "Cwikel inequality, trace ideals, eigenvalue inequalities, Schr\u00f6dinger operators", "note": "\u00a9 2014 European Mathematical Society. \n\nReceived June 14, 2012. \n\nU.S. National Science Foundation grants PHY-1068285 and PHY-1347399 are acknowledged.\n\n

Submitted - 1206.3325v1.pdf

", "abstract": "We give a short proof of the CLR bound on the number of negative eigenvalues of Schr\u00f6dinger operators. The argument, which is based on work of Rumin, leads to remarkably good constants and applies to the case of operator-valued potentials as well. Moreover, we obtain the general form of Cwikel's estimate about the singular values of operators of the form f(X)g(\u2212i\u2207).", "date": "2014", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "4", "number": "1", "publisher": "European Mathematical Society", "pagerange": "1-21", "id_number": "CaltechAUTHORS:20140530-072438434", "issn": "1664-039X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140530-072438434", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1347399" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JST/59", "primary_object": { "basename": "1206.3325v1.pdf", "url": "https://authors.library.caltech.edu/records/7vfyh-mbc97/files/1206.3325v1.pdf" }, "pub_year": "2014", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/jeks1-rav12", "eprint_id": 53251, "eprint_status": "archive", "datestamp": "2023-08-19 22:44:37", "lastmod": "2026-03-09 20:35:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Angel-O", "name": { "family": "Angel", "given": "Omer" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Lyons-R", "name": { "family": "Lyons", "given": "Russell" } } ] }, "title": "Random orderings and unique ergodicity of automorphism groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Graphs, hypergraphs, the random graph, metric spaces, Fra\u00efss\u00e9, Ramsey, minimal flow, Urysohn space", "note": "\u00a9 2014 European Mathematical Society. Received August 12, 2012 and in revised form November 19, 2012.\n\nWe would like to thank Gregory Cherlin and the anonymous referee for many useful comments. Research of O. Angel partially supported by NSERC and the Sloan Foundation. Research of A. S. Kechris partially supported by NSF grant DMS-0968710. Research of R. Lyons partially supported by NSF grant DMS-1007244 and Microsoft Research.\n\n

Submitted - 1208.2389v1.pdf

", "abstract": "We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner and Weiss's example of the group of all permutations of the integers. We also contrast these results to those for certain special classes of graphs and metric spaces in which such random orderings can be found that are not uniform.", "date": "2014", "date_type": "published", "publication": "Journal of the European Mathematical Society", "volume": "16", "number": "10", "publisher": "European Mathematical Society", "pagerange": "2059-2095", "id_number": "CaltechAUTHORS:20150107-075104911", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150107-075104911", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "DMS-0968710" }, { "agency": "NSF", "grant_number": "DMS-1007244" }, { "agency": "Microsoft Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JEMS/483", "primary_object": { "basename": "1208.2389v1.pdf", "url": "https://authors.library.caltech.edu/records/jeks1-rav12/files/1208.2389v1.pdf" }, "pub_year": "2014", "author_list": "Angel, Omer; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/px2v0-v9389", "eprint_id": 46330, "eprint_status": "archive", "datestamp": "2023-08-19 22:42:12", "lastmod": "2026-03-09 21:53:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Zhang-Xingru", "name": { "family": "Zhang", "given": "Xingru" } } ] }, "title": "Characterizing slopes for torus knots", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2014 Geometry & Topology Publications. First published in\nAlgebraic & Geometric Topology in volume 14, number 3, published by Mathematical Sciences Publishers\n\nReceived: 1 December 2012; Revised: 22 July 2013; Accepted: 29 July 2013; Published: 7 April 2014.\n\nThe first author was partially supported by an AIM Five-Year Fellowship, NSF grant number DMS-1103976 and an Alfred P Sloan Research Fellowship. We are grateful to the organizers of the \"Workshop on Topics in Dehn Surgery\" at University of Texas at Austin for making our collaboration possible. We wish to thank John Baldwin for a conversation which made us realize a mistake in an earlier version of this paper.\n\n

Published - agt-2014-14-041s.pdf

Submitted - 1206.5577v2.pdf

", "abstract": "A slope p/q is called a characterizing slope for a given knot K_0 in S^3 if whenever the p/q\u2013surgery on a knot K in S^3 is homeomorphic to the p/q\u2013surgery on K_0 via\nan orientation preserving homeomorphism, then K D K0 . In this paper we try to find characterizing slopes for torus knots T_(r,s). We show that any slope p/q which is\nlarger than the number 30(r^(2)-1)(s^(2)-1)/67 is a characterizing slope for T_(r,s). The proof uses Heegaard Floer homology and Agol\u2013Lackenby's 6\u2013theorem. In the case\nof T(5,2), we obtain more specific information about its set of characterizing slopes by applying further Heegaard Floer homology techniques.", "date": "2014", "date_type": "published", "publication": "Algebraic and Geometric Topology", "volume": "14", "number": "3", "publisher": "Geometry & Topology Publications", "pagerange": "1249-1274", "id_number": "CaltechAUTHORS:20140618-104801586", "issn": "1472-2747", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140618-104801586", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/agt.2014.14.1249", "primary_object": { "basename": "1206.5577v2.pdf", "url": "https://authors.library.caltech.edu/records/px2v0-v9389/files/1206.5577v2.pdf" }, "related_objects": [ { "basename": "agt-2014-14-041s.pdf", "url": "https://authors.library.caltech.edu/records/px2v0-v9389/files/agt-2014-14-041s.pdf" } ], "pub_year": "2014", "author_list": "Ni, Yi and Zhang, Xingru" }, { "id": "https://authors.library.caltech.edu/records/b4b5w-07n42", "eprint_id": 51770, "eprint_status": "archive", "datestamp": "2023-08-19 22:43:33", "lastmod": "2026-03-09 21:41:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "\u0106a\u0107i\u0107-Branimir", "name": { "family": "\u0106a\u0107i\u0107", "given": "Branimir" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Teh-Kevin", "name": { "family": "Teh", "given": "Kevin" } } ] }, "title": "Coupling of gravity to matter, spectral action and cosmic topology", "ispublished": "pub", "full_text_status": "public", "keywords": "Spectral action, cosmic topology, gravity coupled to matter, Poisson summation formula, heat kernel", "note": "\u00a9 2014 European Mathematical Society. \n\nReceived December 15, 2011; revised June 26, 2012. \n\nThis work is partially supported by NSF grants DMS-0901221,\nDMS-1007207, DMS-1201512, PHY-1205440. The second author thanks Jos\u00e9 Luis Cisneros-Molina for a useful conversation and for pointing out to us the results of [9], and the first author thanks Mathai Varghese for useful conversations.\n\n

Submitted - 1106.5473.pdf

", "abstract": "We consider a model of modified gravity based on the spectral action functional, for a cosmic topology given by a spherical space form, and the associated slow-roll inflation scenario. We consider then the coupling of gravity to matter determined by an almost-commutative geometry over the spherical space form. We show that this produces a multiplicative shift of the amplitude of the power spectra for the density fluctuations and the gravitational waves, by a multiplicative factor equal to the total number of fermions in the matter sector of the model. We obtain the result by an explicit nonperturbative computation, based on the Poisson summation formula and the spectra of twisted Dirac operators on spherical space forms, as well as, for more general spacetime manifolds, using a heat kernel computation.", "date": "2014", "date_type": "published", "publication": "Journal of Noncommutative Geometry", "volume": "8", "number": "2", "publisher": "European Mathematical Society", "pagerange": "473-504", "id_number": "CaltechAUTHORS:20141114-110040989", "issn": "1661-6952", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141114-110040989", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JNCG/162", "primary_object": { "basename": "1106.5473.pdf", "url": "https://authors.library.caltech.edu/records/b4b5w-07n42/files/1106.5473.pdf" }, "pub_year": "2014", "author_list": "\u0106a\u0107i\u0107, Branimir; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/dcjgq-cd410", "eprint_id": 43471, "eprint_status": "archive", "datestamp": "2023-08-19 22:35:38", "lastmod": "2026-04-09 21:19:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakamura-Shin", "name": { "family": "Nakamura", "given": "Shin" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Out of equilibrium temperature from holography", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 American Physical Society.\n\nReceived 4 October 2013; published 13 December 2013.\n\nWe thank S. S. Gubser, C. P. Herzog, A. Karch, E. Kiritsis, K. Kobayashi, H. Liu, S. Sasa, T. Takayanagi, D. Teaney and Y. Utsumi for discussions and comments. The work of H. O. is supported in part by U.S. DOE Grant No. DE-FG03-92-ER40701, the Simons Foundation, JSPS Grant-in-Aid for Scientific Research C-23540285, and the WPI Initiative of MEXT of Japan. He also thanks the hospitality of the Aspen Center for Physics and the National Science Foundation, which supports the Center under Grant No. PHY-1066293, and of the Simons Center for Geometry and Physics. The work of S. N. was supported in part by the Grant-in-Aid for Scientific Research on Innovative Areas No. 2104, and Grant-in-Aid for Challenging Exploratory Research No. 23654132.\n\n

Published - PhysRevD.88.126003.pdf

Submitted - 1309.4089v2.pdf

", "abstract": "We define an effective temperature and study its properties for a class of out-of-equilibrium steady states in a heat bath. Our analysis is based on the anti-de Sitter spacetime/conformal field theory (AdS/CFT) correspondence, and examples include systems driven by applied electric fields and branes dragged in plasmas. We found that the effective temperature can be lower than that of the heat bath and that the out-of-equilibrium noise can be smaller than that in equilibrium. We show that a generalization of the fluctuation-dissipation relation holds for the effective temperature. In particular, we generalize the Johnson-Nyquist relation for a large electric field.", "date": "2013-12-13", "date_type": "published", "publication": "Physical Review D", "volume": "88", "number": "12", "publisher": "American Physical Society", "pagerange": "Art. No. 126003", "id_number": "CaltechAUTHORS:20140122-121855825", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140122-121855825", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Simons Foundation" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Grant-in-Aid for Scientific Research on Innovative Areas", "grant_number": "2104" }, { "agency": "Grant-in-Aid for Challenging Exploratory Research", "grant_number": "23654132" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.88.126003", "primary_object": { "basename": "1309.4089v2.pdf", "url": "https://authors.library.caltech.edu/records/dcjgq-cd410/files/1309.4089v2.pdf" }, "related_objects": [ { "basename": "PhysRevD.88.126003.pdf", "url": "https://authors.library.caltech.edu/records/dcjgq-cd410/files/PhysRevD.88.126003.pdf" } ], "pub_year": "2013", "author_list": "Nakamura, Shin and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/5shpz-p9366", "eprint_id": 71910, "eprint_status": "archive", "datestamp": "2023-08-19 22:26:01", "lastmod": "2026-04-09 17:58:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Making Consensus Tractable", "ispublished": "pub", "full_text_status": "public", "keywords": "Bayesian agents, decision by consensus", "note": "\u00a9 2013 ACM, Inc. \n\nReceived May 2012; revised September 2012, January 2013; accepted February 2013. \n\nE. Mossel is supported by a Sloan fellowship in Mathematics, by BSF grant 2004105, by an NSF Career Award (DMS 054829), by ONR award N00014-07-1-0506, and by ISF grant 1300/08. O. Tamuz is supported by ISF grant 1300/08 and is a recipient of the Google Europe Fellowship in Social Computing. This research is supported in part by this Google Fellowship.\n\n

Submitted - 1007.0959.pdf

", "abstract": "We study a model of consensus decision making in which a finite group of Bayesian agents has to choose between one of two courses of action. Each member of the group has a private and independent signal at his or her disposal, giving some indication as to which action is optimal. To come to a common decision, the participants perform repeated rounds of voting. In each round, each agent casts a vote in favor of one of the two courses of action, reflecting his or her current belief, and observes the votes of the rest. \n\nWe provide an efficient algorithm for the calculation the agents have to perform and show that consensus is always reached and that the probability of reaching a wrong decision decays exponentially with the number of agents.", "date": "2013-12", "date_type": "published", "publication": "ACM Transactions on Economics and Computation", "volume": "1", "number": "4", "publisher": "ACM", "pagerange": "Art. No. 20", "id_number": "CaltechAUTHORS:20161110-081650257", "issn": "2167-8375", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-081650257", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2004105" }, { "agency": "NSF", "grant_number": "DMS 054829" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-07-1-0506" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/2542174.2542176", "primary_object": { "basename": "1007.0959.pdf", "url": "https://authors.library.caltech.edu/records/5shpz-p9366/files/1007.0959.pdf" }, "pub_year": "2013", "author_list": "Mossel, Elchanan and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/063mn-3cn50", "eprint_id": 43578, "eprint_status": "archive", "datestamp": "2023-08-19 22:22:49", "lastmod": "2026-04-09 21:20:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Monotonicity of a relative R\u00e9nyi entropy", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 AIP Publishing LLC. Received 15 July 2013. Accepted 10 October 2013. Published online 13 December 2013. We thank E. Carlen, V. Jaksic, C.-A. Pillet, and A. Vershynina for valuable comments on a first draft of this paper. We are grateful to the referee for various suggestions that helped to improve this paper. U.S. National Science Foundation Grants Nos. PHY-1347399 (R.L.F.), PHY-0965859 and\nPHY-1265118 (E.H.L.), and the Simons Foundation Grant No. 230207 (E.H.L.) are acknowledged.\nJ. Math. Phys.54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].\n\n

Published - 1.4838835.pdf

Submitted - 1306.5358v3.pdf

", "abstract": "We show that a recent definition of relative R\u00e9nyi entropy is monotone\nunder completely positive, trace preserving maps. This proves a recent\nconjecture of M\u00fcller-Lennert et al. [\"On quantum R\u00e9nyi entropies: A\nnew definition, some properties,\" J. Math. Phys. 54, 122203 (2013); e-print\narXiv:1306.3142v1; see also e-print arXiv:1306.3142].", "date": "2013-12", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "54", "number": "12", "publisher": "American Institute of Physics", "pagerange": "Art. No. 122201", "id_number": "CaltechAUTHORS:20140130-111730599", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140130-111730599", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1347399" }, { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "NSF", "grant_number": "PHY-1265118" }, { "agency": "Simons Foundation", "grant_number": "230207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.4838835", "primary_object": { "basename": "1306.5358v3.pdf", "url": "https://authors.library.caltech.edu/records/063mn-3cn50/files/1306.5358v3.pdf" }, "related_objects": [ { "basename": "1.4838835.pdf", "url": "https://authors.library.caltech.edu/records/063mn-3cn50/files/1.4838835.pdf" } ], "pub_year": "2013", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/ryxaq-f1122", "eprint_id": 97829, "eprint_status": "archive", "datestamp": "2023-08-19 22:18:42", "lastmod": "2026-04-09 22:45:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Two extensions of Ramsey's theorem", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Duke University Press. \n\nReceived 6 January 2012. Revision received 26 February 2013. First available in Project Euclid 28 November 2013. \n\nConlon's work partially supported by a Royal Society University Research Fellowship. Fox's work partially supported by a Simons Fellowship, by National Science Foundation grant DMS-1069197, by an Alfred P. Sloan Fellowship, and by an MIT NEC Corporation Award. Sudakov's work partially supported by National Science Foundation grant DMS-1101185 and by a US-Israel Binational Science Foundation grant. \n\nWe would like to thank Noga Alon for helpful discussions and, in particular, for raising the question of what other weight functions might work in Erd\u0151s's conjecture. We would also like to thank the referees for their many helpful remarks.\n\n

Submitted - 1112.1548.pdf

", "abstract": "Ramsey's theorem, in the version of Erd\u0151s and Szekeres, states that every 2-coloring of the edges of the complete graph on {1, 2, . . ., n} contains a monochromatic clique of order (1/2)log n. In this article, we consider two well-studied extensions of Ramsey's theorem. Improving a result of R\u00f6dl, we show that there is a constant c > 0 such that every 2-coloring of the edges of the complete graph on {2, 3, . . ., n} contains a monochromatic clique S for which the sum of 1/log i over all vertices i \u2208 S is at least c log log log n. This is tight up to the constant factor c and answers a question of Erd\u0151s from 1981. Motivated by a problem in model theory, V\u00e4\u00e4n\u00e4nen asked whether for every k there is an n such that the following holds: for every permutation \u03c0 of 1, . . ., k\u22121, every 2-coloring of the edges of the complete graph on {1, 2, . . ., n} contains a monochromatic clique a_1 < \u2022 \u2022 \u2022 < a_k with\n\na_(\u03c0(1)+1) \u2212 a_(\u03c0(1)) > a_\u03c0((2)+1) \u2212 a_(\u03c0(2)) > \u2022 \u2022 \u2022 > a_(\u03c0(k\u22121)+1) \u2212 a_(\u03c0(k\u22121)).\n\nThat is, not only do we want a monochromatic clique, but the differences between consecutive vertices must satisfy a prescribed order. Alon and, independently, Erd\u0151s, Hajnal, and Pach answered this question affirmatively. Alon further conjectured that the true growth rate should be exponential in k. We make progress towards this conjecture, obtaining an upper bound on n which is exponential in a power of k. This improves a result of Shelah, who showed that n is at most double-exponential in k.", "date": "2013-11-28", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "162", "number": "15", "publisher": "Duke University Press", "pagerange": "2903-2927", "id_number": "CaltechAUTHORS:20190812-162959551", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959551", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "NSF", "grant_number": "DMS-1101185" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/00127094-2382566", "primary_object": { "basename": "1112.1548.pdf", "url": "https://authors.library.caltech.edu/records/ryxaq-f1122/files/1112.1548.pdf" }, "pub_year": "2013", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/ex9gs-37q03", "eprint_id": 71919, "eprint_status": "archive", "datestamp": "2023-08-19 22:13:18", "lastmod": "2026-03-10 00:00:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gur-Tom", "name": { "family": "Gur", "given": "Tom" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Testing Booleanity and the Uncertainty Principle", "ispublished": "pub", "full_text_status": "public", "keywords": "discrete Fourier analysis, property testing, Boolean functions", "note": "\u00a9 2013 Tom Gur and Omer Tamuz.\nLicensed under a Creative Commons Attribution License (CC-BY).\n\nSubmitted December 26, 2012, revised November 6, 2013; published November 10, 2013.\n\nResearch supported by an Israel Science Foundation grant and by the I-CORE Program of the Planning and Budgeting\nCommittee and the Israel Science Foundation.\nSupported by ISF grant 1300/08. Omer Tamuz is a recipient of the Google Europe Fellowship in Social Computing, and\nthis research is supported in part by this Google Fellowship.\n\nThe authors would like to thank Elchanan Mossel for a helpful initial discussion of the problem and\nfor suggesting the application to property testing. We would like to thank Adi Shamir for suggesting\nthe relevance to cryptography, and we would like to thank Oded Goldreich for discussions regarding\nthe relevance to property testing. Last, we would like to thank the anonymous referees for the helpful\ncomments that allowed us to improve the presentation of the results.\n\n

Published - cj13-14.pdf

Submitted - 1204.0944.pdf

Submitted - 1204.0944v1.pdf

Supplemental Material - cj13-14.zip

", "abstract": "Let f : {-1,1}^n \u2192 R be a real function on the hypercube, given by its discrete\nFourier expansion, or, equivalently, represented as a multilinear polynomial. We say that it is\nBoolean if its image is in {-1;1}.\nWe show that every function on the hypercube with a sparse Fourier expansion must\neither be Boolean or far from Boolean. In particular, we show that a multilinear polynomial\nwith at most k terms must either be Boolean, or output values different than -1 or 1 for a\nfraction of at least 2=(k+2)\u00b2 of its domain.\nIt follows that given oracle access to f, together with the guarantee that its representation\nas a multilinear polynomial has at most k terms, one can test Booleanity using O(k\u00b2) queries.\nWe show an \u03a9(k) queries lower bound for this problem.\nOur proof crucially uses Hirschman's entropic version of Heisenberg's uncertainty principle.", "date": "2013-11-10", "date_type": "published", "publication": "Chicago Journal of Theoretical Computer Science", "volume": "2013", "publisher": "Theory of Computing Exchange", "pagerange": "Art. No. 14", "id_number": "CaltechAUTHORS:20161110-144803099", "issn": "1073-0486", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-144803099", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "I-CORE Program of the Planning and Budgeting Committee" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4086/cjtcs.2013.014", "primary_object": { "basename": "cj13-14.zip", "url": "https://authors.library.caltech.edu/records/ex9gs-37q03/files/cj13-14.zip" }, "related_objects": [ { "basename": "1204.0944.pdf", "url": "https://authors.library.caltech.edu/records/ex9gs-37q03/files/1204.0944.pdf" }, { "basename": "1204.0944v1.pdf", "url": "https://authors.library.caltech.edu/records/ex9gs-37q03/files/1204.0944v1.pdf" }, { "basename": "cj13-14.pdf", "url": "https://authors.library.caltech.edu/records/ex9gs-37q03/files/cj13-14.pdf" } ], "pub_year": "2013", "author_list": "Gur, Tom and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/rjrv2-yzw72", "eprint_id": 42350, "eprint_status": "archive", "datestamp": "2023-08-19 22:02:51", "lastmod": "2026-04-09 16:13:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Keller-C-A", "name": { "family": "Keller", "given": "Christoph A." }, "orcid": "0000-0003-2592-2012" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Modular Constraints on Calabi-Yau Compactifications", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag Berlin Heidelberg. \n\nReceived: 18 October 2012; Accepted: 28 January 2013. \n\nWe thank T. Eguchi, M. Freedman, M. Gaberdiel, S. Hellerman, C. Schmidt-Colinet, W. Taylor, C. Vafa and S.-T. Yau for useful discussions. We thank D. Friedan and T. H\u00fcbsch for their comments on the earlier version of the paper. We thank the hospitality of the Aspen Center for Physics (NSF grant 1066293) and the Simons Center for Geometry and Physics. This work is supported in part by U.S. DOE grant DE-FG03-92-ER40701. The work of CAK is also supported in part by the John A. McCone Postdoctoral Fellowship at Caltech and U.S. DOE grant DE-FG02-96ER40959. The work of HO is also supported in part by a Simons Investigator award from the Simons Foundation, the Fred Kavli Professorship at Caltech, and by the WPI Initiative of MEXT of Japan and JSPS Grant-in-Aid for Scientific Research C-23540285.\n\n

Submitted - 1209.4649.pdf

", "abstract": "We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primary states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.", "date": "2013-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "324", "number": "1", "publisher": "Springer", "pagerange": "107-127", "id_number": "CaltechAUTHORS:20131111-095649297", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131111-095649297", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "John A. McCone Postdoctoral Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40959" }, { "agency": "Simons Foundation" }, { "agency": "Caltech Fred Kavli Professorship" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" } ] }, "other_numbering_system": { "items": [ { "id": "68-2885", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-013-1797-8", "primary_object": { "basename": "1209.4649.pdf", "url": "https://authors.library.caltech.edu/records/rjrv2-yzw72/files/1209.4649.pdf" }, "pub_year": "2013", "author_list": "Keller, Christoph A. and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/fsang-0q918", "eprint_id": 43022, "eprint_status": "archive", "datestamp": "2023-08-19 22:05:16", "lastmod": "2026-04-09 15:25:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conley-C-T", "name": { "family": "Conley", "given": "Clinton T." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Miller-B-D", "name": { "family": "Miller", "given": "Benjamin D." } } ] }, "title": "Stationary probability measures and topological realizations", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2013 Springer. Received July 23. 2012 and in revised form September 16. 2012. The first and third authors were supported in part by SFB Grant 878. The second author was supported in part by NSF Grant DMS-0968710.", "abstract": "We establish the generic inexistence of stationary Borel probability measures for aperiodic Borel actions of countable groups on Polish spaces. Using this, we show that every aperiodic continuous action of a countable group on a compact Polish space has an invariant Borel set on which it has no \u03c3-compact realization.", "date": "2013-11", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "198", "number": "1", "publisher": "Springer", "pagerange": "333-345", "id_number": "CaltechAUTHORS:20131216-115036936", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131216-115036936", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "SFB", "grant_number": "878" }, { "agency": "NSF", "grant_number": "DMS-0968710" } ] }, "other_numbering_system": { "items": [ { "id": "MR3096642", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-013-0025-8", "pub_year": "2013", "author_list": "Conley, Clinton T.; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/h2wbt-97x06", "eprint_id": 43200, "eprint_status": "archive", "datestamp": "2023-08-19 21:40:42", "lastmod": "2026-04-09 16:28:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hedden-M", "name": { "family": "Hedden", "given": "Matthew" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Khovanov module and the detection of unlinks", "ispublished": "pub", "full_text_status": "public", "keywords": "Khovanov module, Heegaard Floer homology, unlinks, branched double cover", "note": "\u00a9 2013 Mathematical Sciences Publishers.\nReceived: 6 May 2013;\nAccepted: 15 June 2013;\nPublished: 17 October 2013.\n\nThis work was initiated when the authors participated the \"Homology\nTheories of Knots and Links\" program at MSRI, and was carried out further\nwhen the authors visited the Simons Center for Geometry and Physics. We are grateful\nto Ciprian Manolescu and Tomasz Mrowka for helpful conversations. We also wish to\nthank Robert Lipshitz, Sucharit Sarkar and the referee for pointing out a mistake in the\nproof of Proposition 2.2. Special thanks are due to Sucharit Sarkar for suggesting a\nway to fix the mistake. The first author was partially supported by NSF grant numbers\nDMS-0906258 and DMS-1150872 and an Alfred P Sloan Research Fellowship. The\nsecond author was partially supported by an AIM Five-Year Fellowship, NSF grant\nnumbers DMS-1021956, DMS-1103976 and an Alfred P Sloan Research Fellowship.\n\n

Published - Downloads-2.pdf

", "abstract": "We study a module structure on Khovanov homology, which we show is natural under the Ozsv\u00e1th\u2013Szab\u00f3 spectral sequence to the Floer homology of the branched double cover. As an application, we show that this module structure detects trivial links. A key ingredient of our proof is that the \u039b\u2217H_1\u2013module structure on Heegaard Floer homology detects S^1 \u00d7 S^2 connected summands.", "date": "2013-10", "date_type": "published", "publication": "Geometry and Topology", "volume": "17", "number": "5", "publisher": "Geometry & Topology Publications", "pagerange": "3027-3076", "id_number": "CaltechAUTHORS:20140103-093828720", "issn": "1465-3060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140103-093828720", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0906258" }, { "agency": "NSF", "grant_number": "DMS-1150872" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1021956" }, { "agency": "NSF", "grant_number": "DMS-1103976" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/gt.2013.17.3027", "primary_object": { "basename": "Downloads-2.pdf", "url": "https://authors.library.caltech.edu/records/h2wbt-97x06/files/Downloads-2.pdf" }, "pub_year": "2013", "author_list": "Hedden, Matthew and Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/9yds7-ya050", "eprint_id": 41197, "eprint_status": "archive", "datestamp": "2023-08-22 10:26:23", "lastmod": "2026-04-09 20:08:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cornelissen-G", "name": { "family": "Cornelissen", "given": "Gunther" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Graph reconstruction and quantum statistical mechanics", "ispublished": "pub", "full_text_status": "public", "keywords": "Graph; Graph reconstruction; Quantum statistical mechanics; Graph C\u2217-algebra", "note": "\u00a9 2013 Elsevier B.V. Received 26 September 2012. Received in revised form 27 December 2012. Available online 29 March 2013.\n\n

Submitted - 1209.5783v1.pdf

", "abstract": "We study how far it is possible to reconstruct a graph from various Banach algebras associated to its universal covering, and extensions thereof to quantum statistical mechanical systems. It turns out that most the boundary operator algebras reconstruct only topological information, but the statistical mechanical point of view allows for complete reconstruction of multigraphs with minimal degree three.", "date": "2013-10", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "72", "publisher": "Elsevier", "pagerange": "110-117", "id_number": "CaltechAUTHORS:20130909-153558798", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130909-153558798", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2013.03.021", "primary_object": { "basename": "1209.5783v1.pdf", "url": "https://authors.library.caltech.edu/records/9yds7-ya050/files/1209.5783v1.pdf" }, "pub_year": "2013", "author_list": "Cornelissen, Gunther and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/6aqj4-q2365", "eprint_id": 77106, "eprint_status": "archive", "datestamp": "2023-08-19 21:45:15", "lastmod": "2026-04-09 20:30:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\n\nReceived: 5 June 2012.\nAccepted: 3 January 2013.\nPublished online: 11 August 2013.\n\nWe thank Zhihao Ma for helpful correspondence. U.S. National Science Foundation grants PHY-1068285 (R.F.) and PHY-0965859 (E.L.) and the Simons Foundation grant 230207 (E.L.) are acknowledged.\n\n

Published - art_3A10.1007_2Fs00220-013-1775-1.pdf

Submitted - 1204.0825.pdf

", "abstract": "Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum. Recently these inequalities have been generalized to the tensor product of several Hilbert spaces and we show here how their derivations can be shortened to a few lines and how they can be generalized. Our proofs utilize the technique of the original derivation of strong subadditivity of the von Neumann entropy.", "date": "2013-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "323", "number": "2", "publisher": "Springer", "pagerange": "487-495", "id_number": "CaltechAUTHORS:20170501-112412599", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-112412599", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "Simons Foundation", "grant_number": "230207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-013-1775-1", "primary_object": { "basename": "1204.0825.pdf", "url": "https://authors.library.caltech.edu/records/6aqj4-q2365/files/1204.0825.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs00220-013-1775-1.pdf", "url": "https://authors.library.caltech.edu/records/6aqj4-q2365/files/art_3A10.1007_2Fs00220-013-1775-1.pdf" } ], "pub_year": "2013", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/9xkv9-1s605", "eprint_id": 42237, "eprint_status": "archive", "datestamp": "2023-08-19 21:27:11", "lastmod": "2026-04-09 15:28:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" } ] }, "title": "Surface defects and resolvents", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Nonperturbative Effects, Sigma Models", "note": "\u00a9 SISSA 2013. Published for SISSA by Springer. \n\nReceived: July 27, 2013. Accepted: August 21, 2013. Published: September 12, 2013. \n\nWe are grateful to A. Kapustin for collaboration at an early stage of the project, and many important discussions. The research of DG was supported by the Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701FG-02. The work of NS was supported in part by DOE grant DE-SC0009988 and by the United States-Israel Binational Science Foundation (BSF) under grant number 2010/629. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Submitted - 1307.2578v2.pdf

", "abstract": "We study a large class of BPS surface defects in 4d N=2 gauge theories. They are defined by coupling a 2d N=(2,2) gauged linear sigma model to the 4d bulk degrees of freedom. Our main result is an efficient computation of the effective twisted superpotential for all these models in terms of a basic object closely related to the resolvent of the 4d gauge theory, which encodes the curve describing the 4d low energy dynamics. We reproduce and extend the results of brane constructions and compute the effective twisted superpotential for general monodromy surface defects. We encounter novel, puzzling field theory phenomena in the low energy dynamics of the simplest surface defects and we propose some local models to explain them. We also study in some detail the behavior of surface defects near monopole points of the bulk theory's Coulomb branch. Finally, we explore the effect on the defect of breaking the bulk supersymmetry from N=2 to N=1 and show that certain quantities are independent of this breaking.", "date": "2013-09-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 70", "id_number": "CaltechAUTHORS:20131105-071959496", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20131105-071959496", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Perimeter Institute for Theoretical Physics" }, { "agency": "Industry Canada" }, { "agency": "Ontario Ministry of Economic Development and Innovation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-SC0009988" }, { "agency": "Binational Science Foundation (United States-Israel)", "grant_number": "2010/629" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP09(2013)070", "primary_object": { "basename": "1307.2578v2.pdf", "url": "https://authors.library.caltech.edu/records/9xkv9-1s605/files/1307.2578v2.pdf" }, "pub_year": "2013", "author_list": "Gaiotto, Davide; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/ee3ak-awj41", "eprint_id": 71969, "eprint_status": "archive", "datestamp": "2023-08-22 10:15:49", "lastmod": "2026-04-09 16:12:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "A lower bound on seller revenue in single buyer monopoly auctions", "ispublished": "pub", "full_text_status": "public", "keywords": "Auctions; Monopoly; Geometric expectation", "note": "\u00a9 2013 Elsevier B.V.\n\nReceived 30 May 2012, Revised 29 May 2013, Accepted 29 May 2013, Available online 6 June 2013.\n\nWe would like to thank Elchanan Mossel for commenting on a preliminary version of this paper. We owe a debt of gratitude to the anonymous reviewer who helped us improve the paper significantly through many helpful suggestions.\n\nThis research is supported by ISF grant 1300/08, and by a Google Europe Fellowship in Social Computing.\n\n

Submitted - 1204.5551.pdf

", "abstract": "We consider a monopoly seller who optimally auctions a single object to a single potential buyer, with a known distribution of valuations. We show that a tight lower bound on the seller's expected revenue is 1/e times the geometric expectation of the buyer's valuation, and that this bound is uniquely achieved for the equal revenue distribution. We show also that when the valuation's expectation and geometric expectation are close, then the seller's expected revenue is close to the expected valuation.", "date": "2013-09", "date_type": "published", "publication": "Operations Research Letters", "volume": "41", "number": "5", "publisher": "Elsevier", "pagerange": "474-476", "id_number": "CaltechAUTHORS:20161114-065718415", "issn": "0167-6377", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-065718415", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.orl.2013.05.011", "primary_object": { "basename": "1204.5551.pdf", "url": "https://authors.library.caltech.edu/records/ee3ak-awj41/files/1204.5551.pdf" }, "pub_year": "2013", "author_list": "Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/brbhf-5w298", "eprint_id": 41568, "eprint_status": "archive", "datestamp": "2023-08-22 10:11:46", "lastmod": "2026-04-09 22:00:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chee-Y-M", "name": { "family": "Chee", "given": "Yeow Meng" } }, { "id": "Colbourn-C-J", "name": { "family": "Colbourn", "given": "Charles J." } }, { "id": "Ling-A-C-H", "name": { "family": "Ling", "given": "Alan C. H." } }, { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "Covering and packing for pairs", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Balanced incomplete block design; Pair packing; Pair covering; Group divisible design; Pairwise balanced design", "note": "\u00a9 2013 Elsevier Inc. Received 24 September 2011. Available online 23 April 2013. We thank an anonymous referee for helpful comments on the presentation.", "abstract": "When a v-set can be equipped with a set of k-subsets so that every 2-subset of the v-set appears in exactly (or at most, or at least) one of the chosen k-subsets, the result is a balanced incomplete block design (or packing, or covering, respectively). For each k, balanced incomplete block designs are known to exist for all sufficiently large values of v that meet certain divisibility conditions. When these conditions are not met, one can ask for the packing with the most blocks and/or the covering with the fewest blocks. Elementary necessary conditions furnish an upper bound on the number of blocks in a packing and a lower bound on the number of blocks in a covering. In this paper it is shown that for all sufficiently large values of v, a packing and a covering on v elements exist whose numbers of blocks differ from the basic bounds by no more than an additive constant depending only on k.", "date": "2013-09", "date_type": "published", "publication": "Journal of Combinatorial Theory. Series A", "volume": "120", "number": "7", "publisher": "Elsevier", "pagerange": "1440-1449", "id_number": "CaltechAUTHORS:20130930-153617380", "issn": "0097-3165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130930-153617380", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jcta.2013.04.005", "pub_year": "2013", "author_list": "Chee, Yeow Meng; Colbourn, Charles J.; et al." }, { "id": "https://authors.library.caltech.edu/records/1aqs2-grd16", "eprint_id": 34007, "eprint_status": "archive", "datestamp": "2023-08-22 09:57:18", "lastmod": "2026-04-09 22:51:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Estrada-C", "name": { "family": "Estrada", "given": "Christopher" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models", "ispublished": "pub", "full_text_status": "public", "keywords": "Noncommutative geometry; Higgs mass; hypergeometric functions", "note": "\u00a9 2013 World Scientific Publishing Company. \n\nReceived 10 October 2012; Accepted 20 December 2012; Published 27 March 2013. \n\nThe first author was supported by a Mellon Mays Undergraduate Fellowship. The second author was partially supported by NSF Grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440.\n\n

Submitted - 1208.5023v1.pdf

", "abstract": "We study the renormalization group flow for the Higgs self coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.", "date": "2013-08", "date_type": "published", "publication": "International Journal of Geometric Methods in Modern Physics", "volume": "10", "number": "7", "publisher": "World Scientific Publishing", "pagerange": "Art. No. 1350036", "id_number": "CaltechAUTHORS:20120911-145601334", "issn": "0219-8878", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120911-145601334", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Mellon Mays Undergraduate Fellowship" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219887813500369", "primary_object": { "basename": "1208.5023v1.pdf", "url": "https://authors.library.caltech.edu/records/1aqs2-grd16/files/1208.5023v1.pdf" }, "pub_year": "2013", "author_list": "Estrada, Christopher and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/cj1sj-bm485", "eprint_id": 38885, "eprint_status": "archive", "datestamp": "2023-08-19 20:30:55", "lastmod": "2026-04-09 16:05:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bejleri-D", "name": { "family": "Bejleri", "given": "Dori" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Quantum field theory over F_1", "ispublished": "pub", "full_text_status": "public", "keywords": "Field with one element\nPerturbative quantum field theory\nGraph hypersurfaces and configuration\nspaces\nModuli spaces of curves\nTorified-schemes\nGrothendieck ring of varieties", "note": "\u00a9 2013 Elsevier B.V. \n\nReceived 7 October 2012. Received in revised form 20 February 2013. Accepted 2 March 2013. Available online 14 March 2013. \n\nThe first author was supported for this project by a Caltech Summer Undergraduate Research Fellowship. The second author is supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The second author thanks Paolo Aluffi for many useful discussions and for a careful reading of the manuscript, Javier L\u00f3pez-Pe\u00f1a for reading an earlier draft of the paper and offering comments and suggestions, and Spencer Bloch for useful conversations about [2]. The authors thank the referee for useful comments and remarks.\n\n

Submitted - 1209.4837.pdf

", "abstract": "In this paper we discuss some questions about geometry over the field with one element, motivated by the properties of algebraic varieties that arise in perturbative quantum field theory. We follow the approach to F_1-geometry based on torified-schemes. We first discuss some simple necessary conditions in terms of the Euler characteristic and classes in the Grothendieck ring, then we give a blowup formula for torified varieties and we show that the wonderful compactifications of the graph configuration spaces, that arise in the computation of Feynman integrals in position space, admit an F_1-structure. By a similar argument we show that the moduli spaces of curves M_(0,n) admit an F_1-structure, thus answering a question of Manin. We also discuss conditions on hyperplane arrangements, a possible notion of embedded F_1-structure and its relation to Chern classes, and questions on Chern classes of varieties with regular torifications.", "date": "2013-07", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "69", "publisher": "Elsevier", "pagerange": "40-59", "id_number": "CaltechAUTHORS:20130611-084746994", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130611-084746994", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2013.03.002", "primary_object": { "basename": "1209.4837.pdf", "url": "https://authors.library.caltech.edu/records/cj1sj-bm485/files/1209.4837.pdf" }, "pub_year": "2013", "author_list": "Bejleri, Dori and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/ms0zy-2xs42", "eprint_id": 39526, "eprint_status": "archive", "datestamp": "2023-08-19 20:08:47", "lastmod": "2026-04-09 17:11:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" }, { "id": "Ruijsenaars-S", "name": { "family": "Ruijsenaars", "given": "Simon" } } ] }, "title": "Difference Operators of Sklyanin and van Diejen Type", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Springer-Verlag Berlin Heidelberg. \n\nReceived: 6 March 2012; Accepted: 6 October 2012; Published online: 5 March 2013. \n\nThis collaboration was begun while the authors were visiting the Liu Bie Ju Centre at City University of Hong Kong. We would like to thank the Centre and M. Ismail for the invitation, hospitality and financial support. The first author was supported in part by a grant (DMS-1001645) from the National Science Foundation. Finally, thanks are due to the referee for a careful report, which helped to improve the exposition.\n\n

Submitted - 1203.0042.pdf

", "abstract": "The Sklyanin algebra S\u03b7 has a well-known family of infinite-dimensional representations D(\u03bc),\u03bc\u2208C\u2217 , in terms of difference operators with shift \u03b7 acting on even meromorphic functions. We show that for generic \u03b7 the coefficients of these operators have solely simple poles, with linear residue relations depending on their locations. More generally, we obtain explicit necessary and sufficient conditions on a difference operator for it to belong to D(\u03bc) . By definition, the even part of D(\u03bc) is generated by twofold products of the Sklyanin generators. We prove that any sum of the latter products yields a difference operator of van Diejen type. We also obtain kernel identities for the Sklyanin generators. They give rise to order-reversing involutive automorphisms of D(\u03bc) , and are shown to entail previously known kernel identities for the van Diejen operators. Moreover, for special \u03bc they yield novel finite-dimensional representations of S\u03b7 .", "date": "2013-06", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "320", "number": "3", "publisher": "Springer", "pagerange": "851-889", "id_number": "CaltechAUTHORS:20130723-114503880", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130723-114503880", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1001645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-013-1692-3", "primary_object": { "basename": "1203.0042.pdf", "url": "https://authors.library.caltech.edu/records/ms0zy-2xs42/files/1203.0042.pdf" }, "pub_year": "2013", "author_list": "Rains, Eric and Ruijsenaars, Simon" }, { "id": "https://authors.library.caltech.edu/records/ckvbq-w1z41", "eprint_id": 40930, "eprint_status": "archive", "datestamp": "2023-08-19 20:10:41", "lastmod": "2026-04-09 20:01:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Is quantum mechanics exact?", "ispublished": "pub", "full_text_status": "public", "keywords": "group theory, quantum theory", "note": "\u00a9 2013 AIP Publishing LLC.\nReceived 17 April 2013; accepted 31 May 2013; published online 27 June 2013.\n\nThis work was supported in part by the Department of Energy grant DE-FG02-92ER40701.\n\n

Published - JMathPhys_54_062107.pdf

", "abstract": "We formulate physically motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to quantum mechanics as the only nontrivial consistent theory. Complex numbers and the existence of the Planck constant common to all systems arise naturally in this approach. The axioms are divided into two groups covering kinematics and basic measurement theory, respectively. We show that even if the second group of axioms is dropped, there are no deformations of quantum mechanics which preserve the kinematic axioms. Thus, any theory going beyond quantum mechanics must represent a radical departure from the usual a priori assumptions about the laws of nature.", "date": "2013-06", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "54", "number": "6", "publisher": "American Institute of Physics", "pagerange": "Art. No. 062107", "id_number": "CaltechAUTHORS:20130826-131734670", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130826-131734670", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.4811217", "primary_object": { "basename": "JMathPhys_54_062107.pdf", "url": "https://authors.library.caltech.edu/records/ckvbq-w1z41/files/JMathPhys_54_062107.pdf" }, "pub_year": "2013", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/ns44h-fp852", "eprint_id": 39812, "eprint_status": "archive", "datestamp": "2023-08-19 20:09:32", "lastmod": "2026-04-09 20:48:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lenzmann-E", "name": { "family": "Lenzmann", "given": "Enno" } } ] }, "title": "Uniqueness of non-linear ground states for fractional Laplacians in R", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2013 Institut Mittag-Leffler. Received May 24, 2011. R. F. acknowledges support from NSF grant PHY-0652854. E. L. was supported by a\nSteno fellowship from the Danish science research council, and he also gratefully acknowledges partial support from NSF grant DMS-0702492.", "abstract": "We prove uniqueness of ground state solutions Q = Q(|x|) \u2265 0 of the non-linear equation (\u2212\u0394)^sQ+Q\u2212Q^(\u03b1+1)=0inR,\n( \u2212 \u0394 ) s Q + Q \u2212 Q \u03b1 + 1 = 0 i n R , where 0 < s < 1 and 0 < \u03b1 < 4s/(1\u22122s) for s<12 s < 1 2 and 0 < \u03b1 < \u221e for s\u226512 s \u2265 1 2 . Here (\u2212\u0394)^s denotes the fractional Laplacian in one dimension. In particular, we answer affirmatively an open question recently raised by Kenig\u2013Martel\u2013Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 s = 1 2 and \u03b1 = 1 in [5] for the Benjamin\u2013Ono equation.\nAs a technical key result in this paper, we show that the associated linearized operator L_+ = (\u2212\u0394)^s +1\u2212(\u03b1+1)Q^\u03b1 is non-degenerate; i.e., its kernel satisfies ker L_+ = span{Q\u2032}. This result about L_+ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for non-linear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin\u2013Ono (BO) and Benjamin\u2013Bona\u2013Mahony (BBM) water wave equations.", "date": "2013-06", "date_type": "published", "publication": "Acta Mathematica", "volume": "210", "number": "2", "publisher": "Springer", "pagerange": "261-318", "id_number": "CaltechAUTHORS:20130807-152723442", "issn": "0001-5962", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130807-152723442", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0652854" }, { "agency": "Danish science research council Steno fellowship" }, { "agency": "NSF", "grant_number": "DMS-0702492" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11511-013-0095-9", "pub_year": "2013", "author_list": "Frank, Rupert L. and Lenzmann, Enno" }, { "id": "https://authors.library.caltech.edu/records/5hz8p-e8k15", "eprint_id": 97807, "eprint_status": "archive", "datestamp": "2023-08-22 09:34:57", "lastmod": "2026-04-09 21:10:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "An improved bound for the stepping-up lemma", "ispublished": "pub", "full_text_status": "public", "keywords": "Hypergraph Ramsey numbers; Stepping-up lemma", "note": "\u00a9 2010 Elsevier B.V. Under an Elsevier user license. \n\nReceived 1 July 2009; received in revised form 18 October 2010; accepted 24 October 2010; available online 27 November 2010. \n\nThe first author's research was supported by a research fellowship from St John's College. The second author's research was supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. The third author's research was supported by NSF CAREER award DMS-0812005 and by a USA-Israeli BSF grant.\n\n

Submitted - 0711.5004.pdf

", "abstract": "The partition relation N \u2192 (n)^(k)_(\u2113) means that whenever the k-tuples of an N-element set are \u2113-colored, there is a monochromatic set of size n, where a set is called monochromatic if all its k-tuples have the same color. The logical negation of N \u2192 (n)^(k)_(\u2113) is written as N / \u2192 (n)^(k)_(\u2113). An ingenious construction of Erd\u0151s and Hajnal known as the stepping-up lemma gives a negative partition relation for higher uniformity from one of lower uniformity, effectively gaining an exponential in each application. Namely, if \u2113 \u2265 2, k \u2265 3, and N / \u2192 (n)^(k)_(\u2113), then 2^N / \u2192 (2n + k - 4)^(k+1)_(\u2113). In this paper we give an improved construction for k \u2265 4. We introduce a general class of colorings which extends the framework of Erd\u0151s and Hajnal and can be used to establish negative partition relations. We show that if \u2113 \u2265 2, k \u2265 4 and N / \u2192 (n)^(k)_(\u2113), then 2^N / \u2192 (n + 3)^(k+1)_(\u2113). If also k is odd or \u2113 \u2265 3, then we get the better bound 2^N / \u2192 (n + 2)^(k+1)_(\u2113). This improved bound gives a coloring of the k-tuples whose largest monochromatic set is a factor \u03a9(2^k) smaller than that given by the original version of the stepping-up lemma. We give several applications of our result to lower bounds on hypergraph Ramsey numbers. In particular, for fixed \u2113 \u2265 4 we determine up to an absolute constant factor (which is independent of k) the size of the largest guaranteed monochromatic set in an \u2113-coloring of the k-tuples of an N-set.", "date": "2013-06", "date_type": "published", "publication": "Discrete Applied Mathematics", "volume": "161", "number": "9", "publisher": "Elsevier", "pagerange": "1191-1196", "id_number": "CaltechAUTHORS:20190812-162957165", "issn": "0166-218X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957165", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" }, { "agency": "NSF" }, { "agency": "Princeton University" }, { "agency": "NSF", "grant_number": "DMS-0812005" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.dam.2010.10.013", "primary_object": { "basename": "0711.5004.pdf", "url": "https://authors.library.caltech.edu/records/5hz8p-e8k15/files/0711.5004.pdf" }, "pub_year": "2013", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/sp7g8-vxr43", "eprint_id": 98016, "eprint_status": "archive", "datestamp": "2023-08-19 20:20:09", "lastmod": "2026-04-09 15:22:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "The Ramsey number of dense graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 London Mathematical Society. \n\nReceived 15 July 2009; revised 16 August 2012; published online 20 December 2012. \n\nThis research was supported by a research fellowship at St John's College, Cambridge.\n\n

Submitted - 0907.2657.pdf

", "abstract": "The Ramsey number r(H) of a graph H is the smallest number n such that, in any two-colouring of the edges of K_n, there is a monochromatic copy of H. We study the Ramsey number of graphs H with t vertices and density \u03c1, proving that r(H) \u2264 2^(c\u221a(\u03c1)log(2/\u03c1)t). We also investigate some related problems, such as the Ramsey number of graphs with t vertices and maximum degree \u03c1t and the Ramsey number of random graphs in G(t, \u03c1), that is, graphs on t vertices where each edge has been chosen independently with probability \u03c1.", "date": "2013-06", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "volume": "45", "number": "3", "publisher": "London Mathematical Society", "pagerange": "483-496", "id_number": "CaltechAUTHORS:20190819-170836067", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-170836067", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/blms/bds097", "primary_object": { "basename": "0907.2657.pdf", "url": "https://authors.library.caltech.edu/records/sp7g8-vxr43/files/0907.2657.pdf" }, "pub_year": "2013", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/2vptm-r0943", "eprint_id": 41043, "eprint_status": "archive", "datestamp": "2023-08-22 09:32:28", "lastmod": "2026-04-09 22:52:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Willett-B", "name": { "family": "Willett", "given": "Brian" } }, { "id": "Yaakov-I", "name": { "family": "Yaakov", "given": "Itamar" } } ] }, "title": "Exact results for supersymmetric abelian vortex loops in 2+1 dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory; Duality in Gauge Field Theories; Solitons Monopoles and Instantons", "note": "\u00a9 2013 SISSA.\n\nPublished for SISSA by Springer.\n\nReceived: April 30, 2013;\nAccepted: May 30, 2013;\nPublished: June 26, 2013.\n\n

Submitted - 1211.2861v2.pdf

", "abstract": "We define a class of supersymmetric defect loop operators in N = 2 gauge theories in 2 + 1 dimensions. We give a prescription for computing the expectation value of such operators in a generic N = 2 theory on the three-sphere using localization. We elucidate the role of defect loop operators in IR dualities of supersymmetric gauge theories, and write down their transformation properties under the SL(2, Z ) action on conformal theories with abelian global symmetries.", "date": "2013-06", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "6", "publisher": "Springer", "pagerange": "Art. No. 099", "id_number": "CaltechAUTHORS:20130903-090622964", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130903-090622964", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP06(2013)099", "primary_object": { "basename": "1211.2861v2.pdf", "url": "https://authors.library.caltech.edu/records/2vptm-r0943/files/1211.2861v2.pdf" }, "pub_year": "2013", "author_list": "Kapustin, Anton; Willett, Brian; et al." }, { "id": "https://authors.library.caltech.edu/records/r815a-caj21", "eprint_id": 39245, "eprint_status": "archive", "datestamp": "2023-08-19 19:58:38", "lastmod": "2026-04-09 22:13:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Liu-Hong", "name": { "family": "Liu", "given": "Hong" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Stoica-B", "name": { "family": "Stoica", "given": "Bogdan" } }, { "id": "Yunes-N", "name": { "family": "Yunes", "given": "Nicol\u00e1s" }, "orcid": "0000-0001-6147-1736" } ] }, "title": "Spontaneous Generation of Angular Momentum in Holographic Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 American Physical Society. \n\nReceived 11 January 2013; published 21 May 2013. \n\nWe thank J. Alicea, R. Loganayagam, L. Motrunich, M. Oshikawa, N. Read, D. T. Son, and G. Volovik for discussion and, in particular, O. Saremi for sharing with us his previous unpublished work. H. O. is thankful for the hospitality of the Aspen Center for Physics (NSF Grant No. 1066293). The work of H. O. and B. S. is supported in part by U.S. DOE Grant No. DE-FG03-92-ER40701. The work of H. O. is also supported in part by a Simons Investigator grant from the Simons Foundation, JSPS Grant-in-Aid for Scientific Research C-23540285, and the WPI Initiative of MEXT of Japan. H. L. is thankful\nfor the hospitality of Caltech. The work of H. L. is partially supported by a Simons Fellowship and by the U.S. Department of Energy (DOE) under cooperative research agreement DE-FG0205ER41360. The work of N.Y. is partially supported by NSF Grant No. PHY-1114374 and NASA Grant No. NNX11AI49G, under 00001944.\n\n

Published - PhysRevLett.110.211601.pdf

Submitted - 1212.3666v2.pdf

", "abstract": "The Schwarzschild black two-brane in four-dimensional anti\u2013de Sitter space is dual to a finite temperature state in three-dimensional conformal field theory. We show that the solution acquires a nonzero angular momentum density when a gravitational Chern-Simons coupling is turned on in the bulk, even though the solution is not modified. A similar phenomenon is found for the Reissner-Nordstr\u00f6m black two-brane with axionic coupling to the gauge field. We discuss interpretation of this phenomenon from the point of view of the boundary three-dimensional conformal field theory.", "date": "2013-05-21", "date_type": "published", "publication": "Physical Review Letters", "volume": "110", "number": "21", "publisher": "American Physical Society", "pagerange": "Art. No. 211601", "id_number": "CaltechAUTHORS:20130708-104924811", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130708-104924811", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Simons Foundation" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" }, { "agency": "Ministry of Education and Science of the Russian Federation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-05ER41360" }, { "agency": "NSF", "grant_number": "PHY-1114374" }, { "agency": "NASA", "grant_number": "NNX11AI49G" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.110.211601", "primary_object": { "basename": "1212.3666v2.pdf", "url": "https://authors.library.caltech.edu/records/r815a-caj21/files/1212.3666v2.pdf" }, "related_objects": [ { "basename": "PhysRevLett.110.211601.pdf", "url": "https://authors.library.caltech.edu/records/r815a-caj21/files/PhysRevLett.110.211601.pdf" } ], "pub_year": "2013", "author_list": "Liu, Hong; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/1f057-24g21", "eprint_id": 38378, "eprint_status": "archive", "datestamp": "2023-08-22 09:22:22", "lastmod": "2026-04-09 15:26:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Overgroup lattices in finite groups of Lie type containing a parabolic", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Finite groups; Groups of Lie type; Subgroup lattices", "note": "\u00a9 2013 Elsevier Inc. \nReceived 26 June 2012;\nAvailable online 6 March 2013.\nCommunicated by Leonard L. Scott, Jr.\n\nThis work was partially supported by NSF grants DMS-0504852 and DMS-0969009.", "abstract": "The main theorem is a step in a program to show there exist finite lattices that are not an interval in the lattice of subgroups of any finite group. As part of the proof of the main theorem, we prove a theorem on the structure of maximal parabolics in finite groups of Lie type, which is of independent interest.", "date": "2013-05-15", "date_type": "published", "publication": "Journal of Algebra", "volume": "382", "publisher": "Elsevier", "pagerange": "71-99", "id_number": "CaltechAUTHORS:20130509-100832818", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130509-100832818", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" }, { "agency": "NSF", "grant_number": "DMS-0969009" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2013.01.034", "pub_year": "2013", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/5rgr0-v8w85", "eprint_id": 39949, "eprint_status": "archive", "datestamp": "2023-08-19 19:54:32", "lastmod": "2026-04-09 22:20:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Kova\u0159\u00edk-H", "name": { "family": "Kova\u0159\u00edk", "given": "Hynek" } } ] }, "title": "Heat kernels of metric trees and applications", "ispublished": "pub", "full_text_status": "public", "keywords": "heat kernel, metric tree, eigenvalue estimate, Sobolev inequality", "note": "\u00a9 2013 SIAM.\n\nReceived by the editors July 27, 2012; accepted for publication December 14, 2012; published\nelectronically May 7, 2013.\n\nThis author's work was supported through DFG grant FR 2664/1-1 and U.S. NSF grant PHY-0652854.\n\nThis author was partially supported by the MIUR-PRIN08 grant\nfor the project \"Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni.\"\n\n

Published - 120886297.pdf

Submitted - 1108.6145v1.pdf

", "abstract": "We consider the heat semigroup generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schr\u00f6dinger operators on metric trees.", "date": "2013-05-07", "date_type": "published", "publication": "SIAM Journal on Mathematical Analysis", "volume": "45", "number": "3", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "1027-1046", "id_number": "CaltechAUTHORS:20130815-102433930", "issn": "0036-1410", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130815-102433930", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "FR 2664/1-1" }, { "agency": "NSF", "grant_number": "PHY-0652854" }, { "agency": "MIUR-PRIN08 Grant" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/120886297", "primary_object": { "basename": "1108.6145v1.pdf", "url": "https://authors.library.caltech.edu/records/5rgr0-v8w85/files/1108.6145v1.pdf" }, "related_objects": [ { "basename": "120886297.pdf", "url": "https://authors.library.caltech.edu/records/5rgr0-v8w85/files/120886297.pdf" } ], "pub_year": "2013", "author_list": "Frank, Rupert L. and Kova\u0159\u00edk, Hynek" }, { "id": "https://authors.library.caltech.edu/records/v84kc-nd242", "eprint_id": 38982, "eprint_status": "archive", "datestamp": "2023-08-19 19:53:19", "lastmod": "2026-04-16 01:39:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Brooks-P", "name": { "family": "Brooks", "given": "Peter" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Protected gates for superconducting qubits", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 American Physical Society\nReceived 21 February 2013; published 6 May 2013.\nWe thank David DiVincenzo for helpful discussions. This\nwork was supported in part by the Intelligence Advanced\nResearch Projects Activity (IARPA) via Department of Interior\nNational Business Center Contract No. D11PC20165. The US\ngovernment is authorized to reproduce and distribute reprints\nfor governmental purposes notwithstanding any copyright\nannotation thereon. The views and conclusions contained\nherein are those of the author and should not be interpreted\nas necessarily representing the official policies or\nendorsements, either expressed or implied, of Intelligence\nAdvanced Research Projects Activity, DoINBC, or the US\ngovernment. We also acknowledge support from National\nScience Foundation (NSF) Grant No. PHY-0803371, Department\nof Energy Grant No. DE-FG03-92-ER40701, and\nNational Security Agency/Army Research Office Grant No.\nW911NF-09-1-0442. The Institute for Quantum Information\nand Matter (IQIM) is an NSF Physics Frontiers Center with\nsupport from the Gordon and Betty Moore Foundation.\n\n

Published - PhysRevA.87.052306.pdf

Submitted - 1302.4122v1.pdf

", "abstract": "We analyze the accuracy of quantum phase gates acting on \"0-\u03c0 qubits\" in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an LC oscillator and a qubit or pair of qubits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance \u221aL/C is large compared to \u210f/4e^2\u22481 k\u03a9. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.", "date": "2013-05-06", "date_type": "published", "publication": "Physical Review A", "volume": "87", "number": "5", "publisher": "American Physical Society", "pagerange": "Art. No. 052306", "id_number": "CaltechAUTHORS:20130619-094717394", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130619-094717394", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Intelligence Advanced Research Projects Activity (IARPA)" }, { "agency": "Department of Interior National Business Center", "grant_number": "D11PC20165" }, { "agency": "NSF", "grant_number": "PHY-0803371" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "National Security Agency (NSA)/Army Research Office (ARO)", "grant_number": "W911NF-09-1-0442" }, { "agency": "Institute for Quantum Information and Matter (IQIM)" }, { "agency": "NSF Physics Frontiers Center" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevA.87.052306", "primary_object": { "basename": "PhysRevA.87.052306.pdf", "url": "https://authors.library.caltech.edu/records/v84kc-nd242/files/PhysRevA.87.052306.pdf" }, "related_objects": [ { "basename": "1302.4122v1.pdf", "url": "https://authors.library.caltech.edu/records/v84kc-nd242/files/1302.4122v1.pdf" } ], "pub_year": "2013", "author_list": "Brooks, Peter; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/g3624-qce87", "eprint_id": 41323, "eprint_status": "archive", "datestamp": "2023-08-19 19:45:35", "lastmod": "2026-04-09 17:41:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Chern-Simons theory and S-duality", "ispublished": "pub", "full_text_status": "public", "keywords": "Duality in Gauge Field Theories, Chern-Simons Theories, Topological Field\nTheories, Supersymmetric gauge theory", "note": "\u00a9 2013 SISSA. Published for SISSA by Springer.\n\nReceived: March 16, 2013. Accepted: April 20, 2013. Published: May 21, 2013. \n\nWe wish thank G. Mikhalkin, G. Moore, A. Neitzke, R. van der Veen, D. Zagier, and especially D. Gaiotto and J. Teschner for many enlightening and helpful discussions. We would also like to thank the Aspen Center for Physics for their hospitality during the 2010 Summer Program, where some of the ideas presented here originated. The work of TD is supported in part by NSF Grant PHY-0969448. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the\nviews of funding agencies.\n\n

Submitted - 1106.4550v1.pdf

", "abstract": "We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example, the space of flat SL(2, C ) connections on M is identified with the space of supersymmetric vacua in a dual 3d gauge theory. The hidden symmetry h \u2192 -4\u03c0^2/h of SL(2) Chern-Simons theory can be identified as the S-duality transformation of N=4 super-Yang-Mills theory (obtained by compactifying the five-brane theory on a torus); whereas the mapping class group action in Chern-Simons theory on a three-manifold M with boundary C is realized as S-duality in 4d N=2 super-Yang-Mills theory associated with the Riemann surface C. We illustrate these symmetries by considering simple examples of 3-manifolds that include knot complements and punctured torus bundles, on the one hand, and mapping cylinders associated with mapping class group transformations, on the other. A generalization of mapping class group actions further allows us to study the transformations between several distinguished coordinate systems on the phase space of Chern-Simons theory, the SL(2) Hitchin moduli space.", "date": "2013-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 109", "id_number": "CaltechAUTHORS:20130913-112827417", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130913-112827417", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0969448" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP05(2013)109", "primary_object": { "basename": "1106.4550v1.pdf", "url": "https://authors.library.caltech.edu/records/g3624-qce87/files/1106.4550v1.pdf" }, "pub_year": "2013", "author_list": "Dimofte, Tudor and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/tb04d-par72", "eprint_id": 38136, "eprint_status": "archive", "datestamp": "2023-08-22 09:11:11", "lastmod": "2026-04-09 17:52:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Vazirani-Monica-J", "name": { "family": "Vazirani", "given": "Monica J." } } ] }, "title": "Deformations of permutation representations of Coxeter groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Coxeter group; Permutation representation; Hecke algebra; Bruhat order", "note": "\u00a9 2012 Springer Science+Business Media, LLC. \n\nReceived: 26 January 2011. Accepted: 6 April 2012. Published online: 28 April 2012. \n\nFirst author partially supported by NSF grant DMS-0833464. Second author partially supported by NSA grant H982300910076, and by Caltech and DMS-0833464 during her visits.\n\n

Submitted - 1008.1037.pdf

", "abstract": "The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat order and a flat deformation over \u2124[q] to a representation of the corresponding Hecke algebra. In this paper we define a larger class of \"quasiparabolic\" subgroups (more generally, quasiparabolic W-sets), and show that they also inherit these properties. Our motivating example is the action of the symmetric group on fixed-point-free involutions by conjugation.", "date": "2013-05", "date_type": "published", "publication": "Journal of Algebraic Combinatorics", "volume": "37", "number": "3", "publisher": "Springer Verlag", "pagerange": "455-502", "id_number": "CaltechAUTHORS:20130426-134058196", "issn": "0925-9899", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130426-134058196", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0833464" }, { "agency": "National Security Agency", "grant_number": "H982300910076" }, { "agency": "Caltech" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10801-012-0371-3", "primary_object": { "basename": "1008.1037.pdf", "url": "https://authors.library.caltech.edu/records/tb04d-par72/files/1008.1037.pdf" }, "pub_year": "2013", "author_list": "Rains, Eric M. and Vazirani, Monica J." }, { "id": "https://authors.library.caltech.edu/records/70skd-czv09", "eprint_id": 39434, "eprint_status": "archive", "datestamp": "2023-08-19 19:35:43", "lastmod": "2026-03-09 21:52:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Nonseparating spheres and twisted Heegaard Floer homology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Mathematical Sciences Publishers.\nReceived: 1 September 2010.\nAccepted: 10 December 2012.\nPublished: 17 April 2013.\n\nWe are very grateful to David Gabai, Cameron Gordon and\nMatthew Hedden for helpful communications. This work was carried out when the\nauthor was at MIT. The author was partially supported by an AIM Five-Year Fellowship\nand NSF grant number DMS-0805807.\n\n

Published - agt-2013-13-037p.pdf

", "abstract": "If a 3\u2013manifold Y contains a nonseparating sphere, then some twisted Heegaard\nFloer homology of Y is zero. This simple fact allows us to prove several results\nabout Dehn surgery on knots in such manifolds. Similar results have been proved for\nknots in L\u2013spaces.", "date": "2013-04-17", "date_type": "published", "publication": "Algebraic and Geometric Topology", "volume": "13", "number": "2", "publisher": "Geometry & Topology Publications", "pagerange": "1143-1159", "id_number": "CaltechAUTHORS:20130718-082647773", "issn": "1472-2747", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130718-082647773", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-0805807" } ] }, "other_numbering_system": { "items": [ { "id": "MR3044606", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/agt.2013.13.1143", "primary_object": { "basename": "agt-2013-13-037p.pdf", "url": "https://authors.library.caltech.edu/records/70skd-czv09/files/agt-2013-13-037p.pdf" }, "pub_year": "2013", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/22xvc-qcf35", "eprint_id": 37774, "eprint_status": "archive", "datestamp": "2023-08-19 19:09:40", "lastmod": "2026-04-09 17:08:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conley-C-T", "name": { "family": "Conley", "given": "Clinton T." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Tucker-Drob-R-D", "name": { "family": "Tucker-Drob", "given": "Robin D." } } ] }, "title": "Ultraproducts of measure preserving actions and graph combinatorics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Cambridge University Press.\nReceived 14 May 2011 and accepted in revised form 1 December 2011.\nPublished online: 16 February 2012.\nThe research of ASK and RDT-D was partially supported by NSF\ngrant DMS-0968710 and of CTC by Marie Curie grant no. 249167 from the European\nUnion. We would like to thank Russell Lyons for many useful conversations.\n\n

Published - S0143385711001143a.pdf

", "abstract": "Ultraproducts of measure preserving actions of countable groups are used to study the graph combinatorics associated with such actions, including chromatic, independence and matching numbers. Applications are also given to the theory of random colorings of Cayley graphs and sofic actions and equivalence relations.", "date": "2013-04", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "33", "publisher": "Cambridge University Press", "pagerange": "334-374", "id_number": "CaltechAUTHORS:20130405-083026269", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130405-083026269", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968710" }, { "agency": "European Union Marie Curie Grant", "grant_number": "249167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/S0143385711001143", "primary_object": { "basename": "S0143385711001143a.pdf", "url": "https://authors.library.caltech.edu/records/22xvc-qcf35/files/S0143385711001143a.pdf" }, "pub_year": "2013", "author_list": "Conley, Clinton T.; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/n7rfs-gs792", "eprint_id": 77131, "eprint_status": "archive", "datestamp": "2023-08-19 19:27:43", "lastmod": "2026-04-09 22:38:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Symmetry of Bipolaron Bound States for Small Coulomb Repulsion", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nWe are grateful to Herbert Spohn for making us aware of this problem. We also thank the referees for important suggestions. Partial financial support from the U.S. National Science Foundation through grants PHY-1068285 (R.F.), PHY-0965859 (E.L.) and the NSERC (R.S.) is acknowledged.\n\n

Published - art_3A10.1007_2Fs00220-012-1604-y.pdf

Submitted - 1201.3954.pdf

", "abstract": "We consider the bipolaron in the Pekar\u2013Tomasevich approximation and address the question whether the ground state is spherically symmetric or not. Numerical analysis has, so far, not completely settled the question. Our contribution is to prove rigorously that the ground state remains spherical for small values of the electron-electron Coulomb repulsion.", "date": "2013-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "319", "number": "2", "publisher": "Springer", "pagerange": "557-573", "id_number": "CaltechAUTHORS:20170502-144700862", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170502-144700862", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-012-1604-y", "primary_object": { "basename": "1201.3954.pdf", "url": "https://authors.library.caltech.edu/records/n7rfs-gs792/files/1201.3954.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs00220-012-1604-y.pdf", "url": "https://authors.library.caltech.edu/records/n7rfs-gs792/files/art_3A10.1007_2Fs00220-012-1604-y.pdf" } ], "pub_year": "2013", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/bqndt-z3281", "eprint_id": 38324, "eprint_status": "archive", "datestamp": "2023-08-22 09:00:21", "lastmod": "2026-04-09 22:07:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Su-Jessica", "name": { "family": "Su", "given": "Jessica" } } ] }, "title": "Arithmetic of Potts Model Hypersurfaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Potts models; points over finite fields; zeta function; mixed Tate motives", "note": "\u00a9 2013 World Scientific Publishing Company. \n\nReceived 4 April 2012. Accepted 25 July 2012. Published 14 December 2012. \n\nThis paper is based on the results of the second author's summer research project, supported by the Summer Undergraduate Research Fellowship program at Caltech. The first author was partly supported by NSF Grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The authors thank Paolo Aluffi and Bill Dubuque for useful conversations.\n\n

Submitted - 1112.5667v1.pdf

", "abstract": "We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the \"fibration condition\" in the dependence of the Grothendieck class on the number of spin states and of the polynomial countability condition for these Potts model hypersurfaces. We then show that a period computation, formally similar to the parametric Feynman integrals of quantum field theory, arises by considering certain thermodynamic averages. One can show that these evaluate to combinations of multiple zeta values for Potts models on polygon polymer chains, while silicate tetrahedral chains provide a candidate for a possible occurrence of non-mixed Tate periods.", "date": "2013-04", "date_type": "published", "publication": "International Journal of Geometric Methods in Modern Physics", "volume": "10", "number": "4", "publisher": "World Scientific Publishing", "pagerange": "Art. No. 1350005", "id_number": "CaltechAUTHORS:20130507-112308486", "issn": "0219-8878", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130507-112308486", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219887813500059", "primary_object": { "basename": "1112.5667v1.pdf", "url": "https://authors.library.caltech.edu/records/bqndt-z3281/files/1112.5667v1.pdf" }, "pub_year": "2013", "author_list": "Marcolli, Matilde and Su, Jessica" }, { "id": "https://authors.library.caltech.edu/records/npe69-kz005", "eprint_id": 37651, "eprint_status": "archive", "datestamp": "2023-08-22 08:55:31", "lastmod": "2026-04-09 15:27:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Fusion systems of F_2-type", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Fusion systems; Finite groups", "note": "\u00a9 2013 Elsevier Inc. Received 19 January 2012. Available online 24 January 2013. Communicated by Ronald Solomon. This work was partially supported by NSF grants DMS-0504852 and DMS-0969009.", "abstract": "We prove results on 2-fusion systems related to the 2-fusion systems of groups of Lie type over the field of order 2 and certain sporadic groups. The results are used in a later paper to determine the N-systems: the 2-fusion systems of N-groups.", "date": "2013-03-15", "date_type": "published", "publication": "Journal of Algebra", "volume": "378", "publisher": "Elsevier", "pagerange": "217-262", "id_number": "CaltechAUTHORS:20130327-114824399", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130327-114824399", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" }, { "agency": "NSF", "grant_number": "DMS-0969009" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2012.12.018", "pub_year": "2013", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/5ghck-hnt78", "eprint_id": 37558, "eprint_status": "archive", "datestamp": "2023-08-19 14:42:27", "lastmod": "2026-04-09 15:01:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lewin-M", "name": { "family": "Lewin", "given": "Mathieu" } }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "A positive density analogue of the Lieb\u2013Thirring inequality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 Duke University Press. \n\nReceived 4 September 2011. Revision received 1 March 2012. \n\nFrank's work partially supported by National Science Foundation grant PHY-1068285. \n\nLewin's work partially supported by European Research Council grant MNIQS-258023. \n\nLieb's work partially supported by National Science Foundation grant PHY-0965859. \n\nSeiringer's work partially supported by the Natural Sciences and Engineering Research Council. \n\nThe first author would like to thank Ari Laptev for stimulating discussions.\n\n

Submitted - 1108.4246.pdf

", "abstract": "The Lieb\u2013Thirring inequalities give a bound on the negative eigenvalues of a Schr\u00f6dinger operator in terms of an L^p-norm of the potential. These are dual to bounds on the H^1-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of the Fermi sea of noninteracting particles (i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials).", "date": "2013-02-15", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "162", "number": "3", "publisher": "Duke University Press", "pagerange": "435-495", "id_number": "CaltechAUTHORS:20130319-101032718", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130319-101032718", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "European Research Council (ERC)", "grant_number": "MNIQS-258023" }, { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/00127094-2019477", "primary_object": { "basename": "1108.4246.pdf", "url": "https://authors.library.caltech.edu/records/5ghck-hnt78/files/1108.4246.pdf" }, "pub_year": "2013", "author_list": "Frank, Rupert L.; Lewin, Mathieu; et al." }, { "id": "https://authors.library.caltech.edu/records/70w97-98w52", "eprint_id": 36133, "eprint_status": "archive", "datestamp": "2023-08-19 14:39:28", "lastmod": "2026-04-09 15:33:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fuji-Hiroyuki", "name": { "family": "Fuji", "given": "Hiroyuki" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "Super-A-polynomial for knots and BPS states", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Elsevier B.V. \n\nReceived 6 June 2012; accepted 9 October 2012. Available online 13 October 2012. \n\nWe thank M. Aganagic, R. Dijkgraaf, E. Gorsky, A. Mironov, A. Morozov, L. Ng, M. Sto\u0161i\u0107, and C. Vafa for useful discussions on related topics. The work of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [# 21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, \"Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos\". The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The research of P.S. is supported by the DOE grant DE-FG03-92-ER40701FG-02, the European Commission under the Marie-Curie International Outgoing Fellowship Programme, and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Submitted - 1205.1515.pdf

", "abstract": "We introduce and compute a 2-parameter family deformation of the A-polynomial that encodes the color dependence of the superpolynomial and that, in suitable limits, reduces to various deformations of the A-polynomial studied in the literature. These special limits include the t-deformation which leads to the \"refined A-polynomial\" introduced in the previous work of the authors and the Q-deformation which leads, by the conjecture of Aganagic and Vafa, to the augmentation polynomial of knot contact homology. We also introduce and compute the quantum version of the super-A-polynomial, an operator that encodes recursion relations for S^r-colored HOMFLY homology. Much like its predecessor, the super-A-polynomial admits a simple physical interpretation as the defining equation for the space of SUSY vacua (= critical points of the twisted superpotential) in a circle compactification of the effective 3d N = 2 theory associated to a knot or, more generally, to a 3-manifold M. Equivalently, the algebraic curve defined by the zero locus of the super-A-polynomial can be thought of as the space of open string moduli in a brane system associated with M. As an inherent outcome of this work, we provide new interesting formulas for colored superpolynomials for the trefoil and the figure-eight knot.", "date": "2013-02-11", "date_type": "published", "publication": "Nuclear Physics B", "volume": "867", "number": "2", "publisher": "Elsevier", "pagerange": "506-546", "id_number": "CaltechAUTHORS:20130103-082610853", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130103-082610853", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "21740179" }, { "agency": "Nagoya University" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Foundation for Polish Science" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2012.10.005", "primary_object": { "basename": "1205.1515.pdf", "url": "https://authors.library.caltech.edu/records/70w97-98w52/files/1205.1515.pdf" }, "pub_year": "2013", "author_list": "Fuji, Hiroyuki; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/tecsz-6kh56", "eprint_id": 38848, "eprint_status": "archive", "datestamp": "2023-08-22 08:36:48", "lastmod": "2026-04-09 17:48:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "S_3-free 2-fusion systems", "ispublished": "pub", "full_text_status": "public", "keywords": "finite groups; fusion systems; Sylow subgroups", "note": "\u00a9 2012 Edinburgh Mathematical Society.\n\nPublished online: 05 December 2012.\n\nThis work was partly supported by NSF Grants DMS-0504852\nand DMS-0969009. The author thanks the referee for a number of suggestions leading to\nimprovements in the paper.\n\n

Published - Aschbacher_2013p27.pdf

", "abstract": "We develop a theory of 2-fusion systems of even characteristic, and use that theory to show that all S_3-free saturated 2-fusion systems are constrained. This supplies a new proof of Glauberman's Theorem on S_4-free groups and its various corollaries.", "date": "2013-02", "date_type": "published", "publication": "Proceedings of the Edinburgh Mathematical Society", "volume": "56", "number": "1", "publisher": "Edinburgh Mathematical Society", "pagerange": "27-48", "id_number": "CaltechAUTHORS:20130607-083326320", "issn": "0013-0915", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130607-083326320", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" }, { "agency": "NSF", "grant_number": "DMS-0969009" } ] }, "other_numbering_system": { "items": [ { "id": "MR3021403", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/S0013091512000235", "primary_object": { "basename": "Aschbacher_2013p27.pdf", "url": "https://authors.library.caltech.edu/records/tecsz-6kh56/files/Aschbacher_2013p27.pdf" }, "pub_year": "2013", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/3j4nr-btf78", "eprint_id": 37786, "eprint_status": "archive", "datestamp": "2023-08-22 08:06:54", "lastmod": "2026-03-09 02:16:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fuji-Hiroyuki", "name": { "family": "Fuji", "given": "Hiroyuki" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sto\u0161i\u0107-M", "name": { "family": "Sto\u0161i\u0107", "given": "Marko" } }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "3d analogs of Argyres-Douglas theories and knot homologies", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory; Duality in Gauge Field Theories; ChernSimons Theories; Differential and Algebraic Geometry", "note": "\u00a9 2013 Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: September 18, 2012; Accepted: December 23, 2012; Published: January 29, 2013. \n\nWe thank M. Aganagic, T. Dimofte, S. Nawata, L. Ng, V. Pestun, and C. Vafa for useful discussions. We also would like to thank the Institute for Theoretical Physics at University of Amsterdam (ITFA), Bethe Center for Theoretical Physics (BCTP) and Physikalisches Institut Universit\u00e4t in Bonn, the Simons Center for Geometry and Physics at Stony Brook, and Mathematical Sciences Center (MSC) of Tsinghua University for hospitality during\nvarious stages of this work. The work of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [# 21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, \"Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos.\" The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The work of M.S. is partially supported by Portuguese funds via the FCT - Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, through project number PTDC/MAT/101503/2008, New Geometry and Topology. M.S. is also\npartially supported by the Ministry of Science of Serbia, project no. 174012. The research of P.S. is supported by the European Commission under the Marie-Curie International\nOutgoing Fellowship Programme and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views\nof funding agencies.\n\n

Published - Fuji_2013p175.pdf

Submitted - 1209.1416v1.pdf

", "abstract": "We study singularities of algebraic curves associated with 3d N=2 theories that have at least one global flavor symmetry. Of particular interest is a class of theories T_K labeled by knots, whose partition functions package Poincar\u00e9 polynomials of the S^r -colored HOMFLY homologies. We derive the defining equation, called the super-A-polynomial, for algebraic curves associated with many new examples of 3d N=2 theories T K and study its singularity structure. In particular, we catalog general types of singularities that presumably exist for all knots and propose their physical interpretation. A computation of super-A-polynomials is based on a derivation of corresponding superpolynomials, which is interesting in its own right and relies solely on a structure of differentials in S^r -colored HOMFLY homologies.", "date": "2013-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2013", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 175", "id_number": "CaltechAUTHORS:20130405-104147281", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130405-104147281", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "21740179" }, { "agency": "Nagoya University Global COE Program" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PTDC/MAT/101503/2008" }, { "agency": "Ministry of Science of Serbia", "grant_number": "174012" }, { "agency": "Marie Curie International Outgoing Fellowship" }, { "agency": "Foundation for Polish Science" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP01(2013)175", "primary_object": { "basename": "1209.1416v1.pdf", "url": "https://authors.library.caltech.edu/records/3j4nr-btf78/files/1209.1416v1.pdf" }, "related_objects": [ { "basename": "Fuji_2013p175.pdf", "url": "https://authors.library.caltech.edu/records/3j4nr-btf78/files/Fuji_2013p175.pdf" } ], "pub_year": "2013", "author_list": "Fuji, Hiroyuki; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/hhdjh-a5t89", "eprint_id": 36450, "eprint_status": "archive", "datestamp": "2023-08-22 08:04:07", "lastmod": "2026-03-09 21:37:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aluffi-P", "name": { "family": "Aluffi", "given": "Paolo" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "A motivic approach to phase transitions in Potts models", "ispublished": "pub", "full_text_status": "public", "keywords": "Potts models; Feynman motives; Grothendieck group; Phase transitions", "note": "\u00a9 2012 Elsevier B.V. \n\nReceived 22 April 2012. Accepted 6 September 2012. Available online 17 September 2012.\n\n

Submitted - 1102.3462.pdf

", "abstract": "We describe an approach to the study of phase transitions in Potts models based on an estimate of the complexity of the locus of real zeros of the partition function, computed in terms of the classes in the Grothendieck ring of the affine algebraic varieties defined by the vanishing of the multivariate Tutte polynomial. We give completely explicit calculations for the examples of the chains of linked polygons and of the graphs obtained by replacing the polygons with their dual graphs. These are based on a deletion\u2013contraction formula for the Grothendieck classes and on generating functions for splitting and doubling edges.", "date": "2013-01", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "63", "publisher": "Elsevier", "pagerange": "6-31", "id_number": "CaltechAUTHORS:20130117-104305431", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130117-104305431", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2012.09.003", "primary_object": { "basename": "1102.3462.pdf", "url": "https://authors.library.caltech.edu/records/hhdjh-a5t89/files/1102.3462.pdf" }, "pub_year": "2013", "author_list": "Aluffi, Paolo and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/ph1ec-73643", "eprint_id": 38483, "eprint_status": "archive", "datestamp": "2023-08-22 08:07:36", "lastmod": "2026-03-09 21:42:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Estrada-C", "name": { "family": "Estrada", "given": "Christopher" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Noncommutative Mixmaster Cosmologies", "ispublished": "pub", "full_text_status": "public", "keywords": "Anisotropic cosmology; mixmaster universe; slow-roll inflation; noncommutative tori; spectral action", "note": "\u00a9 2013 World Scientific Publishing Company. R\n\neceived 3 May 2012. Accepted 4 July 2012. Published 26 October 2012. \n\nThe first author was supported for this project by a Caltech Summer Undergraduate Research Fellowship and by a Richter Scholarship, provided by the Richter Memorial Fund. The second author is supported by NSF Grants DMS-0901221,\nDMS-1007207, DMS-1201512, and PHY-1205440.\n\n

Submitted - 1203.2679v1.pdf

", "abstract": "In this paper we investigate a variant of the classical mixmaster universe model of anisotropic cosmology, where the spatial sections are noncommutative 3-tori. We consider ways in which the discrete dynamical system describing the mixmaster dynamics can be extended to act on the noncommutative torus moduli, and how the resulting dynamics differs from the classical one, for example, in the appearance of exotic smooth structures. We discuss properties of the spectral action, focussing on how the slow-roll inflation potential determined by the spectral action affects the mixmaster dynamics. We relate the model to other recent results on spectral action computation and we identify other physical contexts in which this model may be relevant.", "date": "2013-01", "date_type": "published", "publication": "International Journal of Geometric Methods in Modern Physics", "volume": "10", "number": "1", "publisher": "World Scientific Publishing", "pagerange": "Art. No. 1250086", "id_number": "CaltechAUTHORS:20130514-095557537", "issn": "0219-8878", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130514-095557537", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Richter Scholarship" }, { "agency": "Richter Memorial Funds" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219887812500867", "primary_object": { "basename": "1203.2679v1.pdf", "url": "https://authors.library.caltech.edu/records/ph1ec-73643/files/1203.2679v1.pdf" }, "pub_year": "2013", "author_list": "Estrada, Christopher and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/7hctb-0zp70", "eprint_id": 38418, "eprint_status": "archive", "datestamp": "2023-08-22 08:07:27", "lastmod": "2026-03-09 21:53:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Liu-Yi", "name": { "family": "Liu", "given": "Yi" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Sun-Hongbin", "name": { "family": "Sun", "given": "Hongbin" } }, { "id": "Wang-Shicheng", "name": { "family": "Wang", "given": "Shicheng" } } ] }, "title": "On slope genera of knotted tori in 4-space", "ispublished": "pub", "full_text_status": "public", "keywords": "knotted surface; genus; extendable subgroup", "note": "\u00a9 2013 Pacific Journal of Mathematics.\nReceived: 7 December 2011; Revised: 9 September 2012; Accepted: 17 September 2012; Published: 28 February 2013.\n\nThe second author was partially supported by an AIM Five-Year Fellowship and NSF grant numbers\nDMS-1021956 and DMS-1103976. The fourth author was partially supported by grant No.10631060\nof the National Natural Science Foundation of China.\nThe authors are grateful to Seiichi Kamada for clarifying some points during the\ndevelopment of the paper and for very helpful guidance to the literature. The authors\nalso thank David Gabai, Cameron Gordon, and Charles Livingston for suggestions\nand comments, and thank the referee for encouraging us to improve the structure of\nthis paper.\n\n

Published - pjm-v261-n1-p07-s.pdf

", "abstract": "We investigate genera of slopes of a knotted torus in the 4-sphere analogous to the genus of a classical knot. We compare various formulations of this notion, and use this notion to study the extendable subgroup of the mapping class group of a knotted torus.", "date": "2013-01", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "261", "number": "1", "publisher": "Pacific Journal of Mathematics", "pagerange": "117-144", "id_number": "CaltechAUTHORS:20130510-101747198", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130510-101747198", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-1021956" }, { "agency": "NSF", "grant_number": "DMS-1103976" }, { "agency": "National Natural Science Foundation of China", "grant_number": "10631060" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/pjm.2013.261.117", "primary_object": { "basename": "pjm-v261-n1-p07-s.pdf", "url": "https://authors.library.caltech.edu/records/7hctb-0zp70/files/pjm-v261-n1-p07-s.pdf" }, "pub_year": "2013", "author_list": "Liu, Yi; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/5fpz2-tn671", "eprint_id": 38607, "eprint_status": "archive", "datestamp": "2023-08-19 13:57:50", "lastmod": "2026-03-09 20:35:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conley-C-T", "name": { "family": "Conley", "given": "Clinton T." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Measurable chromatic and independence numbers for ergodic\n graphs and group actions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Ergodic actions, Borel combinatorics, chromatic numbers, amenable groups, free\ngroups.", "note": "\u00a9 2013 European Mathematical Society. Received July 9, 2010; revised August 2, 2011. The authors would like to thank M. Ab\u00e9rt, G. Elek, G. Hjorth, A. Ioana, R. Lyons, B. Miller, Y. Shalom, B. Sudakov, S. Thomas, B. Weiss and the\nreferees for many useful conversations and suggestions, and wish to extend additional thanks to B. Miller for allowing inclusion of Lemma 3.2. M.Ab\u00e9rt and G. Elek pointed out an error in our original proof of a version of Theorem 0.1 (ii). This has now been repaired by an alternative argument (see 2.19, 2.20). G. Elek has also independently suggested a somewhat related proof. A. S. Kechris was partially supported by NSF Grant DMS-0968710, the E. Schr\u00f6dinger Institute, Vienna, and the Mittag-Leffler Institute, Djursholm.", "abstract": "We study in this paper combinatorial problems concerning graphs generated by measure preserving actions of countable groups on standard measure spaces. In particular we study chromatic and independence numbers, in both the measure-theoretic and the Borel context, and relate the behavior of these parameters to properties of the acting group such as amenability, Kazhdan's property (T), and freeness. We also prove a Borel analog of the classical Brooks' Theorem in finite combinatorics for actions of groups with finitely many ends.", "date": "2013", "date_type": "published", "publication": "Groups, Geometry, and Dynamics", "volume": "7", "number": "1", "publisher": "European Mathematical Society", "pagerange": "127-180", "id_number": "CaltechAUTHORS:20130521-131021822", "issn": "1661-7207", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-131021822", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968710" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/GGD/179", "pub_year": "2013", "author_list": "Conley, Clinton T. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/6c9yk-x1577", "eprint_id": 46170, "eprint_status": "archive", "datestamp": "2023-08-19 14:03:30", "lastmod": "2026-03-09 02:18:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "3-Manifolds and 3d indices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2013 International Press.\n\nWe would like to thank Christopher Beem, Abhijit Gadde, Daniel Green,\nAnton Kapustin, Sara Pasquetti, Leonardo Rastelli, Schlomo Razamat,\nNathan Seiberg, Cumrun Vafa, Roland van der Veen, and Edward Witten\nfor illuminating discussions. The work of TD is supported primarily by\nthe Friends of the Institute for Advanced Study, and in part by DOE grant\nDE-FG02-90ER40542. The work of DG is supported in part by NSF grant\nPHY-0503584 and in part by the Roger Dashen membership in the Institute\nfor Advanced Study. The work of SG is supported in part by DOE Grant\nDE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. TD and\nSG thank the Simons Center for Geometry and Physics for their hospitality\nduring the Simons Workshop in Mathematics and Physics, 2011, where\npart of this work was initiated. Opinions and conclusions expressed here\nare those of the authors and do not necessarily reflect the views of funding\nagencies.\n\n

Published - ATMP-2013-0017-0005-a003.pdf

Submitted - 1112.5179v1.pdf

", "abstract": "We identify a large class R of three-dimensional N = 2 superconformal\nfield theories. This class includes the effective theories T_M of M5-branes\nwrapped on 3-manifolds M, discussed in previous work by the authors,\nand more generally comprises theories that admit a UV description as\nabelian Chern\u2013Simons-matter theories with (possibly non-perturbative)\nsuperpotential. Mathematically, class R might be viewed as an extreme\nquantum generalization of the Bloch group; in particular, the equivalence\nrelation among theories in class R is a quantum-field-theoretic \"2 to 3\nmove.\" We proceed to study the supersymmetric index of theories in\nclass R, uncovering its physical and mathematical properties, including\nrelations to algebras of line operators and to 4d indices. For 3-manifold\ntheories T_M, the index is a new topological invariant, which turns out to\nbe equivalent to non-holomorphic SL(2,\u2102) Chern\u2013Simons theory on M\nwith a previously unexplored \"integration cycle.\"", "date": "2013", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "17", "number": "5", "publisher": "International Press", "pagerange": "975-1076", "id_number": "CaltechAUTHORS:20140610-081020607", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140610-081020607", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Friends of the Institute for Advanced Study" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "Institute for Advanced Study" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2013.v17.n5.a3", "primary_object": { "basename": "1112.5179v1.pdf", "url": "https://authors.library.caltech.edu/records/6c9yk-x1577/files/1112.5179v1.pdf" }, "related_objects": [ { "basename": "ATMP-2013-0017-0005-a003.pdf", "url": "https://authors.library.caltech.edu/records/6c9yk-x1577/files/ATMP-2013-0017-0005-a003.pdf" } ], "pub_year": "2013", "author_list": "Dimofte, Tudor; Gaiotto, Davide; et al." }, { "id": "https://authors.library.caltech.edu/records/ptt91-kq190", "eprint_id": 77212, "eprint_status": "archive", "datestamp": "2023-08-19 13:44:46", "lastmod": "2026-04-10 17:26:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Geisinger-L", "name": { "family": "Geisinger", "given": "Leander" } } ] }, "title": "Semi-classical analysis of the Laplace operator with Robin boundary conditions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. \n\nReceived: 11 August 2012. Accepted: 24 August 2012. Published online: 5 October 2012. \n\nThe authors wish to thank A. Laptev for stimulating their interest in this problem. U.S. NSF grants PHY-1068285 (R.L.F.) and PHY-1122309 (L.G.) and DFG grant GE 2369/1-1 (L.G.) are acknowledged. \n\nCommunicated by A. Laptev.\n\n

Published - art_3A10.1007_2Fs13373-012-0028-5.pdf

Submitted - 1208.2327.pdf

", "abstract": "We prove a two-term asymptotic expansion of eigenvalue sums of the Laplacian on a bounded domain with Neumann, or more generally, Robin boundary conditions. We formulate and prove the asymptotics in terms of semi-classical analysis. In this reformulation it is natural to allow the function describing the boundary conditions to depend on the semi-classical parameter and we identify and analyze three different regimes for this dependence.", "date": "2012-12", "date_type": "published", "publication": "Bulletin of Mathematical Sciences", "volume": "2", "number": "2", "publisher": "Springer", "pagerange": "281-319", "id_number": "CaltechAUTHORS:20170505-092151992", "issn": "1664-3615", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170505-092151992", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-1122309" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "GE 2369/1-1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s13373-012-0028-5", "primary_object": { "basename": "1208.2327.pdf", "url": "https://authors.library.caltech.edu/records/ptt91-kq190/files/1208.2327.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs13373-012-0028-5.pdf", "url": "https://authors.library.caltech.edu/records/ptt91-kq190/files/art_3A10.1007_2Fs13373-012-0028-5.pdf" } ], "pub_year": "2012", "author_list": "Frank, Rupert L. and Geisinger, Leander" }, { "id": "https://authors.library.caltech.edu/records/5b3p0-nke27", "eprint_id": 77103, "eprint_status": "archive", "datestamp": "2023-08-19 13:44:40", "lastmod": "2026-04-10 17:43:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Entropy and the Uncertainty Principle", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 The Author. This paper may be reproduced, in its entirety, for noncommercial purposes. \n\nThe work was partially supported by NSF Grants PHY-1068285 (R.L.F.) and PHY-0965859 (E.H.L.).\n\n

Published - art_3A10.1007_2Fs00023-012-0175-y.pdf

Submitted - 1109.1209.pdf

", "abstract": "We generalize, improve and unify theorems of Rumin, and Maassen\u2013Uffink about classical entropies associated with quantum density matrices. These theorems refer to the classical entropies of the diagonals of a density matrix in two different bases. Thus, they provide a kind of uncertainty principle. Our inequalities are sharp because they are exact in the high-temperature or semi-classical limit.", "date": "2012-12", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "13", "number": "8", "publisher": "Springer", "pagerange": "1711-1717", "id_number": "CaltechAUTHORS:20170501-103316603", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-103316603", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-0965859" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-012-0175-y", "primary_object": { "basename": "1109.1209.pdf", "url": "https://authors.library.caltech.edu/records/5b3p0-nke27/files/1109.1209.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs00023-012-0175-y.pdf", "url": "https://authors.library.caltech.edu/records/5b3p0-nke27/files/art_3A10.1007_2Fs00023-012-0175-y.pdf" } ], "pub_year": "2012", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/dbxgb-ff025", "eprint_id": 36131, "eprint_status": "archive", "datestamp": "2023-08-19 13:36:52", "lastmod": "2026-03-09 23:14:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Blasius-D", "name": { "family": "Blasius", "given": "Don" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" }, { "id": "Varadarajan-V-S", "name": { "family": "Varadarajan", "given": "V. S." } } ] }, "title": "In memoriam: Jonathan Rogawski", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Pacific Journal of Mathematics.\nReceived: 30 September 2012.\n\nAccepted: 30 September 2012.\n\nPublished: 30 November 2012.\n\n

Published - pjm-v260-n2-p01-p.pdf

", "abstract": "Jonathan Rogawski is no more. In loving memory, his friends and collaborators\nand admirers have contributed to this garland of articles that you will find in the\npages to follow. He was of course a gifted mathematician, one of the earliest\nworkers on the Langlands Program, but much more. He wrote papers, textbooks,\nsupervised students, and served for many years with great distinction as an editor\nfor the Pacific Journal of Mathematics.", "date": "2012-12", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "260", "number": "2", "publisher": "Pacific Journal of Mathematics", "pagerange": "257-257", "id_number": "CaltechAUTHORS:20130103-082012333", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130103-082012333", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/pjm.2012.260.257", "primary_object": { "basename": "pjm-v260-n2-p01-p.pdf", "url": "https://authors.library.caltech.edu/records/dbxgb-ff025/files/pjm-v260-n2-p01-p.pdf" }, "pub_year": "2012", "author_list": "Blasius, Don; Ramakrishnan, Dinakar; et al." }, { "id": "https://authors.library.caltech.edu/records/ddbyt-wk891", "eprint_id": 36123, "eprint_status": "archive", "datestamp": "2023-08-19 13:18:52", "lastmod": "2026-04-10 18:03:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Tabuada-G", "name": { "family": "Tabuada", "given": "Gon\u00e7alo" } } ] }, "title": "Kontsevich's noncommutative numerical motives", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Foundation Compositio Mathematica. \n\nReceived 27 September 2011, accepted in final form 27 April 2012, published online 12 October 2012. \n\nThe first author was partially supported by the NSF grants DMS-0901221, DMS-1007207 and DMS-1201512. The second author was partially supported by the NEC award 2742738 and by the Portuguese Foundation for Science and Technology through PEst-OE/MAT/UI0297/2011 (CMA).\n\nThe authors are very grateful to Yuri Manin for stimulating discussions and to the anonymous referees for their comments, corrections and questions, which have greatly improved the article.\n\n

Submitted - 1108.3785.pdf

", "abstract": "In this article we prove that Kontsevich's category NC_(num)(k)_F of noncommutative numerical motives is equivalent to the one constructed by the authors in [Marcolli and Tabuada, Noncommutative motives, numerical equivalence, and semisimplicity, Amer. J. Math., to appear, available at arXiv:1105.2950]. As a consequence, we conclude that NC_(num)(k)_F is abelian semi-simple as conjectured by Kontsevich.", "date": "2012-11", "date_type": "published", "publication": "Compositio Mathematica", "volume": "148", "number": "6", "publisher": "Cambridge University Press", "pagerange": "1811-1820", "id_number": "CaltechAUTHORS:20130102-141740985", "issn": "0010-437X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130102-141740985", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "NSF", "grant_number": "DMS-1201512" }, { "agency": "NEC", "grant_number": "2742738" }, { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "PEst-OE/MAT/UI0297/2011" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0010437X12000383", "primary_object": { "basename": "1108.3785.pdf", "url": "https://authors.library.caltech.edu/records/ddbyt-wk891/files/1108.3785.pdf" }, "pub_year": "2012", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/ga32c-ryy04", "eprint_id": 32413, "eprint_status": "archive", "datestamp": "2023-08-19 13:05:11", "lastmod": "2026-04-16 01:39:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Faoro-L", "name": { "family": "Faoro", "given": "Lara" } }, { "id": "Ioffe-L-B", "name": { "family": "Ioffe", "given": "Lev" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Dissipationless dynamics of randomly coupled spins at high temperatures", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 American Physical Society. \n\nReceived 1 February 2012; published 15 October 2012. \n\nWe are grateful to R. McDermott for the discussion of the experimental situation. This work was supported, in part, by Triangle de la physique 2007-36, ANR-06-BLAN-0218, ECS-0608842, ARO W911-09-1-0395, DARPA HR0011-09-1-0009. A.K. acknowledges funding by the Institute of Quantum Information under NSF Grant No. PHY-0803371.\n\n

Published - PhysRevB.86.134414.pdf

Submitted - 1112.3855v1.pdf

", "abstract": "We develop a technique to compute the high-frequency asymptotics of spin correlators in weakly interacting disordered spin systems. We show that the dynamical spin correlator decreases exponentially at high frequencies \u27e8SS\u27e9_\u03c9 \u223c exp(\u2212\u03c4\u2217\u03c9) and compute the characteristic time \u03c4\u2217 of this dependence. In a typical random configuration, some fraction of spins form strongly coupled pairs, which behave as two-level systems. Their switching dynamics is driven by the high-frequency noise from the surrounding spins, resulting in low-frequency 1/f noise in the magnetic susceptibility and other physical quantities. We discuss application of these results to the problem of susceptibility and flux noise in superconducting circuits at mK temperatures.", "date": "2012-10-01", "date_type": "published", "publication": "Physical Review B", "volume": "86", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 134414", "id_number": "CaltechAUTHORS:20120713-092458311", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120713-092458311", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Triangle de la physique", "grant_number": "2007-36" }, { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "ANR-06-BLAN-0218" }, { "agency": "NSF", "grant_number": "ECS-0608842" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911-09-1-0395" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0009" }, { "agency": "NSF", "grant_number": "PHY-0803371" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.86.134414", "primary_object": { "basename": "1112.3855v1.pdf", "url": "https://authors.library.caltech.edu/records/ga32c-ryy04/files/1112.3855v1.pdf" }, "related_objects": [ { "basename": "PhysRevB.86.134414.pdf", "url": "https://authors.library.caltech.edu/records/ga32c-ryy04/files/PhysRevB.86.134414.pdf" } ], "pub_year": "2012", "author_list": "Faoro, Lara; Ioffe, Lev; et al." }, { "id": "https://authors.library.caltech.edu/records/92w3f-nhw77", "eprint_id": 32794, "eprint_status": "archive", "datestamp": "2023-08-22 06:58:29", "lastmod": "2026-04-10 13:40:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Elliptic Littlewood identities", "ispublished": "pub", "full_text_status": "public", "keywords": "Elliptic special functions; Macdonald polynomials; Koornwinder polynomials; Quadratic transformations", "note": "\u00a9 2012 Elsevier Inc.\n\nReceived 1 June 2011. Available online 23 March 2012.\n\n\nThe author would like to thank V. Spiridonov and O. Warnaar for helpful comments on an earlier\ndraft, along with R. Askey and M. Rahman for helpful discussions regarding the analogue of\nCorollary 4.12 for Askey\u2013Wilson polynomials, and F. van de Bult for settling one conjecture from\nthe original version and providing substantial additional evidence for several more. The author would\nalso like to thank P. Forrester for hosting the author's sabbatical at the University of Melbourne, during\nwhich several key portions of the work were done. This work was supported in part by NSF Grants\nNos. DMS-0401387, DMS-0833464, and DMS-1001645; in addition, much of the work was performed\nwhile the author was affiliated with the University of California at Davis.\n\n

Submitted - 0806.0871.pdf

", "abstract": "We prove analogues for elliptic interpolation functions of Macdonald's version of the Littlewood identity for (skew) Macdonald polynomials, in the process developing an interpretation of general elliptic \"hypergeometric\" sums as skew interpolation functions. One such analogue has an interpretation as a \"vanishing integral\", generalizing a result of Rains and Vazirani (2007) [17]; the structure of this analogue gives sufficient insight to enable us to conjecture elliptic versions of most of the other vanishing integrals of Rains and Vazirani (2007) [17] as well. We are thus led to formulate ten conjectures, each of which can be viewed as a multivariate quadratic transformation, and can be proved in a number of special cases.", "date": "2012-10", "date_type": "published", "publication": "Journal of Combinatorial Theory. Series A", "volume": "119", "number": "7", "publisher": "Elsevier", "pagerange": "1558-1609", "id_number": "CaltechAUTHORS:20120730-134423880", "issn": "0097-3165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120730-134423880", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" }, { "agency": "NSF", "grant_number": "DMS-0833464" }, { "agency": "NSF", "grant_number": "DMS-1001645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jcta.2012.03.001", "primary_object": { "basename": "0806.0871.pdf", "url": "https://authors.library.caltech.edu/records/92w3f-nhw77/files/0806.0871.pdf" }, "pub_year": "2012", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/5dhpf-yek21", "eprint_id": 97827, "eprint_status": "archive", "datestamp": "2023-08-22 07:06:02", "lastmod": "2026-04-10 15:01:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } } ] }, "title": "Bounds for graph regularity and removal lemmas", "ispublished": "pub", "full_text_status": "public", "keywords": "Bipartite Graph; Random Graph; Edge Density; Graph Regularity; Regularity Lemma", "note": "\u00a9 2012 Springer Basel AG. \n\nReceived 23 July 2011; revised 03 May 2012; accepted 07 May 2012; first online 25 August 2012. \n\nDavid Conlon's research was supported by a Royal Society University Research Fellowship and Jacob Fox's research was supported by a Simons Fellowship and NSF grant DMS-1069197. \n\nWe would like to thank Noga Alon for helpful comments. We also thank the anonymous referee for carefully reading the article and making several useful remarks.\n\n

Submitted - 1107.4829.pdf

", "abstract": "We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^(2)/log^* k pairs of parts which are not \u03f5-regular, where c, \u03f5 > 0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemer\u00e9di's regularity lemma. In order to gain some control over irregular pairs, another regularity lemma, known as the strong regularity lemma, was developed by Alon, Fischer, Krivelevich, and Szegedy. For this lemma, we prove a lower bound of wowzer-type, which is one level higher in the Ackermann hierarchy than the tower function, on the number of parts in the strong regularity lemma, essentially matching the upper bound. On the other hand, for the induced graph removal lemma, the standard application of the strong regularity lemma, we find a different proof which yields a tower-type bound. We also discuss bounds on several related regularity lemmas, including the weak regularity lemma of Frieze and Kannan and the recently established regular approximation theorem. In particular, we show that a weak partition with approximation parameter \u03f5 may require as many as 2^\u03a9(\u03f5^(\u22122)) parts. This is tight up to the implied constant and solves a problem studied by Lov\u00e1sz and Szegedy.", "date": "2012-10", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "22", "number": "5", "publisher": "Springer", "pagerange": "1191-1256", "id_number": "CaltechAUTHORS:20190812-162959355", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959355", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-012-0171-x", "primary_object": { "basename": "1107.4829.pdf", "url": "https://authors.library.caltech.edu/records/5dhpf-yek21/files/1107.4829.pdf" }, "pub_year": "2012", "author_list": "Conlon, David and Fox, Jacob" }, { "id": "https://authors.library.caltech.edu/records/4nt3p-d2p84", "eprint_id": 35130, "eprint_status": "archive", "datestamp": "2023-08-19 12:55:08", "lastmod": "2026-04-16 01:39:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bell-M-T", "name": { "family": "Bell", "given": "M. T." } }, { "id": "Sadovskyy-I-A", "name": { "family": "Sadovskyy", "given": "I. A." } }, { "id": "Ioffe-L-B", "name": { "family": "Ioffe", "given": "L. B." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A. Yu." }, "orcid": "0000-0002-5777-642X" }, { "id": "Gershenson-M-E", "name": { "family": "Gershenson", "given": "M. E." } } ] }, "title": "Quantum Superinductor with Tunable Nonlinearity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 American Physical Society.\n\nReceived 6 July 2012; published 27 September 2012.\nWe would like to thank V. Manucharyan and A.\nZamolodchikov for helpful discussions. The work was\nsupported by DARPA (HR0011-09-1-0009), NSF (DMR\n1006265), and ARO (W911NF-09-1-0395).\n\n

Published - PhysRevLett.109.137003.pdf

Supplemental Material - README.TXT

Supplemental Material - Supplement_v9.41.pdf

", "abstract": "We report on the realization of a superinductor, a dissipationless element whose microwave impedance greatly exceeds the resistance quantum R_Q. The design of the superinductor, implemented as a ladder of nanoscale Josephson junctions, enables tuning of the inductance and its nonlinearity by a weak magnetic field. The Rabi decay time of the superinductor-based qubit exceeds 1\u2009\u2009\u03bcs. The high kinetic inductance and strong nonlinearity offer new types of functionality, including the development of qubits protected from both flux and charge noises, fault tolerant quantum computing, and high-impedance isolation for electrical current standards based on Bloch oscillations.", "date": "2012-09-27", "date_type": "published", "publication": "Physical Review Letters", "volume": "109", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 137003", "id_number": "CaltechAUTHORS:20121026-145953727", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121026-145953727", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0009" }, { "agency": "NSF", "grant_number": "DMR 1006265" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-09-1-0395" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.109.137003", "primary_object": { "basename": "PhysRevLett.109.137003.pdf", "url": "https://authors.library.caltech.edu/records/4nt3p-d2p84/files/PhysRevLett.109.137003.pdf" }, "related_objects": [ { "basename": "README.TXT", "url": "https://authors.library.caltech.edu/records/4nt3p-d2p84/files/README.TXT" }, { "basename": "Supplement_v9.41.pdf", "url": "https://authors.library.caltech.edu/records/4nt3p-d2p84/files/Supplement_v9.41.pdf" } ], "pub_year": "2012", "author_list": "Bell, M. T.; Sadovskyy, I. A.; et al." }, { "id": "https://authors.library.caltech.edu/records/r5mq8-5n617", "eprint_id": 37668, "eprint_status": "archive", "datestamp": "2023-08-22 06:49:35", "lastmod": "2026-04-10 01:18:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Perez-C", "name": { "family": "Perez", "given": "Christopher" } } ] }, "title": "Codes as Fractals and Noncommutative Spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Error-correcting codes; Noncommutative spaces; Fractals; CSS algorithm; Noncommutative tori; Cuntz algebras", "note": "\u00a9 2012 Springer Basel AG. \n\nReceived: 23 August 2011; Revised: 10 April 2012; Accepted: 21 April 2012; Published online 02 June 2012. \n\nM. Marcolli is partially supported by NSF grants DMS-0901221 and DMS-1007207. C. Perez was supported for this project by a Caltech Summer Undergraduate Research Fellowship.\n\n

Submitted - 1107.5782v1.pdf

", "abstract": "We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from noncommutative geometry, arising from rational noncommutative tori and finite abelian group actions on Cuntz algebras and fractals associated to the classical codes.", "date": "2012-09-01", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "6", "number": "3", "publisher": "Springer Verlag", "pagerange": "199-215", "id_number": "CaltechAUTHORS:20130328-095244455", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130328-095244455", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-012-0114-9", "primary_object": { "basename": "1107.5782v1.pdf", "url": "https://authors.library.caltech.edu/records/r5mq8-5n617/files/1107.5782v1.pdf" }, "pub_year": "2012", "author_list": "Marcolli, Matilde and Perez, Christopher" }, { "id": "https://authors.library.caltech.edu/records/69ssa-jy057", "eprint_id": 97810, "eprint_status": "archive", "datestamp": "2023-09-22 22:35:05", "lastmod": "2026-04-10 02:48:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Erd\u0151s-Hajnal-type theorems in hypergraphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey theory; Erd\u0151s\u2013Hajnal conjecture; Hypergraphs", "note": "\u00a9 2012 Elsevier. Under an Elsevier user license. \n\nReceived 28 April 2011; available online 18 June 2012. \n\nConlon research supported by a Royal Society University Research Fellowship. Fox research supported by a Simons Fellowship and NSF grant DMS-1069197. Sudakov research supported in part by NSF grant DMS-1101185 and by a USA\u2013Israeli BSF grant. \n\nCredit and thanks are due to Vojta R\u00f6dl and Mathias Schacht, who brought the question regarding tripartite subgraphs of \u210b-free hypergraphs to our attention.\n\n

Submitted - 1104.5544.pdf

", "abstract": "The Erd\u0151s\u2013Hajnal conjecture states that if a graph on n vertices is H-free, that is, it does not contain an induced copy of a given graph H, then it must contain either a clique or an independent set of size n^\u03b4(H), where \u03b4(H) > 0 depends only on the graph H. Except for a few special cases, this conjecture remains wide open. However, it is known that an H-free graph must contain a complete or empty bipartite graph with parts of polynomial size.\n\nWe prove an analogue of this result for 3-uniform hypergraphs, showing that if a 3-uniform hypergraph on n vertices is \u210b-free, for any given \u210b, then it must contain a complete or empty tripartite subgraph with parts of order c(log n)^\u00bd + \u03b4(\u210b), where \u03b4(\u210b) > 0 depends only on \u210b. This improves on the bound of c(log n)^\u00bd, which holds in all 3-uniform hypergraphs, and, up to the value of the constant \u03b4(\u210b), is best possible.\n\nWe also prove that, for k \u2265 4, no analogue of the standard Erd\u0151s\u2013Hajnal conjecture can hold in k-uniform hypergraphs. That is, there are k-uniform hypergraphs \u210b and sequences of \u210b-free hypergraphs which do not contain cliques or independent sets of size appreciably larger than one would normally expect.", "date": "2012-09", "date_type": "published", "publication": "Journal of Combinatorial Theory, Series B", "volume": "102", "number": "5", "publisher": "Elsevier", "pagerange": "1142-1154", "id_number": "CaltechAUTHORS:20190812-162957444", "issn": "0095-8956", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957444", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "Simons Foundation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "NSF", "grant_number": "DMS-1101185" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jctb.2012.05.005", "primary_object": { "basename": "1104.5544.pdf", "url": "https://authors.library.caltech.edu/records/69ssa-jy057/files/1104.5544.pdf" }, "pub_year": "2012", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/t73n9-4z936", "eprint_id": 77107, "eprint_status": "archive", "datestamp": "2023-08-19 12:35:35", "lastmod": "2026-04-10 14:19:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Lieb-Thirring inequality for a model of particles with point interactions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 American Institute of Physics. \n\nReceived 23 December 2011; accepted 17 February 2012; published online 14 May 2012. \n\nPartial financial support by NSF (Grant No. PHY-1068285) to R.F. and the NSERC to R.S. is gratefully acknowledged.\n\n

Submitted - 1112.5617.pdf

", "abstract": "We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power 5/3.", "date": "2012-09", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "53", "number": "9", "publisher": "American Institute of Physics", "pagerange": "Art. No. 095201", "id_number": "CaltechAUTHORS:20170501-113527750", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-113527750", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.3697416", "primary_object": { "basename": "1112.5617.pdf", "url": "https://authors.library.caltech.edu/records/t73n9-4z936/files/1112.5617.pdf" }, "related_objects": [ { "basename": "1_2E3697416.pdf", "url": "https://authors.library.caltech.edu/records/t73n9-4z936/files/1_2E3697416.pdf" } ], "pub_year": "2012", "author_list": "Frank, Rupert L. and Seiringer, Robert" }, { "id": "https://authors.library.caltech.edu/records/6q7np-qtf73", "eprint_id": 33342, "eprint_status": "archive", "datestamp": "2023-08-19 11:49:39", "lastmod": "2026-04-10 13:59:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bhuyain-T-A", "name": { "family": "Bhuyain", "given": "Tanvir Ahamed" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "The Ricci Flow on Noncommutative Two-Tori", "ispublished": "pub", "full_text_status": "public", "keywords": "Ricci flow, noncommutative tori, pseudodifferential calculus", "note": "\u00a9 2012 Springer. \n\nReceived: 25 August 2011. Revised: 9 January 2012. Accepted: 19 February 2012. Published online: 14 March 2012. \n\nThis paper is based on the results of the first author's summer research project within the Caltech program Summer Undergraduate Research Fellowships (SURF) [7]. The first author acknowledges support given from the bequest of Herbert J. Ryser (1923\u20131985) through the Caltech mathematics department. The second author acknowledges support from NSF Grants DMS-0901221, DMS-1007207.\n\n

Submitted - 1107.4788v1.pdf

", "abstract": "In this paper we construct a version of Ricci flow for noncommutative two-tori, based on a spectral formulation in terms of the eigenvalues and eigenfunction of the Laplacian and recent results on the Gauss\u2013Bonnet theorem for noncommutative tori.", "date": "2012-08", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "101", "number": "2", "publisher": "Springer", "pagerange": "173-194", "id_number": "CaltechAUTHORS:20120820-083919381", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120820-083919381", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Caltech Mathematics Department" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-012-0550-0", "primary_object": { "basename": "1107.4788v1.pdf", "url": "https://authors.library.caltech.edu/records/6q7np-qtf73/files/1107.4788v1.pdf" }, "pub_year": "2012", "author_list": "Bhuyain, Tanvir Ahamed and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/vqexy-d3q50", "eprint_id": 77093, "eprint_status": "archive", "datestamp": "2023-08-19 11:37:25", "lastmod": "2026-04-10 17:52:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hainzl-C", "name": { "family": "Hainzl", "given": "Christian" } }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } }, { "id": "Solovej-J-P", "name": { "family": "Solovej", "given": "Jan Philip" } } ] }, "title": "Microscopic Derivation of Ginzburg-Landau Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived by the editors February 20, 2011 and, in revised form, November 14, 2011. Published electronically: March 26, 2012. \n\nThe first author gratefully acknowledges financial support received via U.S. NSF grant PHY-1068285. \n\nThe second author gratefully acknowledges financial support received via U.S. NSF grant DMS-0800906. \n\nThe third author gratefully acknowledges financial support received via U.S. NSF grant PHY-0845292 and NSERC. \n\nThe last author gratefully acknowledges financial support received via a grant from the Danish council for independent research. \n\nPart of this work was carried out at the Erwin Schr\u00f6dinger\nInstitute for Mathematical Physics in Vienna, Austria, and the authors are grateful for the support and hospitality during their visit. R.S. would also like to thank the Departamento de Fisica at the Pontificia Universidad Cat\u03cclica de Chile for their hospitality.\n\n

Published - S0894-0347-2012-00735-8.pdf

Submitted - 1102.4001.pdf

", "abstract": "We give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis, with minimal regularity assumptions, plays an important part in our proof.", "date": "2012-07", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "25", "number": "3", "publisher": "American Mathematical Society", "pagerange": "667-713", "id_number": "CaltechAUTHORS:20170501-090207067", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-090207067", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "DMS-0800906" }, { "agency": "NSF", "grant_number": "PHY-0845292" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Danish Council for Independent Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-2012-00735-8", "primary_object": { "basename": "1102.4001.pdf", "url": "https://authors.library.caltech.edu/records/vqexy-d3q50/files/1102.4001.pdf" }, "related_objects": [ { "basename": "S0894-0347-2012-00735-8.pdf", "url": "https://authors.library.caltech.edu/records/vqexy-d3q50/files/S0894-0347-2012-00735-8.pdf" } ], "pub_year": "2012", "author_list": "Frank, Rupert L.; Hainzl, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/yreyx-gys95", "eprint_id": 32320, "eprint_status": "archive", "datestamp": "2023-08-19 11:30:41", "lastmod": "2026-04-10 19:32:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ceyhan-\u00d6", "name": { "family": "Ceyhan", "given": "\u00d6zg\u00fcr" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Feynman Integrals and Motives of Configuration Spaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Springer-Verlag. \n\nReceived: 11 January 2011; Accepted: 15 December 2011; Published online: 25 May 2012. \n\nPart of this work was carried out during a visit of the first author to the California Institute of Technology and during a visit of both authors to the Max Planck Institute for Mathematics in Bonn. The first author is partially supported by a NWO grant; the second author is partially supported by NSF grants DMS-0651925, DMS-0901221, and DMS-1007207. \n\nCommunicated by A. Connes.\n\n

Submitted - 1012.5485v1.pdf

", "abstract": "We formulate the problem of renormalization of Feynman integrals and its relation to periods of motives in configuration space instead of momentum space. The algebro-geometric setting is provided by the wonderful compactifications Conf \u0393(X) of arrangements of subvarieties associated to the subgraphs of a Feynman graph \u0393, with X a (quasi)projective variety. The motive and the class in the Grothendieck ring are computed explicitly for these wonderful compactifications, in terms of the motive of X and the combinatorics of the Feynman graph, using recent results of Li Li. The pullback to the wonderful compactification of the form defined by the unrenormalized Feynman amplitude has singularities along a hypersurface, whose real locus is contained in the exceptional divisors of the iterated blowup that gives the wonderful compactification. A regularization of the Feynman integrals can be obtained by modifying the cycle of integration, by replacing the divergent locus with a Leray coboundary. The ambiguities are then defined by Poincar\u00e9 residues. While these residues give periods associated to the cohomology of the exceptional divisors and their intersections, the regularized integrals give rise to periods of the hypersurface complement in the wonderful compactification.", "date": "2012-07", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "313", "number": "1", "publisher": "Springer", "pagerange": "35-70", "id_number": "CaltechAUTHORS:20120710-100433105", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120710-100433105", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" }, { "agency": "NSF", "grant_number": "DMS-0651925" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-012-1484-1", "primary_object": { "basename": "1012.5485v1.pdf", "url": "https://authors.library.caltech.edu/records/yreyx-gys95/files/1012.5485v1.pdf" }, "pub_year": "2012", "author_list": "Ceyhan, \u00d6zg\u00fcr and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/f6k80-j2g14", "eprint_id": 32603, "eprint_status": "archive", "datestamp": "2023-08-19 11:31:18", "lastmod": "2026-04-16 01:41:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Kong-Liang", "name": { "family": "Kong", "given": "Liang" } } ] }, "title": "Models for Gapped Boundaries and Domain Walls", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Springer-Verlag.\n\n24 May 2011; Accepted: 18 January 2012; Published online: 7 June 2012.\n\nLK thanks Robert K\u00f6nig for introducing the Levin-Wen model to him, and Xiao-Gang Wen for a valuable comment on the physical meaning of defects of codimension 3. We thank John Preskill, Hector Bombin, Anton Kapustin and Yong-ShiWu for many inspiring conversations. This work was supported\nin part by NSF under Grant No. PHY-0803371. AK is also supported by ARO under Grant No. W911NF-09-1-0442. LK is supported by the Gordon and Betty Moore Foundation through Caltech's Center for the Physics of Information, and NSF under Grant No. PHY-0803371, the Basic Research Young Scholars Program and the Initiative Scientific Research Program of Tsinghua University, and NSFC under Grant No. 11071134.\n\n

Submitted - 1104.5047.pdf

", "abstract": "We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk\npart is constructed using a unitary tensor category C as in the Levin-Wen model, whereas the boundary is associated with amodule category over C.We also consider domainwalls\n(or defect lines) between different bulk phases.Adomainwall is transparent to bulk excitations if the corresponding unitary tensor categories are Morita equivalent. Defects of\nhigher codimension will also be studied. In summary, we give a dictionary between physical ingredients of lattice models and tensor-categorical notions.", "date": "2012-07", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "313", "number": "2", "publisher": "Springer", "pagerange": "351-373", "id_number": "CaltechAUTHORS:20120720-094651607", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120720-094651607", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0803371" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-09-1-0442" }, { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Caltech Center for the Physics of Information" }, { "agency": "NSF", "grant_number": "PHY-0803371" }, { "agency": "Tsinghua University Basic Research Young Scholars Program" }, { "agency": "Tsinghua University Initiative Scientific Research Program" }, { "agency": "NSFC", "grant_number": "11071134" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-012-1500-5", "primary_object": { "basename": "1104.5047.pdf", "url": "https://authors.library.caltech.edu/records/f6k80-j2g14/files/1104.5047.pdf" }, "pub_year": "2012", "author_list": "Kitaev, Alexei and Kong, Liang" }, { "id": "https://authors.library.caltech.edu/records/67q6z-wvz03", "eprint_id": 35436, "eprint_status": "archive", "datestamp": "2023-08-19 11:11:43", "lastmod": "2026-04-10 14:15:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Prasad-D", "name": { "family": "Prasad", "given": "Dipendra" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Self-dual representations of division algebras and Weil groups: A contrast", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 The Johns Hopkins University Press.\n\nManuscript received September 29, 2009; revised September 27, 2010.\n\nResearch of the first author supported in part by grants from the Friends of the Institute (of Advanced Study)\nand the von Neumann Fund; research of the second author supported in part by NSF grant DMS-0701089.\n\n

Published - Prasad2012p19433Amer._J._Math.pdf

", "abstract": "Irreducible selfdual representations of any group fall into two classes: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the irreducible representations \u03c3 of the Weil group of a local field k of dimension n with the irreducible representations \u03c0 of the invertible elements of a division algebra D over k of index n, takes selfdual representations to selfdual representations. In this paper we use global methods to study how the Langlands correspondence behaves relative to this distinction among selfdual representations. We prove in particular that for n even, \u03c3 is symplectic if and only if \u03c3 is orthogonal. More generally, we treat the case of GL_(m)(B), for B a division algebra over k of index r, and n = mr.", "date": "2012-06", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "134", "number": "3", "publisher": "Johns Hopkins University Press", "pagerange": "749-772", "id_number": "CaltechAUTHORS:20121113-123411958", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121113-123411958", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Friends of the Institute of Advanced Study" }, { "agency": "von Neumann Fund" }, { "agency": "NSF", "grant_number": "DMS-0701089" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1353/ajm.2012.0017", "primary_object": { "basename": "Prasad2012p19433Amer._J._Math.pdf", "url": "https://authors.library.caltech.edu/records/67q6z-wvz03/files/Prasad2012p19433Amer._J._Math.pdf" }, "pub_year": "2012", "author_list": "Prasad, Dipendra and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/0k1qp-a0g45", "eprint_id": 32467, "eprint_status": "archive", "datestamp": "2023-08-19 11:07:19", "lastmod": "2026-04-10 01:01:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Weak containment in the space of actions of a free group", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 Springer. \n\nReceived July 2, 2009 and in revised form September 1, 2010. \n\nI would like to thank M. Ab\u00e9rt, L. Bowen, D. Gaboriau, A. Ioana, N. Monod, Y. Shalom and T. Tsankov for many useful discussions or comments concerning this paper, and G. Hjorth for allowing me to include 6.3 below. The research of the author was partially supported by NSF Grant DMS-0455285.\n\n

Submitted - weakcontainment02.pdf

", "abstract": "It is shown that the translation action of the free group with n generators\non its profinite completion is the maximum, in the sense of weak containment,\nmeasure preserving action of this group. Using also a result of\nAb\u00e9rt\u2013Nikolov this is used to give a new proof of Gaboriau's theorem that\nthe cost of this group is equal to n. A similar maximality result is proved\nfor generalized shift actions. Finally a study is initiated of the class of\nresidually finite, countable groups for which the finite actions are dense in\nthe space of measure preserving actions.", "date": "2012-06", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "189", "number": "1", "publisher": "Springer", "pagerange": "461-507", "id_number": "CaltechAUTHORS:20120716-102713726", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120716-102713726", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0455285" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-011-0182-6", "primary_object": { "basename": "weakcontainment02.pdf", "url": "https://authors.library.caltech.edu/records/0k1qp-a0g45/files/weakcontainment02.pdf" }, "pub_year": "2012", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/148nq-15p36", "eprint_id": 71906, "eprint_status": "archive", "datestamp": "2023-08-22 05:51:34", "lastmod": "2026-04-10 15:35:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Complete Characterization of Functions Satisfying the Conditions of Arrow's Theorem", "ispublished": "pub", "full_text_status": "public", "keywords": "Equivalence Class; Complete Characterization; Social Welfare Function; Strict Preference; Social Alternative", "note": "\u00a9 2011 Springer-Verlag. \n\nReceived: 14 October 2009; Accepted: 22 March 2011; Published online: 2 April 2011. \n\nE. Mossel was supported by a Sloan fellowship in Mathematics, by BSF grant 2004105, NSF Career Award (DMS 054829), ONR award N00014-07-1-0506, and ISF grant 1300/08, and O. Tamuz was supported by ISF grant 1300/08.\n\n

Submitted - 0910.2465.pdf

", "abstract": "Arrow's theorem implies that a social welfare function satisfying Transitivity, the Weak Pareto Principle (Unanimity), and Independence of Irrelevant Alternatives (IIA) must be dictatorial. When non-strict preferences are also allowed, a dictatorial social welfare function is defined as a function for which there exists a single voter whose strict preferences are followed. This definition allows for many different dictatorial functions, since non-strict preferences of the dictator are not necessarily followed. In particular, we construct examples of dictatorial functions which do not satisfy Transitivity and IIA. Thus Arrow's theorem, in the case of non-strict preferences, does not provide a complete characterization of all social welfare functions satisfying Transitivity, the Weak Pareto Principle, and IIA. The main results of this article provide such a characterization for Arrow's theorem, as well as for follow up results by Wilson. In particular, we strengthen Arrow's and Wilson's result by giving an exact if and only if condition for a function to satisfy Transitivity and IIA (and the Weak Pareto Principle). Additionally, we derive formulae for the number of functions satisfying these conditions.", "date": "2012-06", "date_type": "published", "publication": "Social Choice and Welfare", "volume": "39", "number": "1", "publisher": "Springer", "pagerange": "127-140", "id_number": "CaltechAUTHORS:20161110-073042338", "issn": "0176-1714", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-073042338", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2004105" }, { "agency": "NSF", "grant_number": "DMS 054829" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-07-1-0506" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00355-011-0547-0", "primary_object": { "basename": "0910.2465.pdf", "url": "https://authors.library.caltech.edu/records/148nq-15p36/files/0910.2465.pdf" }, "pub_year": "2012", "author_list": "Mossel, Elchanan and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/s358b-c8d04", "eprint_id": 97822, "eprint_status": "archive", "datestamp": "2023-08-19 10:53:10", "lastmod": "2026-04-10 13:56:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "On two problems in graph Ramsey theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 J\u00e1nos Bolyai Mathematical Society and Springer-Verlag. \n\nReceived 29 January 2010; first online 04 October 2012. \n\nConlon research supported by a Junior Research Fellowship at St John's College. Fox research supported by a Simons Fellowship, an MIT NEC Corp. award and NSF grant DMS-1069197. Sudakov research supported in part by NSF grant DMS-1101185, by AFOSR MURI grant FA9550-10-1-0569 and by a USA-Israel BSF grant.\n\n

Submitted - 1002.0045.pdf

", "abstract": "We study two classical problems in graph Ramsey theory, that of determining the Ramsey number of bounded-degree graphs and that of estimating the induced Ramsey number for a graph with a given number of vertices. \n\nThe Ramsey number r(H) of a graph H is the least positive integer N such that every two-coloring of the edges of the complete graph K_N contains a monochromatic copy of H. A famous result of Chv\u00e1tal, R\u00f6dl, Szemer\u00e9di and Trotter states that there exists a constant c(\u0394) such that r(H) \u2264 c(\u0394)n for every graph H with n vertices and maximum degree \u0394. The important open question is to determine the constant c(\u0394). The best results, both due to Graham, R\u00f6dl and Ruci\u0144ski, state that there are positive constants c and c' such that 2^(c'\u0394) \u2264 c(\u0394) \u2264 c^(\u0394log^(2)\u0394). We improve this upper bound, showing that there is a constant c for which c(\u0394) \u2264 2^(c\u0394log\u0394).", "date": "2012-05", "date_type": "published", "publication": "Combinatorica", "volume": "32", "number": "5", "publisher": "Springer", "pagerange": "513-535", "id_number": "CaltechAUTHORS:20190812-162958859", "issn": "0209-9683", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958859", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" }, { "agency": "Simons Foundation" }, { "agency": "MIT NEC Corporation" }, { "agency": "NSF", "grant_number": "DMS-1069197" }, { "agency": "NSF", "grant_number": "DMS-1101185" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "FA9550-10-1-0569" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-012-2710-3", "primary_object": { "basename": "1002.0045.pdf", "url": "https://authors.library.caltech.edu/records/s358b-c8d04/files/1002.0045.pdf" }, "pub_year": "2012", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/t481e-f9768", "eprint_id": 28628, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:48", "lastmod": "2026-04-10 13:59:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oshikawa-Masaki", "name": { "family": "Oshikawa", "given": "Masaki" } } ] }, "title": "Instability in Magnetic Materials with a Dynamical Axion Field", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 American Physical Society. \n\nReceived 14 December 2011; published 20 April 2012. \n\nWe thank Y. Ando, O. Bergman, J. Gauntlett, D. Hsieh, J. Maldacena, and X.-L. Qi for useful discussions. We thank the hospitality of the Aspen Center for Physics (NSF Grant No. 1066293) and the Kavli Institute for Theoretical Physics, UC Santa Barbara (NSF Grant No. PHY05-51164). The work of H. O. is supported in part by U.S. DOE Grant No. DE-FG03-92-ER40701, the WPI Initiative of MEXT of Japan, and JSPS Grant-in-Aid for Scientific Research No. C-23540285. The work of M. O. is supported in part by JSPS Grant-in-Aid for Scientific Research No. 21540381.\n\n

Published - PhysRevLett.108.161803.pdf

Submitted - 1112.1414v1.pdf

", "abstract": "It has been pointed out that axion electrodynamics exhibits instability in the presence of a background electric field. We show that the instability leads to a complete screening of an applied electric field above a certain critical value and the excess energy is converted into a magnetic field. We clarify the physical origin of the screening effect and discuss its possible experimental realization in magnetic materials where magnetic fluctuations play the role of the dynamical axion field.", "date": "2012-04-20", "date_type": "published", "publication": "Physical Review Letters", "volume": "108", "number": "16", "publisher": "American Physical Society", "pagerange": "Art. No. 161803", "id_number": "CaltechAUTHORS:20120103-143444619", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120103-143444619", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1066293" }, { "agency": "NSF", "grant_number": "PHY05-51164" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "21540381" } ] }, "other_numbering_system": { "items": [ { "id": "11-273", "name": "KITP" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.108.161803", "primary_object": { "basename": "1112.1414v1.pdf", "url": "https://authors.library.caltech.edu/records/t481e-f9768/files/1112.1414v1.pdf" }, "related_objects": [ { "basename": "PhysRevLett.108.161803.pdf", "url": "https://authors.library.caltech.edu/records/t481e-f9768/files/PhysRevLett.108.161803.pdf" } ], "pub_year": "2012", "author_list": "Ooguri, Hirosi and Oshikawa, Masaki" }, { "id": "https://authors.library.caltech.edu/records/wfg1j-aye22", "eprint_id": 29765, "eprint_status": "archive", "datestamp": "2023-08-22 05:16:49", "lastmod": "2026-04-10 02:34:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "Finite Gap Jacobi Matrices, III. Beyond the Szeg\u0151 Class", "ispublished": "pub", "full_text_status": "public", "keywords": "Szeg\u0151 asymptotics; Orthogonal polynomials; Almost periodic\nsequences; Slowly decaying perturbations", "note": "\u00a9 2012 Springer Science. Received: 1 July 2011. Accepted: 18 October 2011. Published online: 25 January 2012. Communicated by Vilmos Totik. J.S.C. and M.Z. gratefully acknowledge the kind invitation and hospitality of the Mathematics Department of Caltech where this work was completed. J.S.C. was supported in part by a Steno Research Grant (09-064947) from the Danish Research Council for Nature and Universe. B.S. was supported in part by NSF grant DMS-0968856. M.Z. was supported in part by NSF grant DMS-0965411.\n\n

Submitted - 1108.0183

", "abstract": "Let e \u2282 R be a finite union of \u2113+1 disjoint closed intervals, and denote by \u03c9_j the harmonic measure of the j left-most bands. The frequency module for e is the set of all integral combinations of \u03c9_1,\u2026,\u03c9_\u2113. Let {a_nb_n}^\u221e_(n=\u2212\u221e) be a point in the isospectral torus for e and p_n its orthogonal polynomials. Let {a_nb_n}^\u221e_(n=1) be a half-line Jacobi matrix with a_n=a_n+\u03b4a_n, b_n=b_n+\u03b4b_n. Suppose \u2211^\u221e_(n=1)\u2502\u03b4an\u2502^2 + \u2502\u03b4b_n\u2502^2 < \u221e and \u2211^N_n=1^e^(2\u03c0i\u03c9n), \u03b4a_n \u2211^N_n=1^e^(2\u03c0i\u03c9n) \u03b4b_n have finite limits as N \u2192 \u221e for all \u03c9 in the frequency module. If, in addition, these partial sums grow at most subexponentially with respect to \u03c9, then for z\u2208\u2102\u2216\u211d, p_n(z)p_n(z) has a limit as n\u2192\u221e. Moreover, we show that there are non-Szeg\u0151 class J's for which this holds.", "date": "2012-04", "date_type": "published", "publication": "Constructive Approximation", "volume": "35", "number": "2", "publisher": "Springer", "pagerange": "259-272", "id_number": "CaltechAUTHORS:20120319-093342145", "issn": "0176-4276", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120319-093342145", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Danish Natural Science Research Council", "grant_number": "09-064947" }, { "agency": "NSF", "grant_number": "DMS-0968856" }, { "agency": "NSF", "grant_number": "DMS-0965411" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00365-012-9152-4", "primary_object": { "basename": "1108.0183", "url": "https://authors.library.caltech.edu/records/wfg1j-aye22/files/1108.0183" }, "pub_year": "2012", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/td2h0-tae78", "eprint_id": 88631, "eprint_status": "archive", "datestamp": "2023-08-19 10:34:20", "lastmod": "2026-03-07 16:31:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Lyons-R", "name": { "family": "Lyons", "given": "Richard" } }, { "id": "Smith-S", "name": { "family": "Smith", "given": "Steve" } }, { "id": "Solomon-R", "name": { "family": "Solomon", "given": "Ronald" } } ] }, "title": "2012 Steele Prizes", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2012 American Mathematical Society.", "abstract": "The 2012 Leroy P. Steele Prize for Mathematical\nExposition is awarded to Michael Aschbacher,\nRichard Lyons, Steve Smith, and Ronald Solomon\nfor their work, The Classification of Finite Simple\nGroups: Groups of Characteristic 2 Type, Mathematical\nSurveys and Monographs, 172, American\nMathematical Society, Providence, RI, 2011. In this\npaper, the authors, who have done foundational\nwork in the classification of finite simple groups,\noffer to the general mathematical public an articulate\nand readable exposition of the classification\nof characteristic 2 type groups.", "date": "2012-04", "date_type": "published", "publication": "Notices of the American Mathematical Society", "volume": "59", "number": "4", "publisher": "American Mathematical Society", "pagerange": "563-566", "id_number": "CaltechAUTHORS:20180807-133142929", "issn": "0002-9920", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180807-133142929", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/noti826", "pub_year": "2012", "author_list": "Aschbacher, Michael; Lyons, Richard; et al." }, { "id": "https://authors.library.caltech.edu/records/fbbgs-7rb71", "eprint_id": 29463, "eprint_status": "archive", "datestamp": "2023-08-19 10:15:32", "lastmod": "2026-04-10 17:09:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakayama-Yu", "name": { "family": "Nakayama", "given": "Yu" }, "orcid": "0000-0002-1747-5147" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Comments on worldsheet description of the Omega background", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Elsevier B.V. \n\nReceived 27 July 2011; received in revised form 4 November 2011; accepted 8 November 2011. Available online 12 November 2011. \n\nWe thank Nathan Berkovits, Nikita Nekrasov, Jaewon Song, and Cumrun Vafa for discussion. This work is supported in part by US Department of Energy grant DE-FG03-92-ER40701 and by the World Premier International Research Center Initiative of MEXT of Japan. H.O. is also supported in part by Grant-in-Aid for Scientific Research C-20540256 and C-23540285 of Japan Society for the Promotion of Science.\n\n

Submitted - 1106.5503.pdf

", "abstract": "Nekrasov's partition function is defined on a flat bundle of R^4 over S^1 called the Omega background. When the fibration is self-dual, the partition function is known to be equal to the topological string partition function, which computes scattering amplitudes of self-dual gravitons and graviphotons in type II superstring compactified on a Calabi\u2013Yau manifold. We propose a generalization of this correspondence when the fibration is not necessarily self-dual.", "date": "2012-03-11", "date_type": "published", "publication": "Nuclear Physics B", "volume": "856", "number": "2", "publisher": "Elsevier", "pagerange": "342-359", "id_number": "CaltechAUTHORS:20120224-134308688", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120224-134308688", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-20540256" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-23540285" } ] }, "other_numbering_system": { "items": [ { "id": "68-2837", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2011.11.010", "primary_object": { "basename": "1106.5503.pdf", "url": "https://authors.library.caltech.edu/records/fbbgs-7rb71/files/1106.5503.pdf" }, "pub_year": "2012", "author_list": "Nakayama, Yu and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/60yc2-spk66", "eprint_id": 97821, "eprint_status": "archive", "datestamp": "2023-08-19 10:11:12", "lastmod": "2026-04-10 19:25:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "On the Ramsey multiplicity of complete graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 J\u00e1nos Bolyai Mathematical Society and Springer Verlag.\n\nReceived 30 November 2007; first online 06 June 2012.\n\nThe author is supported by a research fellowship at St John's College, Cambridge, but was also supported for part of the time that this work was being carried out by the MRTN-CT-2004-511953 project at the Alfr\u00e9d R\u00e9nyi Institute of Mathematics in Budapest.\n\n

Submitted - 0711.4999.pdf

", "abstract": "We show that, for n large, there must exist at least \n\n(n^t)/(C^((1+o(1))t^2)) \n\nmonochromatic K_(t)s in any two-colouring of the edges of K_n, where C \u2248 2.18 is an explicitly defined constant. The old lower bound, due to Erd\u0151s [2], and based upon the standard bounds for Ramsey's theorem, is \n\n(n^t)/(4^((1+o(1))t^2)).", "date": "2012-03", "date_type": "published", "publication": "Combinatorica", "volume": "32", "number": "2", "publisher": "Springer", "pagerange": "171-186", "id_number": "CaltechAUTHORS:20190812-162958767", "issn": "0209-9683", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958767", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" }, { "agency": "Marie Curie Fellowship", "grant_number": "MRTN-CT-2004-511953" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00493-012-2465-x", "primary_object": { "basename": "0711.4999.pdf", "url": "https://authors.library.caltech.edu/records/60yc2-spk66/files/0711.4999.pdf" }, "pub_year": "2012", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/9saf3-dsg11", "eprint_id": 31651, "eprint_status": "archive", "datestamp": "2023-08-19 10:07:40", "lastmod": "2026-04-10 01:28:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Lower signalizer lattices in alternating and symmetric groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 de Gruyter.\n\nReceived September 18, 2010; revised November 28, 2011.\nPublished Online: 06/03/2012.\nCommunicated by Robert M. Guralnick.\nThis work was partially supported by NSF DMS-0504852 and NSF DMS-0969009.\n\n

Published - Aschbacher2012p18270J_Group_Theory.pdf

", "abstract": "We prove that the subgroup lattices of finite alternating and symmetric groups\ndo not contain so-called lower signalizer lattices in the class D\ufffd\u0394. This result is one step\nin a program to show that the lattices in the class D\ufffd\u0394 are not isomorphic to an interval in\nthe subgroup lattice of any finite group.", "date": "2012-03", "date_type": "published", "publication": "Journal of Group Theory", "volume": "15", "number": "2", "publisher": "Walter de Gruyter", "pagerange": "151-225", "id_number": "CaltechAUTHORS:20120525-104153526", "issn": "1433-5883", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120525-104153526", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" }, { "agency": "NSF", "grant_number": "DMS-0969009" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/jgt-2011-0112", "primary_object": { "basename": "Aschbacher2012p18270J_Group_Theory.pdf", "url": "https://authors.library.caltech.edu/records/9saf3-dsg11/files/Aschbacher2012p18270J_Group_Theory.pdf" }, "pub_year": "2012", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/2dtqs-sey14", "eprint_id": 31436, "eprint_status": "archive", "datestamp": "2023-08-22 04:52:12", "lastmod": "2026-04-10 17:34:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" } ] }, "title": "A-polynomial, B-model, and quantization", "ispublished": "pub", "full_text_status": "public", "keywords": "Matrix Models; Non-Commutative Geometry; Chern-Simons Theories; Topological Strings", "note": "\u00a9 2012 Springer, Part of Springer Science+Business Media.\nPublished for SISSA by Springer.\nThis article is distributed under the terms of the Creative Commons\nAttribution License which permits any use, distribution and reproduction in any medium,\nprovided the original author(s) and source are credited.\nReceived: November 2, 2011; accepted: January 31, 2012; published: February 20, 2012.\n\nIt is pleasure to thank Vincent Bouchard, Tudor Dimofte, Nathan Dunfield, Bertrand\nEynard, Maxim Kontsevich, and Don Zagier for helpful discussions and correspondence.\nThe work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and\nin part by NSF Grant PHY-0757647. The research of P.S. is supported by the DOE\ngrant DE-FG03-92-ER40701FG-02 and the European Commission under the Marie-Curie\nInternational Outgoing Fellowship Programme. Opinions and conclusions expressed here\nare those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - Gukov2012p18084J_High_Energy_Phys.pdf

", "abstract": "Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly in a suitable semi-classical limit, as \u0127 \u2192 0, and becomes non-commutative or \"quantum\" away from this limit. For a classical curve defined by the zero locus of a polynomial A(x, y), we provide a construction of its non-commutative counterpart \u00c2(^x, ^y) using the technique of the topological recursion. This leads to a powerful and systematic algorithm for computing \u00a0that, surprisingly, turns out to be much simpler than any of the existent methods. In particular, as a bonus feature of our approach comes a curious observation that, for all curves that come from knots or topological strings, their non-commutative counterparts can be determined just from the first few steps of the topological recursion. We also propose a Ktheory criterion for a curve to be \"quantizable,\" and then apply our construction to many examples that come from applications to knots, strings, instantons, and random matrices.", "date": "2012-02", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2012", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 070", "id_number": "CaltechAUTHORS:20120511-113608838", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120511-113608838", "rights": "This article is distributed under the terms of the Creative Commons\nAttribution License which permits any use, distribution and reproduction in any medium,\nprovided the original author(s) and source are credited.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Marie Curie Fellowship" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP02(2012)070", "primary_object": { "basename": "Gukov2012p18084J_High_Energy_Phys.pdf", "url": "https://authors.library.caltech.edu/records/2dtqs-sey14/files/Gukov2012p18084J_High_Energy_Phys.pdf" }, "pub_year": "2012", "author_list": "Gukov, Sergei and Su\u0142kowski, Piotr" }, { "id": "https://authors.library.caltech.edu/records/5v8pf-zyz48", "eprint_id": 29716, "eprint_status": "archive", "datestamp": "2023-08-19 09:46:41", "lastmod": "2026-04-10 01:28:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Springer-Verlag. Received: 26 January 2011. Accepted: 15 February 2011. Published online: 18 August 2011. Communicated by S. Zelditch. The contribution to the preparation of this paper by Wendy Baratta and James Saunderson is acknowledged. This work was supported by the Australian Research Council.\n\n

Submitted - 1011.1654.pdf

", "abstract": "We characterize averages of \u220f^N_(l=1)\u2502x\u2212t_l\u2502^(\u0251\u22121) with respect to the Selberg density, further constrained so that t_l \u0454 [0,x](l=1,...,q) and t_l \u0454 [x,1](l=q^+1,...,N), in terms of a basis of solutions of a particular Fuchsian matrix differential equation. By making use of the Dotsenko-Fateev integrals, the explicit form of the connection matrix from the Frobenius type power series basis to this basis is calculated, thus allowing us to explicitly compute coefficients in the power series expansion of the averages. From these we are able to compute power series for the marginal distributions of the t_j(j=1,...,N) . In the case q = 0 and \u03b1 < 1 we compute the explicit leading order term in the x \u2192 0 asymptotic expansion, which is of interest to the study of an effect known as singularity dominated strong fluctuations. In the case q = 0 and \u0251 \u0454 Z^+, and with the absolute values removed, the average is a polynomial, and we demonstrate that its zeros are highly structured.", "date": "2012-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "309", "number": "3", "publisher": "Springer", "pagerange": "771-792", "id_number": "CaltechAUTHORS:20120314-084236569", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120314-084236569", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-011-1305-y", "primary_object": { "basename": "1011.1654.pdf", "url": "https://authors.library.caltech.edu/records/5v8pf-zyz48/files/1011.1654.pdf" }, "pub_year": "2012", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/xargs-prw72", "eprint_id": 29131, "eprint_status": "archive", "datestamp": "2023-08-19 09:21:00", "lastmod": "2026-03-09 21:40:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Pierpaoli-Elena", "name": { "family": "Pierpaoli", "given": "Elena" }, "orcid": "0000-0002-7957-8993" }, { "id": "Teh-Kevin", "name": { "family": "Teh", "given": "Kevin" } } ] }, "title": "The Coupling of Topology and Inflation in Noncommutative Cosmology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Springer-Verlag. \n\nReceived: 9 December 2010. Accepted: 26 April 2011. Published online: 4 October 2011. Communicated by A. Connes.\n\n

Submitted - 1012.0780.pdf

", "abstract": "We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained in the model from the nonperturbative form of the spectral action is sensitive not only to the geometry (flat or positively curved) of the universe, but also to the different possible non-simply connected topologies. We show this by explicitly computing the nonperturbative spectral action for some candidate flat cosmic topologies given by Bieberbach manifolds and showing that the resulting inflation potential differs from that of the flat torus by a multiplicative factor, similarly to what happens in the case of the spectral action of the spherical forms in relation to the case of the 3-sphere. We then show that, while the slow-roll parameters differ between the spherical and flat manifolds but do not distinguish different topologies within each class, the power spectra detect the different scalings of the slow-roll potential and therefore distinguish between the various topologies, both in the spherical and in the flat case.", "date": "2012-01", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "309", "number": "2", "publisher": "Springer", "pagerange": "341-369", "id_number": "CaltechAUTHORS:20120203-142242831", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120203-142242831", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "TAPIR" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-011-1352-4", "primary_object": { "basename": "1012.0780.pdf", "url": "https://authors.library.caltech.edu/records/xargs-prw72/files/1012.0780.pdf" }, "pub_year": "2012", "author_list": "Marcolli, Matilde; Pierpaoli, Elena; et al." }, { "id": "https://authors.library.caltech.edu/records/7zy71-zzw53", "eprint_id": 97847, "eprint_status": "archive", "datestamp": "2023-08-22 04:39:40", "lastmod": "2026-03-07 16:33:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "H\u00e0n-Hi\u00eap", "name": { "family": "H\u00e0n", "given": "Hi\u00eap" } }, { "id": "Person-Y", "name": { "family": "Person", "given": "Yury" } }, { "id": "Schacht-M", "name": { "family": "Schacht", "given": "Mathias" } } ] }, "title": "Weak quasi-randomness for uniform hypergraphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Hypergraphs; quasi\u2010randomness; regularity lemma; forcing conjecture for graphs", "note": "\u00a9 2011 Wiley. \n\nIssue online 23 November 2011; version of record online 10 November 2011; manuscript accepted 25 November 2010; manuscript received 30 March 2009.", "abstract": "We study quasi\u2010random properties of k\u2010uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung\u2010Graham\u2010Wilson theorem for quasi\u2010random graphs.\n\nMoreover, let K_k be the complete graph on k vertices and M(k) the line graph of the graph of the k\u2010dimensional hypercube. We will show that the pair of graphs (K_(k),M(k)) has the property that if the number of copies of both K_k and M(k) in another graph G are as expected in the random graph of density d, then G is quasi\u2010random (in the sense of the Chung\u2010Graham\u2010Wilson theorem) with density close to d.", "date": "2012-01", "date_type": "published", "publication": "Random Structures & Algorithms", "volume": "40", "number": "1", "publisher": "Wiley", "pagerange": "1-38", "id_number": "CaltechAUTHORS:20190812-163001217", "issn": "1042-9832", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001217", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.20389", "pub_year": "2012", "author_list": "Conlon, David; H\u00e0n, Hi\u00eap; et al." }, { "id": "https://authors.library.caltech.edu/records/fp6pr-q3t12", "eprint_id": 28350, "eprint_status": "archive", "datestamp": "2023-08-22 04:33:17", "lastmod": "2026-03-09 22:11:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Poonen-B", "name": { "family": "Poonen", "given": "Bjorn" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Random maximal isotropic subspaces and Selmer groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Selmer group; Shafarevich-Tate group; maximal isotropic; quadratic space; Weil pairing; theta characteristic", "note": "\u00a9 2011 American Mathematical Society. The copyright for this article reverts to public domain after 28 years from publication. \n\nReceived by editor(s): September 21, 2010; Received by editor(s) in revised form: April 20, 2011, and May 20, 2011; Posted: July 12, 2011. \n\nThe first author was partially supported by NSF grant DMS-0841321. \n\nThe authors thank Christophe Delaunay, Benedict Gross, Robert Guralnick, Karl Rubin, and the referee for comments.\n\n

Published - Poonen2012p16424J_Am_Math_Soc.pdf

Submitted - 1009.0287.pdf

", "abstract": "Under suitable hypotheses, we construct a probability measure on the set of closed maximal isotropic subspaces of a locally compact quadratic space over F_p. A random subspace chosen with respect to this measure is discrete with probability 1, and the dimension of its intersection with a fixed compact open maximal isotropic subspace is a certain nonnegative-integer-valued random variable.\nWe then prove that the p-Selmer group of an elliptic curve is naturally the intersection of a discrete maximal isotropic subspace with a compact open maximal isotropic subspace in a locally compact quadratic space over F_p. By modeling the first subspace as being random, we can explain the known phenomena regarding distribution of Selmer ranks, such as the theorems of Heath-Brown, Swinnerton-Dyer, and Kane for 2-Selmer groups in certain families of quadratic twists, and the average size of 2- and 3-Selmer groups as computed by Bhargava and Shankar. Our model is compatible with Delaunay's heuristics for p-torsion in Shafarevich-Tate groups, and predicts that the average rank of elliptic curves over a fixed number field is at most 1/2. Many of our results generalize to abelian varieties over global fields.", "date": "2012-01", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "25", "number": "1", "publisher": "American Mathematical Society", "pagerange": "245-269", "id_number": "CaltechAUTHORS:20111207-112922811", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111207-112922811", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0841321" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-2011-00710-8", "primary_object": { "basename": "1009.0287.pdf", "url": "https://authors.library.caltech.edu/records/fp6pr-q3t12/files/1009.0287.pdf" }, "related_objects": [ { "basename": "Poonen2012p16424J_Am_Math_Soc.pdf", "url": "https://authors.library.caltech.edu/records/fp6pr-q3t12/files/Poonen2012p16424J_Am_Math_Soc.pdf" } ], "pub_year": "2012", "author_list": "Poonen, Bjorn and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/a54r5-26k02", "eprint_id": 77092, "eprint_status": "archive", "datestamp": "2023-08-22 04:39:36", "lastmod": "2026-03-09 02:14:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Loss-M", "name": { "family": "Loss", "given": "Michael" } } ] }, "title": "Hardy-Sobolev-Maz'ya inequalities for arbitrary domains", "ispublished": "pub", "full_text_status": "public", "keywords": "Sobolev inequality; Hardy inequality; Schr\u00f6dinger operator", "note": "\u00a9 2011 Elsevier Masson SAS. \n\nReceived 11 February 2011; Available online 14 April 2011. \n\nThe work of M.L. is partially funded by NSF grant DMS\u201301304.\n\n

Submitted - 1102.4394.pdf

", "abstract": "We prove a Hardy-Sobolev-Maz'ya inequality for arbitrary domains \u03a9 \u2282 R^N with a constant depending only on the dimension N \u2265 3. In particular, for convex domains this settles a conjecture by Filippas, Maz'ya and Tertikas. As an application we derive Hardy-Lieb-Thirring inequalities for eigenvalues of Schr\u00f6dinger operators on domains.", "date": "2012-01", "date_type": "published", "publication": "Journal de Math\u00e9matiques Pures et Appliqu\u00e9es", "volume": "97", "number": "1", "publisher": "Elsevier", "pagerange": "39-54", "id_number": "CaltechAUTHORS:20170501-085309159", "issn": "0021-7824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-085309159", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-901304" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.matpur.2011.04.004", "primary_object": { "basename": "1102.4394.pdf", "url": "https://authors.library.caltech.edu/records/a54r5-26k02/files/1102.4394.pdf" }, "pub_year": "2012", "author_list": "Frank, Rupert L. and Loss, Michael" }, { "id": "https://authors.library.caltech.edu/records/fbr4r-txt06", "eprint_id": 77077, "eprint_status": "archive", "datestamp": "2023-08-19 09:28:20", "lastmod": "2026-03-09 02:16:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Sharp constants in several inequalities on the Heisenberg group", "ispublished": "pub", "full_text_status": "public", "keywords": "Hardy-Littlewood-Sobolev inequality, Heisenberg group, sharp constants", "note": "\u00a9 2011 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 8 March 2010; Accepted: 16 November 2011; Published online: 1 July 2012. \n\nSupport by U.S. NSF grant PHY 1068285 (R.L.F.) and PHY 0965859 (E.H.L.) is gratefully acknowledged.\n\n

Published - annals-v176-n1-p06-p.pdf

Submitted - 1009.1410.pdf

", "abstract": "We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to Jerison-Lee more than twenty years ago. From these inequalities we obtain the sharp constants for their duals, which are the Sobolev inequalities for the Laplacian and conformally invariant fractional Laplacians. By considering limiting cases of these inequalities sharp constants for the analogues of the Onofri and log-Sobolev inequalities on H^n are obtained. The methodology is completely different from that used to obtain the R^n inequalities and can be (and has been) used to give a new, rearrangement free, proof of the HLS inequalities.", "date": "2012-01", "date_type": "published", "publication": "Annals of Mathematics", "volume": "176", "number": "1", "publisher": "Princeton University", "pagerange": "349-381", "id_number": "CaltechAUTHORS:20170501-064349426", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-064349426", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" }, { "agency": "NSF", "grant_number": "PHY-0965859" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2012.176.1.6", "primary_object": { "basename": "1009.1410.pdf", "url": "https://authors.library.caltech.edu/records/fbr4r-txt06/files/1009.1410.pdf" }, "related_objects": [ { "basename": "annals-v176-n1-p06-p.pdf", "url": "https://authors.library.caltech.edu/records/fbr4r-txt06/files/annals-v176-n1-p06-p.pdf" } ], "pub_year": "2012", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/dqgqx-nvk43", "eprint_id": 35632, "eprint_status": "archive", "datestamp": "2023-08-22 04:30:07", "lastmod": "2026-03-09 20:34:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Soki\u0107-M", "name": { "family": "Soki\u0107", "given": "Miodrag" } } ] }, "title": "Dynamical properties of the automorphism groups of the random poset and random distributive lattice", "ispublished": "pub", "full_text_status": "restricted", "keywords": "automorphism groups; amenability; random poset; random distributive lattice; universal minimal flow; Ramsey theory", "note": "\u00a9 2012 Instytut Matematyczny PAN.\n\nReceived 24 October 2011; in revised form 7 June 2012.\n\nThe research of the rst author was partially supported by NSF Grant DMS-0968710.", "abstract": "A method is developed for proving non-amenability of certain automorphism groups of countable structures and is used to show that the automorphism groups of the random poset and random distributive lattice are not amenable. The universal minimal flow of the automorphism group of the random distributive lattice is computed as a canonical space of linear orderings but it is also shown that the class of finite distributive lattices does not admit hereditary order expansions with the Amalgamation Property.", "date": "2012", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "218", "number": "1", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "69-94", "id_number": "CaltechAUTHORS:20121126-103335875", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121126-103335875", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968710" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4064/fm218-1-4", "pub_year": "2012", "author_list": "Kechris, Alexander S. and Soki\u0107, Miodrag" }, { "id": "https://authors.library.caltech.edu/records/pbr1f-jad54", "eprint_id": 33284, "eprint_status": "archive", "datestamp": "2023-08-19 09:10:18", "lastmod": "2026-03-08 18:14:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "M." }, "orcid": "0000-0002-4523-9467" }, { "id": "Moring-B", "name": { "family": "Morin", "given": "B." } } ] }, "title": "On the Weil-\u00c9tale Topos of Regular Arithmetic Schemes", "ispublished": "pub", "full_text_status": "restricted", "note": "The first author is supported by grant DMS-0701029 from\nthe National Science Foundation. He would also like to thank Spencer Bloch\nfor a helpful discussion about the material in section 10 and the MPI Bonn for\nits hospitality during the final preparation of this paper.", "abstract": "We define and study a Weil-\u00e9tale topos for any regular,\nproper scheme X over Spec(Z) which has some of the properties suggested by Lichtenbaum for such a topos. In particular, the cohomology with \u02dcR-coefficients has the expected relation to \u03b6(X, s) at s = 0 if the Hasse-Weil L-functions L(h^(i)(X_(Q)), s) have the expected meromorphic\ncontinuation and functional equation. If X has characteristic p the cohomology with Z-coefficients also has the expected relation to \u03b6(X, s) and our cohomology groups recover those previously studied by Lichtenbaum and Geisser.", "date": "2012", "date_type": "published", "publication": "Documenta Mathematica", "volume": "17", "publisher": "Universit\u00e4t Bielefeld Fakultat Mathematik", "pagerange": "313-400", "id_number": "CaltechAUTHORS:20120817-095043547", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120817-095043547", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0701029" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "2012", "author_list": "Flach, M. and Morin, B." }, { "id": "https://authors.library.caltech.edu/records/nbhb2-rc397", "eprint_id": 37237, "eprint_status": "archive", "datestamp": "2023-08-19 09:14:09", "lastmod": "2026-03-09 20:29:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Trigonometric series and set theory", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2012 Polskie Towarzystwo Matematyczne.\nWork on this paper was partially supported by NSF Grant\nDMS-0968710. I would like to thank Ben Miller and Slawek Solecki for\nvaluable comments and other help in the preparation of this paper.", "abstract": "This is a short historical survey concerning the interactions between the\ntheory of trigonometric series and descriptive set theory. We concentrate\nhere on the area related to problems of uniqueness for trigonometric\nseries. Detailed historical and bibliographical references can be found in the\nbooks and survey papers listed at the end.", "date": "2012", "date_type": "published", "publication": "Roczniki. Seria 2: Wiadomo\u015bci Matematyczne", "volume": "48", "number": "2", "publisher": "Polskie Towarzystwo Matematyczne", "pagerange": "109-118", "id_number": "CaltechAUTHORS:20130301-104948205", "issn": "2080-5519", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130301-104948205", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968710" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "2012", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/853k8-bb920", "eprint_id": 39761, "eprint_status": "archive", "datestamp": "2023-08-19 09:15:31", "lastmod": "2026-03-09 02:19:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fuji-Hiroyuki", "name": { "family": "Fuji", "given": "Hiroyuki" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" }, { "id": "Awata-Hidetoshi", "name": { "family": "Awata", "given": "Hidetoshi" } } ] }, "title": "Volume conjecture: refined and categorified", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2012 International Press.\n\nWe thank H.-J. Chung and R.H. Dijkgraaf for useful discussions during the early stages of this work. We thank M. Aganagic, A. Iqbal, D. Krefl, and Sh. Shakirov for discussions and comments. The authors would also like to\nthank the following institutions for their hospitality: California Institute of Technology (H.F.), the Banff International Research Station (H.F., P.S.), and the Simons Center for Geometry and Physics (H.F., S.G., P.S.). The\nwork of H.F. is supported by the Grant-in-Aid for Young Scientists (B) [#21740179] from the Japan Ministry of Education, Culture, Sports, Science and Technology, and the Grant-in-Aid for Nagoya University Global COE Program, \"Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos.\" The work of S.G. is supported in part by DOE Grant DE-FG03-92-ER40701FG-02 and in part by NSF Grant PHY-0757647. The research of P.S. is supported by the DOE grant\nDE-FG03-92-ER40701FG-02, the European Commission under the Marie-Curie International Outgoing Fellowship Programme, and the Foundation for Polish Science. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - ATMP-2012-0016-0006-00026542.pdf

Submitted - 1203.2182v1.pdf

", "abstract": "The generalized volume conjecture relates asymptotic behavior of the colored Jones polynomials to objects naturally defined on an algebraic curve, the zero locus of the A-polynomial A(x,y). Another \"family version\" of the volume conjecture depends on a quantization parameter, usually denoted q or \u0127; this quantum volume conjecture (also known as the AJ-conjecture) can be stated in a form of a q-difference equation that annihilates the colored Jones polynomials and SL(2,C) Chern\u2013 Simons partition functions. We propose refinements/categorifications of both conjectures that include an extra deformation parameter t and describe similar properties of homological knot invariants and refined BPS invariants. Much like their unrefined/decategorified predecessors, that correspond to t=\u22121, the new volume conjectures involve objects naturally defined on an algebraic curve A^(ref)(x,y;t) obtained by a particular deformation of the A-polynomial, and its quantization \u00c2^(ref)(x\u02c6,\u0177;q,t). We compute both classical and quantum t-deformed curves in a number of examples coming from colored knot homologies and refined BPS invariants.", "date": "2012", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "16", "number": "6", "publisher": "International Press", "pagerange": "1669-1777", "id_number": "CaltechAUTHORS:20130805-101410619", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130805-101410619", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)", "grant_number": "21740179" }, { "agency": "Nagoya University" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701FG-02" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Foundation for Polish Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1203.2182", "primary_object": { "basename": "1203.2182v1.pdf", "url": "https://authors.library.caltech.edu/records/853k8-bb920/files/1203.2182v1.pdf" }, "related_objects": [ { "basename": "ATMP-2012-0016-0006-00026542.pdf", "url": "https://authors.library.caltech.edu/records/853k8-bb920/files/ATMP-2012-0016-0006-00026542.pdf" } ], "pub_year": "2012", "author_list": "Fuji, Hiroyuki; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/xhs25-gsc63", "eprint_id": 28438, "eprint_status": "archive", "datestamp": "2023-08-19 04:04:23", "lastmod": "2026-04-10 23:28:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Berkooz-M", "name": { "family": "Berkooz", "given": "Micha" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "A Comment on Nonsupersymmetric Fixed Points and Duality at large N", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 International Press. \n\nWe would like to thank O. Aharony, S. Kachru, E. Silverstein, and M. Strassler for useful discussions. The work of MB is supported by NSF grant PHY-9513835. The work of AK is supported by DOE grant DE-FG02-90ER40542.\n\n

Published - BERatmp99.pdf

Submitted - BERatmp99_preprint.pdf

", "abstract": "We review some of the problems associated with deriving field theoretic results from nonsupersymmetric AdS, focusing on how to control the behavior of the field theory along the flat directions. We discuss an example in which the origin of the moduli space remains a stable vacuum at finite N, and argue that it corresponds to an interacting CFT in three dimensions. Associated to this fixed point is a statement of nonsupersymmetric duality. Because 1/N corrections may change the global picture of the RG flow, the statement of duality is much weaker than in the supersymmetric case.", "date": "2011-12-16", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "3", "number": "3", "publisher": "International Press", "pagerange": "479-494", "id_number": "CaltechAUTHORS:20111213-095612198", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111213-095612198", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.1999.v3.n3.a2", "primary_object": { "basename": "BERatmp99_preprint.pdf", "url": "https://authors.library.caltech.edu/records/xhs25-gsc63/files/BERatmp99_preprint.pdf" }, "related_objects": [ { "basename": "BERatmp99.pdf", "url": "https://authors.library.caltech.edu/records/xhs25-gsc63/files/BERatmp99.pdf" } ], "pub_year": "2011", "author_list": "Berkooz, Micha and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/jhnm6-zqs39", "eprint_id": 28935, "eprint_status": "archive", "datestamp": "2023-08-19 08:46:34", "lastmod": "2026-04-10 23:15:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "Matthias" }, "orcid": "0000-0002-4523-9467" } ] }, "title": "On the cyclotomic main conjecture for the prime 2", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Walter de Gruyter Berlin. Received: 30/01/2009; Revised: 20/08/2010; Published Online: 25/12/2011. The author was supported by grant DMS-0701029 from the National Science Foundation.\n\n

Published - Flach2011p16840J_Reine_Angew_Math.pdf

", "abstract": "We complete the proof of the equivariant Tamagawa number conjecture for Tate motives over absolutely abelian fields by proving a refined cyclotomic main conjecture at the prime 2.", "date": "2011-12", "date_type": "published", "publication": "Journal F\u00fcr Die Reine und Angewandte Mathematik", "volume": "661", "publisher": "Walter de Gruyter", "pagerange": "1-36", "id_number": "CaltechAUTHORS:20120124-104112461", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120124-104112461", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0701029" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1515/CRELLE.2011.082", "primary_object": { "basename": "Flach2011p16840J_Reine_Angew_Math.pdf", "url": "https://authors.library.caltech.edu/records/jhnm6-zqs39/files/Flach2011p16840J_Reine_Angew_Math.pdf" }, "pub_year": "2011", "author_list": "Flach, Matthias" }, { "id": "https://authors.library.caltech.edu/records/6zq6y-a4z78", "eprint_id": 28768, "eprint_status": "archive", "datestamp": "2023-08-19 08:45:22", "lastmod": "2026-04-11 00:19:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Quantization via mirror symmetry", "ispublished": "pub", "full_text_status": "public", "keywords": "mirror symmetry, derived category, branes, quantization, symplectic geometry", "note": "\u00a9 2011 The Mathematical Society of Japan and Springer. \n\nReceived: 5 November 2010; Revised: 1 November 2011; Accepted: 8 November 2011. Published online: 25 December 2011. \n\nThis article is based on the 8th Takagi Lectures that the author delivered at Research Institute for Mathematical Sciences, Kyoto University on November 23, 2010. I would like to thank the organizing committee of the Takagi Lectures for inviting me, and to acknowledge helpful discussions with E. Frenkel, T. Hausel, and E. Witten.\nI also would like to thank E. Witten for collaboration on the A-model approach to quantization reviewed in Section 2. Special thanks are in order to referees for careful reading of the manuscript and suggesting many useful improvements.\nThis work is supported in part by DOE Grant DE-FG03-92-ER40701 and in part by NSF Grant PHY-0757647. Opinions and conclusions expressed here are those of the author and do not necessarily reflect the views of funding agencies.\n\n

Submitted - 1011.2218v2.pdf

", "abstract": "When combined with mirror symmetry, the A-model approach to quantization leads to a fairly simple and tractable problem. The most interesting part of the problem then becomes finding the mirror of the coisotropic brane. We illustrate how it can be addressed in a number of\ninteresting examples related to representation theory and gauge theory, in which mirror geometry is naturally associated with the Langlands dual group. Hyperholomorphic sheaves and (B, B, B) branes play an important role in the B-model approach to quantization.", "date": "2011-12", "date_type": "published", "publication": "Japanese Journal of Mathematics", "volume": "6", "number": "2", "publisher": "Springer", "pagerange": "65-119", "id_number": "CaltechAUTHORS:20120113-091504097", "issn": "0289-2316", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120113-091504097", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11537-011-1033-2", "primary_object": { "basename": "1011.2218v2.pdf", "url": "https://authors.library.caltech.edu/records/6zq6y-a4z78/files/1011.2218v2.pdf" }, "pub_year": "2011", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/2yb7y-r8q43", "eprint_id": 29377, "eprint_status": "archive", "datestamp": "2023-08-22 04:17:48", "lastmod": "2026-04-11 00:12:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Kim-Hyungchul", "name": { "family": "Kim", "given": "Hyungchul" } }, { "id": "Park-Jaemo", "name": { "family": "Park", "given": "Jaemo" } } ] }, "title": "Dualities for 3d theories with tensor matter", "ispublished": "pub", "full_text_status": "public", "keywords": "Field Theories in Lower Dimensions; Duality in Gauge Field Theories; Chern-Simons Theories", "note": "\u00a9 2011 SISSA. \nPublished for SISSA by Springer.\nReceived: October 20, 2011; accepted: December 7, 2011; published: December 23, 2011.\n\nA.K. is supported in part by the DOE grant DE-FG02-92ER40701. J.P. is supported by the KOSEF Grant R01-2008-000-20370-0, the National Research Foundation of Korea (NRF) Grants No. 2009-0085995 and 2005-0049409 through the Center for Quantum Spacetime (CQUeST) of Sogang University. J.P. also appreciates APCTP for its stimulating environment for research. A.K. and J.P. acknowledge Simons Summer Workshop on Mathematics and Physics 2011 for hospitality while the current work was initiated.\n\n

Submitted - 1110.2547v2.pdf

", "abstract": "We study dualities for N = 2 3d Chern-Simons matter theories with gauge groups U/Sp/O, matter in the two-index tensor representations (adjoint/symmetric/antisymmetric)\nin addition to the fundamental representation, and a superpotential. These dualities are analogous to Kutasov-Schwimmer-Seiberg dualities in 4d. We test them by\ncomputing the superconformal index and the partition function on S^3 for many dual pairs and find perfect agreement. In some cases we find a simple dual description for theories with tensor matter and no superpotential, thereby generalizing the \"Duality Appetizer\" of Jafferis and Yin to an infinite class of theories. We also investigate nonperturbative truncation of the chiral ring proposed in the context of 4d dualities.", "date": "2011-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2011", "number": "12", "publisher": "Springer", "pagerange": "87", "id_number": "CaltechAUTHORS:20120217-154342890", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120217-154342890", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" }, { "agency": "Korea Science and Engineering Foundation (KOSEF)", "grant_number": "R01-2008-000-20370-0" }, { "agency": "National Research Foundation of Korea", "grant_number": "2009-0085995" }, { "agency": "National Research Foundation of Korea", "grant_number": "2005-0049409" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP12(2011)087", "primary_object": { "basename": "1110.2547v2.pdf", "url": "https://authors.library.caltech.edu/records/2yb7y-r8q43/files/1110.2547v2.pdf" }, "pub_year": "2011", "author_list": "Kapustin, Anton; Kim, Hyungchul; et al." }, { "id": "https://authors.library.caltech.edu/records/fxgbh-qhn04", "eprint_id": 28396, "eprint_status": "archive", "datestamp": "2023-08-22 04:12:46", "lastmod": "2026-04-10 22:43:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Hollands-L", "name": { "family": "Hollands", "given": "Lotte" } } ] }, "title": "Vortex Counting and Lagrangian 3-Manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "gauge theory; vortex equations; BPS invariants; D-branes; conformal field theory", "note": "\u00a9 2011 Springer. \n\nReceived: 3 March 2011; Revised: 30 August 2011; Accepted: 9 September 2011. Published online: 5 October 2011. \n\nWe would like to thank M. Aganagic, C. Beem, A. Borodin, A. Braverman, A. Gorsky, C. Keller, H. Nakajima, J. Song, and E. Witten for very useful discussions, and C. Vafa for collaboration at an earlier stage of this project. The work of SG and LH is supported in part by NSF grant PHY-0757647. The work of SG\nis also supported in part by DOE grant DE-FG03-92-ER40701 and in part by the Alfred P. Sloan Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Submitted - 1006.0977v1.pdf

", "abstract": "To every 3-manifold M one can associate a two-dimensional N=(2,2) supersymmetric field theory by compactifying five-dimensional N=2 super-Yang\u2013Mills theory on M. This system naturally appears in the study of half-BPS surface operators in four-dimensional N=2 gauge theories on one hand, and in the geometric approach to knot homologies, on the other. We study the relation between vortex counting in such two-dimensional N=(2,2) supersymmetric field theories and the refined BPS invariants of the dual geometries. In certain cases, this counting can also be mapped to the computation of degenerate conformal blocks in two-dimensional CFT's. Degenerate limits of vertex operators\nin CFT receive a simple interpretation via geometric transitions in BPS counting.", "date": "2011-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "98", "number": "3", "publisher": "Springer", "pagerange": "225-287", "id_number": "CaltechAUTHORS:20111209-105547167", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111209-105547167", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-011-0531-8", "primary_object": { "basename": "1006.0977v1.pdf", "url": "https://authors.library.caltech.edu/records/fxgbh-qhn04/files/1006.0977v1.pdf" }, "pub_year": "2011", "author_list": "Dimofte, Tudor; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/adjag-pfq98", "eprint_id": 27239, "eprint_status": "archive", "datestamp": "2023-08-22 03:56:51", "lastmod": "2026-04-10 23:35:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eguchi-Tohru", "name": { "family": "Eguchi", "given": "Tohru" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Tachikawa-Yuji", "name": { "family": "Tachikawa", "given": "Yuji" } } ] }, "title": "Notes on the K3 Surface and the Mathieu Group M_(24)", "ispublished": "pub", "full_text_status": "public", "keywords": "K3 surface; elliptic genus; Mathieu groups", "note": "\u00a9 2011 Taylor & Francis Group, LLC. \n\nReceived April 21, 2010; accepted May 5, 2010. Available online: 14 Oct 2011. \n\nThe authors thank the hospitality of the Aspen Center of Physics during the workshop \"Unity of String Theory,\" when the observation reported in this paper was made. We would like to thank S. Mukai for discussions. T. E. is supported in part by a Grant in Aid from the Japan Ministry of Education, Culture, Sports, Science, and Technology (MEXT). H. O. is supported in part by U.S. Department of Energy grant DE-FG03-92-ER40701, the World Premier International Research Center Initiative, Grant-in-Aid for Scientific Research (C) 20540256 of MEXT, and the Humboldt Research Award. Y. T. is supported in part by NSF grant PHY-0503584, and by a Marvin L. Goldberger membership at the Institute for Advanced Study.\n\n

Submitted - 1004.0956v2.pdf

", "abstract": "We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M_(24). The reason remains a mystery.", "date": "2011-10-14", "date_type": "published", "publication": "Experimental Mathematics", "volume": "20", "number": "1", "publisher": "Taylor and Francis", "pagerange": "91-96", "id_number": "CaltechAUTHORS:20111014-150332394", "issn": "1058-6458", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111014-150332394", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science, and Technology (MEXT)", "grant_number": "20540256" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Alexander von Humboldt Foundation" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "Institute for Advanced Study" } ] }, "other_numbering_system": { "items": [ { "id": "68-2783", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1080/10586458.2011.544585", "primary_object": { "basename": "1004.0956v2.pdf", "url": "https://authors.library.caltech.edu/records/adjag-pfq98/files/1004.0956v2.pdf" }, "pub_year": "2011", "author_list": "Eguchi, Tohru; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/rgb7g-cgs47", "eprint_id": 97816, "eprint_status": "archive", "datestamp": "2023-08-19 08:18:10", "lastmod": "2026-04-10 22:27:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Inevitable randomness in discrete mathematics [Book Review]", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2011 London Mathematical Society.\n\nIssue online 17 July 2011; version of record online 17 July 2011.\n\nBook review of: Inevitable randomness in discrete mathematics (University Lecture Series 49) by J\u00f3zsef Beck: 250 pp., ISBN 978\u20100\u20108218\u20104756\u20105 (American Mathematical Society, Providence, RI, 2009).", "abstract": "Complex systems arise naturally throughout mathematics, computer science, economics and the physical sciences. However, when faced with such intricate systems, we are often powerless to understand their behaviour. Without simplifying assumptions, such as that of the rational agent in economics, the size of the space of possibilities and its apparent lack of order can become overwhelming.\n\nIn this book, J\u00f3zsef Beck explores this issue, suggesting that discrete systems which are not simple should always behave in a random-like fashion, even when different parts of the system do not behave independently.\n\nThe central focus of the book is, to use the author's own term, the following 'vague' metaconjecture.", "date": "2011-10", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "volume": "43", "number": "5", "publisher": "London Mathematical Society", "pagerange": "1021-1023", "id_number": "CaltechAUTHORS:20190812-162958247", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958247", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/blms/bdr063", "pub_year": "2011", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/043n9-qpr29", "eprint_id": 28550, "eprint_status": "archive", "datestamp": "2023-08-19 08:14:39", "lastmod": "2026-04-10 21:59:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Su\u0142kowski-Piotr", "name": { "family": "Su\u0142kowski", "given": "Piotr" }, "orcid": "0000-0002-6176-6240" }, { "id": "Yamazaki-Masahito", "name": { "family": "Yamazaki", "given": "Masahito" } } ] }, "title": "Wall Crossing as Seen by Matrix Models", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 The Author(s). This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 4 June 2010; Accepted: 31 March 2011. \n\nCommunicated by A. Kapustin. We thank Mina Aganagic, Vincento Bouchard, Kentaro Hori, and Yan Soibelman for discussions. H. O. and P. S. thank Hermann Nicolai and the Max-Planck-Institut f\u00fcr Gravitationsphysik for hospitality. Our work is supported in part by the DOE grant DE-FG03-92-ER40701. H. O. and M. Y. are also supported in part by the World Premier International Research Center Initiative of MEXT. H. O. is supported in part by JSPS Grant-in-Aid for Scientific Research (C) 20540256 and by the Humboldt Research Award. P. S. acknowledges the support of the European Commission under the Marie-Curie International Outgoing Fellowship Programme and the Foundation for Polish Science. M. Y. is supported in part by the JSPS Research Fellowship for Young Scientists and the Global COE Program for Physical Science Frontier at the University of Tokyo.\n\n

Published - Ooguri2011p16531Commun_Math_Phys.pdf

", "abstract": "The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally related to the K\u00e4hler moduli space M(X). We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite 't Hooft coupling. The matrix model for the BPS counting on X turns out to give the topological string partition function for another Calabi-Yau manifold Y, whose K\u00e4hler moduli space M(Y) contains two copies of M(X), one related to the BPS charges and another to the stability conditions. The two sets of data are unified in M(Y). The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite 't Hooft coupling they give rise to yet more general geometry Y containing Y.", "date": "2011-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "307", "number": "2", "publisher": "Springer", "pagerange": "429-462", "id_number": "CaltechAUTHORS:20111221-133839011", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111221-133839011", "rights": "This article is distributed under the terms of the Creative Commons Attribution Noncommercial\nLicense which permits any noncommercial use, distribution, and reproduction in any medium, provided the\noriginal author(s) and source are credited.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Alexander von Humboldt Foundation" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Foundation for Polish Science Foundation" }, { "agency": "University of Tokyo" } ] }, "other_numbering_system": { "items": [ { "id": "68-2786", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-011-1330-x", "primary_object": { "basename": "Ooguri2011p16531Commun_Math_Phys.pdf", "url": "https://authors.library.caltech.edu/records/043n9-qpr29/files/Ooguri2011p16531Commun_Math_Phys.pdf" }, "pub_year": "2011", "author_list": "Ooguri, Hirosi; Su\u0142kowski, Piotr; et al." }, { "id": "https://authors.library.caltech.edu/records/b3s9m-dxz32", "eprint_id": 28633, "eprint_status": "archive", "datestamp": "2023-08-19 08:08:47", "lastmod": "2026-04-10 22:01:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Dehn surgeries on knots in product manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 London Mathematical Society.\nReceived 27 January 2010; revised 20 June 2011.\nFirst published online: September 23, 2011 \nThe author was partially supported by an AIM Five-Year Fellowship and NSF grant number DMS-0805807.\nWe are grateful to Danny Calegari for helpful discussions on mapping\nclass groups. This article is dedicated to the memory of Professor Andrew Lange.\n\n

Submitted - 1001.5242v1.pdf

", "abstract": "We show that if a surgery on a knot in a product sutured manifold yields the same product sutured manifold, then this knot is a 0- or 1-crossing knot. The proof uses techniques from sutured manifold theory.", "date": "2011-09-23", "date_type": "published", "publication": "Journal of Topology", "volume": "4", "number": "4", "publisher": "Oxford University Press", "pagerange": "799-816", "id_number": "CaltechAUTHORS:20120103-152321356", "issn": "1753-8416", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120103-152321356", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-0805807" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/jtopol/jtr020", "primary_object": { "basename": "1001.5242v1.pdf", "url": "https://authors.library.caltech.edu/records/b3s9m-dxz32/files/1001.5242v1.pdf" }, "pub_year": "2011", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/51jc4-r5463", "eprint_id": 25495, "eprint_status": "archive", "datestamp": "2023-08-22 03:40:01", "lastmod": "2026-03-09 22:11:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "An Isomonodromy Interpretation of the Hypergeometric Solution of the Elliptic Painlev\u00e9 Equation (and Generalizations)", "ispublished": "pub", "full_text_status": "public", "keywords": "isomonodromy; hypergeometric; Painlev\u00e9; biorthogonal functions.", "note": "\u00a9 2011 The author. The authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. \n \nReceived April 25, 2011, in final form September 06, 2011; Published online September 09, 2011. The author would like to thank N. Witte for some helpful discussions of the orthogonal polynomial approach to isomonodromy (and the University of Melbourne for hosting the author's sabbatical when the discussions took place), and D. Arinkin and A. Borodin for discussions leading to [3] (and thus clarifying what needed (and, perhaps more importantly, what did not\nneed) to be established here). The author was supported in part by NSF grant numbered DMS-0401387, with additional work on the project supported by NSF grants numbered DMS-0833464 and DMS-1001645.\n\n

Published - Rains2011p15869Symmetry_Integr_Geom.pdf

", "abstract": "We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlev\u00e9 equation (or higher-order analogues),\nand admitting a large family of monodromy-preserving deformations. The solutions are certain semiclassical biorthogonal functions (and their Cauchy transforms), biorthogonal with respect to higher-order analogues of Spiridonov's elliptic beta integral.", "date": "2011-09-09", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "7", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 088", "id_number": "CaltechAUTHORS:20110929-113549134", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110929-113549134", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" }, { "agency": "NSF", "grant_number": "DMS-1001645" }, { "agency": "NSF", "grant_number": "DMS-0833464" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2011.088", "primary_object": { "basename": "Rains2011p15869Symmetry_Integr_Geom.pdf", "url": "https://authors.library.caltech.edu/records/51jc4-r5463/files/Rains2011p15869Symmetry_Integr_Geom.pdf" }, "pub_year": "2011", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/dkbbm-c5f35", "eprint_id": 25345, "eprint_status": "archive", "datestamp": "2023-08-22 03:30:39", "lastmod": "2026-04-10 19:55:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "The Birman-Murakami-Wenzl algebras of type E_n", "ispublished": "pub", "full_text_status": "public", "keywords": "Associative algebra; Birman-Murakami-Wenzl algebra; BMW algebra; Brauer algebra; cellular algebra; Coxeter group; generalized Temperley-Lieb algebra; root system; semisimple algebra; word problem in semigroups", "note": "\u00a9 2011 Birkh\u00e4user Boston. \n\nDedicated to professor T. A. Springer on the occasion of his 85th birthday. \n\nReceived January 7, 2011. Accepted April 28, 2011. Published online June 17, 2011.\n\n

Submitted - 1101.3544.pdf

", "abstract": "The Birman-Murakami-Wenzl algebras (BMW algebras) of type E_ n for n\u2009=\u20096, 7, 8 are shown to be semisimple and free over the integral domain Z[\u03b4^(\u00b11),l^(\u00b11),m]/(m1\u2212\u03b4)(l\u2212l^(\u22121)) of ranks 1,440,585; 139,613,625; and 53,328, 069,225. We also show they are cellular over suitable rings. The Brauer algebra of type E_n is a homomorphic ring image and is also semisimple and free of the same rank as an algebra over the ring Z[\u03b4^(\u00b11)]. A rewrite system for the Brauer algebra is used in bounding the rank of the BMW algebra above. The generalized Temperley-Lieb algebra of type E_n turns out to be a subalgebra of the BMW algebra of the same type. So, the BMW algebras of type E_n share many structural properties with the classical ones (of type A_n) and those of type D_n .", "date": "2011-09", "date_type": "published", "publication": "Transformation Groups", "volume": "16", "number": "3", "publisher": "Springer", "pagerange": "681-715", "id_number": "CaltechAUTHORS:20110914-114035979", "issn": "1083-4362", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110914-114035979", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00031-011-9150-9", "primary_object": { "basename": "1101.3544.pdf", "url": "https://authors.library.caltech.edu/records/dkbbm-c5f35/files/1101.3544.pdf" }, "pub_year": "2011", "author_list": "Cohen, Arjeh M. and Wales, David B." }, { "id": "https://authors.library.caltech.edu/records/3rb7n-cbz70", "eprint_id": 88853, "eprint_status": "archive", "datestamp": "2023-08-19 07:57:54", "lastmod": "2026-03-09 20:41:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "In Memoriam: Gregory Hjorth, 1963-2011", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Association for Symbolic Logic. \n\nI am indebted to Jen Davoren and Guy West for their help concerning Greg Hjorth's school/university days and chess career and to BenMiller and Simon Thomas for many useful comments.\n\n

Published - in_memoriam_gregory_hjorth_19632011.pdf

", "abstract": "Greg Hjorth suddenly and unexpectedly passed away on January 13, 2011 in Melbourne, at the age of 47, due to a heart attack. He was a remarkable person, a chess prodigy who competed internationally at a high level until his early 20s, then devoted himself to the study of philosophy and mathematics and went on to become a leading figure in the field of mathematical logic and its applications.", "date": "2011-09", "date_type": "published", "publication": "Bulletin of Symbolic Logic", "volume": "17", "number": "3", "publisher": "Association for Symbolic Logic", "pagerange": "471-477", "id_number": "CaltechAUTHORS:20180816-103208698", "issn": "1079-8986", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-103208698", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "in_memoriam_gregory_hjorth_19632011.pdf", "url": "https://authors.library.caltech.edu/records/3rb7n-cbz70/files/in_memoriam_gregory_hjorth_19632011.pdf" }, "pub_year": "2011", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/30892-c4y04", "eprint_id": 77082, "eprint_status": "archive", "datestamp": "2023-08-22 03:35:33", "lastmod": "2026-04-11 01:29:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Olofsson-R", "name": { "family": "Olofsson", "given": "Rikard" } } ] }, "title": "Eigenvalue bounds for Schr\u00f6dinger operators with a homogeneous magnetic field", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator; Lieb-Thirring inequalities; magnetic field", "note": "\u00a9 2011 The Author(s). This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 13 January 2011; Revised: 10 May 2011; Accepted: 10 May 2011. Published online: 9 June 2011. \n\nR. Olofsson acknowledges support through the Swedish Research Council.\n\n

Published - art_3A10.1007_2Fs11005-011-0499-4.pdf

Submitted - 1102.0329.pdf

", "abstract": "We prove Lieb-Thirring inequalities for Schr\u00f6dinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength of the magnetic field, and hence quantifies the diamagnetic behavior of the system. For a harmonic oscillator in a homogenous magnetic field, we obtain the sharp constants in the inequalities.", "date": "2011-09", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "97", "publisher": "Springer", "pagerange": "227-241", "id_number": "CaltechAUTHORS:20170501-072120225", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-072120225", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-011-0499-4", "primary_object": { "basename": "1102.0329.pdf", "url": "https://authors.library.caltech.edu/records/30892-c4y04/files/1102.0329.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs11005-011-0499-4.pdf", "url": "https://authors.library.caltech.edu/records/30892-c4y04/files/art_3A10.1007_2Fs11005-011-0499-4.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L. and Olofsson, Rikard" }, { "id": "https://authors.library.caltech.edu/records/9gbkd-x2c34", "eprint_id": 28337, "eprint_status": "archive", "datestamp": "2023-08-22 03:21:56", "lastmod": "2026-04-10 21:11:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Building Cosmological Models via Noncommutative Geometry", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Noncommutative geometry; spectral action; early universe; inflationary cosmology; cosmic topology.", "note": "\u00a9 2011 World Scientific Publishing Company. Received 17 January 2011. Accepted 19 February 2011. Dedicated to Alan Carey, on the occasion of his 60th birthday.", "abstract": "This is an overview of new and ongoing research developments aimed at constructing cosmological\nmodels based on noncommutative geometry, via the spectral action functional,\nthought of as a modified gravity action, which includes the coupling with matter when\ncomputed on an almost commutative geometry. This survey is mostly based on recent\nresults obtained in collaboration with Elena Pierpaoli and Kevin Teh. We describe various\naspects of cosmological models of the very early universe, developed by the author\nand Pierpaoli, based on the asymptotic expansion of the spectral action functional and\non renormalization group analysis of the associated particle physics model (an extension\nof the standard model with right-handed neutrinos and Majorana mass terms previously\ndeveloped in collaboration with Chamseddine and Connes). We also describe nonperturbative\nresults, more recently obtained by Pierpaoli, Teh, and the author, which extend\nto the more modern universe, which show that, for different candidate cosmic topologies,\nthe form of the slow-roll inflation potentials obtained from the nonperturbative calculation\nof the spectral action are strongly coupled to the underlying geometry and topology.\nWe discuss some ongoing directions of research and open questions in this new field of\n\"noncommutative cosmology\". The paper is based on the talk given by the author at\nthe conference \"Geometry and Quantum Field Theory\" at the MPI, in honor of Alan\nCarey.", "date": "2011-08", "date_type": "published", "publication": "International Journal of Geometric Methods in Modern Physics", "volume": "8", "number": "5", "publisher": "World Scientific Publishing", "pagerange": "1131-1168", "id_number": "CaltechAUTHORS:20111207-093921796", "issn": "0219-8878", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111207-093921796", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219887811005592", "pub_year": "2011", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/9r784-gwh77", "eprint_id": 77079, "eprint_status": "archive", "datestamp": "2023-08-19 07:39:16", "lastmod": "2026-04-10 23:17:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Eigenvalue bounds for Schr\u00f6dinger operators with complex potentials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 London Mathematical Society. \n\nReceived 17 May 2010; revised 20 January 2011; published online 6 April 2011. \n\nThe author wishes to thank A. Laptev and O. Safronov for useful correspondence.\n\n

Submitted - 1005.2785.pdf

", "abstract": "We show that the absolute values of non-positive eigenvalues of Schr\u00f6dinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz and Sogge.", "date": "2011-08", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "volume": "43", "number": "4", "publisher": "Wiley", "pagerange": "745-750", "id_number": "CaltechAUTHORS:20170501-065723391", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/blms/bdr008", "primary_object": { "basename": "1005.2785.pdf", "url": "https://authors.library.caltech.edu/records/9r784-gwh77/files/1005.2785.pdf" }, "pub_year": "2011", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/n5zhq-7pn49", "eprint_id": 24528, "eprint_status": "archive", "datestamp": "2023-08-22 03:10:08", "lastmod": "2026-03-09 22:45:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "On Algebraically Integrable Differential Operators on an Elliptic Curve", "ispublished": "pub", "full_text_status": "public", "keywords": "finite gap differential operator; monodromy; elliptic Calogero-Moser system", "note": "\u00a9 2011 Institute of Mathematics of National Academy of Sciences of Ukraine.\n\nReceived April 25, 2011, in final form June 30, 2011; Published online July 07, 2011.\nThis paper is a contribution to the Special Issue \"Relationship of Orthogonal Polynomials and Special\nFunctions with Quantum Groups and Integrable Systems\". The full collection is available at\nhttp://www.emis.de/journals/SIGMA/OPSF.html.\nThe authors are grateful to I. Krichever, E. Previato, and A. Veselov for useful discussions. The work of P.E. was partially supported by the the NSF grants DMS-0504847 and DMS-0854764. The work of E.R. was partially supported by the NSF grant DMS-1001645.\n\n

Published - Etingof2011p15152Symmetry_Integr_Geom.pdf

Submitted - 1011.6410.pdf

", "abstract": "We study differential operators on an elliptic curve of order higher than 2 which are algebraically integrable (i.e., finite gap). We discuss classification of such operators of order 3 with one pole, discovering exotic operators on special elliptic curves defined over Q which do not deform to generic elliptic curves. We also study algebraically integrable operators of higher order with several poles and with symmetries, and (conjecturally) relate them to crystallographic elliptic Calogero-Moser systems (which is a generalization of the results of Airault, McKean, and Moser).", "date": "2011-07-07", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "7", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "pagerange": "Art. No. 62", "id_number": "CaltechAUTHORS:20110725-113214387", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110725-113214387", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504847" }, { "agency": "NSF", "grant_number": "DMS-0854764" }, { "agency": "NSF", "grant_number": "DMS-1001645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2011.062", "primary_object": { "basename": "1011.6410.pdf", "url": "https://authors.library.caltech.edu/records/n5zhq-7pn49/files/1011.6410.pdf" }, "related_objects": [ { "basename": "Etingof2011p15152Symmetry_Integr_Geom.pdf", "url": "https://authors.library.caltech.edu/records/n5zhq-7pn49/files/Etingof2011p15152Symmetry_Integr_Geom.pdf" } ], "pub_year": "2011", "author_list": "Etingof, Pavel and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/8c1y5-jgr12", "eprint_id": 23323, "eprint_status": "archive", "datestamp": "2023-08-22 02:46:29", "lastmod": "2026-04-11 00:47:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "Finite Gap Jacobi Matrices, II. The Szeg\u0151 Class", "ispublished": "pub", "full_text_status": "public", "keywords": "Isospectral torus; Szego asymptotics; Orthogonal polynomials", "note": "\u00a9 2010 Springer Science+Business Media, LLC. \n\nReceived: 31 May 2009. Revised: 9 October 2009. Accepted: 10 November 2009. Published online: 13 April 2010. \n\nCommunicated by Vilmos Totik. \n\nJ.S. Christiansen was supported in part by a Steno Research Grant from FNU, the Danish Research Council. B. Simon was supported in part by NSF grant DMS-0652919. Maxim Zinchenko was supported in part by NSF grant DMS-0965411. We would like to thank F. Peherstorfer and P. Yuditskii for the private communication [14]. J.S.C. would like to thank M. Flach and A. Lange for the hospitality of Caltech where this work\nwas completed.\n\n

Submitted - 0906.1630

", "abstract": "Let e \u2282 R be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szeg\u0151 condition is equivalent to lim sup a_1...a_n/cap e_n >0 (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a new proof of Szego asymptotics, including L^2 asymptotics on the spectrum. We make heavy use of the covering map formalism of Sodin-Yuditskii as presented in our first paper in this series.", "date": "2011-06", "date_type": "published", "publication": "Constructive Approximation", "volume": "33", "number": "3", "publisher": "Springer", "pagerange": "365-403", "id_number": "CaltechAUTHORS:20110414-085411774", "issn": "0176-4276", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110414-085411774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" }, { "agency": "NSF", "grant_number": "DMS-0965411" }, { "agency": "Danish Natural Science Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00365-010-9094-7", "primary_object": { "basename": "0906.1630", "url": "https://authors.library.caltech.edu/records/8c1y5-jgr12/files/0906.1630" }, "pub_year": "2011", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/0t188-7j679", "eprint_id": 28495, "eprint_status": "archive", "datestamp": "2023-08-22 02:51:11", "lastmod": "2026-04-10 23:07:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aganagic-M", "name": { "family": "Aganagic", "given": "Mina" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } }, { "id": "Yamazaki-Masahito", "name": { "family": "Yamazaki", "given": "Masahito" } } ] }, "title": "Wall Crossing and M-Theory", "ispublished": "pub", "full_text_status": "public", "keywords": "string theory; bound state; Fock space; Calabi-Yau manifold", "note": "\u00a9 2011 Research Institute for Mathematical Sciences, Kyoto University. \n\nThis is a contribution to the special issue \"The golden jubilee of algebraic analysis\". Communicated by M. Kashiwara. \n\nReceived September 15, 2009. Revised January 7, 2010. \n\nWe would like to thank G. Moore, H. Nakajima and K. Nagao for stimulating discussions. \n\nM. A. is supported in part by the UC Berkeley Center for Theoretical Physics and the NSF grant PHYS-0457317. H. O. and M. Y. are supported in part by DOE grant DE-FG03-92-ER40701 and by the World Premier International Research Center Initiative of MEXT of Japan. H. O. is also supported in part by a Grant-in-Aid for Scientific Research (C) 20540256 of JSPS and by the Kavli Foundation.\n\nC. V. is supported in part by NSF grant PHY-0244821. M. Y. is also supported in part by the JSPS fellowships for Young Scientists and by the Global COE Program for Physical Sciences Frontier at the University of Tokyo. \n\nH. O. thanks for the hospitality at the Aspen Center for Physics. C. V. and M. Y. thank Simons Center for Geometry and Physics at Stony Brook for hospitality.\n\n

Submitted - 0908.1194.pdf

", "abstract": "We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi-Yau 3-fold X. When X has no compact 4-cycles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M-theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. The generating function of the D-brane bound states is expressed as a reduction of the square of the topological string partition function, in all chambers of the K\u00e4hler moduli space.", "date": "2011-06", "date_type": "published", "publication": "Publications of the Research Institute for Mathematical Sciences", "volume": "47", "number": "2", "publisher": "European Mathematical Society", "pagerange": "569-584", "id_number": "CaltechAUTHORS:20111216-141905707", "issn": "0034-5318", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111216-141905707", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "UC Berkeley Center for Theoretical Physics" }, { "agency": "NSF", "grant_number": "PHYS-0457317" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Kavli Foundation" }, { "agency": "University of Tokyo" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "other_numbering_system": { "items": [ { "id": "68-2746", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.2977/PRIMS/44", "primary_object": { "basename": "0908.1194.pdf", "url": "https://authors.library.caltech.edu/records/0t188-7j679/files/0908.1194.pdf" }, "pub_year": "2011", "author_list": "Aganagic, Mina; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/gecbz-afj02", "eprint_id": 23968, "eprint_status": "archive", "datestamp": "2023-08-22 02:47:02", "lastmod": "2026-04-10 20:32:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mart\u00ednez-Finkelshtein-A", "name": { "family": "Mart\u00ednez-Finkelshtein", "given": "Andrei" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Asymptotics of the L^2 norm of derivatives of OPUC", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials; Derivative asymptotics", "note": "\u00a9 2010 Elsevier Inc. Received 28 May 2010; received in revised form 23 August 2010; accepted 15 September 2010.\nAvailable online 21 September 2010. Communicated by Leonid Golinskii. We dedicate this paper in fond memory of Franz Peherstorfer from whom we learned so much. The first author was supported in part by Junta de Andaluc\u00eda grants FQM-229, P06-FQM-01735 and P09-FQM-4643, and by the Ministry of Science and Innovation of Spain (project code MTM2008-06689-C02-01). The second author was supported in part by NSF grant DMS-0652919.\n\n

Submitted - p330.pdf

", "abstract": "We show that for many families of OPUC, one has \u2016\u03c6'_n\u20162/n \u2192 l, a condition we call normal behavior. We prove that this implies |\u03b1_n|\u21920 and that it holds if \u2211^\u221e_(n=0)\u2502\u03b1_n\u2502< \u221e. We also prove it is true for many sparse sequences. On the other hand, it is often destroyed by the insertion of a mass point.", "date": "2011-06", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "163", "number": "6", "publisher": "Elsevier", "pagerange": "747-778", "id_number": "CaltechAUTHORS:20110610-081439616", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110610-081439616", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Junta de Andaluc\u00eda", "grant_number": "FQM-229" }, { "agency": "Junta de Andaluc\u00eda", "grant_number": "P06-FQM-01735" }, { "agency": "Junta de Andaluc\u00eda", "grant_number": "P09-FQM-4643" }, { "agency": "NSF", "grant_number": "DMS-0652919" }, { "agency": "Ministry of Science and Innovation (Spain)", "grant_number": "MTM2008-06689-C02-01" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2010.09.002", "primary_object": { "basename": "p330.pdf", "url": "https://authors.library.caltech.edu/records/gecbz-afj02/files/p330.pdf" }, "pub_year": "2011", "author_list": "Mart\u00ednez-Finkelshtein, Andrei and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/s1mbd-yas15", "eprint_id": 77081, "eprint_status": "archive", "datestamp": "2023-08-19 07:01:32", "lastmod": "2026-04-10 21:47:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } }, { "id": "Thomas-L-E", "name": { "family": "Thomas", "given": "Lawrence E." } } ] }, "title": "Stability and Absence of Binding for Multi-Polaron Systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The author(s) 2011. The authors retain the copyright for this article. The paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 28 April 2010; Accepted: 06 January 2011; First Online: 24 February 2011. \n\nWe are grateful to Herbert Spohn for making us aware of the problem of proving absence of binding for large U. We also thank Marcel Griesemer and Jacob Schach M\u00f8ller for helpful comments on an early version of our manuscript. Partial financial support from the U.S. National Science Foundation through grants PHY-0652854 (E.L. and R.F.) and PHY-0845292 (R.S.) are gratefully acknowledged. L.T. would like to thank the PIMS Institute, University of British Columbia, for their hospitality and support.\n\n

Published - art_3A10.1007_2Fs10240-011-0031-5.pdf

Submitted - 1004.4892.pdf

", "abstract": "We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N \u2265 2 polarons. Fr\u00f6hlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \u221a\u0251, and with each other by Coulomb repulsion of strength U. We prove the following: (i)While there is a known thermodynamic instability for U < 2\u0251, stability of matter does hold for U > 2\u0251, that is, the ground state energy per particle has a finite limit as N \u2192 \u221e. (ii) There is no binding of any kind if U exceeds a critical value that depends on \u0251 but not on N. The same results are shown to hold for the Pekar-Tomasevich model.", "date": "2011-06", "date_type": "published", "publication": "Publications math\u00e9matiques de l'IH\u00c9S", "volume": "113", "number": "1", "publisher": "Springer", "pagerange": "39-67", "id_number": "CaltechAUTHORS:20170501-071121790", "issn": "0073-8301", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-071121790", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0652854" }, { "agency": "NSF", "grant_number": "PHY-0845292" }, { "agency": "University of British Columbia" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10240-011-0031-5", "primary_object": { "basename": "1004.4892.pdf", "url": "https://authors.library.caltech.edu/records/s1mbd-yas15/files/1004.4892.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs10240-011-0031-5.pdf", "url": "https://authors.library.caltech.edu/records/s1mbd-yas15/files/art_3A10.1007_2Fs10240-011-0031-5.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/dxkb0-r7s18", "eprint_id": 78983, "eprint_status": "archive", "datestamp": "2023-08-19 07:01:40", "lastmod": "2026-04-10 22:26:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Manin-Y-I", "name": { "family": "Manin", "given": "Yuri I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Error-Correcting Codes and Phase Transitions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Birkh\u00e4user Springer. \n\nReceived: 24 November 2009. Accepted: 17 February 2010. Published online: 23 March 2010.\n\n

Submitted - 0910.5135.pdf

", "abstract": "The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous curve in the space of parameters. The main goal of this paper is to relate the asymptotic bound to phase diagrams of quantum statistical mechanical systems. We first identify the code parameters with Hausdorff and von Neumann dimensions, by considering fractals consisting of infinite sequences of code words. We then construct operator algebras associated to individual codes. These are Toeplitz algebras with a time evolution for which the KMS state at critical temperature gives the Hausdorff measure on the corresponding fractal. We extend this construction to algebras associated to limit points of codes, with non-uniform multi-fractal measures, and to tensor products over varying parameters.", "date": "2011-06", "date_type": "published", "publication": "Mathematics in Computer Science", "volume": "5", "number": "2", "publisher": "Springer Verlag", "pagerange": "133-170", "id_number": "CaltechAUTHORS:20170712-080808371", "issn": "1661-8270", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-080808371", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11786-010-0031-8", "primary_object": { "basename": "0910.5135.pdf", "url": "https://authors.library.caltech.edu/records/dxkb0-r7s18/files/0910.5135.pdf" }, "pub_year": "2011", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/6rbhj-c9209", "eprint_id": 24437, "eprint_status": "archive", "datestamp": "2023-08-19 06:21:50", "lastmod": "2026-04-10 22:16:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bashkirov-D", "name": { "family": "Bashkirov", "given": "Denis" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Supersymmetry enhancement by monopole operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory, Duality in Gauge Field Theories", "note": "\u00a9 2011 SISSA. Received: March 16, 2011. Accepted: April 25, 2011. Published: May 3, 2011. A.K. would like to thank E. Witten for a useful discussion and I. Klebanov for comments on the draft. A.K. is also grateful to the Aspen Center for Physics for hospitality during the last stages of this work. This work was supported in part by the DOE grant DE-FG02-92ER40701.\n\n

Submitted - 1007.4861v1.pdf

", "abstract": "We describe a method which allows one to study hidden symmetries in a large class of strongly coupled supersymmetric gauge theories in three dimensions. We apply this method to the ABJM theory and to the infrared limit of =4 SQCD with adjoint and fundamental matter. We show that the U(N) ABJM model with Chern-Simons level k = 1or k = 2 has hidden =8 supersymmetry. Hidden supersymmetry is also shown to occur in =4 d = 3 SQCD with one fundamental and one adjoint hypermultiplet. The latter theory, as well as the U(N) ABJM theory at k = 1, are shown to have a decoupled free sector. This provides evidence that both models are dual to the infrared limit of =8 U(N) super-Yang-Mills theory.", "date": "2011-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2011", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 015", "id_number": "CaltechAUTHORS:20110718-080735915", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110718-080735915", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP05(2011)015", "primary_object": { "basename": "1007.4861v1.pdf", "url": "https://authors.library.caltech.edu/records/6rbhj-c9209/files/1007.4861v1.pdf" }, "pub_year": "2011", "author_list": "Bashkirov, Denis and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/bnmcf-y8j10", "eprint_id": 24517, "eprint_status": "archive", "datestamp": "2023-08-19 06:22:20", "lastmod": "2026-04-10 20:44:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bashkirov-D", "name": { "family": "Bashkirov", "given": "Denis" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Dualities between N = 8 superconformal field theories in three dimensions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Extended Supersymmetry \u2013 Duality in Gauge Field Theories \u2013 Chern-Simons Theories", "note": "\u00a9 2011 SISSA. Received: April 27, 2011. Accepted: May 7, 2011. Published: May 16, 2011. This work was supported in part by the DOE grant DE-FG02-92ER40701.", "abstract": "We show that an infinite family of N=6 d=3 superconformal Chern-Simons-matter theories has hidden N=8 superconformal symmetry and hidden parity on the quantum level. This family of theories is different from the one found by Aharony, Bergman, Jafferis and Maldacena, as well as from the theories constructed by Bagger and Lambert, and Gustavsson. We also test several conjectural dualities between BLG theories and ABJ theories by comparing superconformal indices of these theories.", "date": "2011-05", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2011", "number": "5", "publisher": "Springer", "pagerange": "Art. No. 074", "id_number": "CaltechAUTHORS:20110725-084744097", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110725-084744097", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP05(2011)074", "pub_year": "2011", "author_list": "Bashkirov, Denis and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/acv60-f4w82", "eprint_id": 23595, "eprint_status": "archive", "datestamp": "2023-08-19 06:19:28", "lastmod": "2026-04-10 22:18:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Pierpaoli-Elena", "name": { "family": "Pierpaoli", "given": "Elena" }, "orcid": "0000-0002-7957-8993" }, { "id": "Teh-Kevin", "name": { "family": "Teh", "given": "Kevin" } } ] }, "title": "The Spectral Action and Cosmic Topology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Springer-Verlag. \n\nReceived: 20 May 2010; Accepted: 21 October 2010; Published online: 22 February 2011. \n\nCommunicated by A. Connes.\n\n

Submitted - 1005.2256.pdf

", "abstract": "The spectral action functional, considered as a model of gravity coupled to\nmatter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose\nform and corresponding slow-roll parameters can be sensitive to the underlying cosmic\ntopology. We explicitly compute the non-perturbative spectral action for some of the\nmain candidates for cosmic topologies, namely the quaternionic space, the Poincar\u00e9\ndodecahedral space, and the flat tori. We compute the corresponding slow-roll parameters\nand we check that the resulting inflation model behaves in the same way as for\na simply-connected spherical topology in the case of the quaternionic space and the\nPoincar\u00e9 homology sphere, while it behaves differently in the case of the flat tori. We\nadd an appendix with a discussion of the case of lens spaces.", "date": "2011-05", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "304", "number": "1", "publisher": "Springer", "pagerange": "125-174", "id_number": "CaltechAUTHORS:20110509-092722190", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110509-092722190", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "TAPIR" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-011-1211-3", "primary_object": { "basename": "1005.2256.pdf", "url": "https://authors.library.caltech.edu/records/acv60-f4w82/files/1005.2256.pdf" }, "pub_year": "2011", "author_list": "Marcolli, Matilde; Pierpaoli, Elena; et al." }, { "id": "https://authors.library.caltech.edu/records/tf4pg-fsv96", "eprint_id": 22798, "eprint_status": "archive", "datestamp": "2023-08-19 06:15:55", "lastmod": "2026-04-10 23:18:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Saulina-N", "name": { "family": "Saulina", "given": "Natalia" } } ] }, "title": "Topological boundary conditions in abelian Chern-Simons theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Elsevier B.V. \n\nReceived 24 September 2010; accepted 27 December 2010. Available online 30 December 2010. \n\nWe would like to thank D. Freed, A. Kitaev, J. Lurie, G. Moore, V. Ostrik, and L. Rozansky for\nuseful discussions and advice. We are grateful to the Aspen Center for Physics for an excellent\nworking atmosphere. This work was supported in part by the DOE grant DE-FG02-92ER40701.\n\n

Submitted - 1008.0654v2.pdf

", "abstract": "We study topological boundary conditions in abelian Chern\u2013Simons theory and line operators confined\nto such boundaries. From the mathematical point of view, their relationships are described by a certain\n2-category associated to an even integer-valued symmetric bilinear form (the matrix of Chern\u2013Simons couplings).\nWe argue that boundary conditions correspond to Lagrangian subgroups in the finite abelian group\nclassifying bulk line operators (the discriminant group). We describe properties of boundary line operators;\nin particular we compute the boundary associator. We also study codimension one defects (surface operators)\nin abelian Chern\u2013Simons theories. As an application, we obtain a classification of such theories up to\nisomorphism, in general agreement with the work of Belov and Moore.", "date": "2011-04-21", "date_type": "published", "publication": "Nuclear Physics B", "volume": "845", "number": "3", "publisher": "Elsevier", "pagerange": "393-435", "id_number": "CaltechAUTHORS:20110310-100106179", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110310-100106179", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92ER40701" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2010.12.017", "primary_object": { "basename": "1008.0654v2.pdf", "url": "https://authors.library.caltech.edu/records/tf4pg-fsv96/files/1008.0654v2.pdf" }, "pub_year": "2011", "author_list": "Kapustin, Anton and Saulina, Natalia" }, { "id": "https://authors.library.caltech.edu/records/ax1vm-6jz20", "eprint_id": 77098, "eprint_status": "archive", "datestamp": "2023-08-19 06:14:01", "lastmod": "2026-04-10 22:53:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lewin-M", "name": { "family": "Lewin", "given": "Mathieu" } }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Energy Cost to Make a Hole in the Fermi Sea", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 American Physical Society. \n\nReceived 7 February 2011. \n\nGrants from the U.S. NSF PHY-0965859 (E.\u2009L. and R.\u2009F.), PHY-0845292 (R.\u2009S.) and from the ERC MNIQS-258023 (M.\u2009L.) are acknowledged.\n\n

Published - PhysRevLett.106.150402.pdf

Submitted - 1102.1414.pdf

", "abstract": "The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.", "date": "2011-04-15", "date_type": "published", "publication": "Physical Review Letters", "volume": "106", "number": "15", "publisher": "American Physical Society", "pagerange": "Art. No. 150402", "id_number": "CaltechAUTHORS:20170501-093433748", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-093433748", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0965859" }, { "agency": "NSF", "grant_number": "PHY-0845292" }, { "agency": "European Research Council (ERC)", "grant_number": "MNIQS-258023" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.106.150402", "primary_object": { "basename": "1102.1414.pdf", "url": "https://authors.library.caltech.edu/records/ax1vm-6jz20/files/1102.1414.pdf" }, "related_objects": [ { "basename": "PhysRevLett.106.150402.pdf", "url": "https://authors.library.caltech.edu/records/ax1vm-6jz20/files/PhysRevLett.106.150402.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L.; Lewin, Mathieu; et al." }, { "id": "https://authors.library.caltech.edu/records/c54x4-pn733", "eprint_id": 23521, "eprint_status": "archive", "datestamp": "2023-08-19 06:13:33", "lastmod": "2026-04-11 01:34:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Critical Lieb-Thirring bounds in gaps and the generalized Nevai conjecture for finite gap Jacobi matrices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 Duke University Press.\n\nReceived 16 March 2010; Revision received 4 July 2010.\nSimon's work supported in part by National Science Foundation grant DMS-0652919.\nWe thank Alexander Pushnitski and Robert Seiringer for valuable discussions.\n\n

Published - Frank2011p13678Duke_Math_J.pdf

Submitted - 1003.4703

", "abstract": "We prove bounds of the form \u2211_(e\u2208I\u22c2\u03c3_d(H)) dist(e, \u03c3_e(H)^(1/2) \u2264 L^1 -norm of a perturbation, where I is a gap. Included are gaps in continuum one-dimensional periodic Schr\u00f6dinger operators and finite gap Jacobi matrices, where we get a generalized Nevai conjecture about an L^(1)-condition implying a Szeg\u0151 condition. One key is a general new form of the Birman-Schwinger bound in gaps.", "date": "2011-04-15", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "157", "number": "3", "publisher": "Duke University Press", "pagerange": "461-493", "id_number": "CaltechAUTHORS:20110502-112300651", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110502-112300651", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1215/00127094-1272912", "primary_object": { "basename": "1003.4703", "url": "https://authors.library.caltech.edu/records/c54x4-pn733/files/1003.4703" }, "related_objects": [ { "basename": "Frank2011p13678Duke_Math_J.pdf", "url": "https://authors.library.caltech.edu/records/c54x4-pn733/files/Frank2011p13678Duke_Math_J.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/6t771-58x04", "eprint_id": 77398, "eprint_status": "archive", "datestamp": "2023-08-19 06:09:30", "lastmod": "2026-04-10 22:45:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-T", "name": { "family": "Ekholm", "given": "Tomas" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Kova\u0159\u00edk-H", "name": { "family": "Kova\u0159\u00edk", "given": "Hynek" } } ] }, "title": "Eigenvalue estimates for Schr\u00f6dinger operators on metric trees", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operatorMetric treeEigenvalue estimateLieb\u2013Thirring inequalityCwikel\u2013Lieb\u2013Rozenblum inequality", "note": "\u00a9 2011 Elsevier Inc. \n\nReceived 11 October 2007, Accepted 3 January 2011, Available online 13 January 2011. \n\nCommunicated by the Managing Editors of AIM. \n\nThe authors are grateful to Robert Seiringer and Timo Weidl for several useful discussions, and to the organizers of the workshop 'Analysis on Graphs' at the Isaac Newton Institute in Cambridge for their kind invitation. This work has been supported by Vetenskapsr\u00e5det/Swedish Research Council (T.E.) and DAAD grant D/06/49117 (R.F.). Partial support by the ESF programme SPECT (T.E. and H.K.) and the DAAD-STINT PPP programme (R.F.) is gratefully acknowledged.\n\n

Submitted - 0710.5500.pdf

", "abstract": "We consider Schr\u00f6dinger operators on radial metric trees and prove Lieb\u2013Thirring and Cwikel\u2013Lieb\u2013Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.", "date": "2011-04-01", "date_type": "published", "publication": "Advances in Mathematics", "volume": "226", "number": "6", "publisher": "Elsevier", "pagerange": "5165-5197", "id_number": "CaltechAUTHORS:20170512-094610802", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-094610802", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Vetenskapsr\u00e5det/Swedish Research Council" }, { "agency": "Deutscher Akademischer Austauschdienst (DAAD)", "grant_number": "D/06/49117" }, { "agency": "European Science Foundation" }, { "agency": "Swedish Foundation for International Cooperation in Research and Higher Education (STINT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2011.01.001", "primary_object": { "basename": "0710.5500.pdf", "url": "https://authors.library.caltech.edu/records/6t771-58x04/files/0710.5500.pdf" }, "pub_year": "2011", "author_list": "Ekholm, Tomas; Frank, Rupert L.; et al." }, { "id": "https://authors.library.caltech.edu/records/f536n-wb594", "eprint_id": 23128, "eprint_status": "archive", "datestamp": "2023-08-22 02:26:51", "lastmod": "2026-04-11 00:23:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Natural boundaries and spectral theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Reflectionless; Right limit; Natural boundary", "note": "\u00a9 2011 Elsevier Inc. \n\nReceived 9 August 2010; accepted 21 December 2010. Available online 30 December 2010. \n\nCommunicated by Charles Fefferman. \n\nSupported in part by NSF grant DMS-0652919. \n\nWe would like to thank Shmuel Agmon, John Garnett, Jean-Pierre Kahane, Rowan Killip, and Genadi Levin for useful discussions.\n\n

Submitted - p328.pdf

", "abstract": "We present and exploit an analogy between lack of absolutely continuous spectrum for Schr\u00f6dinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke's example and natural boundary examples for random power series where independence is not assumed.", "date": "2011-04-01", "date_type": "published", "publication": "Advances in Mathematics", "volume": "226", "number": "6", "publisher": "Elsevier", "pagerange": "4902-4920", "id_number": "CaltechAUTHORS:20110328-100710731", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110328-100710731", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.aim.2010.12.019", "primary_object": { "basename": "p328.pdf", "url": "https://authors.library.caltech.edu/records/f536n-wb594/files/p328.pdf" }, "pub_year": "2011", "author_list": "Breuer, Jonathan and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/wd916-xk848", "eprint_id": 23044, "eprint_status": "archive", "datestamp": "2023-08-22 02:09:24", "lastmod": "2026-04-10 21:23:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Paolucci-A-M", "name": { "family": "Paolucci", "given": "Anna Maria" } } ] }, "title": "Cuntz\u2013Krieger Algebras and Wavelets on Fractals", "ispublished": "pub", "full_text_status": "public", "keywords": "Cuntz\u2013Krieger; Wavelets; Fractals; Cantor set; Hilbert space; Perron\u2013Frobenius operator; Ruelle operator", "note": "\u00a9 2011 Springer. This article is distributed under the terms of the Creative Commons Attribution Noncommercial\nLicense which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.\n\nReceived: 6 August 2009; Accepted: 2 November 2009; Published online: 21 November 2009.\nCommunicated by Palle Jorgensen.\nPart of this work was done during a stay of the authors at the Max Planck Institute for Mathematics, which we thank for the hospitality and support. M. Marcolli was partially supported by NSF grant DMS-0651925.\n\n

Published - Marcolli2011p13123Complex_Anal_Oper_Th.pdf

Submitted - 0908.0596.pdf

", "abstract": "We consider representations of Cuntz\u2013Krieger algebras on the Hilbert space of square integrable functions on the limit set, identified with a Cantor set in the unit interval. We use these representations and the associated Perron\u2013Frobenius and Ruelle operators to construct families of wavelets on these Cantor sets.", "date": "2011-03", "date_type": "published", "publication": "Complex Analysis and Operator Theory", "volume": "5", "number": "1", "publisher": "Springer", "pagerange": "41-81", "id_number": "CaltechAUTHORS:20110322-095729744", "issn": "1661-8254", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110322-095729744", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0651925" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11785-009-0044-y", "primary_object": { "basename": "0908.0596.pdf", "url": "https://authors.library.caltech.edu/records/wd916-xk848/files/0908.0596.pdf" }, "related_objects": [ { "basename": "Marcolli2011p13123Complex_Anal_Oper_Th.pdf", "url": "https://authors.library.caltech.edu/records/wd916-xk848/files/Marcolli2011p13123Complex_Anal_Oper_Th.pdf" } ], "pub_year": "2011", "author_list": "Marcolli, Matilde and Paolucci, Anna Maria" }, { "id": "https://authors.library.caltech.edu/records/csyfa-1vk23", "eprint_id": 22977, "eprint_status": "archive", "datestamp": "2023-08-19 05:40:58", "lastmod": "2026-04-10 21:51:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aluffi-P", "name": { "family": "Aluffi", "given": "Paolo" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Graph Hypersurfaces and a Dichotomy in the Grothendieck Ring", "ispublished": "pub", "full_text_status": "public", "keywords": "graph hypersurfaces, Grothendieck ring, stable birational equivalence", "note": "\u00a9 2011 Springer.\nReceived: 1 June 2010; Revised: 14 December 2010; Accepted: 12 January 2011; Published online: 29 January 2011.\n\n

Submitted - 1005.4470.pdf

", "abstract": "The subring of the Grothendieck ring of varieties generated by the graph\nhypersurfaces of quantum field theory maps to the monoid ring of stable birational equivalence\nclasses of varieties. We show that the image of this map is the copy of Z generated\nby the class of a point. This clarifies the extent to which the graph hypersurfaces 'generate\nthe Grothendieck ring of varieties': while it is known that graph hypersurfaces generate\nthe Grothendieck ring over a localization of Z[L] in which L becomes invertible, the span\nof the graph hypersurfaces in the Grothendieck ring itself is nearly killed by setting the\nLefschetz motive L to zero. In particular, this shows that the graph hypersurfaces do not\ngenerate the Grothendieck ring prior to localization. The same result yields some information\non the mixed Hodge structures of graph hypersurfaces, in the form of a constraint on\nthe terms in their Deligne\u2013Hodge polynomials. These observations are certainly not surprising\nfor the expert reader, but are somewhat hidden in the literature. The treatment in\nthis note is straightforward and self-contained.", "date": "2011-03", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "95", "number": "3", "publisher": "Springer", "pagerange": "223-232", "id_number": "CaltechAUTHORS:20110318-142126748", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110318-142126748", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-011-0461-5", "primary_object": { "basename": "1005.4470.pdf", "url": "https://authors.library.caltech.edu/records/csyfa-1vk23/files/1005.4470.pdf" }, "pub_year": "2011", "author_list": "Aluffi, Paolo and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/wzfgq-ewr80", "eprint_id": 22711, "eprint_status": "archive", "datestamp": "2023-08-19 05:34:12", "lastmod": "2026-04-16 01:39:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fidkowski-L", "name": { "family": "Fidkowski", "given": "Lukasz" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Topological phases of fermions in one dimension", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 American Physical Society. Received 13 September 2010; published 8 February 2011. We would like to acknowledge useful discussions with\nJason Alicea, Matthew Hastings, Netanel Lindner, John\nPreskill, Gil Refael, Ari Turner, and Dan Freed. A.K. is\ngrateful to the Aspen Center for Physics for hospitality.\nThis work was supported in part by the Institute for Quantum\nInformation under National Science Foundation Grant\nNo. PHY-0803371.\n\n

Published - Fidkowski2011p12796Phys_Rev_B.pdf

", "abstract": "In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the time-reversal-invariant Majorana chain (BDI symmetry class).While the band classification yields an integer topological index k, it is known that phases characterized by values of k in the same equivalence class modulo 8 can be adiabatically transformed one to another by adding suitable interaction terms. Here we show that the eight equivalence classes are distinct and exhaustive, and provide a physical interpretation for the interacting invariant modulo 8. The different phases realize different Altland-Zirnbauer classes of the reduced density matrix for an entanglement bipartition into two half chains. We generalize these results to the classification of all one-dimensional gapped phases of fermionic systems with possible antiunitary symmetries, utilizing the algebraic framework of central extensions. We use matrix product state methods to prove our results.", "date": "2011-02-15", "date_type": "published", "publication": "Physical Review B", "volume": "83", "number": "7", "publisher": "American Physical Society", "pagerange": "Art. No. 075103", "id_number": "CaltechAUTHORS:20110308-123056073", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110308-123056073", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Institute for Quantum Information", "grant_number": "PHY-0803371" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.83.075103", "primary_object": { "basename": "Fidkowski2011p12796Phys_Rev_B.pdf", "url": "https://authors.library.caltech.edu/records/wzfgq-ewr80/files/Fidkowski2011p12796Phys_Rev_B.pdf" }, "pub_year": "2011", "author_list": "Fidkowski, Lukasz and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/6gt2j-qw665", "eprint_id": 22954, "eprint_status": "archive", "datestamp": "2023-08-19 05:33:21", "lastmod": "2026-04-10 23:47:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } } ] }, "title": "Spatially Modulated Phase in the Holographic Description of Quark-Gluon Plasma", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 American Physical Society. \n\nReceived 30 November 2010; published 11 February 2011. \n\nWe would like to thank M. Natsuume, D. Son, S. Sugimoto, and C.-P. Yeh for stimulating discussions. H. O. thanks the Aspen Center for Physics and the Simons Center for Geometry and Physics, and C. S. P. thanks the IPMU for their hospitalities. This work is supported in part by DOE Grant No. DE-FG03-92-ER40701 and by the World Premier International Research Center Initiative of MEXT. H.O. is also supported in part by a Grant-in-Aid for Scientific Research (C) 20540256 of JSPS. C. S. P. is also supported in part by DOE Grant No. DE-FG02-04ER41286.\n\n

Published - Ooguri2011p12936Phys_Rev_Lett.pdf

", "abstract": "We present a string theory construction of a gravity dual of a spatially modulated phase. Our earlier work shows that the Chern-Simons\n term in the five-dimensional Maxwell theory destabilizes the\n Reissner-Nordstrom black holes in anti-de Sitter space if the\n Chern-Simons coupling is sufficiently high. In this Letter, we show\n that a similar instability is realized on the world volume of 8-branes\n in the Sakai-Sugimoto model in the quark-gluon plasma phase. Our result\n suggests a new spatially modulated phase in quark-gluon plasma when the\n baryon density is above 0.8N_f fm(^-3) at temperature 150 MeV.", "date": "2011-02-11", "date_type": "published", "publication": "Physical Review Letters", "volume": "106", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 061601", "id_number": "CaltechAUTHORS:20110317-104913163", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110317-104913163", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-04ER41286" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.106.061601", "primary_object": { "basename": "Ooguri2011p12936Phys_Rev_Lett.pdf", "url": "https://authors.library.caltech.edu/records/6gt2j-qw665/files/Ooguri2011p12936Phys_Rev_Lett.pdf" }, "pub_year": "2011", "author_list": "Ooguri, Hirosi and Park, Chang-Soon" }, { "id": "https://authors.library.caltech.edu/records/pcj8r-qnk44", "eprint_id": 22949, "eprint_status": "archive", "datestamp": "2023-08-19 05:33:17", "lastmod": "2026-04-16 01:39:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tikhonov-K-S", "name": { "family": "Tikhonov", "given": "K. S." } }, { "id": "Feigel'man-M-V", "name": { "family": "Feigel'man", "given": "M. V." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A. Yu." }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Power-Law Spin Correlations in a Perturbed Spin Model on a Honeycomb Lattice", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 American Physical Society. Received 12 September 2010; revised 3 January 2011; published 11 February 2011. We are grateful to L. B. Ioffe and A. S. Ioselevich for\nuseful discussions. This research was supported by the\nRFBR Grant No. 10-02-00554.\n\n

Published - Tikhonov2011p12931Phys_Rev_Lett.pdf

", "abstract": "We consider the spin- 12 model on the honeycomb lattice in the presence of a weak magnetic field\nh_\u03b1 \u226a 1. Such a perturbation destroys the exact integrability of the model in terms of gapless fermions and\nstatic Z_2 fluxes. We show that it results in the appearance of a long-range tail in the irreducible dynamic\nspin correlation function: \u226as^z(t,r)s^z(0,0)\u226b \u03b1 h^2_z\nf(tr), where f(t,r) \u03b1 [max(t,r]^(-4) is proportional to the\ndensity polarization function of fermions.", "date": "2011-02-11", "date_type": "published", "publication": "Physical Review Letters", "volume": "106", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 067203", "id_number": "CaltechAUTHORS:20110316-161521086", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110316-161521086", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research (RFBR)", "grant_number": "10-02-00554" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.106.067203", "primary_object": { "basename": "Tikhonov2011p12931Phys_Rev_Lett.pdf", "url": "https://authors.library.caltech.edu/records/pcj8r-qnk44/files/Tikhonov2011p12931Phys_Rev_Lett.pdf" }, "pub_year": "2011", "author_list": "Tikhonov, K. S.; Feigel'man, M. V.; et al." }, { "id": "https://authors.library.caltech.edu/records/phjsx-gsv45", "eprint_id": 28295, "eprint_status": "archive", "datestamp": "2023-08-22 02:01:36", "lastmod": "2026-04-10 20:36:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aluffi-P", "name": { "family": "Aluffi", "given": "Paolo" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Algebro-Geometric Feynman Rules", "ispublished": "pub", "full_text_status": "public", "keywords": "Feynman rules; parametric Feynman integrals; graph hypersurfaces; Grothendieck ring of varieties; Chern\u2013Schwartz\u2013MacPherson classes.", "note": "\u00a9 2011 World Scientific Publishing Co. Received 24 September 2010. Accepted 26 September 2010.\n\n

Submitted - 0811.2514.pdf

", "abstract": "We give a general procedure to construct \"algebro-geometric Feynman rules\", that is, characters of the Connes\u2013Kreimer Hopf algebra of Feynman graphs that factor through a Grothendieck ring of immersed conical varieties, via the class of the complement of the affine graph hypersurface. In particular, this maps to the usual Grothendieck ring of varieties, defining \"motivic Feynman rules\". We also construct an algebro-geometric Feynman rule with values in a polynomial ring, which does not factor through the usual Grothendieck ring, and which is defined in terms of characteristic classes of singular varieties. This invariant recovers, as a special value, the Euler characteristic of the projective graph hypersurface complement. The main result underlying the construction of this invariant is a formula for the characteristic classes of the join of two projective varieties. We discuss the BPHZ renormalization procedure in this algebro-geometric context and some motivic zeta functions arising from the partition functions associated to motivic Feynman rules.", "date": "2011-02", "date_type": "published", "publication": "International Journal of Geometric Methods in Modern Physics", "volume": "8", "number": "1", "publisher": "World Scientific Publishing", "pagerange": "203-237", "id_number": "CaltechAUTHORS:20111205-113131774", "issn": "0219-8878", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111205-113131774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219887811005099", "primary_object": { "basename": "0811.2514.pdf", "url": "https://authors.library.caltech.edu/records/phjsx-gsv45/files/0811.2514.pdf" }, "pub_year": "2011", "author_list": "Aluffi, Paolo and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/trqfz-dwt03", "eprint_id": 77804, "eprint_status": "archive", "datestamp": "2023-08-19 05:13:24", "lastmod": "2026-04-10 20:26:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Morozov-S-I", "name": { "family": "Morozov", "given": "Sergey" }, "orcid": "0000-0001-6226-5811" }, { "id": "Vugalter-S", "name": { "family": "Vugalter", "given": "Semjon" } } ] }, "title": "Weakly coupled bound states of Pauli operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 27 March 2009. Accepted: 2 May 2010. Published online: 14 July 2010. \n\nCommunicated by L. Ambrosio. \n\nThe authors would like to thank T. Weidl for drawing their attention to this problem and for helpful discussions. R.F. has profitted from discussions with T. Ekholm and H. Kovarik. The authors gratefully acknowledge the hospitality at Stuttgart University, KTH Stockholm and ESI Vienna, where parts of this work were done. This work was partially supported through Deutsche Forschungsgemeinschaft's (DFG) grant FR 2664/1-1, US National Science Foundation's grant PHY 06 52854 (R.F.), DFG grant SI 348/12-2, Engineering and Physical Sciences Research Council's grant EP/F029721/1 (S.M.) and DFG grant WE 1964/2 (S.V.).\n\n

Published - art_3A10.1007_2Fs00526-010-0339-x.pdf

Submitted - 0903.5333.pdf

", "abstract": "We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.", "date": "2011-01-01", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "40", "number": "1", "publisher": "Springer", "pagerange": "253-271", "id_number": "CaltechAUTHORS:20170526-094859466", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-094859466", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "FR 2664/1-1" }, { "agency": "NSF", "grant_number": "PHY-0652854" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "SI 348/12-2" }, { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "EP/F029721/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-010-0339-x", "primary_object": { "basename": "0903.5333.pdf", "url": "https://authors.library.caltech.edu/records/trqfz-dwt03/files/0903.5333.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs00526-010-0339-x.pdf", "url": "https://authors.library.caltech.edu/records/trqfz-dwt03/files/art_3A10.1007_2Fs00526-010-0339-x.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L.; Morozov, Sergey; et al." }, { "id": "https://authors.library.caltech.edu/records/kcpmw-sdn19", "eprint_id": 22923, "eprint_status": "archive", "datestamp": "2023-08-22 01:45:25", "lastmod": "2026-03-09 02:20:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Soibelman-Y", "name": { "family": "Soibelman", "given": "Yan" } } ] }, "title": "Quantum Wall Crossing in N=2 Gauge Theories", "ispublished": "pub", "full_text_status": "public", "keywords": "motivic Donaldson-Thomas invariants; BPS invariants; wall-crossing; supersymmetric gauge theory", "note": "\u00a9 Springer 2010. \n\nReceived: 2 July 2010. Accepted: 20 September 2010. Published online: 16 October 2010. \n\nWe would like to thank D. Jafferis, M. Kontsevich, A. Neitzke, and M. Reineke for very useful discussions, and S. Deser and C. Silberstein for providing important clues. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701, in part by NSF Grant PHY-0757647, and in part by the Alfred P. Sloan Foundation. Y.S. is grateful to IHES for excellent research conditions. His work was partially supported by an NSF grant. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Submitted - 0912.1346v1.pdf

", "abstract": "We study refined and motivic wall-crossing formulas in N = 2 supersymmetric gauge theories with SU(2) gauge group and N _f < 4 matter hypermultiplets in the fundamental representation. Such gauge theories provide an excellent testing ground for the conjecture that \"refined = motivic.\"", "date": "2011-01", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "95", "number": "1", "publisher": "Springer", "pagerange": "1-25", "id_number": "CaltechAUTHORS:20110316-093514240", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110316-093514240", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-010-0437-x", "primary_object": { "basename": "0912.1346v1.pdf", "url": "https://authors.library.caltech.edu/records/kcpmw-sdn19/files/0912.1346v1.pdf" }, "pub_year": "2011", "author_list": "Dimofte, Tudor; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/jmby0-yas06", "eprint_id": 97820, "eprint_status": "archive", "datestamp": "2023-08-22 01:47:59", "lastmod": "2026-03-08 17:36:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Large almost monochromatic subsets in hypergraphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Bipartite Graph; Complete Graph; Complete Bipartite Graph; Pigeonhole Principle; Ramsey Number", "note": "\u00a9 Hebrew University Magnes Press 2011. \n\nReceived 22 January 2009; first online 25 February 2011. \n\nConlon research supported by a research fellowship at St John's College. Fox research supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. Sudakov research supported in part by NSF CAREER award DMS-0812005 and by USA-Israeli BSF grant.\n\n

Submitted - 0901.3912.pdf

", "abstract": "We show that for all \u2113 and \u03b5 > 0 there is a constant c = c(\u2113, \u03b5) > 0 such that every \u2113-coloring of the triples of an N-element set contains a subset S of size c\u221a(log N) such that at least 1 \u2212 \u03b5 fraction of the triples of S have the same color. This result is tight up to the constant c and answers an open question of Erd\u0151s and Hajnal from 1989 on discrepancy in hypergraphs. For \u2113 \u2265 4 colors, it is known that there is an \u2113-coloring of the triples of an N-element set whose largest monochromatic subset has cardinality only \u0398(log log N). Thus, our result demonstrates that the maximum almost monochromatic subset that an \u2113-coloring of the triples must contain is much larger than the corresponding monochromatic subset. This is in striking contrast with graphs, where these two quantities have the same order of magnitude. To prove our result, we obtain a new upper bound on the \u2113-color Ramsey numbers of complete multipartite 3-uniform hypergraphs, which answers another open question of Erd\u0151s and Hajnal.", "date": "2011-01", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "181", "number": "1", "publisher": "Springer", "pagerange": "423-432", "id_number": "CaltechAUTHORS:20190812-162958677", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958677", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" }, { "agency": "NSF" }, { "agency": "Princeton University" }, { "agency": "NSF", "grant_number": "DMS-0812005" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-011-0016-6", "primary_object": { "basename": "0901.3912.pdf", "url": "https://authors.library.caltech.edu/records/jmby0-yas06/files/0901.3912.pdf" }, "pub_year": "2011", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/kkwpb-2f938", "eprint_id": 37671, "eprint_status": "archive", "datestamp": "2023-08-19 04:58:48", "lastmod": "2026-03-09 22:48:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Poonen-B", "name": { "family": "Poonen", "given": "Bjorn" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Self cup products and the theta characteristic torsor", "ispublished": "pub", "full_text_status": "public", "keywords": "Weil pairing, theta characteristic, self cup product", "note": "\u00a9 2011 International Press.\n\nReceived by the editors 23 September 2011.\n\nWe thank Benedict Gross for the suggestion to look at the self cup product on\nH^1(k,A[2]) induced by the Weil pairing e_2 on a Jacobian. We also thank Brian\nConrad and the referee for comments. Bjorn Poonen was partially supported by\nNational Science Foundation grants DMS-0841321 and DMS-1069236.\n\n

Submitted - 1104.2105v1.pdf

", "abstract": "We give a general formula relating self cup products in cohomology to connecting maps in nonabelian cohomology, and apply it to obtain a formula for the self cup product associated to the Weil pairing.", "date": "2011", "date_type": "published", "publication": "Mathematical Research Letters", "volume": "18", "number": "6", "publisher": "International Press", "pagerange": "1305-1318", "id_number": "CaltechAUTHORS:20130328-103531472", "issn": "1073-2780", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130328-103531472", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0841321" }, { "agency": "NSF", "grant_number": "DMS-1069236" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/MRL.2011.v18.n6.a18", "primary_object": { "basename": "1104.2105v1.pdf", "url": "https://authors.library.caltech.edu/records/kkwpb-2f938/files/1104.2105v1.pdf" }, "pub_year": "2011", "author_list": "Poonen, Bjorn and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/vm555-99k41", "eprint_id": 77105, "eprint_status": "archive", "datestamp": "2023-08-19 05:02:17", "lastmod": "2026-03-09 00:46:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "On the uniqueness of ground states of non-local equations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nSubmitted on 19 Sep 2011.\n\nThis work was supported through the U.S. National Science Foundation grant PHY-1068285.\n\n

Published - JEDP_2011____A5_0.pdf

Submitted - 1109.4049.pdf

", "abstract": "We review our joint result with E. Lenzmann about the uniqueness of ground state solutions of non-linear equations involving the fractional Laplacian and provide an alternate uniqueness proof for an equation related to the intermediate long-wave equation.", "date": "2011", "date_type": "published", "publication": "Journ\u00e9es \u00e9quations aux d\u00e9riv\u00e9es partielles", "volume": "2011", "publisher": "Groupement de recherche Analyse des \u00e9quations aux d\u00e9riv\u00e9es partielles", "pagerange": "A5", "id_number": "CaltechAUTHORS:20170501-111716146", "issn": "0752-0360", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-111716146", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-1068285" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.5802/jedp.77", "primary_object": { "basename": "1109.4049.pdf", "url": "https://authors.library.caltech.edu/records/vm555-99k41/files/1109.4049.pdf" }, "related_objects": [ { "basename": "JEDP_2011____A5_0.pdf", "url": "https://authors.library.caltech.edu/records/vm555-99k41/files/JEDP_2011____A5_0.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/pjfqq-pj294", "eprint_id": 28523, "eprint_status": "archive", "datestamp": "2023-08-19 04:55:20", "lastmod": "2026-03-18 00:06:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On the Removal of Finite Discrete Spectrum by Coefficient Stripping", "ispublished": "pub", "full_text_status": "public", "keywords": "Coefficient stripping, block Jacobi matrices", "note": "\u00a9 2011 European Mathematical Society. \n\nReceived July 1, 2010, revised August 26, 2010. \n\nSupported in part by NSF grant DMS-0652919.\n\n

Submitted - p331.pdf

", "abstract": "We prove for a large class of operators, J, including block Jacobi matrices, if \u03c3(J)\\[\u03b1,\u03b2] is a finite set, each point of which is an eigenvalue of finite multiplicity, then a finite coefficient stripped, J_N , has \u03c3(J_N)\u2282[\u03b1,\u03b2]. We use an abstract Dirichlet decoupling.", "date": "2011", "date_type": "published", "publication": "Journal of Spectral Theory", "volume": "1", "number": "1", "publisher": "European Mathematical Society", "pagerange": "81-85", "id_number": "CaltechAUTHORS:20111219-134707644", "issn": "1664-039X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111219-134707644", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4171/JST/3", "primary_object": { "basename": "p331.pdf", "url": "https://authors.library.caltech.edu/records/pjfqq-pj294/files/p331.pdf" }, "pub_year": "2011", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/f4q66-11q30", "eprint_id": 23393, "eprint_status": "archive", "datestamp": "2023-08-19 04:41:55", "lastmod": "2026-04-11 19:19:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } } ] }, "title": "Holographic endpoint of spatially modulated phase transition", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 American Physical Society. \n\nReceived 1 September 2010; published 2 December 2010. \n\nWe thank Michael Cross, Per Kraus, Shin Nakamura, and Dam T. Son for discussions. We also thank Sean Hartnoll and Subir Sachdev for their comments on the earlier version of this paper. We are grateful to Hermann Nicolai and to the Max-Planck-Institut f\u00fcr Gravitationsphysik for hospitality. C. P. thanks the hospitality of the Korea Institute for Advanced Study and the Institute for the Physics and Mathematics of the Universe at the University of Tokyo. H. O. thanks the Aspen Center for Physics, where this work was completed, for the hospitality. This work is supported in part by DOE Grant No. DE-FG03-92-ER40701 and the World Premier International Research Center Initiative of MEXT. H.O. is also supported in part by JSPS Grant-in-Aid for Scientific Research (C) No. 20540256 and by the Humboldt Foundation. \n\nNote added.\u2014After the first version of this paper was completed, we were informed of the work [3], which suggested that an instability to crystalline phases might be a generic feature of phases which are describable by a bulk AdS2 geometry. Such an instability would provide a natural way to understand the ground state entropy.\n\n

Published - Ooguri2010p13459Phys_Rev_D.pdf

", "abstract": "In a previous paper [S. Nakamura, H. Ooguri, and C.\u2009S. Park, Phys. Rev. D 81, 044018 (2010)], we showed that the Reissner-Nordstr\u00f6m black hole in the five-dimensional anti\u2013de Sitter space coupled to the Maxwell theory with the Chern-Simons term is unstable when the Chern-Simons coupling is sufficiently large. In the dual conformal field theory, the instability suggests a spatially modulated phase transition. In this paper, we construct and analyze nonlinear solutions which describe the endpoint of this phase transition. In the limit where the Chern-Simons coupling is large, we find that the phase transition is of the second order with the mean field critical exponent. However, the dispersion relation with the Van Hove singularity enhances quantum corrections in the bulk, and we argue that this changes the order of the phase transition from the second to the first. We compute linear response functions in the nonlinear solution and find an infinite off-diagonal DC conductivity in the new phase.", "date": "2010-12-02", "date_type": "published", "publication": "Physical Review D", "volume": "82", "number": "12", "publisher": "American Physical Society", "pagerange": "Art. No. 126001", "id_number": "CaltechAUTHORS:20110420-110435590", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110420-110435590", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Alexander von Humboldt Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.82.126001", "primary_object": { "basename": "Ooguri2010p13459Phys_Rev_D.pdf", "url": "https://authors.library.caltech.edu/records/f4q66-11q30/files/Ooguri2010p13459Phys_Rev_D.pdf" }, "pub_year": "2010", "author_list": "Ooguri, Hirosi and Park, Chang-Soon" }, { "id": "https://authors.library.caltech.edu/records/xews6-rjx22", "eprint_id": 20971, "eprint_status": "archive", "datestamp": "2023-08-19 04:29:52", "lastmod": "2026-04-11 18:07:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borodin-A", "name": { "family": "Borodin", "given": "Alexei" } }, { "id": "Gorin-V", "name": { "family": "Gorin", "given": "Vadim" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "q-Distributions on boxed plane partitions", "ispublished": "pub", "full_text_status": "public", "keywords": "Plane partitions, q-Racah orthogonal polynomials, Determinantal point processes", "note": "\u00a9 2010 Springer Basel AG. \nPublished online: 15 September 2010. AB was partially supported by NSF grant DMS-0707163. VG was partially supported by the Moebius\nContest Foundation for Young Scientists. EMR was partially supported by NSF grant DMS-0833464. The authors would like to thank Dan Betea for a number of valuable remarks.\n\n

Submitted - 0905.0679.pdf

", "abstract": "We introduce elliptic weights of boxed plane partitions and prove that they give rise to a generalization of MacMahon's product formula for the number of plane partitions in a box. We then focus on the most general positive degenerations of these weights that are related to orthogonal polynomials; they form three 2-D families. For\ndistributions from these families, we prove two types of results. First, we construct explicit Markov chains that preserve these distributions. In particular, this leads to a relatively simple exact sampling algorithm. Second, we consider a limit when all dimensions of the box grow and plane partitions become large and prove that the local correlations converge to those of ergodic translation invariant Gibbs measures. For fixed proportions of the box, the slopes of the limiting Gibbs measures (that can also be viewed as slopes of tangent planes to the hypothetical limit shape) are encoded by a single quadratic polynomial.", "date": "2010-12", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "16", "number": "4", "publisher": "Springer", "pagerange": "731-789", "id_number": "CaltechAUTHORS:20101123-092946208", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101123-092946208", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0707163" }, { "agency": "NSF", "grant_number": "DMS-0833464" }, { "agency": "Young Scientists Moebius Contest Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-010-0034-y", "primary_object": { "basename": "0905.0679.pdf", "url": "https://authors.library.caltech.edu/records/xews6-rjx22/files/0905.0679.pdf" }, "pub_year": "2010", "author_list": "Borodin, Alexei; Gorin, Vadim; et al." }, { "id": "https://authors.library.caltech.edu/records/z6qfe-0dd58", "eprint_id": 97819, "eprint_status": "archive", "datestamp": "2023-08-22 01:31:21", "lastmod": "2026-04-11 23:52:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "An Approximate Version of Sidorenko's Conjecture", "ispublished": "pub", "full_text_status": "public", "keywords": "Sidorenko's conjecture; graph homomorphism; subgraph density", "note": "\u00a9 2010 The Author(s). This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: April 26, 2010. Accepted: June 3, 2010. \n\nD.C.'s research supported by a Junior Research Fellowship at St John's College. J.F.'s research supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. B.S.'s research supported in part by NSF CAREER award DMS-0812005 and by a USA-Israeli BSF grant.\n\n

Published - Conlon2010_Article_AnApproximateVersionOfSidorenk.pdf

Submitted - 1004.4236.pdf

", "abstract": "A beautiful conjecture of Erd\u0151s-Simonovits and Sidorenko states that, if H is a bipartite graph, then the random graph with edge density p has in expectation asymptotically the minimum number of copies of H over all graphs of the same order and edge density. This conjecture also has an equivalent analytic form and has connections to a broad range of topics, such as matrix theory, Markov chains, graph limits, and quasirandomness. Here we prove the conjecture if H has a vertex complete to the other part, and deduce an approximate version of the conjecture for all H. Furthermore, for a large class of bipartite graphs, we prove a stronger stability result which answers a question of Chung, Graham, and Wilson on quasirandomness for these graphs.", "date": "2010-12", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "20", "number": "6", "publisher": "Springer", "pagerange": "1354-1366", "id_number": "CaltechAUTHORS:20190812-162958544", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958544", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" }, { "agency": "NSF" }, { "agency": "Princeton University" }, { "agency": "NSF", "grant_number": "DMS-0812005" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-010-0097-0", "primary_object": { "basename": "1004.4236.pdf", "url": "https://authors.library.caltech.edu/records/z6qfe-0dd58/files/1004.4236.pdf" }, "related_objects": [ { "basename": "Conlon2010_Article_AnApproximateVersionOfSidorenk.pdf", "url": "https://authors.library.caltech.edu/records/z6qfe-0dd58/files/Conlon2010_Article_AnApproximateVersionOfSidorenk.pdf" } ], "pub_year": "2010", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/rfhz6-3np03", "eprint_id": 23145, "eprint_status": "archive", "datestamp": "2023-08-19 04:16:17", "lastmod": "2026-04-11 19:26:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitano-Ryuichiro", "name": { "family": "Kitano", "given": "Ryuichiro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Ookouchi-Yutaka", "name": { "family": "Ookouchi", "given": "Yutaka" } } ] }, "title": "Supersymmetry Breaking and Gauge Mediation", "ispublished": "pub", "full_text_status": "public", "keywords": "model building, dynamical symmetry breaking, string theory", "note": "\u00a9 2010 Annual Reviews. \n\nFirst published online as a Review in Advance on July 19, 2010. \n\nWe thank M. Graesser, Z. Komargodski, and D. Shih for comments on this manuscript. R.K.\nis supported in part by a Grant-in-Aid for Scientific Research, number 21840006, of the Japan\nSociety for the Promotion of Science ( JSPS). H.O. is supported in part by U.S. Department of\nEnergy grant number DE-FG03-92-ER40701; the World Premier International Research Center\nInitiative of the Ministry of Education, Culture, Sports, Science and Technology of Japan; and\na Grant-in-Aid for Scientific Research, number (C) 20540256, of JSPS. Y.O.'s research at the\nPerimeter Institute for Theoretical Physics is supported in part by the Government of Canada through the Natural Sciences and Engineering Research Council of Canada and by the Province\nof Ontario through the Ministry of Research and Innovation.\n\n

Submitted - 1001.4535.pdf

", "abstract": "We review recent works on supersymmetry breaking and gauge mediation. We survey our current understanding of dynamical supersymmetry-breaking mechanisms and describe new model-building tools that use duality, metastability, and stringy construction. We discuss phenomenological constraints and their solutions, paying particular attention to gaugino masses and electroweak symmetry breaking.", "date": "2010-11", "date_type": "published", "publication": "Annual Review of Nuclear and Particle Science", "volume": "60", "publisher": "Annual Reviews", "pagerange": "491-511", "id_number": "CaltechAUTHORS:20110329-080256247", "issn": "0163-8998", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110329-080256247", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "21840006" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Ontario Ministry of Research and Innovation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1146/annurev.nucl.012809.104540", "primary_object": { "basename": "1001.4535.pdf", "url": "https://authors.library.caltech.edu/records/rfhz6-3np03/files/1001.4535.pdf" }, "pub_year": "2010", "author_list": "Kitano, Ryuichiro; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/2wgfd-k8h37", "eprint_id": 20410, "eprint_status": "archive", "datestamp": "2023-08-19 04:09:10", "lastmod": "2026-04-11 19:44:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Denicola-D", "name": { "family": "Denicola", "given": "Domenic" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Zainy-al-Yasry-A", "name": { "family": "Zainy al-Yasry", "given": "Ahmad" } } ] }, "title": "Spin foams and noncommutative geometry", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 IOP Publishing. \n\nReceived 15 May 2010, in final form 30 July 2010. Published 22 September 2010. \n\nThis work was inspired by and partially carried out during the workshop 'Noncommutative Geometry and Loop Quantum Gravity' at the Mathematisches Forschungsinstitut Oberwolfach, which the first two authors thank for hospitality and support. The second author is partially supported by NSF grants DMS-0651925, DMS-0901221 and DMS-1007207. The first author was partially supported by a Richter Memorial Fund Summer Undergraduate Research Fellowship from Caltech.\n\n

Submitted - 1005.1057v1.pdf

", "abstract": "We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of the Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry.", "date": "2010-10-21", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "27", "number": "20", "publisher": "IOP", "pagerange": "Art. No. 205025", "id_number": "CaltechAUTHORS:20101012-141717687", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101012-141717687", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0651925" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" }, { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" }, { "agency": "Mathematisches Forschungsinstitut Oberwolfach" }, { "agency": "Richter Memorial Funds" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/0264-9381/27/20/205025", "primary_object": { "basename": "1005.1057v1.pdf", "url": "https://authors.library.caltech.edu/records/2wgfd-k8h37/files/1005.1057v1.pdf" }, "pub_year": "2010", "author_list": "Denicola, Domenic; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/w3p4r-0es80", "eprint_id": 21699, "eprint_status": "archive", "datestamp": "2023-08-22 01:02:31", "lastmod": "2026-04-11 23:47:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Willett-B", "name": { "family": "Willett", "given": "Brian" } }, { "id": "Yaakov-I", "name": { "family": "Yaakov", "given": "Itamar" } } ] }, "title": "Nonperturbative tests of three-dimensional dualities", "ispublished": "pub", "full_text_status": "public", "keywords": "Matrix Models; Brane Dynamics in Gauge Theories; Extended Supersymmetry; Duality in Gauge Field Theories", "note": "\u00a9 2010 SISSA.\n\nReceived: July 21, 2010; accepted: September 15, 2010; published: October 6, 2010.\n\n

Submitted - 1003.5694.pdf

", "abstract": "We test several conjectural dualities between strongly coupled superconformal field theories in three dimensions by computing their exact partition functions on a three\nsphere as a function of Fayet-Iliopoulos and mass parameters. The calculation is carried out using localization of the path integral and the matrix model previously derived for superconformal N = 2 gauge theories. We verify that the partition functions of quiver theories related by mirror symmetry agree provided the mass parameters and the Fayet-Iliopoulos parameters are exchanged, as predicted. We carry out a similar calculation for the mirror of N = 8 super-Yang-Mills theory and show that its partition function agrees with that of the ABJM theory at unit Chern-Simons level. This provides a nonperturbative test of the conjectural equivalence of the two theories in the conformal limit.", "date": "2010-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2010", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 013", "id_number": "CaltechAUTHORS:20110111-113638601", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110111-113638601", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP10(2010)013", "primary_object": { "basename": "1003.5694.pdf", "url": "https://authors.library.caltech.edu/records/w3p4r-0es80/files/1003.5694.pdf" }, "pub_year": "2010", "author_list": "Kapustin, Anton; Willett, Brian; et al." }, { "id": "https://authors.library.caltech.edu/records/kd18h-cwj91", "eprint_id": 19720, "eprint_status": "archive", "datestamp": "2023-08-22 00:54:17", "lastmod": "2026-04-11 19:33:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Nevai Condition", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials; Regular measures; CD kernel", "note": "\u00a9 2009 Springer Science+Business Media, LLC. \n\nReceived: 4 September 2008. Accepted: 2 March 2009. Published online: 16 May 2009. \n\nWe would like to thank David Damanik and Svetlana Jitomirskaya for valuable correspondence and Benjamin Weiss for valuable discussions. J.B. and B.S. would like to thank Ehud de Shalit for the hospitality of The Hebrew University where some of this work was done. Y.L. would like to thank Matthias Flach for the hospitality of Caltech where some of this work was done.\n\n

Submitted - 0809.2255

", "abstract": "We study Nevai's condition that for orthogonal polynomials on the real\nline, K_n(x, x_0)^2K_n(x_0, x_0)\n^(\u22121) d\u03c1(x) \u2192 \u03b4_(x0), where K_n is the Christoffel\u2013Darboux\nkernel. We prove that it holds for the Nevai class of a finite gap set uniformly on\nthe spectrum, and we provide an example of a regular measure on [\u22122, 2] where it\nfails on an interval.", "date": "2010-10", "date_type": "published", "publication": "Constructive Approximation", "volume": "32", "number": "2", "publisher": "Springer", "pagerange": "221-254", "id_number": "CaltechAUTHORS:20100830-143634133", "issn": "0176-4276", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100830-143634133", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "1169/06" }, { "agency": "Binational Science Foundation (BSF)", "grant_number": "2006483" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00365-009-9055-1", "primary_object": { "basename": "0809.2255", "url": "https://authors.library.caltech.edu/records/kd18h-cwj91/files/0809.2255" }, "pub_year": "2010", "author_list": "Breuer, Jonathan; Last, Yoram; et al." }, { "id": "https://authors.library.caltech.edu/records/e1ja5-m0f90", "eprint_id": 27757, "eprint_status": "archive", "datestamp": "2023-08-19 03:58:51", "lastmod": "2026-04-11 22:18:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Pierpaoli-Elena", "name": { "family": "Pierpaoli", "given": "Elena" }, "orcid": "0000-0002-7957-8993" } ] }, "title": "Early universe models from noncommutative geometry", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2011 International Press. \n\nPart of this work was carried out during visits of the first author at the Mathematical Sciences Research Institute in Berkeley and at the Max Planck Institute for Mathematics in Bonn. The hospitality and support of both institutions is gratefully acknowledged.\n\n

Submitted - 0908.3683v1.pdf

", "abstract": "We investigate cosmological predictions on the early universe based on the noncommutative geometry (NCG) models of gravity coupled to matter. Using the renormalization group analysis for the standard model with right-handed neutrinos and Majorana mass terms, which is the particle\nphysics content of the most recent NCG models, we analyze the behavior of the coefficients of the gravitational and cosmological terms in the Lagrangian derived from the asymptotic expansion of the spectral action functional of NCG. We find emergent Hoyle\u2013Narlikar and conformal\ngravity at the see-saw scales and a running effective gravitational constant, which affects the propagation of gravitational waves and the evaporation law of primordial black holes and provides Linde models of negative gravity in the early universe. The same renormalization group\nanalysis also governs the running of the effective cosmological constant of the model. The model also provides a Higgs-based slow-roll inflationary mechanism, for which one can explicitly compute the slow-roll parameters.\nThe particle physics content allows for dark matter models based on sterile neutrinos with Majorana mass terms.", "date": "2010-10", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "14", "number": "5", "publisher": "International Press", "pagerange": "1373-1432", "id_number": "CaltechAUTHORS:20111111-141226446", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111111-141226446", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Mathematical Sciences Research Institute (MSRI)" }, { "agency": "Max Planck Institute for Mathematics" } ] }, "local_group": { "items": [ { "id": "TAPIR" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2010.v14.n5.a2", "primary_object": { "basename": "0908.3683v1.pdf", "url": "https://authors.library.caltech.edu/records/e1ja5-m0f90/files/0908.3683v1.pdf" }, "pub_year": "2010", "author_list": "Marcolli, Matilde and Pierpaoli, Elena" }, { "id": "https://authors.library.caltech.edu/records/dt8kw-njc19", "eprint_id": 20652, "eprint_status": "archive", "datestamp": "2023-08-22 00:53:20", "lastmod": "2026-04-11 18:25:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kolodrubetz-D", "name": { "family": "Kolodrubetz", "given": "Daniel" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology", "ispublished": "pub", "full_text_status": "public", "keywords": "Noncommutative geometry models of particle physics and cosmology; Renormalization group flow; Majorana neutrinos; Initial conditions at unification; modified gravity models", "note": "\u00a9 2010 Elsevier B.V.\n\nReceived 27 June 2010; revised 26 July 2010; accepted 30 July 2010. Editor: M. Cveti\u010d. Available online 12 August 2010.\n\nThis Letter is based on the results of Daniel Kolodrubetz's summer research project supported by Caltech's Summer Undergraduate Research Richter Memorial Fellowship. We thank the referee for many useful comments.\n\n

Submitted - 1006.4000.pdf

", "abstract": "We investigate the effect of varying boundary conditions on the renormalization group flow in a recently developed noncommutative geometry model of particle physics and cosmology. We first show that there is a sensitive dependence on the initial conditions at unification, so that, varying a parameter even slightly can be shown to have drastic effects on the running of the model parameters. We compare the running in the case of the default and the maximal mixing conditions at unification. We then exhibit explicitly a particular choice of initial conditions at the unification scale, in the form of modified maximal mixing conditions, which have the property that they satisfy all the geometric constraints imposed by the noncommutative geometry of the model at unification, and at the same time, after running them down to lower energies with the renormalization group flow, they still agree in order of magnitude with the predictions at the electroweak scale.", "date": "2010-09-27", "date_type": "published", "publication": "Physics Letters B", "volume": "693", "number": "2", "publisher": "Elsevier", "pagerange": "166-174", "id_number": "CaltechAUTHORS:20101103-111640771", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101103-111640771", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Summer Undergraduate Research Fellowship (SURF)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.physletb.2010.08.018", "primary_object": { "basename": "1006.4000.pdf", "url": "https://authors.library.caltech.edu/records/dt8kw-njc19/files/1006.4000.pdf" }, "pub_year": "2010", "author_list": "Kolodrubetz, Daniel and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/5hb0k-44d56", "eprint_id": 20034, "eprint_status": "archive", "datestamp": "2023-08-19 03:53:00", "lastmod": "2026-04-11 19:44:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ceyhan-\u00d6", "name": { "family": "Ceyhan", "given": "\u00d6zg\u00fcr" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Open string theory and planar algebras", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 IOP Publishing Ltd. \n\nReceived 19 March 2010, in final form 21 March 2010 Published 16 August 2010. \n\nThe first author would like to thank Vaughan Jones for useful discussions. The first author is partially supported by NWO. The second author is partially supported by NSF grants DMS-0651925 and DMS-0901221. Part of this work was carried out during the authors' stay at the Max Planck Institute for Mathematics, which we thank for the hospitality and for support. The first author also thanks to Feza G\u00fcrsey Institute for the hospitality.\n\n

Submitted - 0907.5330v1.pdf

", "abstract": "In this paper, we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov\u2013Witten theory. In particular, through the well-known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry and subfactors of von Neumann algebras.", "date": "2010-09-24", "date_type": "published", "publication": "Journal of Physics A: Mathematical and General", "volume": "43", "number": "38", "publisher": "IOP", "pagerange": "Art. No. 385401", "id_number": "CaltechAUTHORS:20100920-094734398", "issn": "0305-4470", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100920-094734398", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" }, { "agency": "NSF", "grant_number": "DMS-0651925" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "Max Planck Institute for Mathematics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1751-8113/43/38/385401", "primary_object": { "basename": "0907.5330v1.pdf", "url": "https://authors.library.caltech.edu/records/5hb0k-44d56/files/0907.5330v1.pdf" }, "pub_year": "2010", "author_list": "Ceyhan, \u00d6zg\u00fcr and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/av0g1-g3461", "eprint_id": 88594, "eprint_status": "archive", "datestamp": "2023-08-19 03:44:45", "lastmod": "2026-04-11 17:25:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fleischhack-C", "name": { "family": "Fleischhack", "given": "Christian" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Nest-R", "name": { "family": "Nest", "given": "Ryszard" } } ] }, "title": "Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 EMS Publishing House. \n\nPublished online: 2010-09-01.", "abstract": "Spectral triples have recently turned out to be relevant for different approaches that aim at quantizing gravity and the other fundamental forces of nature in a mathematically rigorous way. The purpose of this workshop was to bring together researchers mainly from noncommutative geometry and loop quantum gravity \u2013two major fields that have used spectraltriples independently so far\u2013 in order to share their results and open issues.", "date": "2010-09-01", "date_type": "published", "publication": "Oberwolfach Reports", "volume": "7", "number": "1", "publisher": "European Mathematical Society", "pagerange": "373-413", "id_number": "CaltechAUTHORS:20180806-102243722", "issn": "1660-8933", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-102243722", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/OWR/2010/09", "pub_year": "2010", "author_list": "Fleischhack, Christian; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/eny3v-ty248", "eprint_id": 19275, "eprint_status": "archive", "datestamp": "2023-08-19 03:37:32", "lastmod": "2026-04-11 23:00:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } }, { "id": "Viehmann-E", "name": { "family": "Viehmann", "given": "Eva" } } ] }, "title": "On the Hodge\u2013Newton filtration for p-divisible O-modules", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag 2009. \n\nReceived: 2 January 2008. Accepted: 13 January 2009. Published online: 16 June 2009. \n\nWe thank L. Fargues, M. Harris and R. Kottwitz for their interest in our work and for stimulating discussions. We are grateful to E. Lau, M. Rapoport and T. Wedhorn for helpful comments on a preliminary version of this paper. This project started while the authors were visiting the Institut des Hautes \u00c9tudes Scientifiques (E.M.) and the Universit\u00e9 de Paris-Sud (E.V.).We thank both institutions for their hospitality. During the stay at Orsay, E.V. was supported by a fellowship within the Post-Doc program of the German Academic Exchange Service (DAAD). Later in the project, E.M. was partially supported by NSF Grant DMS-0701310.\n\n

Submitted - 0710.4194v2.pdf

", "abstract": "The notions Hodge\u2013Newton decomposition and Hodge\u2013Newton filtration for F-crystals are due to Katz and generalize Messing's result on the existence of the local-\u00e9tale filtration for p-divisible groups. Recently, some of Katz's classical results have been generalized by Kottwitz to the context of F-crystals with additional structures and by Moonen to \u03bc-ordinary p-divisible groups. In this paper, we discuss further generalizations to the situation of crystals in characteristic p and of p-divisible groups with additional structure by endomorphisms.", "date": "2010-09", "date_type": "published", "publication": "Mathematische Zeitschrift", "volume": "266", "number": "1", "publisher": "Springer Verlag", "pagerange": "193-205", "id_number": "CaltechAUTHORS:20100804-134200820", "issn": "0025-5874", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100804-134200820", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutscher Akademischer Austauschdienst (DAAD)" }, { "agency": "NSF", "grant_number": "DMS-0701310" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00209-009-0561-4", "primary_object": { "basename": "0710.4194v2.pdf", "url": "https://authors.library.caltech.edu/records/eny3v-ty248/files/0710.4194v2.pdf" }, "pub_year": "2010", "author_list": "Mantovan, Elena and Viehmann, Eva" }, { "id": "https://authors.library.caltech.edu/records/7mcnc-6ym17", "eprint_id": 22858, "eprint_status": "archive", "datestamp": "2023-08-19 03:41:17", "lastmod": "2026-04-11 21:58:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Rozansky-L", "name": { "family": "Rozansky", "given": "Lev" } } ] }, "title": "Three-dimensional topological field theory and symplectic algebraic geometry II", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 International Press. \nReceived March 11, 2010.\nL.R. is indebted to D. Arinkin for many patient explanations of the properties of coherent sheaves. He is also grateful to V. Ginzburg for numerous discussions and encouragement. A.K. would like to thank D. Orlov for the\nsame. A.K. is also grateful to D. Ben-Zvi, V. Ostrik, and L. Positselski for advice. Both authors would like to thank Natalia Saulina for collaboration on Part I of the paper. The work of A.K. was supported in part by the DOE grant DE-FG03-92-ER40701. The work of L.R. was supported by the NSF grant DMS-0808974.\n\n

Published - Kapustin2010p12542Commun._Number_Theory_Phys.pdf

", "abstract": "Motivated by the path-integral analysis [6] of boundary conditions in a three-dimensional topological sigma model, we suggest a definition of the two-category \u00a8L(X) associated with a holomorphic symplectic manifold X and study its properties. The simplest objects of \u00a8L(X) are holomorphic lagrangian submanifolds Y \u2282 X. We pay\nspecial attention to the case when X is the total space of the cotangent bundle of a complex manifold U or a deformation thereof. In the latter case, the endomorphism category of the zero section is a monoidal category which is an A_\u221e deformation of the two-periodic derived category of U.", "date": "2010-09", "date_type": "published", "publication": "Communications in Number Theory and Physics", "volume": "4", "number": "3", "publisher": "International Press", "pagerange": "463-549", "id_number": "CaltechAUTHORS:20110314-113130491", "issn": "1931-4523", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110314-113130491", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "DMS-0808974" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CNTP.2010.v4.n3.a1", "primary_object": { "basename": "Kapustin2010p12542Commun._Number_Theory_Phys.pdf", "url": "https://authors.library.caltech.edu/records/7mcnc-6ym17/files/Kapustin2010p12542Commun._Number_Theory_Phys.pdf" }, "pub_year": "2010", "author_list": "Kapustin, Anton and Rozansky, Lev" }, { "id": "https://authors.library.caltech.edu/records/zm2vp-way89", "eprint_id": 77354, "eprint_status": "archive", "datestamp": "2023-08-19 03:43:02", "lastmod": "2026-04-11 19:18:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" } ] }, "title": "Inversion positivity and the sharp Hardy\u2013Littlewood\u2013Sobolev inequality", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 The Authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\n\nReceived: 28 April 2009; Accepted: 25 November 2009; First Online: 23 December 2009.\n\nWe are grateful to E. Carlen for pointing out that the conformal invariance of the HLS functional and the conventional reflection positivity through planes imply the inversion positivity through spheres. This allows us to circumvent our original, direct but complicated proof, which uses properties of Gegenbauer polynomials. Support through DFG grant FR 2664/1-1 (R.F.) and U.S. NSF grant PHY 0652854 (R.F. and E.L.) is gratefully acknowledged.\n\n

Published - art_3A10.1007_2Fs00526-009-0302-x.pdf

Submitted - 0904.4275.pdf

", "abstract": "We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.", "date": "2010-09", "date_type": "published", "publication": "Calculus of Variations and Partial Differential Equations", "volume": "39", "number": "1-2", "publisher": "Springer", "pagerange": "85-99", "id_number": "CaltechAUTHORS:20170510-143424777", "issn": "0944-2669", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-143424777", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "FR 2664/1-1" }, { "agency": "NSF", "grant_number": "PHY-0652854" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00526-009-0302-x", "primary_object": { "basename": "0904.4275.pdf", "url": "https://authors.library.caltech.edu/records/zm2vp-way89/files/0904.4275.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs00526-009-0302-x.pdf", "url": "https://authors.library.caltech.edu/records/zm2vp-way89/files/art_3A10.1007_2Fs00526-009-0302-x.pdf" } ], "pub_year": "2010", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/yq8z6-97a54", "eprint_id": 19810, "eprint_status": "archive", "datestamp": "2023-08-19 03:33:40", "lastmod": "2026-04-16 01:40:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tupitsyn-I-S", "name": { "family": "Tupitsyn", "given": "I. S." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A." }, "orcid": "0000-0002-5777-642X" }, { "id": "Prokof'ev-N-V", "name": { "family": "Prokof'ev", "given": "N. V." } }, { "id": "Stamp-P-C-E", "name": { "family": "Stamp", "given": "P. C. E." } } ] }, "title": "Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 The American Physical Society.\n\nReceived 14 June 2010; published 17 August 2010.\n\nWe thank E. Fradkin, B. Svistunov, S. Trebst, M. Troyer,\nI. Affleck, K. Shtengel, and S. Sachdev for discussions. We\nare also indebted to M. Berciu and J. Heyl whose research\nclusters were used to perform our MC simulations. N.P. acknowledges\nsupport from the National Science Foundation\nunder Grant No. PHY-0653183, a grant from the Army Research\nOffice with funding from the DARPA OLE program,\nand Aspen Center for physics.\n\n

Published - Tupitsyn2010p11258Phys_Rev_B.pdf

", "abstract": "We construct a mapping between the two-dimensional toric code model in external magnetic fields, h_z and h_x, and the three-dimensional classical Ising system with plaquette interactions, which is equivalent to the three-dimensional Z_2 gauge Higgs model with anisotropy between the imaginary time and spatial directions. The isotropic limit of the latter model was studied using Monte Carlo simulations on large (up to 60^3) lattices in order to determine the stability of the topological phase against generic magnetic field perturbations and to resolve fine details of the phase diagram. We find that the topological phase is bounded by second-order transition lines, which merge into a first-order line at what appears to be a multicritical point arising from the competition between the Higgs and confinement transitions in the Z_2 gauge system. An effective field theory for this type of multicritical point (if one actually exists) is not known. Our results have potential applications to frustrated magnets, quantum computation, lattice gauge models in particle physics, and critical phenomena.", "date": "2010-08-17", "date_type": "published", "publication": "Physical Review B", "volume": "82", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 085114", "id_number": "CaltechAUTHORS:20100907-152559860", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100907-152559860", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0653183" }, { "agency": "Army Research Office" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Aspen Center for Physics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.82.085114", "primary_object": { "basename": "Tupitsyn2010p11258Phys_Rev_B.pdf", "url": "https://authors.library.caltech.edu/records/yq8z6-97a54/files/Tupitsyn2010p11258Phys_Rev_B.pdf" }, "pub_year": "2010", "author_list": "Tupitsyn, I. S.; Kitaev, A.; et al." }, { "id": "https://authors.library.caltech.edu/records/pw80h-jdy02", "eprint_id": 98014, "eprint_status": "archive", "datestamp": "2023-08-19 03:30:14", "lastmod": "2026-03-08 18:14:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "An Extremal Theorem in the Hypercube", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Electronic Journal of Combinatorics. \n\nSubmitted May 4, 2010; accepted Jul 18, 2010; published Aug 9, 2010. \n\nConlon supported by a Junior Research Fellowship at St John's College. \n\nI would like to thank Eoin Long for reading carefully through an earlier version of this note.\n\n

Published - EJC17.R111.pdf

Submitted - 1005.0582.pdf

Erratum - HyperCycleErratum.pdf

", "abstract": "The hypercube Q_n is the graph whose vertex set is {0, 1}^n and where two vertices are adjacent if they differ in exactly one coordinate. For any subgraph H of the cube, let ex(Q_(n), H) be the maximum number of edges in a subgraph of Q_n which does not contain a copy of H. We find a wide class of subgraphs H, including all previously known examples, for which ex(Q_(n), H) = o(e(Q_n)). In particular, our method gives a unified approach to proving that ex(Q_(n), C_(2t)) = o(e(Q_n)) for all t \u2265 4 other than 5.", "date": "2010-08-09", "date_type": "published", "publication": "Electronic Journal of Combinatorics", "volume": "17", "publisher": "Electronic Journal of Combinatorics", "pagerange": "Art. No. R111", "id_number": "CaltechAUTHORS:20190819-163059223", "issn": "1077-8926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190819-163059223", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1005.0582", "primary_object": { "basename": "1005.0582.pdf", "url": "https://authors.library.caltech.edu/records/pw80h-jdy02/files/1005.0582.pdf" }, "related_objects": [ { "basename": "EJC17.R111.pdf", "url": "https://authors.library.caltech.edu/records/pw80h-jdy02/files/EJC17.R111.pdf" }, { "basename": "HyperCycleErratum.pdf", "url": "https://authors.library.caltech.edu/records/pw80h-jdy02/files/HyperCycleErratum.pdf" } ], "pub_year": "2010", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/evvb9-rm871", "eprint_id": 19011, "eprint_status": "archive", "datestamp": "2023-08-22 00:26:06", "lastmod": "2026-04-12 00:08:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "Finite Gap Jacobi Matrices, I. The Isospectral Torus", "ispublished": "pub", "full_text_status": "public", "keywords": "Isospectral torus; Covering map; Orthogonal polynomials", "note": "\u00a9 2009 Springer. \n\nReceived: 25 September 2008. Accepted: 11 February 2009.\nPublished online: 22 May 2009. \n\nCommunicated by Vilmos Totik. \n\nWe want to thank D. Calegari, H. Farkas, F. Gesztesy, I. Kra, N. Makarov, F. Peherstorfer, and P. Yuditskii for helpful discussions and comments.\n\n

Submitted - 0810.3273

", "abstract": "Let e \u2282 R be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is e, a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as a tool for ourselves and others to study perturbations. One important result is the expression of Jost functions for the torus in terms of theta functions.", "date": "2010-08", "date_type": "published", "publication": "Constructive Approximation", "volume": "32", "number": "1", "publisher": "Springer", "pagerange": "1-65", "id_number": "CaltechAUTHORS:20100713-080234381", "issn": "0176-4276", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100713-080234381", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00365-009-9057-z", "primary_object": { "basename": "0810.3273", "url": "https://authors.library.caltech.edu/records/evvb9-rm871/files/0810.3273" }, "pub_year": "2010", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/mr5rg-bsq25", "eprint_id": 71904, "eprint_status": "archive", "datestamp": "2023-08-22 00:17:44", "lastmod": "2026-04-11 17:36:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Iterative maximum likelihood on networks", "ispublished": "pub", "full_text_status": "public", "keywords": "Maximum likelihood; Sparse sensing; Learning on networks; Algebraic recursion relation; Bayesian Economics", "note": "\u00a9 2009 Elsevier. \n\nReceived 30 April 2009. Accepted 31 August 2009. Available online 3 December 2009. \n\nSupported by a Sloan fellowship in Mathematics, by BSF grant 2004105, by NSF Career Award (DMS 054829) by ONR award N00014-07-1-0506 and by ISF grant 1300/08. \n\nSupported by ISF grant 1300/08.\n\n

Submitted - 0904.4903.pdf

", "abstract": "We consider n agents located on the vertices of a connected graph. Each agent v receives a signal X_v(0)\u223cN(\u03bc,1) where \u03bc is an unknown quantity. A natural iterative way of estimating \u03bc is to perform the following procedure. At iteration t+1 let X_v(t+1) be the average of X_v(t) and of X_w(t) among all the neighbors w of v. It is well known that this procedure converges to X(\u221e) = 1/2 |E|^(\u22121) \u03a3 d_v X_v where dv is the degree of v. \n\nIn this paper we consider a variant of simple iterative averaging, which models \"greedy\" behavior of the agents. At iteration t, each agent v declares the value of its estimator X_v(t) to all of its neighbors. Then, it updates X_v(t+1) by taking the maximum likelihood (or minimum variance) estimator of \u03bc, given X_v(t) and X_w(t) for all neighbors w of v, and the structure of the graph. \n\nWe give an explicit efficient procedure for calculating X_v(t), study the convergence of the process as t\u2192\u221e and show that if the limit exists then X_v(\u221e)=X_w(\u221e) for all v and w. For graphs that are symmetric under actions of transitive groups, we show that the process is efficient. Finally, we show that the greedy process is in some cases more efficient than simple averaging, while in other cases the converse is true, so that, in this model, \"greed\" of the individual agents may or may not have an adverse affect on the outcome. \n\nThe model discussed here may be viewed as the maximum likelihood version of models studied in Bayesian Economics. The ML variant is more accessible and allows in particular to show the significance of symmetry in the efficiency of estimators using networks of agents.", "date": "2010-07", "date_type": "published", "publication": "Advances in Applied Mathematics", "volume": "45", "number": "1", "publisher": "Elsevier", "pagerange": "36-49", "id_number": "CaltechAUTHORS:20161109-165317769", "issn": "0196-8858", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-165317769", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2004105" }, { "agency": "NSF", "grant_number": "DMS 054829" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-07-1-0506" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aam.2009.11.004", "primary_object": { "basename": "0904.4903.pdf", "url": "https://authors.library.caltech.edu/records/mr5rg-bsq25/files/0904.4903.pdf" }, "pub_year": "2010", "author_list": "Mossel, Elchanan and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/mmsks-jf624", "eprint_id": 20038, "eprint_status": "archive", "datestamp": "2023-08-22 00:07:27", "lastmod": "2026-04-11 19:53:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hedden-M", "name": { "family": "Hedden", "given": "Matthew" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Manifolds with small Heegaard Floer ranks", "ispublished": "pub", "full_text_status": "public", "keywords": "Heegaard Floer homology; Khovanov homology; two-component unlink; torus bundle", "note": "\u00a9 2010 Mathematical Sciences Publishers. \n\nReceived: 11 August 2009; Revised: 26 May 2010; Accepted: 24 February 2010; Published: 11 June 2010; Proposed: Ron Fintushel; Seconded: Peter Ozsv\u00e1th, Ron Stern.\n\n

Published - Hedden2010p11401Geom_Topol.pdf

", "abstract": "We show that the only irreducible three-manifold with positive first Betti number and Heegaard Floer homology of rank two is homeomorphic to zero-framed surgery on the trefoil. We classify links whose branched double cover gives rise to this manifold. Together with a spectral sequence from Khovanov homology to the Floer homology of the branched double cover, our results show that Khovanov\nhomology detects the unknot if and only if it detects the two component unlink.", "date": "2010-06-11", "date_type": "published", "publication": "Geometry and Topology", "volume": "14", "number": "3", "publisher": "Geometry & Topology Publications", "pagerange": "1479-1501", "id_number": "CaltechAUTHORS:20100920-101712597", "issn": "1465-3060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100920-101712597", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/gt.2010.14.1479", "primary_object": { "basename": "Hedden2010p11401Geom_Topol.pdf", "url": "https://authors.library.caltech.edu/records/mmsks-jf624/files/Hedden2010p11401Geom_Topol.pdf" }, "pub_year": "2010", "author_list": "Hedden, Matthew and Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/ch1t4-h8378", "eprint_id": 24514, "eprint_status": "archive", "datestamp": "2023-08-19 02:42:06", "lastmod": "2026-04-11 17:11:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aluffi-P", "name": { "family": "Aluffi", "given": "Paolo" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Parametric Feynman integrals and determinant hypersurfaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 International Press. \n\nThe first author acknowledges partial support by NSA grant H98230-07-1-0024. The second author is partially supported by NSF grants DMS-0651925, DMS-0901221, and DMS-1007207. This work was partly carried out during stays of the authors at the MPI and MSRI. The first author also thanks the California Institute of Technology, where part of this work was done.\n\n

Published - Aluffi2010p15170Adv_Theor_Math_Phys.pdf

", "abstract": "The purpose of this paper is to show that, under certain combinatorial conditions on the graph, parametric Feynman integrals can be realized as periods on the complement of the determinant hypersurface in an affine space depending on the number of loops of the Feynman graph. The question of whether the Feynman integrals are periods of mixed Tate motives can then be reformulated (modulo divergences) as a question on a relative cohomology being a realization of a mixed Tate motive. This is the cohomology of the pair of the determinant hypersurface complement and a normal crossings divisor depending only on the number of loops and the genus of the graph. We show explicitly that this relative cohomology is a realization of a mixed Tate motive in the case of three loops and we give alternative formulations of the main question in the general case, by describing the locus of intersection of the divisor with the determinant hypersurface complement in terms of intersections of unions of Schubert cells in flag varieties. We also discuss different methods of regularization aimed at removing the divergences of the Feynman integral.", "date": "2010-06", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "14", "number": "3", "publisher": "International Press", "pagerange": "911-963", "id_number": "CaltechAUTHORS:20110725-070951650", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110725-070951650", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSA", "grant_number": "H98230-07-1-0024" }, { "agency": "NSF", "grant_number": "DMS-0651925" }, { "agency": "NSF", "grant_number": "DMS-0901221" }, { "agency": "NSF", "grant_number": "DMS-1007207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0901.2107", "primary_object": { "basename": "Aluffi2010p15170Adv_Theor_Math_Phys.pdf", "url": "https://authors.library.caltech.edu/records/ch1t4-h8378/files/Aluffi2010p15170Adv_Theor_Math_Phys.pdf" }, "pub_year": "2010", "author_list": "Aluffi, Paolo and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/7hptf-y4j30", "eprint_id": 77078, "eprint_status": "archive", "datestamp": "2023-08-19 02:37:45", "lastmod": "2026-04-11 19:18:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } }, { "id": "Thomas-L-E", "name": { "family": "Thomas", "given": "Lawrence E." } } ] }, "title": "Bipolaron and N-Polaron Binding Energies", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 The American Physical Society. \n\nReceived 7 April 2010; published 27 May 2010. \n\nThe authors are grateful to Herbert Spohn for making us aware of the problem of proving the absence of binding for large U. Grants from the U.S. National Science Foundation are gratefully acknowledged: PHY-0652854 (E.\u2009L. and R.\u2009F.), PHY-0845292 (R.\u2009S.).\n\n

Published - PhysRevLett.104.210402.pdf

Submitted - 1004.1196.pdf

", "abstract": "The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2\u03b1, where U is the electronic Coulomb repulsion and \u03b1 is the polaron coupling constant. Second, if U is large enough, there is no multipolaron binding of any kind. Considering the known fact that there is binding for some U>2\u03b1, these conclusions are not obvious and their proof has been an open problem for some time.", "date": "2010-05-28", "date_type": "published", "publication": "Physical Review Letters", "volume": "104", "number": "21", "publisher": "American Physical Society", "pagerange": "Art. No. 210402", "id_number": "CaltechAUTHORS:20170501-064924933", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-064924933", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0652854" }, { "agency": "NSF", "grant_number": "PHY-0845292" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.104.210402", "primary_object": { "basename": "1004.1196.pdf", "url": "https://authors.library.caltech.edu/records/7hptf-y4j30/files/1004.1196.pdf" }, "related_objects": [ { "basename": "PhysRevLett.104.210402.pdf", "url": "https://authors.library.caltech.edu/records/7hptf-y4j30/files/PhysRevLett.104.210402.pdf" } ], "pub_year": "2010", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/3468f-8xb76", "eprint_id": 21947, "eprint_status": "archive", "datestamp": "2023-08-19 02:23:41", "lastmod": "2026-04-11 22:59:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Poltoratski-A", "name": { "family": "Poltoratski", "given": "Alexei" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "The Hilbert transform of a measure", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Springer. \n\nReceived December 9, 2008. \n\nSupported in part by NSF grant DMS-0800300; Supported in part by NSF grant DMS-0652919; Supported in part by NSF grant DMS-0965411.\n\n

Submitted - 0811.0791

", "abstract": "Let e be a homogeneous subset of R in the sense of Carleson. Let \u03bc be a finite positive measure on R and H_\u03bc(x) its Hilbert transform. We prove that if lim_(t\u2192\u221e)t|e\u2229{x||H_\u03bc(x)|>t}| = 0, then \u03bc_s(e) = 0, where \u03bc_s is the singular part of \u03bc.", "date": "2010-05", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "111", "number": "1", "publisher": "Springer Verlag", "pagerange": "247-265", "id_number": "CaltechAUTHORS:20110201-094527717", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110201-094527717", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0800300" }, { "agency": "NSF", "grant_number": "DMS-0652919" }, { "agency": "NSF", "grant_number": "DMS-0965411" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s11854-010-0017-0", "primary_object": { "basename": "0811.0791", "url": "https://authors.library.caltech.edu/records/3468f-8xb76/files/0811.0791" }, "pub_year": "2010", "author_list": "Poltoratski, Alexei; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/bgvds-kvv30", "eprint_id": 18302, "eprint_status": "archive", "datestamp": "2023-08-19 02:18:54", "lastmod": "2026-04-11 17:26:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Generation of fusion systems of characteristic 2-type", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2009 Springer-Verlag. \n\nReceived: 9 December 2008. Accepted: 25 November 2009. Published online: 11 December 2009. \n\nThis work was partially supported by NSF-0504852.", "abstract": "We prove that if F is a saturated fusion system on a finite 2-\ngroup S, then either F is known, or F is generated by the normalizers of\ntwo canonically defined F-characteristic subgroups of S. There are various\ncorollaries for finite groups of characteristic 2-type.", "date": "2010-05", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "180", "number": "2", "publisher": "Springer", "pagerange": "225-299", "id_number": "CaltechAUTHORS:20100513-152930353", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100513-152930353", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-009-0229-z", "pub_year": "2010", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/6pvht-fny80", "eprint_id": 19264, "eprint_status": "archive", "datestamp": "2023-08-19 02:23:26", "lastmod": "2026-04-11 22:04:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "David" }, "orcid": "0000-0001-5924-3849" }, { "id": "Killip-R", "name": { "family": "Killip", "given": "Rowan" }, "orcid": "0000-0002-4272-7916" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Perturbations of orthogonal polynomials with periodic recursion coefficients", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Annals of Mathematics. \n\nReceived February 2, 2007. Revised September 3, 2008. Published 25 April 2010. \n\nIt is a pleasure to thank Leonid Golinskii, Irina Nenciu, Leonid Pastur, and Peter Yuditskii for useful discussions. Note Added August, 2008. During the refereeing of this paper, Remling (in\n[94]), motivated in part by this paper, found a positive resolution of the conjecture that, in the language of our Theorem 9.5, every set in G is a Denisov-Rakhmanov set. His analysis depends on a very interesting theorem on right limits of Jacobi\nmatrices with absolutely continuous spectrum\u2014it provides a new approach to Denisov-Rakhmanov theorems. \n\nD.D. was supported in part by NSF grants DMS-0500910 and DMS-0653720. R.K. was supported in part by NSF grant DMS-0401277 and a Sloan Foundation Fellowship. B.S. was supported in part by NSF grant DMS-0140592 and U.S.-Israel Binational Science Foundation (BSF) Grant No. 2002068.\n\n

Submitted - 0702388

", "abstract": "The results of Denisov-Rakhmanov, Szeg\u0151-Shohat-Nevai, and Killip-Simon are extended from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a characterization of the isospectral torus that is well adapted to the study of perturbations.", "date": "2010-05", "date_type": "published", "publication": "Annals of Mathematics", "volume": "171", "number": "3", "publisher": "Annals of Mathematics", "pagerange": "1931-2010", "id_number": "CaltechAUTHORS:20100803-145828608", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100803-145828608", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0500910" }, { "agency": "NSF", "grant_number": "DMS-0653720" }, { "agency": "NSF", "grant_number": "DMS-0401277" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4007/annals.2010.171.1931", "primary_object": { "basename": "0702388", "url": "https://authors.library.caltech.edu/records/6pvht-fny80/files/0702388" }, "pub_year": "2010", "author_list": "Damanik, David; Killip, Rowan; et al." }, { "id": "https://authors.library.caltech.edu/records/xt2ry-nbk16", "eprint_id": 66693, "eprint_status": "archive", "datestamp": "2023-08-19 02:16:25", "lastmod": "2026-04-11 18:32:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Iqbal-A", "name": { "family": "Iqbal", "given": "Amer" } }, { "id": "Koz\u00e7az-C", "name": { "family": "Koz\u00e7az", "given": "Can" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Link Homologies and the Refined Topological Vertex", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author(s) 2010. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 16 September 2009. Accepted: 14 December 2009. Published online: 20 April 2010. \n\nCommunicated by N.A. Nekrasov. \n\nWe would like to thank C. Doran, J. Rasmussen, and B.Webster for valuable discussions. It is our pleasure to thank the Stony Brook physics department and the 4th Simons Workshop in Mathematics and Physics for hospitality during the initial stages of this work. In addition, C.V. thanks the CTP at MIT for hospitality during his sabbatical leave. The work of S.G. is supported in part by DOE grant DE-FG03-92-ER40701, in part by RFBR grant 04-02-16880, and in part by the grant for support of scientific schools NSh-8004.2006.2. The work of C.V. is supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\n

Published - Gukov,S.757-.pdf

Submitted - 0705.1368.pdf

", "abstract": "We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations (R _1, R _2). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.", "date": "2010-04-20", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "298", "number": "3", "publisher": "Springer", "pagerange": "757-785", "id_number": "CaltechAUTHORS:20160505-114729379", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-114729379", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Russian Foundation for Basic Research (RFBR)", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-010-1045-4", "primary_object": { "basename": "0705.1368.pdf", "url": "https://authors.library.caltech.edu/records/xt2ry-nbk16/files/0705.1368.pdf" }, "related_objects": [ { "basename": "Gukov,S.757-.pdf", "url": "https://authors.library.caltech.edu/records/xt2ry-nbk16/files/Gukov,S.757-.pdf" } ], "pub_year": "2010", "author_list": "Gukov, Sergei; Iqbal, Amer; et al." }, { "id": "https://authors.library.caltech.edu/records/kcz9a-s1223", "eprint_id": 17864, "eprint_status": "archive", "datestamp": "2023-08-21 23:42:26", "lastmod": "2026-04-11 18:06:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Levaillant-C", "name": { "family": "Levaillant", "given": "Claire" } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David" } } ] }, "title": "Parameters for which the Lawrence\u2013Krammer representation is reducible", "ispublished": "pub", "full_text_status": "public", "keywords": "Representation theory; Lawrence-Krammer representation; Braid groups; BMW algebras; Semisimplicity; Iwahori-Hecke algebras", "note": "\u00a9 2010 Elsevier Inc. \n\nReceived 31 August 2008. Available online 2 February 2010. \n\nCommunicated by Michel Brou\u00e9.\n\n

Submitted - 0901.3856.pdf

", "abstract": "We show that the representation, introduced by Lawrence and\nKrammer to show the linearity of the braid group, is generically\nirreducible. However, for some values of its two parameters when\nthese are specialized to complex numbers, it becomes reducible.\nWe construct a representation of degree n(n\u22121)/2 of the BMW algebra\nof type A_(n\u22121). As a representation of the braid group on n strands,\nit is equivalent to the Lawrence\u2013Krammer representation where\nthe two parameters of the BMW algebra are related to those\nappearing in the Lawrence\u2013Krammer representation. We give the\nvalues of the parameters for which the representation is reducible\nand give the proper invariant subspaces in some cases. We use\nthis representation to show that for these special values of the\nparameters, the BMW algebra of type A_(n\u22121) is not semisimple.", "date": "2010-04-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "323", "number": "7", "publisher": "Elsevier", "pagerange": "1966-1982", "id_number": "CaltechAUTHORS:20100406-100411802", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100406-100411802", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jalgebra.2009.12.021", "primary_object": { "basename": "0901.3856.pdf", "url": "https://authors.library.caltech.edu/records/kcz9a-s1223/files/0901.3856.pdf" }, "pub_year": "2010", "author_list": "Levaillant, Claire and Wales, David" }, { "id": "https://authors.library.caltech.edu/records/cnwgn-76b14", "eprint_id": 18459, "eprint_status": "archive", "datestamp": "2023-08-19 02:10:04", "lastmod": "2026-04-16 01:39:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Fidkowski-L", "name": { "family": "Fidkowski", "given": "Lukasz" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Effects of interactions on the topological classification of free fermion systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 The American Physical Society. Received 4 January 2010; published 7 April 2010. We would like to acknowledge useful discussions with\nJohn Preskill and Andreas Ludwig. This work was supported\nin part by the Institute for Quantum Information under National\nScience Foundation, Grant No. PHY-0803371. A.K. is\nalso supported by DARPA under Grant No. HR0011-09-\n0009.\n\n

Published - Fidkowski2010p10059Phys_Rev_B.pdf

", "abstract": "We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one-dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion classification lies in Z, but with the introduction of interactions the Z is broken to Z_8. We illustrate this in the microscopic model of the Majorana chain by constructing an explicit path between two distinct phases whose topological invariants are equal modulo 8, along which the system remains gapped. The path goes through a strongly interacting region. We also find the field-theory interpretation of this phenomenon. There is a second-order phase transition between the two phases in the free theory, which can be avoided by going through the strongly interacting region. We show that this transition is in the two-dimensional Ising universality class, where a first-order phase transition line, terminating at a second-order transition, can be avoided by going through the analog of a high-temperature paramagnetic phase. In fact, we construct the full phase diagram of the system as a function of the thermal operator (i.e., the mass term that tunes between the two phases in the free theory) and two quartic operators, obtaining a first-order Peierls transition region, a second-order transition region, and a region with no transition.", "date": "2010-04-01", "date_type": "published", "publication": "Physical Review B", "volume": "81", "number": "13", "publisher": "American Physical Society", "pagerange": "Art. No. 134509", "id_number": "CaltechAUTHORS:20100526-114410284", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100526-114410284", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Institute for Quantum Information under NSF", "grant_number": "PHY-0803371" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-0009" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.81.134509", "primary_object": { "basename": "Fidkowski2010p10059Phys_Rev_B.pdf", "url": "https://authors.library.caltech.edu/records/cnwgn-76b14/files/Fidkowski2010p10059Phys_Rev_B.pdf" }, "pub_year": "2010", "author_list": "Fidkowski, Lukasz and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/69a6q-4a252", "eprint_id": 17610, "eprint_status": "archive", "datestamp": "2023-08-19 02:03:13", "lastmod": "2026-04-11 22:41:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Ryckman-E", "name": { "family": "Ryckman", "given": "Eric" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Equality of the Spectral and Dynamical Definitions of Reflection", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 12 May 2009. Accepted: 10 August 2009. Published online: 14 November 2009. \n\nCommunicated by M. Aizenman. \n\nSupported in part by NSF grant DMS-0652919.\n\n

Published - Breuer2010p7191Commun_Math_Phys.pdf

Submitted - 0905.3724

", "abstract": "For full-line Jacobi matrices, Schr\u00f6dinger operators, and CMV matrices, we show that being reflectionless, in the sense of the well-known property of m-functions, is equivalent to a lack of reflection in the dynamics in the sense that any state that goes entirely to x = \u2212\u221e as t \u2192 \u2212\u221e goes entirely to x = \u221e as t \u2192 \u221e. This allows us to settle a conjecture of Deift and Simon from 1983 regarding ergodic Jacobi matrices.", "date": "2010-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "295", "number": "2", "publisher": "Springer", "pagerange": "531-550", "id_number": "CaltechAUTHORS:20100301-083137497", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100301-083137497", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-009-0945-7", "primary_object": { "basename": "0905.3724", "url": "https://authors.library.caltech.edu/records/69a6q-4a252/files/0905.3724" }, "related_objects": [ { "basename": "Breuer2010p7191Commun_Math_Phys.pdf", "url": "https://authors.library.caltech.edu/records/69a6q-4a252/files/Breuer2010p7191Commun_Math_Phys.pdf" } ], "pub_year": "2010", "author_list": "Breuer, Jonathan; Ryckman, Eric; et al." }, { "id": "https://authors.library.caltech.edu/records/bzvfv-ae337", "eprint_id": 17899, "eprint_status": "archive", "datestamp": "2023-08-21 23:39:11", "lastmod": "2026-04-11 23:01:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ku-Cheng-Yeaw", "name": { "family": "Ku", "given": "Cheng Yeaw" } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "Eigenvalues of the derangement graph", "ispublished": "pub", "full_text_status": "public", "keywords": "Derangement; Cayley graph; Eigenvalue; Symmetric group", "note": "\u00a9 2009 Elsevier Inc.\n\nReceived 20 March 2008. Available online 12 October 2009. \n\nWe would like to thank the anonymous referees for the comments that helped us make several improvements to this paper.\n\n

Submitted - 0803.2901.pdf

", "abstract": "We consider the Cayley graph on the symmetric group S_n generated by derangements. It is well known that the eigenvalues of this graph are indexed by partitions of n. We investigate how these eigenvalues are determined by the shape of their corresponding partitions. In particular, we show that the sign of an eigenvalue is the parity of the number of cells below the first row of the corresponding Ferrers diagram. We also provide some lower and upper bounds for the absolute values of these eigenvalues.", "date": "2010-04", "date_type": "published", "publication": "Journal of Combinatorial Theory. Series A", "volume": "117", "number": "3", "publisher": "Elsevier", "pagerange": "289-312", "id_number": "CaltechAUTHORS:20100408-101413008", "issn": "0097-3165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100408-101413008", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jcta.2009.10.002", "primary_object": { "basename": "0803.2901.pdf", "url": "https://authors.library.caltech.edu/records/bzvfv-ae337/files/0803.2901.pdf" }, "pub_year": "2010", "author_list": "Ku, Cheng Yeaw and Wales, David B." }, { "id": "https://authors.library.caltech.edu/records/gw5zr-6gz95", "eprint_id": 19279, "eprint_status": "archive", "datestamp": "2023-08-19 01:50:00", "lastmod": "2026-04-11 17:29:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Henriques-A", "name": { "family": "Henriques", "given": "Andr\u00e9" } }, { "id": "Kamnitzer-J", "name": { "family": "Kamnitzer", "given": "Joel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Annals of Mathematics. \n\nReceived July 25, 2005; Revised May 13, 2007. \n\nThe authors are grateful to L. Avramov, C. De Concini, J. Morava, J. Morgan, and B. Sturmfels, for useful discussions and references. P.E. thanks the mathematics department of ETH (Zurich) for hospitality. The work of P.E. was partially supported by the NSF grant DMS-0504847 and the CRDF grant RM1-2545-MO-03. E.R. was supported in part by NSF Grant No. DMS-0401387. J.K. thanks the mathematics department of EPFL for hospitality. The work of J.K. was supported by NSERC and AIM. Finally, we would like to mention that at many\nstages of this work we made significant use of the Magma computer algebra system for algebraic computations.\n\n

Submitted - 0507514.pdf

", "abstract": "We compute the Poincar\u00e9 polynomial and the cohomology algebra with rational coefficients of the manifold M_n of real points of the moduli space of algebraic curves of genus 0 with n labeled points. This cohomology is a quadratic algebra, and we conjecture that it is Koszul. We also compute the 2-local torsion in the cohomology of M_n. As was shown by the fourth author, the cohomology of M_n does not have odd torsion, so that the above determines the additive structure of the integral homology and cohomology. Further, we prove that the rational homology operad of M_n is the operad of 2-Gerstenhaber algebras, which is closely related to the Hanlon-Wachs operad of 2-Lie algebras (generated by a ternary bracket). Finally, using Drinfeld's theory of quantization of coboundary Lie quasibialgebras, we show that a large series of representations of the quadratic dual Lie algebra L_n of H^*(M_n,Q) (associated to such quasibialgebras) factors through the the natural projection of L_n to the associated graded Lie algebra of the prounipotent completion of the fundamental group of M_n. This leads us to conjecture that the said projection is an isomorphism, which would imply a formula for lower central series ranks of the fundamental group. On the other hand, we show that the spaces M_n are not formal starting from n = 6.", "date": "2010-03", "date_type": "published", "publication": "Annals of Mathematics", "volume": "171", "number": "2", "publisher": "Annals of Mathematics", "pagerange": "731-777", "id_number": "CaltechAUTHORS:20100804-142058742", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100804-142058742", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504847" }, { "agency": "NSF", "grant_number": "DMS-0401387" }, { "agency": "Civilian Research & Development Foundation (CRDF)", "grant_number": "RM1-2545-MO-03" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "American Institute of Mathematics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2010.171.731", "primary_object": { "basename": "0507514.pdf", "url": "https://authors.library.caltech.edu/records/gw5zr-6gz95/files/0507514.pdf" }, "pub_year": "2010", "author_list": "Etingof, Pavel; Henriques, Andr\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/dsst3-q2q20", "eprint_id": 18443, "eprint_status": "archive", "datestamp": "2023-08-21 23:29:43", "lastmod": "2026-04-11 19:27:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Willett-B", "name": { "family": "Willett", "given": "Brian" } }, { "id": "Yaakov-I", "name": { "family": "Yaakov", "given": "Itamar" } } ] }, "title": "Exact results for Wilson loops in superconformal Chern-Simons theories with matter", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric gauge theory; Matrix Models; AdS-CFT Correspondence; Chern-Simons Theories", "note": "\u00a9 SISSA 2010.\n\nReceived: 30 November 2009. Revised: 23 February 2010. Accepted: 1 March 2010. Published online: 17 March 2010.\n\n

Submitted - 0909.4559.pdf

", "abstract": "We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any N = 2 theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.", "date": "2010-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2010", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 089", "id_number": "CaltechAUTHORS:20100526-081247508", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100526-081247508", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "68-2750", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP03(2010)089", "primary_object": { "basename": "0909.4559.pdf", "url": "https://authors.library.caltech.edu/records/dsst3-q2q20/files/0909.4559.pdf" }, "pub_year": "2010", "author_list": "Kapustin, Anton; Willett, Brian; et al." }, { "id": "https://authors.library.caltech.edu/records/qta7e-y5811", "eprint_id": 19315, "eprint_status": "archive", "datestamp": "2023-08-19 01:50:14", "lastmod": "2026-03-07 16:33:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Chermak-A", "name": { "family": "Chermak", "given": "Andrew" } } ] }, "title": "A group-theoretic approach to a family of 2-local finite groups constructed by Levi and Oliver", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2009 Annals of Mathematics.\nReceived January 12, 2006.\nRevised December 14, 2006.\nThe work of the first author was partially supported by NSF-0203417.", "abstract": "We extend the notion of a p-local finite group (defined in [BLO03]) to the notion of a p-local group. We define morphisms of p-local groups, obtaining thereby a category, and we introduce the notion of a representation of a p-local group via signalizer functors associated with groups. We construct a chain G = (G_0 \u2192 G_1 \u2192 ...) of 2-local finite groups, via a representation of a chain G^* = (G_0 \u2192 G_1 \u2192 ...) of groups, such that G_0 is the 2-local finite group of the third Conway sporadic group Co_3, and for n > 0, G_n is one of the 2-local finite groups constructed by Levi and Oliver in [LO02]. We show that the direct limit G of G exists in the category of 2-local groups, and that it is the 2-local group of the union of the chain G^*. The 2-completed classifying space of G is shown to be the classifying space B DI(4) of the exotic 2-compact group of Dwyer and Wilkerson [DW93].", "date": "2010-03", "date_type": "published", "publication": "Annals of Mathematics", "volume": "171", "number": "2", "publisher": "Annals of Mathematics", "pagerange": "881-978", "id_number": "CaltechAUTHORS:20100806-092914498", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100806-092914498", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0203417" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "2010", "author_list": "Aschbacher, Michael and Chermak, Andrew" }, { "id": "https://authors.library.caltech.edu/records/e7c9x-taw64", "eprint_id": 17967, "eprint_status": "archive", "datestamp": "2023-08-19 01:39:22", "lastmod": "2026-04-11 19:53:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nakamura-Shin", "name": { "family": "Nakamura", "given": "Shin" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } } ] }, "title": "Gravity dual of spatially modulated phase", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 The American Physical Society. \n\nReceived 26 November 2009; published 10 February 2010. \n\nWe thank M. Fisher, K. Hashimoto, G. Horowitz, S. Kinoshita, A. Kitaev, M. Kitazawa, H. Liu, K. Murata, M. Oshikawa, Y. Tachikawa, and T. Takayanagi for discussions. H. O. and C.-S. P. are supported in part by DOE Grant No. DE-FG03-92-ER40701. H. O. is also supported in part by the World Premier International Research Center Initiative of MEXT of Japan and by a Grant-in-Aid for Scientific Research (C) under Grant No. 20540256 of JSPS. S. N. is supported by the Grant-in-Aid for the Global COE Program ''The Next Generation of Physics, Spun from Universality and Emergence'' of MEXT of Japan. S. N. was also supported by the SRC Program of the KOSEF through the Center for Quantum Space-time of Sogang University under Grant No. R11-2005-021 and by the YST program of Asia Pacific Center for Theoretical Physics at the initial stage of the present work. H. O. thanks the Albert Einstein Institute in Golm, the Aspen Center for Physics, the Galileo Galilei Institute in Florence, the Kavli Institute for Theoretical Physics in Santa Barbara, and the Yukawa Institute for Theoretical Physics in Kyoto for their hospitality.\n\n

Published - Nakamura2010p7451Phys_Rev_D.pdf

Submitted - 0911.0679.pdf

", "abstract": "We show that the five-dimensional Maxwell theory with the Chern-Simons term is tachyonic in the presence of a constant electric field. When coupled to gravity, a sufficiently large Chern-Simons coupling causes instability of the Reissner-Nordstr\u00f6m black holes in anti-de Sitter space. The instability happens only at nonvanishing momenta, suggesting a spatially modulated phase in the holographically dual quantum field theory in (3+1) dimensions, with spontaneous current generation in a helical configuration. The three-charge extremal black hole in the type IIB superstring theory on AdS_5\u00d7S^5 barely satisfies the stability condition.", "date": "2010-02-15", "date_type": "published", "publication": "Physical Review D", "volume": "81", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 044018", "id_number": "CaltechAUTHORS:20100413-155824837", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100413-155824837", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Korea Science and Engineering Foundation", "grant_number": "R11-2005-021" }, { "agency": "Asia Pacific Center for Theoretical Physics" } ] }, "other_numbering_system": { "items": [ { "id": "68-2754", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.81.044018", "primary_object": { "basename": "0911.0679.pdf", "url": "https://authors.library.caltech.edu/records/e7c9x-taw64/files/0911.0679.pdf" }, "related_objects": [ { "basename": "Nakamura2010p7451Phys_Rev_D.pdf", "url": "https://authors.library.caltech.edu/records/e7c9x-taw64/files/Nakamura2010p7451Phys_Rev_D.pdf" } ], "pub_year": "2010", "author_list": "Nakamura, Shin; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/fq4z3-1dv42", "eprint_id": 17518, "eprint_status": "archive", "datestamp": "2023-08-19 01:31:40", "lastmod": "2026-04-11 22:22:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dunfield-N-M", "name": { "family": "Dunfield", "given": "Nathan M." } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Three-manifolds (Topology)", "note": "\u00a9 2010 Johns Hopkins University Press.\n\nManuscript received January 7, 2008; revised October 14, 2008.\n\nResearch of both authors supported in part by the NSF; research of the first author supported in part by\nthe Sloan Foundation.\n\n

Published - Dunfield2010p7073Am_J_Math.pdf

", "abstract": "We exhibit a closed hyperbolic 3-manifold which satisfies a very strong form of Thurston's Virtual Fibration Conjecture. In particular, this manifold has finite covers which fiber over the circle in arbitrarily many ways. More precisely, it has a tower of finite covers where the number of fibered faces of the Thurston norm ball goes to infinity, in fact faster than any power of the logarithm of the degree of the cover, and we give a more precise quantitative lower bound. The example manifold M is arithmetic, and the proof uses detailed number-theoretic information, at the level of the Hecke eigenvalues, to drive a geometric argument based on Fried's dynamical characterization of the fibered faces. The origin of the basic fibration M \u2192 S^1 is the modular elliptic curve E = X_0(49), which admits multiplication by the ring of integers of Q[\u221a(\u22127)]. We first base change the holomorphic\ndifferential on E to a cusp form on GL(2) over K = Q[\u221a(\u22123)], and then transfer over to a quaternion algebra D/K ramified only at the primes above 7; the fundamental group of M is a quotient of the principal congruence subgroup of O^\u2217_D of level 7. To analyze the topological properties of M, we use a new practical method for computing the Thurston norm, which is of independent interest. We also give a noncompact finite-volume hyperbolic 3-manifold with the same properties by using a direct topological argument.", "date": "2010-02", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "132", "number": "1", "publisher": "Johns Hopkins University Press", "pagerange": "53-97", "id_number": "CaltechAUTHORS:20100218-101507964", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100218-101507964", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1353/ajm.0.0098", "primary_object": { "basename": "Dunfield2010p7073Am_J_Math.pdf", "url": "https://authors.library.caltech.edu/records/fq4z3-1dv42/files/Dunfield2010p7073Am_J_Math.pdf" }, "pub_year": "2010", "author_list": "Dunfield, Nathan M. and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/ky9rm-n1391", "eprint_id": 16864, "eprint_status": "archive", "datestamp": "2023-08-19 01:21:24", "lastmod": "2026-04-11 18:06:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } } ] }, "title": "Supersymmetric non-relativistic geometries in M-theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Elsevier B.V. \n\nReceived 8 June 2009; revised 4 August 2009; accepted 31 August 2009. Available online 4 September 2009. \n\nThis article is registered under preprint number 0905.1954. \n\nWe would like to thank Jaewon Song and Masahiko Yamazaki for their participation in an earlier stage of this project and for discussion. We are grateful to Yu Nakayama for helpful discussion. This work is supported in part by DOE grant DE-FG03-92-ER40701. The work of H.O. is also supported in part by a Grant-in-Aid for Scientific Research (C) 20540256 from the Japan Society for the Promotion of Science, by the World Premier International Research Center Initiative of MEXT of Japan, and by the Kavli Foundation. C.P. is supported in part by Samsung Scholarship.\n\n

Submitted - 0905.1954.pdf

", "abstract": "We construct M-theory supergravity solutions with the non-relativistic Schr\u00f6dinger symmetry starting\nfrom the warped AdS_5 metric with N = 1 supersymmetry. We impose the condition that the lightlike direction\nis compact by making it a non-trivial U(1) bundle over the compact space. Sufficient conditions\nfor such solutions are analyzed. The solutions have two supercharges for generic values of parameters,\nbut the number of supercharges increases to six in some special cases. A Schr\u00f6dinger geometry with\nSU(2)\u00d7SU(2)\u00d7U(1) isometry is considered as a specific example.We consider the Kaluza\u2013Klein modes\nand show that the non-relativistic particle number is bounded above by the quantum numbers of the compact\nspace.", "date": "2010-01-01", "date_type": "published", "publication": "Nuclear Physics B", "volume": "824", "number": "1-2", "publisher": "Elsevier", "pagerange": "136-153", "id_number": "CaltechAUTHORS:20091203-101126154", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091203-101126154", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "(C) 20540256" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Kavli Foundation" }, { "agency": "Samsung Scholarship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2731", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2009.08.021", "primary_object": { "basename": "0905.1954.pdf", "url": "https://authors.library.caltech.edu/records/ky9rm-n1391/files/0905.1954.pdf" }, "pub_year": "2010", "author_list": "Ooguri, Hirosi and Park, Chang-Soon" }, { "id": "https://authors.library.caltech.edu/records/9421p-rnq58", "eprint_id": 18651, "eprint_status": "archive", "datestamp": "2023-08-19 01:18:04", "lastmod": "2026-03-09 23:10:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Transformations of elliptic hypergeometric integrals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 Annals of Mathematics. \n\nReceived: 21 April 2005; Published: 8 March 2010.\n\n

Submitted - 0309252.pdf

", "abstract": "We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BC_n and A_n; as a special case, we recover some integral identities conjectured by van Diejen and Spiridonov. For BC_n, we also consider their \"Type II\" integral. Their proof of that integral, together with our transformation, gives rise to pairs of adjoint integral operators; a different proof gives rise to pairs of adjoint difference operators. These allow us to construct a family of biorthogonal abelian functions generalizing the Koornwinder polynomials, and satisfying the analogues of the Macdonald conjectures. Finally, we discuss some transformations of Type II-style integrals. In particular, we find that adding two parameters to the Type II integral gives an integral invariant under an appropriate action of the Weyl group E_7.", "date": "2010-01", "date_type": "published", "publication": "Annals of Mathematics", "volume": "171", "number": "1", "publisher": "Annals of Mathematics", "pagerange": "169-243", "id_number": "CaltechAUTHORS:20100611-112526706", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100611-112526706", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2010.171.169", "primary_object": { "basename": "0309252.pdf", "url": "https://authors.library.caltech.edu/records/9421p-rnq58/files/0309252.pdf" }, "pub_year": "2010", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/tmnj9-7nm31", "eprint_id": 97837, "eprint_status": "archive", "datestamp": "2023-08-19 01:20:17", "lastmod": "2026-03-08 17:36:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Hypergraph Ramsey numbers", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Copyright 2009 American Mathematical Society. The copyright for this article reverts to public domain 28 years after publication. \n\nReceived by editor(s): September 8, 2008. Published electronically: August 18, 2009. \n\nThe research of the first author was supported by a Junior Research Fellowship at St John's College, Cambridge. The research of the second author was supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. The research of the third author was supported in part by NSF CAREER award DMS-0812005 and by a USA-Israeli BSF grant. \n\nThe results in Section 6.1 were obtained in collaboration with Noga Alon, and we thank him for allowing us to include them here. We also thank N. Alon and D. Mubayi for interesting discussions, and the anonymous referee for very useful comments.\n\n

Submitted - 0808.3760.pdf

", "abstract": "The Ramsey number r_(k)(s, n) is the minimum N such that every red-blue coloring of the k-tuples of an N-element set contains a red set of size s or a blue set of size n, where a set is called red (blue) if all k-tuples from this set are red (blue). In this paper we obtain new estimates for several basic hypergraph Ramsey problems. We give a new upper bound for r_(k)(s, n) for k \u2265 3 and s fixed. In particular, we show that \n\nr_(3)(s, n) \u2264 2^(n^(s-2)log n), \n\nwhich improves by a factor of n^(s-2)/polylog n the exponent of the previous upper bound of Erd\u0151s and Rado from 1952. We also obtain a new lower bound for these numbers, showing that there is a constant c > 0 such that \n\nr_(3)(s, n) \u2265 2^(csn log((n/s)+1)) \n\nfor all 4 \u2264 s \u2264 n. For constant s, this gives the first superexponential lower bound for r_(3)(s, n), answering an open question posed by Erd\u0151s and Hajnal in 1972. Next, we consider the 3-color Ramsey number r_(3)(n, n, n), which is the minimum N such that every 3-coloring of the triples of an N-element set contains a monochromatic set of size n. Improving another old result of Erd\u0151s and Hajnal, we show that \n\nr_(3)(n, n, n) \u2265 2^(n^(c log n)). \n\nFinally, we make some progress on related hypergraph Ramsey-type problems.", "date": "2010-01", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "23", "number": "1", "publisher": "American Mathematical Society", "pagerange": "247-266", "id_number": "CaltechAUTHORS:20190812-163000262", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163000262", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" }, { "agency": "Princeton University" }, { "agency": "NSF", "grant_number": "DMS-0812005" }, { "agency": "Binational Science Foundation (USA-Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/s0894-0347-09-00645-6", "primary_object": { "basename": "0808.3760.pdf", "url": "https://authors.library.caltech.edu/records/tmnj9-7nm31/files/0808.3760.pdf" }, "pub_year": "2010", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/fvwqv-cbd70", "eprint_id": 66644, "eprint_status": "archive", "datestamp": "2023-08-19 01:19:21", "lastmod": "2026-03-09 02:16:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Rigid Surface Operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 International Press. \n\nWe would like to thank R. Bezrukavnikov, A. Braverman, A. Elashvili, D. Gaiotto, V. Kac, G. Lusztig, C. Vafa, and especially D. Kazhdan for valuable discussions and correspondence. Research of SG is supported in part by NSF Grant DMS-0635607, in part by RFBR grant 07-02-00645, and in part by the Alfred P. Sloan Foundation. Research of EW is partly supported by NSF Grant PHY-0503584. Conclusions reported here are those of the authors and not of funding agencies.\n\n

Published - euclid.atmp.1283281759.pdf

Submitted - 0804.1561.pdf

", "abstract": "Surface operators in gauge theory are analogous to Wilson and 't Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of half-BPS surface operators in N = 4 super Yang\u2013Mills theory, and determined how they transform under S-duality. Those surface operators depend on a relatively large number of freely adjustable parameters. In the present paper, we consider the opposite case of half-BPS surface operators that are \"rigid\" in the sense that they do not depend on any parameters at all. We present some simple constructions of rigid half-BPS surface operators and attempt to determine how they transform under duality. This attempt is only partially successful, suggesting that our constructions are not the whole story. The partial match suggests interesting connections with quantization. We discuss some possible refinements and some string theory constructions which might lead to a more complete picture.", "date": "2010-01", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "14", "number": "1", "publisher": "International Press", "pagerange": "87-178", "id_number": "CaltechAUTHORS:20160504-103840382", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-103840382", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "07-02-00645" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "PHY-0503584" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2010.v14.n1.a3", "primary_object": { "basename": "0804.1561.pdf", "url": "https://authors.library.caltech.edu/records/fvwqv-cbd70/files/0804.1561.pdf" }, "related_objects": [ { "basename": "euclid.atmp.1283281759.pdf", "url": "https://authors.library.caltech.edu/records/fvwqv-cbd70/files/euclid.atmp.1283281759.pdf" } ], "pub_year": "2010", "author_list": "Gukov, Sergei and Witten, Edward" }, { "id": "https://authors.library.caltech.edu/records/4q3k7-mjj66", "eprint_id": 17582, "eprint_status": "archive", "datestamp": "2023-08-21 23:09:10", "lastmod": "2026-03-09 02:17:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Alday-L-F", "name": { "family": "Alday", "given": "Luis F." } }, { "id": "Gaiotto-D", "name": { "family": "Gaiotto", "given": "Davide" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Tachikawa-Yuji", "name": { "family": "Tachikawa", "given": "Yuji" } }, { "id": "Verlinde-H", "name": { "family": "Verlinde", "given": "Herman" } } ] }, "title": "Loop and surface operators in N = 2 gauge theory and Liouville modular geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetry and Duality; Conformal and W Symmetry; Supersymmetric gauge theory", "note": "\u00a9 2010 Springer. Published for SISSA by Springer. This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. \n\nReceived: 31 October 2009. Accepted: 6 January 2010. Published online: 27 January 2010. \n\nWe have benefited from useful discussions with N. Drukker, J. Gomis, J. Maldacena, N.\nNekrasov, T. Okuda, V. Pestun, N. Seiberg, J. Teschner, C. Vafa, E. Verlinde, and E.\nWitten. L.F.A. and D.G. are supported in part by the DOE grant DE-FG02- 90ER40542.\nD.G. is supported in part by the Roger Dashen membership in the Institute for Advanced\nStudy. YT is supported in part by the NSF grant PHY-0503584, and by the Marvin L.\nGoldberger membership at the Institute for Advanced Study. The research of H.V. is\nsupported by the National Science Foundation under Grant No. PHY-0756966 and by an\nEinstein Fellowship of the Institute for Advanced Study. The work of SG is supported in\npart by DOE grant DE-FG03-92-ER40701, in part by NSF grant PHY07-57647, and in\npart by the Alfred P. Sloan Foundation. Opinions and conclusions expressed here are those\nof the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - Alday2010p7111J_High_Energy_Phys.pdf

", "abstract": "Recently, a duality between Liouville theory and four dimensional N = 2 gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric 't Hooft-Wilson line operators in a variety of N = 2 gauge theories.", "date": "2010-01", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2010", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 113", "id_number": "CaltechAUTHORS:20100224-150755870", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100224-150755870", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02- 90ER40542" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Institute for Advanced Study" }, { "agency": "NSF", "grant_number": "PHY-0503584" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "NSF", "grant_number": "PHY-0756966" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/JHEP01(2010)113", "primary_object": { "basename": "Alday2010p7111J_High_Energy_Phys.pdf", "url": "https://authors.library.caltech.edu/records/4q3k7-mjj66/files/Alday2010p7111J_High_Energy_Phys.pdf" }, "pub_year": "2010", "author_list": "Alday, Luis F.; Gaiotto, Davide; et al." }, { "id": "https://authors.library.caltech.edu/records/513j8-7az43", "eprint_id": 17050, "eprint_status": "archive", "datestamp": "2023-08-21 23:05:25", "lastmod": "2026-03-09 02:16:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Refined, Motivic, and Quantum", "ispublished": "pub", "full_text_status": "public", "keywords": "motivic Donaldson\u2013Thomas invariants; D-branes, BPS invariants; wall-crossing; three-dimensional partitions", "note": "\u00a9 2009 Springer. \n\nReceived: 17 June 2009; accepted: 16 September 2009; published online: 14 November 2009. \n\nWe thank A. Gorsky, E. Gorsky, D. Jafferis, G. Moore, A. Neitzke, H. Ooguri,\nY. Soibelman, and M. Yamazaki for useful discussions and comments. We are\ngrateful to the KITP, Santa Barbara for warm hospitality during the program\n\"Fundamental Aspects of Superstring Theory,\" where part of this work was carried\nout. TD acknowledges support from a National Defense Science and Engineering\nGraduate Fellowship. Research of SG is supported in part by the Alfred\nP. Sloan Foundation, by DARPA under Grant No. HR0011-09-1-0015, and by\nthe National Science Foundation under Grant No. PHY05-51164 and Grant No.\nPHY07-57647. Opinions and conclusions expressed here are those of the authors\nand do not necessarily reflect the views of funding agencies.\n\n

Submitted - 0904.1420v1.pdf

", "abstract": "It is well known that in string compactifications on toric Calabi\u2013Yau manifolds one can introduce refined BPS invariants that carry information not only about the charge of the BPS state but also about the spin content. In this paper we study how these invariants behave under wall crossing. In particular, by applying a refined wall crossing formula, we obtain the refined BPS degeneracies for the conifold in different chambers. The result can be interpreted in terms of a new statistical model that counts \"refined\" pyramid partitions; the model provides a combinatorial realization of wall crossing and clarifies the relation between refined pyramid partitions and the refined topological vertex. We also compare the wall crossing behavior of the refined BPS invariants with that of the motivic Donaldson\u2013Thomas invariants introduced by Kontsevich\u2013Soibelman. In particular, we argue that, in the context of BPS state counting, the three adjectives in the title of this paper are essentially synonymous.", "date": "2010-01", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "91", "number": "1", "publisher": "Springer", "pagerange": "1-27", "id_number": "CaltechAUTHORS:20100104-122110812", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100104-122110812", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Defense Science and Engineering Graduate (NDSEG) Fellowship" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)", "grant_number": "HR0011-09-1-0015" }, { "agency": "NSF", "grant_number": "PHY-0551164" }, { "agency": "NSF", "grant_number": "PHY-0757647" } ] }, "other_numbering_system": { "items": [ { "id": "68-2725", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-009-0357-9", "primary_object": { "basename": "0904.1420v1.pdf", "url": "https://authors.library.caltech.edu/records/513j8-7az43/files/0904.1420v1.pdf" }, "pub_year": "2010", "author_list": "Dimofte, Tudor and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/769bp-zdm75", "eprint_id": 77801, "eprint_status": "archive", "datestamp": "2023-08-19 01:11:31", "lastmod": "2026-03-09 02:16:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } } ] }, "title": "Inequalities between Dirichlet and Neumann eigenvalues on the Heisenberg group", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author 2010. Published by Oxford University Press.\n\nReceived June 8, 2009; Accepted December 2, 2009\nCommunicated by Prof. Peter Sarnak\n\nThe authors acknowledge interesting discussions with A. Hansson concerning the topics of this paper. The first author wishes to thank E. Lieb and R. Seiringer for helpful remarks. Support through DFG grant FR 2664/1-1 and U.S. NSF grant PHY 06 52854 (R.F.) is gratefully acknowledged.\n\nRecently, Bernard Helffer suggested a way of proving similar estimates for a large class of sub-elliptic operators. This will be the subject of a forthcoming publication.\n\n

Submitted - 0906.1402.pdf

", "abstract": "We prove that for any domain in the Heisenberg group the (k+1)'th Neumann eigenvalue of the sub-Laplacian is strictly less than the k'th Dirichlet eigenvalue. As a byproduct we obtain similar inequalities for the Euclidean Laplacian with a homogeneous magnetic field.", "date": "2010", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2010", "number": "15", "publisher": "Oxford University Press", "pagerange": "2889-2902", "id_number": "CaltechAUTHORS:20170526-092032067", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-092032067", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "FR 2664/1-1" }, { "agency": "NSF", "grant_number": "PHY-0652854" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnp230", "primary_object": { "basename": "0906.1402.pdf", "url": "https://authors.library.caltech.edu/records/769bp-zdm75/files/0906.1402.pdf" }, "pub_year": "2010", "author_list": "Frank, Rupert L. and Laptev, Ari" }, { "id": "https://authors.library.caltech.edu/records/8mrfs-5ez75", "eprint_id": 21465, "eprint_status": "archive", "datestamp": "2023-08-19 01:01:08", "lastmod": "2026-03-09 22:47:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "The homology of real subspace arrangements", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2010 London Mathematical Society. \n\nReceived 10 December 2009. Journal of Topology Advance Access published October 14, 2010. \n\nThe author was supported in part by NSF Grant No. DMS-0401387. \n\nThe author would like to thank his coauthors P. Etingof, A. Henriques, and J. Kamnitzer on [7] for introducing him to these questions, and especially Henriques for discussions relating to blow-ups in Z[1/2]-cohomology. In addition, the author would like to thank S. Devadoss and especially S. Yuzvinsky for motivating discussions, as well as several referees for useful comments.\n\n

Published - Rains2010p12227J_Topol.pdf

Submitted - 0610743.pdf

", "abstract": "Associated to any subspace arrangement is a 'De Concini\u2013Procesi model', a certain smooth compactification of its complement, which in the case of the braid arrangement produces the Deligne\u2013Mumford compactification of the moduli space of genus 0 curves with marked points. In the present work, we calculate the integral homology of real De Concini\u2013Procesi models, extending earlier work of Etingof, Henriques, Kamnitzer and the author on the (2-adic) integral cohomology of the real locus of the moduli space. To be precise, we show that the integral homology of a real De Concini\u2013Procesi model is isomorphic modulo its 2-torsion to a sum of cohomology groups of subposets of the intersection lattice of the arrangement. As part of the proof, we construct a large family of natural maps between De Concini\u2013Procesi models (generalizing the operad structure of moduli space), and determine the induced action on poset cohomology. In particular, this determines the ring structure of the cohomology of De Concini\u2013Procesi models (modulo 2-torsion).", "date": "2010", "date_type": "published", "publication": "Journal of Topology", "volume": "3", "number": "4", "publisher": "Oxford University Press", "pagerange": "786-818", "id_number": "CaltechAUTHORS:20101221-082008592", "issn": "1753-8416", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101221-082008592", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/jtopol/jtq027", "primary_object": { "basename": "0610743.pdf", "url": "https://authors.library.caltech.edu/records/8mrfs-5ez75/files/0610743.pdf" }, "related_objects": [ { "basename": "Rains2010p12227J_Topol.pdf", "url": "https://authors.library.caltech.edu/records/8mrfs-5ez75/files/Rains2010p12227J_Topol.pdf" } ], "pub_year": "2010", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/y0xym-ggy09", "eprint_id": 20205, "eprint_status": "archive", "datestamp": "2023-08-19 00:59:49", "lastmod": "2026-03-18 00:08:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avila-Artur", "name": { "family": "Avila", "given": "Artur" } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum", "ispublished": "pub", "full_text_status": "public", "keywords": "orthogonal polynomials, clock behavior, almost Mathieu equation", "note": "\u00a9 2010 Mathematical Sciences Publishers.\n\nReceived 20 Oct 2009. Accepted 19 Nov 2009. Published: 4 March 2010. \n\nY. Last was supported in part by grant 1169/06 from the Israel Science Foundation; B. Simon by grant DMS-0652919 from the\nNSF; and both by grant 2006483 from the United States\u2013Israel Binational Science Foundation (BSF), Jerusalem. \n\nA. Avila thanks M. Flach and T. Tombrello for the hospitality of Caltech. B. Simon would like to thank E. de Shalit for the hospitality of Hebrew University. This research was partially conducted during the period Avila served as a Clay Research Fellow. We would like to thank H. Furstenberg and B. Weiss for\nuseful comments.\n\n

Published - Avila2010p11450Anal._PDE.pdf

", "abstract": "By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of (1/n)K_n(x, x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials. We then show that these hypotheses are always valid for ergodic Jacobi\nmatrices with absolutely continuous spectrum and prove that the limit of (1/n)K_n(x, x) is \u03c1_\u221e(x)/w(x) where \u03c1_\u221e is the density of zeros and w is the absolutely continuous weight of the spectral measure.", "date": "2010", "date_type": "published", "publication": "Analysis & PDE", "volume": "3", "number": "1", "publisher": "Mathematical Sciences Publishers", "pagerange": "81-108", "id_number": "CaltechAUTHORS:20100928-144330506", "issn": "1948-206X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100928-144330506", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "1169/06" }, { "agency": "NSF", "grant_number": "DMS-0652919" }, { "agency": "Binational Science Foundation (BSF)", "grant_number": "2006483" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.2140/apde.2010.3.81", "primary_object": { "basename": "Avila2010p11450Anal._PDE.pdf", "url": "https://authors.library.caltech.edu/records/y0xym-ggy09/files/Avila2010p11450Anal._PDE.pdf" }, "pub_year": "2010", "author_list": "Avila, Artur; Last, Yoram; et al." }, { "id": "https://authors.library.caltech.edu/records/8jwgb-d4638", "eprint_id": 16558, "eprint_status": "archive", "datestamp": "2023-08-19 00:54:07", "lastmod": "2026-04-12 13:35:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Saulina-N", "name": { "family": "Saulina", "given": "Natalia" } } ] }, "title": "Chern\u2013Simons\u2013Rozansky\u2013Witten topological field theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Elsevier B.V. \n\nReceived 11 May 2009; \naccepted 1 July 2009. \nAvailable online 8 July 2009.\n\nA.K. would like to thank Lev Rozansky and Sergey Arkhipov for valuable discussions. This\nwork was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Submitted - 0904.1447v2.pdf

", "abstract": "We construct and study a new topological field theory in three dimensions. It is a hybrid between Chern\u2013Simons and Rozansky\u2013Witten theory and can be regarded as a topologically-twisted version of the N=4 d=3 supersymmetric gauge theory recently discovered by Gaiotto and Witten. The model depends on a gauge group G and a hyper-K\u00e4hler manifold X with a tri-holomorphic action of G. In the case when X is an affine space, we show that the model is equivalent to Chern\u2013Simons theory whose gauge group is a supergroup. This explains the role of Lie superalgebras in the construction of Gaiotto and Witten. For general X, our model appears to be new. We describe some of its properties, focusing on the case when G is simple and X is the cotangent bundle of the flag variety of G. In particular, we show that Wilson loops are labeled by objects of a certain category which is a quantum deformation of the equivariant derived category of coherent sheaves on X.", "date": "2009-12-21", "date_type": "published", "publication": "Nuclear Physics B", "volume": "823", "number": "3", "publisher": "Elsevier", "pagerange": "403-427", "id_number": "CaltechAUTHORS:20091103-111212673", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091103-111212673", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2009.07.006", "primary_object": { "basename": "0904.1447v2.pdf", "url": "https://authors.library.caltech.edu/records/8jwgb-d4638/files/0904.1447v2.pdf" }, "pub_year": "2009", "author_list": "Kapustin, Anton and Saulina, Natalia" }, { "id": "https://authors.library.caltech.edu/records/fff0b-1g810", "eprint_id": 97814, "eprint_status": "archive", "datestamp": "2023-08-19 00:50:40", "lastmod": "2026-04-12 23:50:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "On-line Ramsey Numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey theory, on-line games", "note": "\u00a9 2009 Society for Industrial and Applied Mathematics. \n\nSubmitted 10 February 2009; accepted 08 September 2009; published online 11 December 2009. \n\nThe author was supported by a Junior Research Fellowship at St. John's College, Cambridge. \n\nI would like to thank Jacob Fox for reading carefully through an earlier version of this paper and making several helpful suggestions.\n\n

Published - 090749220.pdf

Submitted - 0902.1715.pdf

", "abstract": "Consider the following game between two players, Builder and Painter. Builder draws edges one at a time and Painter colors them in either red or blue, as each appears. Builder's aim is to force Painter to draw a monochromatic copy of a fixed graph G. The minimum number of edges which Builder must draw, regardless of Painter's strategy, in order to guarantee that this happens is known as the on-line Ramsey number \u02dcr(G) of G. Our main result, relating to the conjecture that [equation; see abstract in PDF for details], is that there exists a constant c > 1 such that [equation; see abstract in PDF for details] for infinitely many values of t. We also prove a more specific upper bound for this number, showing that there exists a positive constant c such that [equation; see abstract in PDF for details]. Finally, we prove a new upper bound for the on-line Ramsey number of the complete bipartite graph K_(t,t).", "date": "2009-12-11", "date_type": "published", "publication": "SIAM Journal on Discrete Mathematics", "volume": "23", "number": "4", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "1954-1963", "id_number": "CaltechAUTHORS:20190812-162958058", "issn": "0895-4801", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958058", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/090749220", "primary_object": { "basename": "0902.1715.pdf", "url": "https://authors.library.caltech.edu/records/fff0b-1g810/files/0902.1715.pdf" }, "related_objects": [ { "basename": "090749220.pdf", "url": "https://authors.library.caltech.edu/records/fff0b-1g810/files/090749220.pdf" } ], "pub_year": "2009", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/pr508-nm281", "eprint_id": 16834, "eprint_status": "archive", "datestamp": "2023-08-21 22:50:41", "lastmod": "2026-04-12 02:56:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Christiansen-J-S", "name": { "family": "Christiansen", "given": "Jacob S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zinchenko-M", "name": { "family": "Zinchenko", "given": "Maxim" } } ] }, "title": "Finite gap Jacobi matrices: An announcement", "ispublished": "pub", "full_text_status": "public", "keywords": "Finite gap Jacobi matrices; Isospectral torus; Szeg\u0151's theorem; Szeg\u0151 asymptotics; Jost function", "note": "\u00a9 2009 Elsevier B.V. \n\nReceived 23 October 2007. Available online 28 February 2009. \n\nThe second author is supported in part by NSF grants DMS0140592 and DMS-0652919.\n\n

Submitted - 0711.4739.pdf

", "abstract": "We consider Jacobi matrices whose essential sectrum is a finite union of closed intervals. We focus on Szeg\u0151's theorem, Jost solutions, and Szeg\u0151 asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.", "date": "2009-12-01", "date_type": "published", "publication": "Journal of Computational and Applied Mathematics", "volume": "233", "number": "3", "publisher": "Elsevier", "pagerange": "652-662", "id_number": "CaltechAUTHORS:20091130-115048841", "issn": "0377-0427", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091130-115048841", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.cam.2009.02.081", "primary_object": { "basename": "0711.4739.pdf", "url": "https://authors.library.caltech.edu/records/pr508-nm281/files/0711.4739.pdf" }, "pub_year": "2009", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/jbyvh-vgz32", "eprint_id": 17330, "eprint_status": "archive", "datestamp": "2023-08-21 22:49:21", "lastmod": "2026-04-12 18:49:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Closed 3-braids are nearly fibred", "ispublished": "pub", "full_text_status": "public", "keywords": "Closed 3-braids; fibred; knot Floer homology; disk decomposition", "note": "\u00a9 2009 World Scientific Publishing Co.\nAccepted 8 October 2009.\n\nWe wish to thank David Gabai and Zolt\u00e1n Szab\u00f3 for some helpful conversations.\nWe are especially grateful to Jacob Rasmussen, who pointed out a crucial mistake\nin an earlier version of this paper, and to Xingru Zhang, from whose lecture the\nauthor learned Xu's work on 3-braids.\nThis paper was written in 2005 when the author was a graduate student at\nPrinceton University. The author was partially supported by a Graduate School\nCentennial fellowship at Princeton University.\n\n

Submitted - 0510243v2.pdf

", "abstract": "We classify fibred closed 3-braids. In particular, given a nontrivial closed 3-braid,\neither it is fibred, or it differs from a fibred link by adding a crossing. The proof uses\nGabai's method of disk decomposition. The topmost term in the knot Floer homology\nof closed 3-braids is also computed.", "date": "2009-12", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "18", "number": "12", "publisher": "World Scientific Publishing Co.", "pagerange": "1637-1649", "id_number": "CaltechAUTHORS:20100128-082614040", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100128-082614040", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Princeton University" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0218216509007701", "primary_object": { "basename": "0510243v2.pdf", "url": "https://authors.library.caltech.edu/records/jbyvh-vgz32/files/0510243v2.pdf" }, "pub_year": "2009", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/zhp2v-74a26", "eprint_id": 16807, "eprint_status": "archive", "datestamp": "2023-08-21 22:45:09", "lastmod": "2026-04-12 14:41:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Katzarkov-L", "name": { "family": "Katzarkov", "given": "Ludmil" } }, { "id": "Orlov-D", "name": { "family": "Orlov", "given": "Dmitri" }, "orcid": "0000-0002-2230-457X" }, { "id": "Yotov-M", "name": { "family": "Yotov", "given": "Mirroslav" } } ] }, "title": "Homological Mirror Symmetry for manifolds of general type", "ispublished": "pub", "full_text_status": "public", "keywords": "Homological mirror Symmetry; K theory; Categories", "note": "\u00a9 2009 Versita Warsaw and Springer-Verlag Berlin Heidelberg. \n\nReceived 22 August 2009; accepted 1 September 2009. \n\nFirst and second authors are partially supported by NSF Grant DMS0600800 and by Clay Math Institute.\nWe have benefited greatly from discussions M. Kontsevich, P. Seidel, K. Hori, C. Vafa and E. Witten. We are very thankful\nto D. Auroux and T. Pantev, without whom this paper would have never been written. We would like to thank IPAM, UCLA\nand especially M. Green and H. D. Cao for the wonderful working conditions of the program Symplectic Geometry and\nPhysics, during which the work on this paper was initiated. The first two authors are grateful to KITP, Santa Barbara\nand especially D. Gross, R. Dijgraaf, D. Freed and T. Pantev, for the wonderful athmosphere during the program Geometry,\nDuality and Strings, when most of this work was done.\n\n

Submitted - 1004.0129v3.pdf

", "abstract": "In this paper we outline the foundations of Homological Mirror Symmetry for manifolds of general type. Both Physics and Categorical prospectives are considered.", "date": "2009-12", "date_type": "published", "publication": "Central European Journal of Mathematics", "volume": "7", "number": "4", "publisher": "Springer", "pagerange": "571-605", "id_number": "CaltechAUTHORS:20091125-095742069", "issn": "1895-1074", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091125-095742069", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0600800" }, { "agency": "Clay Math Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2478/s11533-009-0056-x", "primary_object": { "basename": "1004.0129v3.pdf", "url": "https://authors.library.caltech.edu/records/zhp2v-74a26/files/1004.0129v3.pdf" }, "pub_year": "2009", "author_list": "Kapustin, Anton; Katzarkov, Ludmil; et al." }, { "id": "https://authors.library.caltech.edu/records/377h1-h5425", "eprint_id": 17275, "eprint_status": "archive", "datestamp": "2023-08-19 00:41:49", "lastmod": "2026-04-13 03:49:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Geometry as seen by string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "topological string theory", "note": "\u00a9 The Mathematical Society of Japan and Springer 2009. \n\nReceived: 22 January 2009. Revised: 29 April 2009. Accepted: 6 May 2009. Published online: 25 December 2009. \n\nCommunicated by: Hiraku Nakajima. \n\nThis article is based on the 4th Takagi Lectures that the author delivered at the Kyoto University on June 21, 2008.\n\n

Submitted - 0901.1881.pdf

", "abstract": "This is an introductory review of the topological string theory from physicist's perspective. I start with the definition of the theory and describe its relation to the Gromov\u2013Witten invariants. The BCOV holomorphic anomaly equations, which generalize the Quillen anomaly formula, can be used to compute higher genus partition functions of the theory. The open/closed string duality relates the closed topological string theory to the Chern\u2013Simons gauge theory and the random matrix model. As an application of the topological string theory, I discuss the counting of bound states of D-branes.", "date": "2009-12", "date_type": "published", "publication": "Japanese Journal of Mathematics", "volume": "4", "number": "2", "publisher": "Springer", "pagerange": "95-120", "id_number": "CaltechAUTHORS:20100121-141325818", "issn": "0289-2316", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100121-141325818", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Kavli Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "68-2718", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11537-009-0833-0", "primary_object": { "basename": "0901.1881.pdf", "url": "https://authors.library.caltech.edu/records/377h1-h5425/files/0901.1881.pdf" }, "pub_year": "2009", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/wb4dc-tqs84", "eprint_id": 17990, "eprint_status": "archive", "datestamp": "2023-08-21 22:49:50", "lastmod": "2026-04-12 13:27:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Spiridonov-V-P", "name": { "family": "Spiridonov", "given": "V. P." } } ] }, "title": "Determinants of elliptic hypergeometric integrals", "ispublished": "pub", "full_text_status": "public", "keywords": "elliptic hypergeometric function; difference equation; determinant; difference Galois theory", "note": "Original Russian Text Copyright \u00a9 by E. M. Rains and V. P. Spiridonov.\nTranslated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 43, No. 4, pp. 67\u201386, 2009.\nReceived: 25 December 2007; published online: 22 December 2009.\n\nThe first author was supported in part by NSF grant DMS0833464. The second author was supported in part\nby RFBR grant 08-01-00392 and by the Max Planck Institute for Mathematics (Bonn), during the visit to which part\nof this work was done.\n\n

Submitted - 0712.4253.pdf

", "abstract": "We start from an interpretation of the BC_(2)-symmetric \"Type I\" (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation and then generalize this construction to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding formulas for the elliptic beta integral and symmetry transformation in a new way, by proving that both sides satisfy the same difference equations and that these difference equations satisfy a needed Galois-theoretic condition ensuring the uniqueness of the simultaneous solution.", "date": "2009-12", "date_type": "published", "publication": "Functional Analysis and its Applications", "volume": "43", "number": "4", "publisher": "Springer", "pagerange": "297-311", "id_number": "CaltechAUTHORS:20100415-102226300", "issn": "0016-2663", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100415-102226300", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0833464" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "08-01-00392" }, { "agency": "Max Planck Institute for Mathematics" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10688-009-0037-7", "primary_object": { "basename": "0712.4253.pdf", "url": "https://authors.library.caltech.edu/records/wb4dc-tqs84/files/0712.4253.pdf" }, "pub_year": "2009", "author_list": "Rains, E. M. and Spiridonov, V. P." }, { "id": "https://authors.library.caltech.edu/records/ps58j-7ha97", "eprint_id": 16903, "eprint_status": "archive", "datestamp": "2023-08-19 00:27:33", "lastmod": "2026-04-16 01:39:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gils-C", "name": { "family": "Gils", "given": "Charlotte" } }, { "id": "Trebst-S", "name": { "family": "Trebst", "given": "Simon" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Ludwig-A-W-W", "name": { "family": "Ludwig", "given": "Andreas W. W." } }, { "id": "Troyer-M", "name": { "family": "Troyer", "given": "Matthias" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Topology-driven quantum phase transitions in time-reversal-invariant anyonic quantum liquids", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Macmillan Publishers Limited. \n\nReceived 18 September 2008; accepted 13 August 2009; published online 20 September 2009. \n\nWe thank M. Freedman, X.-G. Wen and P. Fendley for stimulating discussions. Our numerical simulations were based on the ALPS libraries. A.W.W.L. was supported, in part, by NSF DMR-0706140. \n\nAuthor contributions: C.G., S.T. and M.T. contributed to the numerical work. C.G., A.K., A.W.W.L and Z.W. contributed to the analytical solution. All authors contributed to the development of the general picture presented in this manuscript.\n\n

Supplemental Material - Gils2009p6501Nat_Phys_supp.pdf

", "abstract": "Indistinguishable particles in two dimensions can be characterized by anyonic quantum statistics, which is more general than that of bosons or fermions. Anyons emerge as quasiparticles in fractional quantum Hall states and in certain frustrated quantum magnets. Quantum liquids of anyons show degenerate ground states, where the degeneracy depends on the topology of the underlying surface. Here, we present a new type of continuous quantum phase transition in such anyonic quantum liquids, which is driven by quantum fluctuations of the topology. The critical state connecting two anyonic liquids on surfaces with different topologies is reminiscent of the notion of a 'quantum foam' with fluctuations on all length scales. This exotic quantum phase transition arises in a microscopic model of interacting anyons for which we present an exact solution in a linear geometry. We introduce an intuitive physical picture of this model that unifies string nets and loop gases, and provide a simple description of topological quantum phases and their phase transitions.", "date": "2009-11", "date_type": "published", "publication": "Nature Physics", "volume": "5", "number": "11", "publisher": "Nature Publishing Group", "pagerange": "834-839", "id_number": "CaltechAUTHORS:20091208-111910640", "issn": "1745-2473", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091208-111910640", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMR-0706140" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1038/NPHYS1396", "primary_object": { "basename": "Gils2009p6501Nat_Phys_supp.pdf", "url": "https://authors.library.caltech.edu/records/ps58j-7ha97/files/Gils2009p6501Nat_Phys_supp.pdf" }, "pub_year": "2009", "author_list": "Gils, Charlotte; Trebst, Simon; et al." }, { "id": "https://authors.library.caltech.edu/records/41g6c-zjc92", "eprint_id": 97831, "eprint_status": "archive", "datestamp": "2023-08-19 00:31:02", "lastmod": "2026-04-12 20:09:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Hypergraph Packing and Sparse Bipartite Ramsey Numbers", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Cambridge University Press 2009. \n\nReceived 30 July 2007; revised 24 April 2009; first published online 22 June 2009. \n\nThe author is kindly supported by a grant from St John's College, Cambridge. \n\nI would like to thank the referee for several helpful comments.", "abstract": "We prove that there exists a constant c such that, for any integer \u0394, the Ramsey number of a bipartite graph on n vertices with maximum degree \u0394 is less than 2^(c\u0394)n. A probabilistic argument due to Graham, R\u00f6dl and Ruci\u0144ski implies that this result is essentially sharp, up to the constant c in the exponent. Our proof hinges upon a quantitative form of a hypergraph packing result of R\u00f6dl, Ruci\u0144ski and Taraz.", "date": "2009-11", "date_type": "published", "publication": "Combinatorics, Probability and Computing", "volume": "18", "number": "6", "publisher": "Cambridge University Press", "pagerange": "913-923", "id_number": "CaltechAUTHORS:20190812-162959718", "issn": "0963-5483", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959718", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/s0963548309990174", "pub_year": "2009", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/1p5t0-he886", "eprint_id": 15815, "eprint_status": "archive", "datestamp": "2023-08-19 00:26:19", "lastmod": "2026-04-12 03:09:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Yamazaki-Masahito", "name": { "family": "Yamazaki", "given": "Masahito" } } ] }, "title": "Crystal Melting and Toric Calabi-Yau Manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Springer. \n\nReceived: 9 December 2008; Accepted: 12 February 2009; Published online: 19 May 2009.\n\n

Submitted - 0811.2801.pdf

", "abstract": "We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.", "date": "2009-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "292", "number": "1", "publisher": "Springer", "pagerange": "179-199", "id_number": "CaltechAUTHORS:20090911-153603164", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090911-153603164", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "68-2706", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-009-0836-y", "primary_object": { "basename": "0811.2801.pdf", "url": "https://authors.library.caltech.edu/records/1p5t0-he886/files/0811.2801.pdf" }, "pub_year": "2009", "author_list": "Ooguri, Hirosi and Yamazaki, Masahito" }, { "id": "https://authors.library.caltech.edu/records/csk2m-nme21", "eprint_id": 17311, "eprint_status": "archive", "datestamp": "2023-08-21 22:37:40", "lastmod": "2026-04-13 03:14:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Tikhonov-M", "name": { "family": "Tikhonov", "given": "Mikhail" }, "orcid": "0000-0002-9558-1121" } ] }, "title": "Abelian duality, walls and boundary conditions in diverse dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Duality in Gauge Field Theories; Chern-Simons Theories; D-branes", "note": "\u00a9 SISSA 2009.\nThis is an Open Access article.\nReceived 21 September 2009, accepted for publication 14 October 2009.\nPublished 4 November 2009.\n\n

Published - Kapustin2009p6696J_High_Energy_Phys.pdf

", "abstract": "We systematically apply the formalism of duality walls to study the action of duality transformations on boundary conditions and local and nonlocal operators in two, three, and four-dimensional free field theories. In particular, we construct a large class of D-branes for two-dimensional sigma-models with toroidal targets and determine the action of the T-duality group on it. It is manifest in this formalism that T-duality transformations on D-branes are given by a differential-geometric version of the Fourier-Mukai transform.", "date": "2009-11", "date_type": "published", "publication": "Journal of High Energy Physics", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 006", "id_number": "CaltechAUTHORS:20100127-084219140", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100127-084219140", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2009/11/006", "primary_object": { "basename": "Kapustin2009p6696J_High_Energy_Phys.pdf", "url": "https://authors.library.caltech.edu/records/csk2m-nme21/files/Kapustin2009p6696J_High_Energy_Phys.pdf" }, "pub_year": "2009", "author_list": "Kapustin, Anton and Tikhonov, Mikhail" }, { "id": "https://authors.library.caltech.edu/records/be14c-2nz37", "eprint_id": 16939, "eprint_status": "archive", "datestamp": "2023-08-21 22:28:53", "lastmod": "2026-04-12 14:30:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Shareshian-J", "name": { "family": "Shareshian", "given": "John" } } ] }, "title": "Restrictions on the structure of subgroup lattices of finite alternating and symmetric groups", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Subgroup lattice; Symmetric group; Alternating group", "note": "\u00a9 2009 Elsevier Inc. \n\nReceived 9 January 2009. Available online 23 July 2009. \n\nCommunicated by Ronald Solomon. \n\nWe thank the referee for helpful comments. We thank Russ Woodroofe for providing the picture of D\u0394(3, 3).\n\nPartially supported by NSF Grants DMS 0504852 and DMS 0604233.", "abstract": "Let G be a finite alternating or symmetric group. We describe an infinite class of finite lattices, none of which is isomorphic to any interval [H,G] in the subgroup lattice of G.", "date": "2009-10-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "322", "number": "7", "publisher": "Elsevier", "pagerange": "2449-2463", "id_number": "CaltechAUTHORS:20091210-094932243", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091210-094932243", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" }, { "agency": "NSF", "grant_number": "DMS-0604233" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2009.05.042", "pub_year": "2009", "author_list": "Aschbacher, Michael and Shareshian, John" }, { "id": "https://authors.library.caltech.edu/records/t780d-xyj74", "eprint_id": 20708, "eprint_status": "archive", "datestamp": "2023-08-19 00:14:11", "lastmod": "2026-04-12 01:59:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Branes and quantization", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 International Press.\n\nWe would like to thank D. Kazhdan, M. Kontsevich, N. Hitchin, and P. Sarnak for valuable discussions. Research of SG is supported in part by NSF Grants DMS-0635607 and PHY-0757647, in part by RFBR grant 07-02-00645, and in part by the Alfred P. Sloan Foundation. Research of EW is\nsupported in part by NSF Grant PHY-0503584. Conclusions reported here are those of the authors and not of funding agencies.\n\n

Published - Gukov2009p11796Adv_Theor_Math_Phys.pdf

", "abstract": "The problem of quantizing a symplectic manifold (M,\u03c9) can be formulated in terms of the A-model of a complexification of M. This leads to an interesting new perspective on quantization. From this point of view, the Hilbert space obtained by quantization of (M,\u03c9) is the space of (B_(cc), B) strings, where B_(cc) and B are two A-branes; B is an ordinary Lagrangian A-brane, and Bcc is a space-filling coisotropic A-brane. B is supported on M, and the choice of \u03c9 is encoded in the choice of B_(cc). As an example, we describe from this point of view the representations of the\ngroup SL(2,R). Another application is to Chern\u2013Simons gauge theory.", "date": "2009-10", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "13", "number": "5", "publisher": "International Press", "pagerange": "1445-1518", "id_number": "CaltechAUTHORS:20101108-100406383", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20101108-100406383", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "07- 02-00645" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "PHY-0503584" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2009.v13.n5.a5", "primary_object": { "basename": "Gukov2009p11796Adv_Theor_Math_Phys.pdf", "url": "https://authors.library.caltech.edu/records/t780d-xyj74/files/Gukov2009p11796Adv_Theor_Math_Phys.pdf" }, "pub_year": "2009", "author_list": "Gukov, Sergei and Witten, Edward" }, { "id": "https://authors.library.caltech.edu/records/yxaem-bkf13", "eprint_id": 16024, "eprint_status": "archive", "datestamp": "2023-08-19 00:07:58", "lastmod": "2026-04-12 05:18:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Matrix averages relating to Ginibre ensembles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Institute of Physics and IOP Publishing Limited. \n\nReceived 4 July 2009. Published 2 September 2009. Print publication: Issue 38 (25 September 2009). \n\nThe work of PJF was supported by the Australian Research Council.\n\n

Submitted - 0907.0287.pdf

", "abstract": "The theory of zonal polynomials is used to compute the average of a Schur polynomial of argument AX, where A is a fixed matrix and X is from the real Ginibre ensemble. This generalizes a recent result of Sommers and Khoruzhenko (2009 J. Phys. A: Math. Theor. 42 222002), and furthermore allows analogous results to be obtained for the complex and real quaternion Ginibre ensembles. As applications, the positive integer moments of the general variance Ginibre ensembles are computed in terms of generalized hypergeometric functions; these are written in terms of averages over matrices of the same size as the moment to give duality formulas, and the averages of the power sums of the eigenvalues are expressed as finite sums of zonal polynomials.", "date": "2009-09-25", "date_type": "published", "publication": "Journal of Physics A: Mathematical and Theoretical", "volume": "42", "number": "38", "publisher": "IOP", "pagerange": "Art. No. 385205", "id_number": "CaltechAUTHORS:20090923-143135904", "issn": "1751-8113", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090923-143135904", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1751-8113/42/38/385205", "primary_object": { "basename": "0907.0287.pdf", "url": "https://authors.library.caltech.edu/records/yxaem-bkf13/files/0907.0287.pdf" }, "pub_year": "2009", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/3eztb-xvx88", "eprint_id": 56828, "eprint_status": "archive", "datestamp": "2023-08-19 00:05:59", "lastmod": "2026-03-09 21:52:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Link Floer homology detects the Thurston norm", "ispublished": "pub", "full_text_status": "public", "keywords": "link Floer homology, link, rational homology 3-sphere, Thurston norm, taut foliation", "note": "\u00a9 2009 Mathematical Sciences Publishers. \n\nReceived: 8 May 2006. Revised: 2 July 2009. Accepted: 1 August 2009. Published: 18 September 2009. Proposed: Peter Ozsv\u00e1th. Seconded: Ron Fintushel, Walter Neumann. \n\nWe are grateful to David Gabai and Zolt\u00e1n Szab\u00f3 for some helpful conversations. We wish to thank Efstratia Kalfagianni for informing us Kaiser's work [5]. We particularly thank the referee for a thorough reading of an earlier version of this paper, for many constructive suggestions and for pointing out a serious mistake. \n\nThe first version of this paper was carried out when the author was a graduate student at Princeton University. The author was partially supported by a Graduate School Centennial fellowship at Princeton University during the course of this work.\n\n

Published - gt-v13-n5-p09-p.pdf

", "abstract": "We prove that, for a link L in a rational homology 3\u2013sphere, the link Floer homology detects the Thurston norm of its complement. This result has been proved by Ozsv\u00e1th and Szab\u00f3 for links in S^3. As an ingredient of the proof, we show that knot Floer homology detects the genus of null-homologous links in rational homology spheres, which is a generalization of an earlier result of the author. Our argument uses the techniques due to Ozsv\u00e1th and Szab\u00f3, Hedden and the author.", "date": "2009-09-18", "date_type": "published", "publication": "Geometry and Topology", "volume": "13", "number": "5", "publisher": "Geometry & Topology Publications", "pagerange": "2991-3019", "id_number": "CaltechAUTHORS:20150421-115909626", "issn": "1465-3060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115909626", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Princeton University" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/gt.2009.13.2991", "primary_object": { "basename": "gt-v13-n5-p09-p.pdf", "url": "https://authors.library.caltech.edu/records/3eztb-xvx88/files/gt-v13-n5-p09-p.pdf" }, "pub_year": "2009", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/7kxjk-xhy82", "eprint_id": 15117, "eprint_status": "archive", "datestamp": "2023-08-21 22:16:31", "lastmod": "2026-04-12 02:18:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Overgroups of primitive groups, II", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Finite groups; Permutation groups", "note": "\u00a9 2009 Elsevier. \n\nReceived 19 August 2008. Communicated by Ronald Solomon. Available online 30 May 2009.", "abstract": "We continue our study of the overgroup lattices of subgroups of finite alternating and symmetric groups, with applications to the question of Palfy and Pudlak as to whether each finite lattice is an interval in the lattice of subgroups of some finite group.", "date": "2009-09-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "322", "number": "5", "publisher": "Elsevier", "pagerange": "1586-1626", "id_number": "CaltechAUTHORS:20090817-144817879", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090817-144817879", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2009.04.044", "pub_year": "2009", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/mc4h7-vbs78", "eprint_id": 17093, "eprint_status": "archive", "datestamp": "2023-08-21 22:14:36", "lastmod": "2026-04-13 00:16:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-Arjeh-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Frenk-Bart", "name": { "family": "Frenk", "given": "Bart" } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "Brauer algebras of simply laced type", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Irreducible Representation; Positive Root; Invariant Subspace; Coxeter Group; High Element", "note": "\u00a9 Hebrew University Magnes Press 2009. \n\nReceived: 9 May 2007. Revised: 30 January 2008. Published online: 4 December 2009.", "abstract": "The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph A_(n \u2212 1) on n \u2212 1 nodes. Here we describe an algebra depending on an arbitrary graph Q, called the Brauer algebra of type Q, and study its structure in the cases where Q is a Coxeter graph of simply laced spherical type (so its connected components are of type A_(n \u2212 1), D_n , E_6, E_7, E_8). We find its irreducible representations and its dimension, and show that the algebra is cellular. The algebra is generically semisimple and contains the group algebra of the Coxeter group of type Q as a subalgebra. It is a ring homomorphic image of the Birman-Murakami-Wenzl algebra of type Q; this fact will be used in later work determining the structure of the Birman-Murakami-Wenzl algebras of simply laced spherical type.", "date": "2009-09", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "173", "number": "1", "publisher": "Springer", "pagerange": "335-365", "id_number": "CaltechAUTHORS:20100107-113013608", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100107-113013608", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s11856-009-0095-9", "pub_year": "2009", "author_list": "Cohen, Arjeh M.; Frenk, Bart; et al." }, { "id": "https://authors.library.caltech.edu/records/vjwec-s3c53", "eprint_id": 97812, "eprint_status": "archive", "datestamp": "2023-08-19 00:00:39", "lastmod": "2026-04-12 20:19:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "A new upper bound for diagonal Ramsey numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey numbers, graph theory, quasirandomness", "note": "\u00a9 2009 Princeton University.\n\nReceived 11 July 2006; revised 14 November 2007.\n\nThe author is kindly supported by a grant from St John's College, Cambridge.\n\nI would like to thank B\u00e9la Bollob\u00e1s, Tim Gowers, Ben Green and Tom Sanders for their advice and encouragement.\n\n

Submitted - 0607788.pdf

", "abstract": "We prove a new upper bound for diagonal two-colour Ramsey numbers, showing that there exists a constant C such that \n\nr(k + 1, k + 1) \u2264 k^[-C log k/(log log k (2k_k).", "date": "2009-09", "date_type": "published", "publication": "Annals of Mathematics", "volume": "170", "number": "2", "publisher": "Princeton University", "pagerange": "941-960", "id_number": "CaltechAUTHORS:20190812-162957624", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957624", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4007/annals.2009.170.941", "primary_object": { "basename": "0607788.pdf", "url": "https://authors.library.caltech.edu/records/vjwec-s3c53/files/0607788.pdf" }, "pub_year": "2009", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/1fasg-d7h74", "eprint_id": 77396, "eprint_status": "archive", "datestamp": "2023-08-18 23:59:56", "lastmod": "2026-04-13 03:01:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "A Simple Proof of Hardy-Lieb-Thirring Inequalities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 by the author. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 19 September 2008. Accepted: 18 November 2008. Published online: 13 March 2009. \n\nCommunicated by B. Simon \n\nThe author would like to thank E. Lieb and R. Seiringer for very fruitful discussions, as well as J. P. Solovej, T. \u00d8stergaard S\u00f8rensen and W. Spitzer for useful correspondence. Support through DAAD grant D/06/49117 and U.S. National Science Foundation grant PHY 06 52854 is gratefully acknowledged.\n\n

Published - art_3A10.1007_2Fs00220-009-0759-7.pdf

Submitted - 0809.3797.pdf

", "abstract": "We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schr\u00f6dinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, S\u00f8rensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).", "date": "2009-09", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "290", "number": "2", "publisher": "Springer", "pagerange": "789-800", "id_number": "CaltechAUTHORS:20170512-093621400", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-093621400", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutscher Akademischer Austauschdienst (DAAD)", "grant_number": "D/06/49117" }, { "agency": "NSF", "grant_number": "PHY-0652854" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-009-0759-7", "primary_object": { "basename": "0809.3797.pdf", "url": "https://authors.library.caltech.edu/records/1fasg-d7h74/files/0809.3797.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs00220-009-0759-7.pdf", "url": "https://authors.library.caltech.edu/records/1fasg-d7h74/files/art_3A10.1007_2Fs00220-009-0759-7.pdf" } ], "pub_year": "2009", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/wkawb-8zd24", "eprint_id": 17970, "eprint_status": "archive", "datestamp": "2023-08-21 22:14:46", "lastmod": "2026-04-13 05:50:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Cyclotomy and Endomotives", "ispublished": "pub", "full_text_status": "public", "keywords": "field with one element; noncommutative geometry; endomotives; Bost-Connes quantum statistical mechanical system; Lambda-rings; Witten-Reshetikhin-Turaev invariants", "note": "\u00a9 2009 Pleiades Publishing, Ltd.\nReceived: 24 January 2009. Published online: 12 August 2009.\nThe text was submitted by the author in English.\nI thank Yuri Manin for useful conversations and for suggesting the possible relation to \u039b-rings. I thank Jack Morava for several useful discussions and Peter Teichner for useful comments. I also thank James Borger for reading earlier drafts of this manuscript. I especially wish to thank Alain Connes for extensive comments and suggestions that greatly improved the paper. This work is partially supported by NSF grant DMS-0651925. Part of this work was done during stays at the MPI and at MSRI, which I thank for the hospitality and for support.\n\n

Submitted - 0901.3167.pdf

", "abstract": "We compare two different models of noncommutative geometry of the cyclotomic tower, both based on an arithmetic algebra of functions of roots of unity and an action by endomorphisms, the first based on the Bost-Connes (BC) quantum statistical mechanical system and the second on the Habiro ring, where the Habiro functions have, in addition to evaluations at roots of unity, also full Taylor expansions. Both have compatible endomorphisms actions of the multiplicative semigroup of positive integers. As a higher dimensional generalization, we consider a crossed product ring obtained using Manin's multivariable generalizations of the Habiro functions and an action by endomorphisms of the semigroup of integer matrices with positive determinant. We then construct a corresponding class of multivariable BC endomotives, which are obtained geometrically from self maps of higher dimensional algebraic tori, and we discuss some of their quantum statistical mechanical properties. These multivariable BC endomotives are universal for (torsion free) \u039b-rings, compatibly with the Frobenius action. Finally, we discuss briefly how Habiro's universal Witten-Reshetikhin-Turaev invariant of integral homology 3-spheres may relate invariants of 3-manifolds to gadgets over F_1 and semigroup actions on homology 3-spheres to endomotives.", "date": "2009-09", "date_type": "published", "publication": "P-Adic Numbers, Ultrametric Analysis, and Applications", "volume": "1", "number": "3", "publisher": "Springer", "pagerange": "217-263", "id_number": "CaltechAUTHORS:20100414-093452256", "issn": "2070-0474", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100414-093452256", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0651925" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/S2070046609030042", "primary_object": { "basename": "0901.3167.pdf", "url": "https://authors.library.caltech.edu/records/wkawb-8zd24/files/0901.3167.pdf" }, "pub_year": "2009", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/pttjc-1mp74", "eprint_id": 15787, "eprint_status": "archive", "datestamp": "2023-08-18 23:54:23", "lastmod": "2026-04-12 13:40:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lascoux-A", "name": { "family": "Lascoux", "given": "Alain" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Warnaar-S-O", "name": { "family": "Warnaar", "given": "S. Ole" }, "orcid": "0000-0002-9786-0175" } ] }, "title": "Nonsymmetric interpolation macdonald polynomials and gl_n basic hypergeometric series", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Springer. \n\nReceived: 11 September 2008. Accepted: 12 March 2009. Published online: 8 July 2009. \n\nSupported by the ANR project MARS (BLAN06-2 134516).\nSupported by the NSF grant DMS-0401387.\nSupported by the Australian Research Council. \n\nPart of this work was carried out at MSRI during the special programme Combinatorial Representation Theory. AL and SOW thank MSRI for hospitality and financial support.\n\n

Submitted - 0807.1351.pdf

", "abstract": "The Knop-Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gl_n. Our main results include a new q-binomial theorem, a new q-Gauss sum, and several transformation formulae for gl_n series.", "date": "2009-09", "date_type": "published", "publication": "Transformation Groups", "volume": "14", "number": "3", "publisher": "Springer", "pagerange": "613-647", "id_number": "CaltechAUTHORS:20090911-153557865", "issn": "1083-4362", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090911-153557865", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Agence Nationale pour la Recherche (ANR)", "grant_number": "BLAN06-2 134516" }, { "agency": "NSF", "grant_number": "DMS-0401387" }, { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00031-009-9061-1", "primary_object": { "basename": "0807.1351.pdf", "url": "https://authors.library.caltech.edu/records/pttjc-1mp74/files/0807.1351.pdf" }, "pub_year": "2009", "author_list": "Lascoux, Alain; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/9xfrs-qrb35", "eprint_id": 15151, "eprint_status": "archive", "datestamp": "2023-08-20 02:28:58", "lastmod": "2026-04-12 13:56:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Rozansky-L", "name": { "family": "Rozansky", "given": "Lev" } }, { "id": "Saulina-N", "name": { "family": "Saulina", "given": "Natalia" } } ] }, "title": "Three-dimensional topological field theory and symplectic algebraic geometry I", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Elsevier B.V. \nReceived 26 November 2008; accepted 28 January 2009.\nAvailable online 3 February 2009.\nA.K. would like to thank Alexei Bondal, Dennis Gaitsgory, David Ben-Zvi, David Nadler,\nDan Freed, Andrei Mikhailov, and Dima Orlov for discussions. L.R. would like to thank Dima\nArinkin, David Ben-Zvi and David Nadler for discussions. N.S. would like to thank Andrei\nMikhailov for discussions. Part of this work was done during the BIRS workshop \"Matrix Factorizations\nin Physics and Mathematics\", May 2008. A.K. and L.R. are grateful to the organizers\nfor the invitation and to the Banff International Research Station for hospitality. The work of\nA.K. and N.S. was supported in part by the DOE grant DE-FG03-92-ER40701. The work of\nL.R. was supported by NSF grant DMS-0808974.\n\n

Submitted - 0810.5415v2.pdf

", "abstract": "We study boundary conditions and defects in a three-dimensional topological sigma-model with a complex symplectic target space X (the Rozansky\u2013Witten model). We show that boundary conditions correspond to complex Lagrangian submanifolds in X equipped with complex fibrations. The set of boundary conditions has the structure of a 2-category; morphisms in this 2-category are interpreted physically as one-dimensional defect lines separating parts of the boundary with different boundary conditions. This 2-category is a categorification of the Z_2-graded derived category of X; it is also related to categories of matrix factorizations and a categorification of deformation quantization (quantization of symmetric monoidal categories). In Appendix B we describe a deformation of the B-model and the associated category of branes by forms of arbitrary even degree.", "date": "2009-08-01", "date_type": "published", "publication": "Nuclear Physics B", "volume": "816", "number": "3", "publisher": "Elsevier", "pagerange": "295-355", "id_number": "CaltechAUTHORS:20090818-093340561", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090818-093340561", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "DMS-0808974" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2009.01.027", "primary_object": { "basename": "0810.5415v2.pdf", "url": "https://authors.library.caltech.edu/records/9xfrs-qrb35/files/0810.5415v2.pdf" }, "pub_year": "2009", "author_list": "Kapustin, Anton; Rozansky, Lev; et al." }, { "id": "https://authors.library.caltech.edu/records/3m2gh-ec774", "eprint_id": 16403, "eprint_status": "archive", "datestamp": "2023-08-21 21:58:19", "lastmod": "2026-04-12 02:01:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Overgroups of Primitive Groups", "ispublished": "pub", "full_text_status": "restricted", "keywords": "permutation group; lattice", "note": "\u00a9 2009 Australian Mathematical Publishing Association Inc. \n\nReceived September 1 2007, accepted June 6 2008. \n\nThis work was partially supported by grant no. NSF-0504852.", "abstract": "We give a qualitative description of the set O_G(H) of overgroups in G of primitive subgroups H of finite\nalternating and symmetric groups G, and particularly of the maximal overgroups. We then show that\ncertain weak restrictions on the lattice O_G(H) impose strong restrictions on H and its overgroup lattice.", "date": "2009-08", "date_type": "published", "publication": "Journal of the Australian Mathematical Sociey", "volume": "87", "number": "1", "publisher": "Australian Mathematical Society", "pagerange": "37-82", "id_number": "CaltechAUTHORS:20091020-133518121", "issn": "1446-7887", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091020-133518121", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/S1446788708000785", "pub_year": "2009", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/ymmhp-74t66", "eprint_id": 56826, "eprint_status": "archive", "datestamp": "2023-08-20 02:27:18", "lastmod": "2026-04-13 03:56:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Heegaard Floer homology and fibred 3-manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 The Johns Hopkins University Press. \n\nManuscript received July 13, 2007; revised October 3, 2008. \n\nDedicated to the memory of Xiao-Song Lin. \n\nResearch supported in part by a Graduate School Centennial Fellowship at Princeton University, an AIM Five-Year Fellowship, and NSF grant DMS-0805807. \n\nThe author wishes to thank Paolo Ghiggini, whose work [4] has a great influence on this one. He also wishes to thank David Gabai, Feng Luo, Peter Ozsv\u00e1th, Jacob Rasmussen and Zolt\u00e1n Szab\u00f3 for their encouragement during the course of this work. Special thanks are due to Yinghua Ai for a conversation during which the author realized a gap in an earlier version of this paper, and for helpful discussions on twisted Heegaard Floer homology. He is also grateful to the referee for pointing out a mistake and for providing many\nconstructive suggestions. \n\nThe earlier versions of this paper were written when the author was at Princeton University and Columbia University.\n\n

Published - 131.4.ni.pdf

", "abstract": "Given a closed 3 -manifold Y, we show that the Heegaard Floer homology determines whether Y fibres over the circle with a fibre of negative Euler characteristic. This is an analogue of an earlier result about knots proved by Ghiggini and the author.", "date": "2009-08", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "131", "number": "4", "publisher": "Johns Hopkins University Press", "pagerange": "1047-1063", "id_number": "CaltechAUTHORS:20150421-115902536", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115902536", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Princeton University Centennial Fellowship" }, { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-0805807" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1353/ajm.0.0064", "primary_object": { "basename": "131.4.ni.pdf", "url": "https://authors.library.caltech.edu/records/ymmhp-74t66/files/131.4.ni.pdf" }, "pub_year": "2009", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/re97d-vtb21", "eprint_id": 16239, "eprint_status": "archive", "datestamp": "2023-08-21 21:57:32", "lastmod": "2026-04-12 18:23:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Breuer-J", "name": { "family": "Breuer", "given": "Jonathan" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Singular spectrum for radial trees", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operators; quantum graphs; trees; singular spectrum; reflectionless property", "note": "\u00a9 2009 World Scientific. \n\nReceived 25 March 2009; Revised 10 July 2009. \n\nWe are grateful to Barry Simon for useful discussions. RF appreciates the warm hospitality of Caltech, where part of this work has been done, and acknowledges support through DAAD grant D/06/49117.\n\n

Submitted - Breuer2009p5819Rev_Math_Phys.pdf

", "abstract": "We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that, generically (in the sense of Baire), radial trees have purely singular continuous spectrum.", "date": "2009-08", "date_type": "published", "publication": "Reviews in Mathematical Physics", "volume": "21", "number": "7", "publisher": "World Scientific", "pagerange": "929-945", "id_number": "CaltechAUTHORS:20091012-105116089", "issn": "0129-055X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091012-105116089", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutscher Akademischer Austauschdienst (DAAD)", "grant_number": "D/06/49117" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0129055X09003773", "primary_object": { "basename": "Breuer2009p5819Rev_Math_Phys.pdf", "url": "https://authors.library.caltech.edu/records/re97d-vtb21/files/Breuer2009p5819Rev_Math_Phys.pdf" }, "pub_year": "2009", "author_list": "Breuer, Jonathan and Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/gm97y-8m567", "eprint_id": 56825, "eprint_status": "archive", "datestamp": "2023-08-20 02:27:14", "lastmod": "2026-04-12 21:04:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Dehn surgeries that yield fibred 3-manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Springer. \n\nReceived: 28 December 2007 / Revised: 20 October 2008 / Published online: 10 January 2009. \n\nWe are grateful to Michel Boileau, David Gabai and Tao Li for some very interesting discussions, to Marc Lackenby for helpful comments, and to John Luecke for a detailed description of his earlier proof of a special case of Theorem 1.4. The author is partially supported by an AIM Five-Year Fellowship. This research was partially conducted during the period the author was employed by the Clay Mathematics Institute as a Liftoff Fellow, and when the author visited University of Minnesota, Twin Cities. The author wishes to thank the above institutions for their supports, and special thanks are due to Tian-Jun Li for his hospitality.\n\n

Submitted - 0712.4387.pdf

", "abstract": "We study Dehn surgeries on null-homotopic knots that yield fibred 3-manifolds when an additional (but natural) homological restriction is imposed. The major tool used is Gabai's theory of sutured manifold decomposition. Such surgeries are negative examples to a question of Michel Boileau. Another result we will prove is about surgeries which reduce the Thurston norm of a fibred manifold.", "date": "2009-08", "date_type": "published", "publication": "Mathematische Annalen", "volume": "344", "number": "4", "publisher": "Springer Verlag", "pagerange": "863-876", "id_number": "CaltechAUTHORS:20150421-115859030", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115859030", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AIM Five-Year Fellowship" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-008-0331-3", "primary_object": { "basename": "0712.4387.pdf", "url": "https://authors.library.caltech.edu/records/gm97y-8m567/files/0712.4387.pdf" }, "pub_year": "2009", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/4mrey-82r45", "eprint_id": 97851, "eprint_status": "archive", "datestamp": "2023-08-21 21:59:35", "lastmod": "2026-04-12 20:58:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Fox-J", "name": { "family": "Fox", "given": "Jacob" } }, { "id": "Sudakov-B", "name": { "family": "Sudakov", "given": "Benny" } } ] }, "title": "Ramsey numbers of sparse hypergraphs", "ispublished": "pub", "full_text_status": "public", "keywords": "Ramsey numbers; hypergraphs; Tur\u00e1n\u2010type theorems; dependent random choice", "note": "\u00a9 2008 Wiley. \n\nIssue online 15 June 2009; version of record online 17 December 2008; manuscript accepted 07 May 2008; manuscript received 27 September 2007. \n\nFox research supported by an NSF Graduate Research Fellowship and a Princeton Centennial Fellowship. Sudakov research supported in part by NSF CAREER award DMS-0546523, NSF grants DMS-0355497 and DMS-0635607, by a USA-Israeli BSF grant, and by the State of New Jersey. \n\nWe would like to thank Jan Hladky for finding several typos in an earlier version of this paper.\n\n

Submitted - 0710.0027.pdf

", "abstract": "We give a short proof that any k\u2010uniform hypergraph H on n vertices with bounded degree \u0394 has Ramsey number at most c(\u0394,k)n, for an appropriate constant c(\u0394,k). This result was recently proved by several authors, but those proofs are all based on applications of the hypergraph regularity method. Here we give a much simpler, self\u2010contained proof which uses new techniques developed recently by the authors together with an argument of Kostochka and R\u00f6dl. Moreover, our method demonstrates that, for k \u2265 4,\n\n[equation; see abstract in PDF for details],\n\nwhere the tower is of height k and the constant c depends on k. It significantly improves on the Ackermann\u2010type upper bound that arises from the regularity proofs, and we present a construction which shows that, at least in certain cases, this bound is not far from best possible. Our methods also allows us to prove quite sharp results on the Ramsey number of hypergraphs with at most m edges.", "date": "2009-08", "date_type": "published", "publication": "Random Structures & Algorithms", "volume": "35", "number": "1", "publisher": "Wiley", "pagerange": "1-14", "id_number": "CaltechAUTHORS:20190812-163001597", "issn": "1042-9832", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001597", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Princeton University" }, { "agency": "NSF", "grant_number": "DMS-0546523" }, { "agency": "NSF", "grant_number": "DMS-0355497" }, { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "Binational Science Foundation (USA-Israel)" }, { "agency": "State of New Jersey" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/rsa.20260", "primary_object": { "basename": "0710.0027.pdf", "url": "https://authors.library.caltech.edu/records/4mrey-82r45/files/0710.0027.pdf" }, "pub_year": "2009", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/ktekr-d4e52", "eprint_id": 77807, "eprint_status": "archive", "datestamp": "2023-08-20 02:05:15", "lastmod": "2026-04-12 14:54:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "A note on low energy scattering for homogeneous long range potentials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Birkh\u00e4user Verlag Basel/Switzerland. \n\nThe author wishes to thank R. Seiringer for useful discussions. Support through DFG grant FR 2664/1-1 and U.S. NSF grant PHY 06 52854 is gratefully acknowledged.\n\n

Submitted - 0812.2916.pdf

", "abstract": "We explicitly calculate the scattering matrix at energy zero for attractive, radial and homogeneous long-range potentials. This proves a conjecture by Derezinski and Skibsted.", "date": "2009-06-15", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "10", "number": "3", "publisher": "Springer", "pagerange": "573-575", "id_number": "CaltechAUTHORS:20170526-100006703", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-100006703", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "FR 2664/1-1" }, { "agency": "NSF", "grant_number": "PHY-0652854" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-009-0410-3", "primary_object": { "basename": "0812.2916.pdf", "url": "https://authors.library.caltech.edu/records/ktekr-d4e52/files/0812.2916.pdf" }, "pub_year": "2009", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/ap2y2-p2p22", "eprint_id": 14424, "eprint_status": "archive", "datestamp": "2023-08-20 02:02:08", "lastmod": "2026-04-12 02:22:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Saulina-N", "name": { "family": "Saulina", "given": "Natalia" } } ] }, "title": "The algebra of Wilson\u2013't Hooft operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Elsevier B.V. \n\nReceived 26 November 2008; accepted 3 February 2009\nAvailable online 10 February 2009. \n\nWe would like to thank R. Bezrukavnikov, A. Braverman, S. Gukov, M. Finkelberg, I. Mirkovic, L. Positselski and E. Witten for discussions. We are especially grateful to R. Bezrukavnikov for valuable advice without which this work would not be possible.We would like to express our thanks to the Aspen Center for Physics for hospitality. A.K. is also grateful to the Independent University of Moscow for staying open during the winter holidays of 2006\u20132007 and thereby providing an opportunity to share some preliminary results with interested mathematicians and to receive their feedback. This work was supported in part by the DOE grant\nDE-FG03-92-ER40701.\n\n

Submitted - 0710.2097v1.pdf

", "abstract": "We study the Operator Product Expansion of Wilson\u2013't Hooft operators in a twisted N=4 super-Yang\u2013Mills theory with gauge group G. The Montonen\u2013Olive duality puts strong constraints on the OPE and in the case G=SU(2) completely determines it. From the mathematical point of view, the Montonen\u2013Olive duality predicts the L^2 Dolbeault cohomology of certain equivariant vector bundles on Schubert cells in the affine Grassmannian. We verify some of these predictions. We also make some general observations about higher categories and defects in Topological Field Theories.", "date": "2009-06-11", "date_type": "published", "publication": "Nuclear Physics B", "volume": "814", "number": "1-2", "publisher": "Elsevier", "pagerange": "327-365", "id_number": "CaltechAUTHORS:20090623-092906678", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090623-092906678", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2009.02.004", "primary_object": { "basename": "0710.2097v1.pdf", "url": "https://authors.library.caltech.edu/records/ap2y2-p2p22/files/0710.2097v1.pdf" }, "pub_year": "2009", "author_list": "Kapustin, Anton and Saulina, Natalia" }, { "id": "https://authors.library.caltech.edu/records/4vrmb-80d92", "eprint_id": 15634, "eprint_status": "archive", "datestamp": "2023-08-21 21:37:38", "lastmod": "2026-03-09 23:07:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "van-de-Bult-F-J", "name": { "family": "van de Bult", "given": "Fokko J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions", "ispublished": "pub", "full_text_status": "public", "keywords": "elliptic hypergeometric functions; basic hypergeometric functions; transformation formulas", "note": "The authors retain ownership of the copyright with respect to their papers published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. \n\nReceived February 01, 2009; Published online June 10, 2009. \n\nThis paper is a contribution to the Proceedings of the Workshop \"Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions\" (July 21\u201325, 2008, MPIM, Bonn, Germany). The full collection is available at http://www.emis.de/journals/SIGMA/Elliptic-Integrable-Systems.html \n\nThe second author was supported in part by NSF grant DMS-0833464.\n\n

Published - vandeBult2009p4725Symmetry_Integr_Geom.pdf

", "abstract": "We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised _10\u03c6_9's and their Nassrallah-Rahman type integral representation.", "date": "2009-06-10", "date_type": "published", "publication": "Symmetry, Integrability and Geometry, Methods and Applications (SIGMA)", "volume": "5", "number": "059", "publisher": "Institute of Mathematics of National Academy of Sciences of Ukraine", "id_number": "CaltechAUTHORS:20090904-142309890", "issn": "1815-0659", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090904-142309890", "rights": "Creative Commons Attribution-NonCommercial-ShareAlike Licence.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0833464" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.3842/SIGMA.2009.059", "primary_object": { "basename": "vandeBult2009p4725Symmetry_Integr_Geom.pdf", "url": "https://authors.library.caltech.edu/records/4vrmb-80d92/files/vandeBult2009p4725Symmetry_Integr_Geom.pdf" }, "pub_year": "2009", "author_list": "van de Bult, Fokko J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/kkz8m-22b96", "eprint_id": 56823, "eprint_status": "archive", "datestamp": "2023-08-20 02:00:33", "lastmod": "2026-04-12 14:17:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ai-Yinghua", "name": { "family": "Ai", "given": "Yinghua" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Two applications of twisted Floer homology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author 2009. Published by Oxford University Press. \n\nReceived September 4, 2008. Revision received April 28, 2009. Accepted May 1, 2009. Communicated by Prof. Yasha Eliashberg\n\nWe are grateful to Peter Ozsv\u00e1th and Zolt\u00e1n Szab\u00f3 for suggesting us to use twisted Heegaard Floer homology for the genus-1 case. In particular, we thank Peter for helpful conversations and encouragements and for providing the ideas to prove Proposition 3.2. The first author would also like to thank Thomas Peters for many helpful discussions during their joint work [1].\n\nThis work was carried out while the two authors were at Columbia University. Both authors are grateful to the Columbia Mathematics Department for its hospitality.\n\nThis work was supported by the China Scholarship Council (to Y.A.); the American Institute of Mathematics (Five-Year Fellowship to Y.N.); and the National Science Foundation (grant number DMS-0805807 to Y.N.).\n\n

Submitted - 0809.0622.pdf

", "abstract": "Given an irreducible closed three-manifold Y, we show that its twisted Heegaard Floer homology determines whether Y is a torus bundle over the circle. Another result we will prove is, if K is a genus-1 null-homologous knot in an L-space, and the zero surgery on K is fibered, then K itself is fibered. These two results are the missing cases of earlier results due to the second author.", "date": "2009-06-05", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2009", "number": "19", "publisher": "Oxford University Press", "pagerange": "3726-3746", "id_number": "CaltechAUTHORS:20150421-115851747", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115851747", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "China Scholarship Council" }, { "agency": "AIM Five-Year Fellowship" }, { "agency": "NSF", "grant_number": "DMS-0805807" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnp070", "primary_object": { "basename": "0809.0622.pdf", "url": "https://authors.library.caltech.edu/records/kkz8m-22b96/files/0809.0622.pdf" }, "pub_year": "2009", "author_list": "Ai, Yinghua and Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/yzr3e-d7h13", "eprint_id": 14584, "eprint_status": "archive", "datestamp": "2023-08-21 21:30:40", "lastmod": "2026-04-12 13:41:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Consani-C", "name": { "family": "Consani", "given": "Caterina" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Fun with F_1", "ispublished": "pub", "full_text_status": "public", "keywords": "BC-system; Endomotives; Varieties over F_1; Frobenius correspondence", "note": "\u00a9 2008 Elsevier Inc.\n\n\nReceived 14 June 2008.\nRevised 1 August 2008.\nAvailable online 6 November 2008.\n\n\nThe authors are partially supported by NSF grants DMS-FRG-0652164, DMS-0652431, and DMS-\n0651925. The second author gratefully thanks l'Institut des Hautes \u00c9tudes Scientifiques for the hospitality, \nthe pleasant atmosphere and the support received during a visit in January\u2013April 2008. The \nthird author would like to thank Abhijnan Rej for some useful conversations.\n\n

Submitted - 0806.2401.pdf

Presentation - mmc1.mpg

", "abstract": "We show that the algebra and the endomotive of the quantum statistical mechanical system of Bost\u2013Connes naturally arises by extension of scalars from the \"field with one element\" to rational numbers. The inductive structure of the abelian part of the endomotive corresponds to the tower of finite extensions of that \"field,\" while the endomorphisms reflect the Frobenius correspondences. This gives in particular an explicit model over the integers for this endomotive, which is related to the original Hecke algebra description. We study the reduction at a prime of the endomotive and of the corresponding noncommutative crossed product algebra.\n\nVideo. For a video summary of this paper, please visit http://\nwww.youtube.com/watch?v=az_0pxm1jrI.", "date": "2009-06", "date_type": "published", "publication": "Journal of Number Theory", "volume": "129", "number": "6", "publisher": "Elsevier", "pagerange": "1532-1561", "id_number": "CaltechAUTHORS:20090714-095640002", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090714-095640002", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-FRG-0652164" }, { "agency": "NSF", "grant_number": "DMS-0652431" }, { "agency": "NSF", "grant_number": "DMS-0651925" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jnt.2008.08.007", "primary_object": { "basename": "0806.2401.pdf", "url": "https://authors.library.caltech.edu/records/yzr3e-d7h13/files/0806.2401.pdf" }, "related_objects": [ { "basename": "mmc1.mpg", "url": "https://authors.library.caltech.edu/records/yzr3e-d7h13/files/mmc1.mpg" } ], "pub_year": "2009", "author_list": "Connes, Alain; Consani, Caterina; et al." }, { "id": "https://authors.library.caltech.edu/records/0szjb-x0a44", "eprint_id": 15992, "eprint_status": "archive", "datestamp": "2023-08-21 21:34:11", "lastmod": "2026-04-12 01:48:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "The action of S_n on the cohomology of M_(0,n)(R)", "ispublished": "pub", "full_text_status": "public", "keywords": "Cycle index; cohomology; moduli space; real genus 0 curves", "note": "\u00a9 2009 Springer. \n\nPublished online: 27 January 2009. \n\nThe author would like to thank P. Etingof for useful discussions (and for asking the question in the first place); also A. Henderson for helpful comments and references, especially regarding the complex case, and the referees for helpful suggestions about the organization of the exposition. This work was supported in part by NSF Grant No. DMS-0401387.\n\n

Submitted - 0601573.pdf

", "abstract": "In recent work by Etingof, Henriques, Kamnitzer, and the author, a presentation and explicit basis was given for the rational cohomology of the real locus M_(0,n)(R) of the moduli space of stable genus 0 curves with n marked points. We determine the graded character of the action of S_n on this space (induced by permutations of the marked points), both in the form of a plethystic formula for the cycle index, and as an explicit product formula for the value of the character on a given cycle type.", "date": "2009-06", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "15", "number": "1", "publisher": "Springer", "pagerange": "171-188", "id_number": "CaltechAUTHORS:20090922-113504889", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090922-113504889", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-008-0467-8", "primary_object": { "basename": "0601573.pdf", "url": "https://authors.library.caltech.edu/records/0szjb-x0a44/files/0601573.pdf" }, "pub_year": "2009", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/sdgxn-h6z25", "eprint_id": 14686, "eprint_status": "archive", "datestamp": "2023-08-21 21:18:23", "lastmod": "2026-04-12 23:56:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cantero-M-J", "name": { "family": "Cantero", "given": "Mar\u00eda Jos\u00e9" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Poisson brackets of orthogonal polynomials", "ispublished": "pub", "full_text_status": "public", "keywords": "Jacobi matrix; CMV matrix; OPUC; OPRL", "note": "\u00a9 2007 Elsevier Inc. \n\nReceived 9 March 2007; received in revised form 4 June 2007; accepted 9 July 2007. Available online 14 September 2007. \n\nCommunicated by C.K. Chui and H.N. Mhaskar. \n\nDedicated to the memory of G.G. Lorentz. \n\nIt is a pleasure to thank Rafael Hernandez Heredero and Irina Nenciu for useful discussions. M. J. Cantero would like to thank Tom Tombrello and Gary Lorden for the hospitality of Caltech.\nGeorge Lorentz was a giant of approximation theory. It is a pleasure and an honor to dedicate this paper to his memory.\n\n

Submitted - 0603098

", "abstract": "For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.", "date": "2009-05", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "158", "number": "1", "publisher": "Elsevier", "pagerange": "3-48", "id_number": "CaltechAUTHORS:20090728-075326318", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090728-075326318", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2007.07.001", "primary_object": { "basename": "0603098", "url": "https://authors.library.caltech.edu/records/sdgxn-h6z25/files/0603098" }, "pub_year": "2009", "author_list": "Cantero, Mar\u00eda Jos\u00e9 and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/8pkg1-ezf50", "eprint_id": 14783, "eprint_status": "archive", "datestamp": "2023-08-20 01:32:15", "lastmod": "2026-04-13 04:05:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Yamazaki-Masahito", "name": { "family": "Yamazaki", "given": "Masahito" } } ] }, "title": "Emergent Calabi-Yau geometry", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 The American Physical Society. \n\nReceived 27 February 2009; published 21 April 2009. \n\nWe would like to thank Alexei Borodin, Kentaro Hori, Kentaro Nagao, and Andrei Okounkov for stimulating discussions. We thank Mina Aganagic for her comment on the earlier version of this Letter. This work is supported in part by DOE Grant No. DE-FG03-92-ER40701 and by the World Premier International Research Center Initiative of MEXT of Japan. H. O. is also supported in part by a Grant-in-Aid for Scientific Research (C) 20540256 of JSPS and by the Kavli Foundation. M.Y. is also supported in part by JSPS and GCOE for Phys. Sci. Frontier of MEXT of Japan.\n\n

Published - Wu2009p2374Phys_Rev_Lett.pdf

Submitted - 0902.3996.pdf

", "abstract": "We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the characteristic polynomial of the crystal melting model to the holomorphic 3-form on the corresponding Calabi-Yau manifold.", "date": "2009-04-24", "date_type": "published", "publication": "Physical Review Letters", "volume": "102", "number": "16", "publisher": "American Physical Society", "pagerange": "161601", "id_number": "CaltechAUTHORS:20090804-095624246", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090804-095624246", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "C-20540256" }, { "agency": "Kavli Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "68-2721", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.102.161601", "primary_object": { "basename": "0902.3996.pdf", "url": "https://authors.library.caltech.edu/records/8pkg1-ezf50/files/0902.3996.pdf" }, "related_objects": [ { "basename": "Wu2009p2374Phys_Rev_Lett.pdf", "url": "https://authors.library.caltech.edu/records/8pkg1-ezf50/files/Wu2009p2374Phys_Rev_Lett.pdf" } ], "pub_year": "2009", "author_list": "Ooguri, Hirosi and Yamazaki, Masahito" }, { "id": "https://authors.library.caltech.edu/records/vbx73-2xb73", "eprint_id": 14057, "eprint_status": "archive", "datestamp": "2023-08-21 21:06:20", "lastmod": "2026-04-13 05:23:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Limits of elliptic hypergeometric integrals", "ispublished": "pub", "full_text_status": "public", "keywords": "elliptic gamma asymptotics; degeneration; hypergeometric integrals", "note": "\u00a9 2009 Springer. \n\nReceived: 14 April 2007. Accepted: 20 August 2007. Published online: 31 October 2007. \n\nThe author would like to thank P. Forrester, J. Stokman and F. van de Bult for motivating conversations regarding the trigonometric and hyperbolic cases, and R. Askey for suggesting the use of the modular transformation to derive classical limits (as in [10]), which led the author to consider the paper [9]; the author would also like to thank an anonymous referee for pointing out that the original version of Theorem 4.7 was badly stated.\n\n

Submitted - 0607093.pdf

", "abstract": "In Ann. Math., to appear, 2008, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) are indeed limiting cases. We also obtain a number of new trigonometric (q-hypergeometric) integral identities as limits from the elliptic level.", "date": "2009-04", "date_type": "published", "publication": "Ramanujan Journal", "volume": "18", "number": "3", "publisher": "Springer", "pagerange": "257-306", "id_number": "CaltechAUTHORS:20090423-141245409", "issn": "1382-4090", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090423-141245409", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11139-007-9055-3", "primary_object": { "basename": "0607093.pdf", "url": "https://authors.library.caltech.edu/records/vbx73-2xb73/files/0607093.pdf" }, "pub_year": "2009", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/rgyqq-jcx39", "eprint_id": 15568, "eprint_status": "archive", "datestamp": "2023-08-21 21:08:55", "lastmod": "2026-04-12 13:30:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kreimer-Y", "name": { "family": "Kreimer", "given": "Yury" } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Monotone Jacobi parameters and non-Szeg\u0151 weights", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials; Schrodinger operators; Spectral weights; Szego condition", "note": "\u00a9 2009 Elsevier B.V. \n\nReceived 8 November 2007; received in revised form 4 April 2008; accepted 28 April 2008. Available online 9 November 2008. \n\nCommunicated by Sergey Krushchev. \n\nThe first author was supported in part by The Israel Science Foundation (grant no. 1169/06). \n\nThe third author was supported in part by NSF grant DMS-0140592. The second and the third authors' research was supported in part by Grant No. 2002068 and No. 2006483 from the United States\u2013Israel Binational Science Foundation (BSF), Jerusalem, Israel. It is a pleasure to thank Fritz Gesztesy, Uri Kaluzhny, and Doron Lubinsky for useful discussions. The authors would also like to thank Mira Shamis and the referees for pointing out several corrections to the original manuscript. B.S. would like to thank Ehud de Shalit for the hospitality of the Einstein Institute of Mathematics at the Hebrew University where some of this work was done. Y.L. would like to thank Matthias Flach for the hospitality of the Department of Mathematics at Caltech where some of this work was done.\n\n

Submitted - p320.pdf

", "abstract": "We relate asymptotics of Jacobi parameters to asymptotics of the spectral weights near the edges. Typical of our results is that for a_n \u2261 1, b_n = \u2212Cn^(\u2212\u03b2)(0 < \u03b2 , 2/3), one has d\u00b5(x) = w(x) on (\u22122,2), and near x = 2, w(x) = e^(-2Q(x)) where Q(x) = \u03b2^(-1)C^(1/\u03b2) \u0413(3/2)\u0413(1/\u03b2-1/2)(2-x)1/2-1/\u03b2/\u0413(1/\u03b2 +1) (1 + o((2-x)))).", "date": "2009-04", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "157", "number": "2", "publisher": "Elsevier", "pagerange": "144-171", "id_number": "CaltechAUTHORS:20090903-110552245", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090903-110552245", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "1169/06" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2006483" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2008.04.020", "primary_object": { "basename": "p320.pdf", "url": "https://authors.library.caltech.edu/records/rgyqq-jcx39/files/p320.pdf" }, "pub_year": "2009", "author_list": "Kreimer, Yury; Last, Yoram; et al." }, { "id": "https://authors.library.caltech.edu/records/vcgyd-qv434", "eprint_id": 14657, "eprint_status": "archive", "datestamp": "2023-08-21 21:07:38", "lastmod": "2026-04-12 18:37:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Gijsbers-D-A-H", "name": { "family": "Gijsbers", "given": "Di\u00e9 A. H." } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "Tangle and Brauer diagram algebras of type D_n", "ispublished": "pub", "full_text_status": "public", "keywords": "Associative algebra; BMW algebra; Brauer algebra; Temperley\u2013Lieb algebra; tangle; Brauer diagram; Coxeter groups", "note": "\u00a9 2009 World Scientific Publishing Co. \n\nAccepted 3 February 2008. \n\nThe work reported here grew out of the Ph. D. thesis of one of us [7]. The other two authors wish to acknowledge Caltech and Technische Universiteit Eindhoven for enabling mutual visits.\n\n

Submitted - 0704.2754.pdf

", "abstract": "A generalization of the Kauffman tangle algebra is given for Coxeter type D_n. The tangles involve a pole of order 2. The algebra is shown to be isomorphic to the Birman\u2013Murakami\u2013Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which, in our set-up, occurs when the Coxeter type is A_(n - 1). The proof involves a diagrammatic version of the Brauer algebra of type Dn of which the generalized Temperley\u2013Lieb algebra of type D_n is a subalgebra.", "date": "2009-04", "date_type": "published", "publication": "Journal of Knot Theory and its Ramifications", "volume": "18", "number": "4", "publisher": "World Scientific Publishing Co.", "pagerange": "447-483", "id_number": "CaltechAUTHORS:20090723-161051204", "issn": "0218-2165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090723-161051204", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1142/S0218216509007063", "primary_object": { "basename": "0704.2754.pdf", "url": "https://authors.library.caltech.edu/records/vcgyd-qv434/files/0704.2754.pdf" }, "pub_year": "2009", "author_list": "Cohen, Arjeh M.; Gijsbers, Di\u00e9 A. H.; et al." }, { "id": "https://authors.library.caltech.edu/records/s7t0g-2bc28", "eprint_id": 14519, "eprint_status": "archive", "datestamp": "2023-08-20 01:02:57", "lastmod": "2026-04-12 03:04:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A Celebration of J\u00fcrg and Tom", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2009 Springer.\nReceived: 10 September 2008. Accepted: 18 September 2008. Published online: 25 October 2008.\n\nSupported in part by NSF grant DMS-0652919.\n\nIssue in honor of the (recent) sixtieth birthdays of J\u00fcrg Fr\u00f6hlich and Tom Spencer.", "abstract": "Without abstract.", "date": "2009-03", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "134", "number": "5-6", "publisher": "Springer", "pagerange": "809-812", "id_number": "CaltechAUTHORS:20090708-105847182", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090708-105847182", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s10955-008-9627-7", "pub_year": "2009", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/qnxws-hey72", "eprint_id": 15838, "eprint_status": "archive", "datestamp": "2023-08-21 20:51:52", "lastmod": "2026-04-12 02:02:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "On set systems with restricted intersections modulo p and p-ary t-designs", "ispublished": "pub", "full_text_status": "public", "keywords": "t-designs; Incidence matrices; Extremal set theory; Set intersections", "note": "\u00a9 2009 Elsevier B.V.\n\nReceived 13 November 2007; accepted 12 September 2008. Available online 23 October 2008. \nThe author's research was supported by NSA Grant H98230-04-1-0037.\n\n

Published - Wilson2009p1015Discrete_Math.pdf

", "abstract": "We consider bounds on the size of families \u2131 of subsets of a v-set subject to restrictions modulo a prime p on the cardinalities of the pairwise intersections. We improve the known bound when \u2131 is allowed to contain sets of different sizes, but only in a special case. We show that if the bound for uniform families \u2131 holds with equality, then \u2131 is the set of blocks of what we call a p-ary t-design for certain values of t. This motivates us to make a few observations about p-ary t-designs for their own sake.", "date": "2009-02-28", "date_type": "published", "publication": "Discrete Mathematics", "volume": "309", "number": "3", "publisher": "Elsevier", "pagerange": "606-612", "id_number": "CaltechAUTHORS:20090914-121114974", "issn": "0012-365X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090914-121114974", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Security Agency", "grant_number": "H98230-04-1-0" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.disc.2008.09.025", "primary_object": { "basename": "Wilson2009p1015Discrete_Math.pdf", "url": "https://authors.library.caltech.edu/records/qnxws-hey72/files/Wilson2009p1015Discrete_Math.pdf" }, "pub_year": "2009", "author_list": "Wilson, Richard M." }, { "id": "https://authors.library.caltech.edu/records/7my47-98y11", "eprint_id": 15064, "eprint_status": "archive", "datestamp": "2023-08-20 00:53:56", "lastmod": "2026-04-12 13:33:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Ookouchi-Yutaka", "name": { "family": "Ookouchi", "given": "Yutaka" } }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } }, { "id": "Song-Jaewon", "name": { "family": "Song", "given": "Jaewon" }, "orcid": "0000-0002-1238-2435" } ] }, "title": "Current correlators for general gauge mediation", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 Elsevier B.V. \n\nReceived 24 July 2008; accepted 11 September 2008. Available online 19 September 2008. \n\nWe would like to thank H. Goh, M. Ibe, J. Marsano, N. Seiberg and T. Yanagida for discussion. C.P. and J.S. thank the hospitality of the Institute for the Physics and Mathematics of the Universe\nat the University of Tokyo. This work is supported in part by DOE grant DE-FG03-92-ER40701. The work of H.O. is also supported in part by a Grant-in-Aid for Scientific Research (C) 20540256 from the Japan Society for the Promotion of Science, by the World Premier International Research Center Initiative of MEXT of Japan, and by the Kavli Foundation. C.P. and J.S. are also supported in part by Samsung Scholarship.\n\n

Submitted - 0806.4733.pdf

", "abstract": "In the gauge mediation mechanism, the effects of the hidden sector are characterized by a set of correlation functions of the global symmetry current of the hidden sector. We present methods to compute these correlators in cases with strongly coupled hidden sectors. Several examples are presented to demonstrate the technique explicitly.", "date": "2009-02-11", "date_type": "published", "publication": "Nuclear Physics B", "volume": "808", "number": "1-2", "publisher": "Elsevier", "pagerange": "121-136", "id_number": "CaltechAUTHORS:20090817-101240132", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090817-101240132", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Kavli Foundation" }, { "agency": "Samsung Scholarship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2692", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2008.09.017", "primary_object": { "basename": "0806.4733.pdf", "url": "https://authors.library.caltech.edu/records/7my47-98y11/files/0806.4733.pdf" }, "pub_year": "2009", "author_list": "Ooguri, Hirosi; Ookouchi, Yutaka; et al." }, { "id": "https://authors.library.caltech.edu/records/ggcyn-h0f13", "eprint_id": 13478, "eprint_status": "archive", "datestamp": "2023-08-21 20:45:43", "lastmod": "2026-04-12 14:11:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Weak convergence of CD kernels and applications", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials; unit-circle; paraorthogonal polynomials; zeros; asymptotics; quadrature; intervals; operators; matrices", "note": "\u00a9 2009 Duke University Press. \n\nReceived 19 December 2007. Revision received 1 May 2008; publication date 1 February 2009. \n\nIt is a pleasure to thank Jonathan Breuer, Yoram Last, and especially Vilmos Totik for useful conversations. I also thank Ehud de Shalit and Yoram Last for the hospitality of the Einstein Institute of Mathematics of the Hebrew University during part of the preparation of this article.\n\n

Published - SIMdmj09.pdf

", "abstract": "We prove a general result on equality of the weak limits of the zero counting measure, d\u03bdn, of orthogonal polynomials (defined by a measure d\u03bc) and (1/n)Kn(x, x)d\u03bc(x). By combining this with the asymptotic upper bounds of M\u00e1t\u00e9 and Nevai [16] and Totik [33] on n\u03bbn(x), we prove some general results on \u222b \u0399(1/n)Kn(x, x)d\u03bcs \u2192 0 for the singular part of d\u03bc and \u222b \u0399 |\u03c1E(x) \u2212 (w(x)/n)Kn(x, x)| dx \u2192 0, where \u03c1E is the density of the equilibrium measure and w(x) the density of d\u03bc.", "date": "2009-02-01", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "146", "number": "2", "publisher": "Duke University Press", "pagerange": "305-330", "id_number": "CaltechAUTHORS:SIMdmj09", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMdmj09", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1215/00127094-2008-067", "primary_object": { "basename": "SIMdmj09.pdf", "url": "https://authors.library.caltech.edu/records/ggcyn-h0f13/files/SIMdmj09.pdf" }, "pub_year": "2009", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/j4f8j-nem94", "eprint_id": 15968, "eprint_status": "archive", "datestamp": "2023-08-21 20:44:37", "lastmod": "2026-04-12 02:18:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Regularity and the Ces\u00e0ro\u2013Nevai class", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Orthogonal polynomial; Regular measure", "note": "\u00a9 2008 Elsevier Inc. \n\nReceived 23 October 2007; revised 28 February 2008; accepted 10 April 2008. Communicated by Leonid Golinskii. Available online 31 October 2008. \n\nThe research was supported in part by NSF grants DMS-0140592 and DMS-0652919.", "abstract": "We consider OPRL and OPUC with measures regular in the sense of Ullman\u2013Stahl\u2013Totik and prove consequences on the Jacobi parameters or Verblunsky coefficients. For example, regularity on [\u22122,2] implies lim_(N\u2192\u221e)N^(-1)[\u2211_(n=1)^N(a_n-1)^2 + b_n^2] = 0.", "date": "2009-02", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "156", "number": "2", "publisher": "Elsevier", "pagerange": "142-153", "id_number": "CaltechAUTHORS:20090918-112109981", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090918-112109981", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "NSF", "grant_number": "DMS-0652919" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2008.04.016", "pub_year": "2009", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/kfmep-8pp23", "eprint_id": 88783, "eprint_status": "archive", "datestamp": "2023-08-20 00:50:03", "lastmod": "2026-04-12 20:25:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Weak convergence of CD kernels and applications", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 Duke Mathematical Journal. \n\nReceived 19 December 2007. Revision received 1 May 2008. \n\nSimon's work supported in part by National Science Foundation grant DMS-0140592 and U.S.\u2013Israel Binational Science Foundation grant 2002068. \n\nIt is a pleasure to thank Jonathan Breuer, Yoram Last, and especially Vilmos Totik for useful conversations. I also thank Ehud de Shalit and Yoram Last for the hospitality of the Einstein Institute of Mathematics of the Hebrew University during part of the preparation of this article.\n\n

Submitted - 0707.2578

", "abstract": "We prove a general result on equality of the weak limits of the zero counting measure, d\u03bdnd\u03bdn, of orthogonal polynomials (defined by a measure d\u03bc) and (1/n)K_n(x,x)d\u03bc(x). By combining this with the asymptotic upper bounds of M\u00e1t\u00e9 and Nevai [16] and Totik [33] on n\u03bb_n(x), we prove some general results on \u222b_I (1/n)K_n(x,x)d \u03bc_s \u2192 0 for the singular part of d\u03bc and \u222b_ I \u2223\u2223\u03c1_E(x) \u2212 (w(x)/n)K_n(x,x)\u2223\u2223dx \u2192 0, where \u03c1_E is the density of the equilibrium measure and w(x)x) the density of d \u03bc.", "date": "2009-02", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "146", "number": "2", "publisher": "Duke University Press", "pagerange": "305-330", "id_number": "CaltechAUTHORS:20180813-091037545", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180813-091037545", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1215/00127094-2008-067", "primary_object": { "basename": "0707.2578", "url": "https://authors.library.caltech.edu/records/kfmep-8pp23/files/0707.2578" }, "pub_year": "2009", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/f468v-awk92", "eprint_id": 13404, "eprint_status": "archive", "datestamp": "2023-08-20 00:34:51", "lastmod": "2026-03-08 18:15:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "Matthias" }, "orcid": "0000-0002-4523-9467" } ] }, "title": "Iwasawa Theory and Motivic L-functions", "ispublished": "pub", "full_text_status": "public", "keywords": "L-functions", "note": "\u00a9 International Press\nReceived August 17, 2006. \n2000 Mathematics Subject Classification. Primary: 11G40, Secondary: 11R23, 11R33, 11G18\n\n

Published - FLApamq09.pdf

", "abstract": "We illustrate the use of Iwasawa theory in proving cases of the (equivariant) Tamagawa number conjecture.", "date": "2009-01", "date_type": "published", "publication": "Pure and Applied Mathematics Quarterly", "volume": "5", "number": "1, Sp.", "publisher": "International Press", "pagerange": "255-294", "id_number": "CaltechAUTHORS:FLApamq09", "issn": "1558-8602", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FLApamq09", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Science Foundation", "grant_number": "DMS-0401403" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "FLApamq09.pdf", "url": "https://authors.library.caltech.edu/records/f468v-awk92/files/FLApamq09.pdf" }, "pub_year": "2009", "author_list": "Flach, Matthias" }, { "id": "https://authors.library.caltech.edu/records/1g5m5-6kg08", "eprint_id": 15169, "eprint_status": "archive", "datestamp": "2023-08-20 00:16:34", "lastmod": "2026-04-12 20:46:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cook-P-L-H", "name": { "family": "Cook", "given": "Paul L. H." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Yang-Jie", "name": { "family": "Yang", "given": "Jie" } } ] }, "title": "New Anomalies in Topological String Theory", "ispublished": "pub", "full_text_status": "public", "keywords": "string theory", "note": "\u00a9 2008 Progress of Theoretical Physics. \n\nWe thank M. Aganagic, E. Getzler, T. Graber, K. Hori, C. Vafa, K. Vyas and J. Walcher for useful discussions. H.O. thanks T. Eguchi for introducing him to the beautiful area of mathematical physics and for many enjoyable collaborations. This research is supported in part by DOE grant DE-FG03-92-ER40701. H.O. is also supported in part by the Kavli Foundation and by the World Premier International Research Center Initiative of MEXT of Japan.\n\n

Published - Cook2009p2041Prog_Theor_Phys_Supp.pdf

Submitted - 0804.1120.pdf

", "abstract": "We show that the topological string partition function with D-branes on a compact Calabi-Yau manifold has new anomalies that spoil the recursive structure of the holomorphic anomaly equation and introduce dependence on wrong moduli (such as complex structure moduli in the A-model), unless the disk one-point functions vanish. This provides a microscopic explanation for the recent result of Walcher in arXiv:0712.2775 on counting of BPS states in M-theory using the topological string partition function. The relevance of vanishing disk one-point functions to large N duality for compact Calabi-Yau manifolds is noted.", "date": "2009", "date_type": "published", "publication": "Progress of Theoretical Physics Supplement", "volume": "2009", "number": "177", "publisher": "Progress of Theoretical Physics", "pagerange": "120-127", "id_number": "CaltechAUTHORS:20090819-111703735", "issn": "0375-9687", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090819-111703735", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Kavli Foundation" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" } ] }, "other_numbering_system": { "items": [ { "id": "68-2672", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Takayanagi-T", "name": { "family": "Takayanagi", "given": "Tadashi" } }, { "id": "Yahikozawa-S", "name": { "family": "Yahikozawa", "given": "Shigeaki" } } ] }, "doi": "10.1143/PTPS.177.120", "primary_object": { "basename": "0804.1120.pdf", "url": "https://authors.library.caltech.edu/records/1g5m5-6kg08/files/0804.1120.pdf" }, "related_objects": [ { "basename": "Cook2009p2041Prog_Theor_Phys_Supp.pdf", "url": "https://authors.library.caltech.edu/records/1g5m5-6kg08/files/Cook2009p2041Prog_Theor_Phys_Supp.pdf" } ], "pub_year": "2009", "author_list": "Cook, Paul L. H.; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/p2hzh-8r107", "eprint_id": 14942, "eprint_status": "archive", "datestamp": "2023-08-20 00:16:28", "lastmod": "2026-04-12 02:58:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Signalizer lattices in finite groups", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2009 The University of Michigan.\n\nReceived February 12, 2007. Revision received January 31, 2008.\nThis work was partially supported by NSF-0504852.\nZentralblatt MATH identifier: 05566074.", "abstract": "Let G be a finite group and let H be a subgroup of G. We investigate constraints\nimposed upon the structure of G by restrictions on the lattice O_G(H) of overgroups\nof H in G. Call such a lattice a finite group interval lattice. In particular\nwe would like to show that the following question has a positive answer.", "date": "2009", "date_type": "published", "publication": "Michigan Mathematical Journal", "volume": "58", "number": "1", "publisher": "University of Michigan", "pagerange": "79-103", "id_number": "CaltechAUTHORS:20090811-091248605", "issn": "0026-2285", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090811-091248605", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0504852" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1307/mmj/1242071684", "pub_year": "2009", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/k09rz-nhe49", "eprint_id": 17120, "eprint_status": "archive", "datestamp": "2023-08-20 00:17:59", "lastmod": "2026-03-18 00:09:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Killip-R", "name": { "family": "Killip", "given": "Rowan" }, "orcid": "0000-0002-4272-7916" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Sum rules and spectral measures of Schr\u00f6dinger operators with L^2 potentials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Copyright 2009 Annals of Mathematics. \n\nReceived July 11, 2005. \n\nKillip was supported in part by NSF grant DMS-0401277 and a Sloan Foundation Fellowship. Simon was supported in part by NSF grant DMS-0140592 and in part by Grant No. 2002068 from the United States-Israel Science Foundation, Jerusalem, Israel.\n\n

Published - Killip2009p6534Ann_Math.pdf

", "abstract": "Necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half-line Schr\u00f6dinger operator with square integrable potential.", "date": "2009", "date_type": "published", "publication": "Annals of Mathematics", "volume": "170", "number": "2", "publisher": "Princeton University Press", "pagerange": "739-782", "id_number": "CaltechAUTHORS:20100108-193514874", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100108-193514874", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401277" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.48550/arXiv.0608767", "primary_object": { "basename": "Killip2009p6534Ann_Math.pdf", "url": "https://authors.library.caltech.edu/records/k09rz-nhe49/files/Killip2009p6534Ann_Math.pdf" }, "pub_year": "2009", "author_list": "Killip, Rowan and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/0tx4k-my486", "eprint_id": 18723, "eprint_status": "archive", "datestamp": "2023-08-20 00:20:04", "lastmod": "2026-03-18 00:03:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Schr\u00f6dinger operators with purely discrete spectrum", "ispublished": "pub", "full_text_status": "public", "keywords": "compact resolvent, Schr\u00f6dinger operators", "note": "\u00a9 2009 TBiMC Scientific Publishers. \n\nReceived 17/10/2008. \n\nIt is a pleasure to thank Peter Stollmann for useful correspondence and Ehud de Shalit for the hospitality of Hebrew University where some of the work presented here was done. \n\nSupported in part by NSF grant DMS-0652919 and by Grant No. 2006483 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.\n\n

Submitted - p322.pdf

", "abstract": "We prove that \u2013 \u0394 + V has purely discrete spectrum if V \u2265 0 and, for all M, |{x|V(x)", "date": "2009", "date_type": "published", "publication": "Methods of Functional Analysis and Topology", "volume": "15", "number": "1", "publisher": "TBiMC Scientific Publishers", "pagerange": "61-66", "id_number": "CaltechAUTHORS:20100617-144018858", "issn": "1029-3531", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100617-144018858", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0652919" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2006483" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "p322.pdf", "url": "https://authors.library.caltech.edu/records/0tx4k-my486/files/p322.pdf" }, "pub_year": "2009", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/y1pmt-j1802", "eprint_id": 17372, "eprint_status": "archive", "datestamp": "2023-08-20 00:18:04", "lastmod": "2026-04-12 23:49:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dimofte-T-D", "name": { "family": "Dimofte", "given": "Tudor" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Lenells-J", "name": { "family": "Lenells", "given": "Jonatan" } }, { "id": "Zagier-D", "name": { "family": "Zagier", "given": "Don" } } ] }, "title": "Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 International Press. \n\nReceived March 18, 2009. \n\nWe would like to thank D. Auroux, N. Dunfield, S. Garoufalidis, K. Hikami, T. Mrowka,\nW. Neumann, E. Witten, and C. Zickert for useful discussions and correspondence. Research\nof SG is supported in part by NSF Grant PHY-0757647 and in part by the Alfred P.\nSloan Foundation. JL acknowledges support from a Marie Curie Intra-European Fellowship.\nTD acknowledges support from a National Defense Science and Engineering Graduate\nFellowship. Opinions and conclusions expressed here are those of the authors and do not\nnecessarily reflect the views of funding agencies.\n\n

Published - Dimofte2009p6866Commun._Number_Theory_Phys.pdf

", "abstract": "We develop several methods that allow us to compute all-loop partition functions in perturbative Chern-Simons theory with complex gauge group G_C, sometimes\nin multiple ways. In the background of a non-abelian irreducible flat connection, perturbative G_C invariants turn out to be interesting topological invariants, which are very different from finite type (Vassiliev) invariants obtained in a theory with compact gauge group G. We explore various aspects of these invariants and present an example where we compute them explicitly to high loop order. We also introduce a notion of \"arithmetic TQFT\" and conjecture (with supporting numerical evidence) that SL(2,C) Chern-Simons theory is an example of such a theory.", "date": "2009", "date_type": "published", "publication": "Communications in Number Theory and Physics", "volume": "3", "number": "2", "publisher": "International Press", "pagerange": "363-443", "id_number": "CaltechAUTHORS:20100202-111957900", "issn": "1931-4523", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100202-111957900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0757647" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Marie Curie Fellowship" }, { "agency": "National Defense Science and Engineering Graduate (NDSEG) Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CNTP.2009.v3.n2.a4", "primary_object": { "basename": "Dimofte2009p6866Commun._Number_Theory_Phys.pdf", "url": "https://authors.library.caltech.edu/records/y1pmt-j1802/files/Dimofte2009p6866Commun._Number_Theory_Phys.pdf" }, "pub_year": "2009", "author_list": "Dimofte, Tudor; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/s4vpk-ana78", "eprint_id": 16837, "eprint_status": "archive", "datestamp": "2023-08-20 00:17:38", "lastmod": "2026-03-09 23:12:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Remarks on the Symmetric Powers of Cusp Forms on GL(2)", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2009 D. Ramakrishnan.\nFirst published in Contemporary Mathematics in volume 488, 2009, published by the American Mathematical Society.\nPartially supported by NSF grant DMS-0701OS9.\n\n

Published - Ramakrishnan2009p6383.pdf

", "abstract": "In this paper we prove the following conditional result: Let F be a number field, and \u03c0 a cusp form on GL(2)/F which is not solvable polyhedral. Assume that all the symmetric powers sym^(m)(\u03c0) are modular, i.e., define automorphic forms on GL(m + 1)/F. If sym^6(\u03c0) is cuspidal, then\nso are the sym^(m)(\u03c0), for all m. Moreover, sym^(6)(\u03c0) is Eisensteinian iff sym^(5)(\u03c0) is an abelian twist of the functorial product of \u03c0 with the symmetric square of\na cusp form \u03c0' on GL(2)/F.", "date": "2009", "date_type": "published", "publication": "Contemporary Mathematics", "volume": "488", "publisher": "American Mathematical Society", "pagerange": "237-256", "id_number": "CaltechAUTHORS:20091130-134058409", "issn": "0271-4132", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091130-134058409", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0701089" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "Ramakrishnan2009p6383.pdf", "url": "https://authors.library.caltech.edu/records/s4vpk-ana78/files/Ramakrishnan2009p6383.pdf" }, "pub_year": "2009", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/49b17-8qt63", "eprint_id": 15656, "eprint_status": "archive", "datestamp": "2023-08-22 13:57:54", "lastmod": "2026-03-09 20:36:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ioana-A", "name": { "family": "Ioana", "given": "Adrian" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Tsankov-T", "name": { "family": "Tsankov", "given": "Todor" } } ] }, "title": "Subequivalence relations and positive-definite functions", "ispublished": "pub", "full_text_status": "public", "keywords": "Subequivalence relations; positive-definite functions; co-induced action; orbit equivalence; non-amenable groups; classification; percolation, property (T); cost", "note": "\u00a9 2009 EMS Publishing House.\n\nThe research of A.S.K. and T.T. was partially supported by NSF Grant DMS-0455285. We would like to thank I. Epstein for allowing us to include here our joint results. We would also like to thank R. Lyons, S. Popa and Y. Shalom for many valuable comments.\n\n

Published - Ioana2009p5841Group_Geom_Dynam.pdf

", "abstract": "We study a positive-definite function associated with a countable, measure-preserving equivalence relation, which can be used to measure quantitatively the proximity of subequivalence relations. Combined with a co-inducing construction introduced by Epstein and earlier work of Ioana, this can be used to construct many mixing actions of countable groups and establish the non-classifiability, in a strong sense, of orbit equivalence of actions of non-amenable groups. We also discuss connections with percolation on Cayley graphs and the theory of costs.", "date": "2009", "date_type": "published", "publication": "Groups, Geometry, and Dynamics", "volume": "3", "number": "4", "publisher": "European Mathematical Society", "pagerange": "579-625", "id_number": "CaltechAUTHORS:20090908-083705826", "issn": "1661-7207", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090908-083705826", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0455285" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0806.0430", "primary_object": { "basename": "Ioana2009p5841Group_Geom_Dynam.pdf", "url": "https://authors.library.caltech.edu/records/49b17-8qt63/files/Ioana2009p5841Group_Geom_Dynam.pdf" }, "pub_year": "2009", "author_list": "Ioana, Adrian; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/86sf7-2y605", "eprint_id": 77355, "eprint_status": "archive", "datestamp": "2023-08-22 13:53:33", "lastmod": "2026-04-12 21:03:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Non-linear ground state representations and sharp Hardy inequalities", "ispublished": "pub", "full_text_status": "public", "keywords": "Hardy inequality; Sobolev embedding; Ground state substitution; Fractional Sobolev spaces", "note": "\u00a9 2008 Elsevier Inc. \n\nReceived 4 March 2008, Accepted 22 May 2008, Available online 10 July 2008. \n\nThe authors wish to thank E. Lieb for helpful discussions. This work was supported by DAAD grant D/06/49117 (R.L. Frank), by U.S. National Science Foundation grant PHY 06 52356 and an A.P. Sloan Fellowship (R. Seiringer).\n\n

Submitted - 0803.0503.pdf

", "abstract": "We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.", "date": "2008-12-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "255", "number": "12", "publisher": "Elsevier", "pagerange": "3407-3430", "id_number": "CaltechAUTHORS:20170510-155935658", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-155935658", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutscher Akademischer Austauschdienst (DAAD)", "grant_number": "D/06/49117" }, { "agency": "NSF", "grant_number": "PHY-06 52356" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jfa.2008.05.015", "primary_object": { "basename": "0803.0503.pdf", "url": "https://authors.library.caltech.edu/records/86sf7-2y605/files/0803.0503.pdf" }, "pub_year": "2008", "author_list": "Frank, Rupert L. and Seiringer, Robert" }, { "id": "https://authors.library.caltech.edu/records/a4tft-69g20", "eprint_id": 12496, "eprint_status": "archive", "datestamp": "2023-08-22 13:51:44", "lastmod": "2026-04-16 01:40:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Faoro-Lara", "name": { "family": "Faoro", "given": "Lara" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Ioffe-Lev-B", "name": { "family": "Ioffe", "given": "Lev B." } } ] }, "title": "Quasiparticle Poisoning and Josephson Current Fluctuations Induced by Kondo Impurities", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 The American Physical Society. \n\nReceived 25 January 2008; published 10 December 2008. \n\nThis work was supported by the National Security Agency (NSA) under Army Research Office (ARO) Contract No. W911NF-06-1-0208 and NSF ECS 0608842.\n\n

Published - FAOprl08.pdf

", "abstract": "We introduce a toy model that allows us to study the physical properties of a spin impurity coupled to the electrons in the superconducting island. We show that, when the coupling of the spin is of the order of the superconducting gap Delta, two almost degenerate subgap states are formed. By computing the Berry phase that is associated with the superconducting phase rotations in this model, we prove that these subgap states are characterized by a different charge and demonstrate that the switching between these states has the same effect as quasiparticle poisoning (unpoisoning) of the island. We also show that an impurity coupled to both the island and the lead generates Josepshon current fluctuations.", "date": "2008-12-12", "date_type": "published", "publication": "Physical Review Letters", "volume": "101", "number": "24", "publisher": "American Physical Society", "pagerange": "Art. No. 247002", "id_number": "CaltechAUTHORS:FAOprl08", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FAOprl08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Security Agency" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-06-1-0208" }, { "agency": "NSF", "grant_number": "ECS-0608842" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.101.247002", "primary_object": { "basename": "FAOprl08.pdf", "url": "https://authors.library.caltech.edu/records/a4tft-69g20/files/FAOprl08.pdf" }, "pub_year": "2008", "author_list": "Faoro, Lara; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/5t5qc-r1s05", "eprint_id": 78982, "eprint_status": "archive", "datestamp": "2023-08-22 13:45:26", "lastmod": "2026-04-13 04:01:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Zainy-al-Yasry-A", "name": { "family": "Zainy al-Yasry", "given": "Ahmad" } } ] }, "title": "Coverings, correspondences, and noncommutative geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "3-manifolds; Branched coverings; Correspondences; Cobordisms; Time evolution", "note": "\u00a9 2008 Elsevier B.V. \n\nReceived 7 January 2008. Received in revised form 15 June 2008. Accepted 12 July 2008. Available online 20 July 2008. \n\nWe thank the referee for many very useful comments and suggestions. The first author is partially supported by NSF-grant DMS-0651925.\n\n

Submitted - 0807.2924.pdf

", "abstract": "We construct an additive category where objects are embedded graphs in the 3-sphere and morphisms are geometric correspondences given by 3-manifolds realized in different ways as branched covers of the 3-sphere, up to branched cover cobordisms. We consider dynamical systems obtained from associated convolution algebras endowed with time evolutions defined in terms of the underlying geometries. We describe the relevance of our construction to the problem of spectral correspondences in noncommutative geometry.", "date": "2008-12", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "58", "number": "12", "publisher": "Elsevier", "pagerange": "1639-1661", "id_number": "CaltechAUTHORS:20170712-075152597", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-075152597", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0651925" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2008.07.007", "primary_object": { "basename": "0807.2924.pdf", "url": "https://authors.library.caltech.edu/records/5t5qc-r1s05/files/0807.2924.pdf" }, "pub_year": "2008", "author_list": "Marcolli, Matilde and Zainy al-Yasry, Ahmad" }, { "id": "https://authors.library.caltech.edu/records/sbjtp-jde45", "eprint_id": 66981, "eprint_status": "archive", "datestamp": "2023-08-20 00:06:36", "lastmod": "2026-04-12 23:36:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Murakami-Hitoshi", "name": { "family": "Murakami", "given": "Hitoshi" } } ] }, "title": "SL(2,C) Chern\u2013Simons Theory and the Asymptotic Behavior of the Colored Jones Polynomial", "ispublished": "pub", "full_text_status": "public", "keywords": "colored Jones polynomial, volume conjecture, A-polynomial, Chern\u2013Simons theory", "note": "\u00a9 2008 Springer. \n\nReceived: 7 July 2007; Revised: 18 August 2008; Accepted: 6 November 2008. \n\nThe authors would like to thank J\u00e9r\u00f4me Dubois, Stavros Garoufalidis, and Toshiaki Hattori for helpful conversations. It is also a pleasure to thank the organizers of the conference \"Around the Volume Conjecture\" at Columbia University in March 2006 and the conference \"Modular Forms and String Duality\" at Banff in June 2006, which stimulated much of this work. This work was supported in part by the DOE under grant number DE-FG03-92-ER40701, in part by RFBR grant 04-02-16880, and in part by the grant for support of scientific schools NSh-8004.2006.2 (S.G.), and in part by Grant-in-Aid for Scientific Research (B) (15340019) (H.M.).\n\n

Published - art_3A10.1007_2Fs11005-008-0282-3.pdf

Submitted - 0608324.pdf

", "abstract": "It has been proposed that the asymptotic behavior of the colored Jones polynomial is equal to the perturbative expansion of the Chern\u2013Simons gauge theory with complex gauge group SL(2,C) on the hyperbolic knot complement. In this note we make the first step toward verifying this relation beyond the semi-classical approximation. This requires a careful understanding of some delicate issues, such as normalization of the colored Jones polynomial and the choice of polarization in Chern\u2013Simons theory. Addressing these issues allows us to go beyond the volume conjecture and to verify some predictions for the behavior of the subleading terms in the asymptotic expansion of the colored Jones polynomial.", "date": "2008-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "86", "number": "2-3", "publisher": "Springer", "pagerange": "79-98", "id_number": "CaltechAUTHORS:20160511-094807499", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-094807499", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "15340019" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-008-0282-3", "primary_object": { "basename": "0608324.pdf", "url": "https://authors.library.caltech.edu/records/sbjtp-jde45/files/0608324.pdf" }, "related_objects": [ { "basename": "art_3A10.1007_2Fs11005-008-0282-3.pdf", "url": "https://authors.library.caltech.edu/records/sbjtp-jde45/files/art_3A10.1007_2Fs11005-008-0282-3.pdf" } ], "pub_year": "2008", "author_list": "Gukov, Sergei and Murakami, Hitoshi" }, { "id": "https://authors.library.caltech.edu/records/9q9g7-rbr36", "eprint_id": 12503, "eprint_status": "archive", "datestamp": "2023-08-22 13:39:05", "lastmod": "2026-04-13 06:00:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } } ] }, "title": "Superconformal Chern-Simons theories and the squashed seven sphere", "ispublished": "pub", "full_text_status": "public", "keywords": "dS-CFT Correspondence; M-Theory; Gauge-gravity correspondence", "note": "\u00a9 2008 SISSA. \n\nReceived 9 October 2008, accepted for publication 10 November 2008. Published 26 November 2008. \n\nWe would like to thank J. Schwarz for discussions. C.P. thanks the students and organizers of Prospects in Theoretical Physics 2008 where the work was initiated. H.O. thanks the Aspen Center for Physics for the hospitality. \n\nThis work is supported in part by DOE grant DE-FG03-92-ER40701. The work of H.O. is also supported in part by a Grant-in-Aid for Scientific Research (C) 20540256 from the Japan Society for the Promotion of Science, by the World Premier International Research Center Initiative of MEXT of Japan, and by the Kavli Foundation. C.P. is supported in part by Samsung Scholarship.\n\n

Published - OOGjhep08.pdf

Accepted Version - arXiv-0808.0500v2.pdf

", "abstract": "We show that there are two supersymmetric completions of the three-dimensional Chern-Simons theory of level k with gauge group U(N) \u00d7 U(N) coupled to four sets of massless scalars and spinors in the bi-fundamental representation, if we require Sp(2) \u2282 SU(4) global symmetry with the matter fields in the fundamental representation of SU(4). One is the Script N = 6 superconformal theory recently studied in hep-th/0806.1218 and another is a new theory with Script N = 1 superconformal symmetry. We conjecture that the Script N = 1 theory is dual to M theory on AdS4 \u00d7 squashed S^7/Bbb Zk.", "date": "2008-11-26", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2008", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 082", "id_number": "CaltechAUTHORS:OOGjhep08", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Kavli Foundation" }, { "agency": "Samsung Scholarship" } ] }, "other_numbering_system": { "items": [ { "id": "IPMU-08-0052", "name": "Institute for the Physics and Mathematics of the Universe, University of Tokyo" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2008/11/082", "primary_object": { "basename": "arXiv-0808.0500v2.pdf", "url": "https://authors.library.caltech.edu/records/9q9g7-rbr36/files/arXiv-0808.0500v2.pdf" }, "related_objects": [ { "basename": "OOGjhep08.pdf", "url": "https://authors.library.caltech.edu/records/9q9g7-rbr36/files/OOGjhep08.pdf" } ], "pub_year": "2008", "author_list": "Ooguri, Hirosi and Park, Chang-Soon" }, { "id": "https://authors.library.caltech.edu/records/w7f43-ym034", "eprint_id": 56824, "eprint_status": "archive", "datestamp": "2023-08-22 13:31:02", "lastmod": "2026-04-12 23:34:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Boileau-M", "name": { "family": "Boileau", "given": "Michel" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wang-Shicheng", "name": { "family": "Wang", "given": "Shicheng" } } ] }, "title": "On standard forms of 1-dominations between knots with same Gromov volumes", "ispublished": "pub", "full_text_status": "public", "keywords": "Standard forms; 1-dominations; knots", "note": "\u00a9 2008 World Scientific Publishing Co. \n\nReceived: 10 January 2008; Revised: 19 March 2008. \n\nThis research was conducted during the periods the second author was a graduate student at Princeton University and was employed by the Clay Mathematics Institute as a Liftoff Fellow. The second author was partially supported by a Graduate School Centennial Fellowship at Princeton University. The third author is partially supported by grant No.10631060 of the National Natural Science Foundation of China.\n\n

Submitted - 0801.1943.pdf

", "abstract": "Let k and k\u2032 be two knots in the 3-sphere. Say k 1-dominates k\u2032, if there is a proper degree 1 map f: E(k) \u2192 E(k\u2032).\n\nTheorem: Suppose that any companion of k is prime. If k 1-dominates k\u2032 with the same Gromov volume, then k\u2032 can be obtained from k by finitely many de-satellizations.\n\nThe condition of \"same Gromov volume\" clearly cannot be removed. We also give a new construction of 1-domination between knots with the same Gromov volume to show that the condition \"any companion of k is prime\" cannot be removed.", "date": "2008-11", "date_type": "published", "publication": "Communications in Contemporary Mathematics", "volume": "10", "number": "S1", "publisher": "World Scientific Publishing Company", "pagerange": "857-870", "id_number": "CaltechAUTHORS:20150421-115855236", "issn": "0219-1997", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115855236", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Princeton University Centennial Fellowship" }, { "agency": "National Natural Science Foundation of China", "grant_number": "10631060" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219199708003071", "primary_object": { "basename": "0801.1943.pdf", "url": "https://authors.library.caltech.edu/records/w7f43-ym034/files/0801.1943.pdf" }, "pub_year": "2008", "author_list": "Boileau, Michel; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/js3z3-npm25", "eprint_id": 66982, "eprint_status": "archive", "datestamp": "2023-08-19 23:46:56", "lastmod": "2026-03-09 02:20:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Gauge Theory, Ramification, And The Geometric Langlands Program", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 International Press. \n\nWe thank A. Braverman, D. Gaitsgory, E. Frenkel, and D. Kazhdan for patient and extremely helpful explanations. We also thank J. Andersen, P. Aspinwall, M. F. Atiyah, D. Ben-Zvi, R. Bezrukavnikov, R. Bielawski, R. Dijkgraaf, R. Donagi, N. Hitchin, L. Jeffrey, A. Kapustin, P. Kronheimer, Y. Laszlo, H. Nakajima, C. Sorger, and M. Thaddeus, among others, for a wide variety of helpful comments and advice. Research of SG was partly supported by DOE grant DE-FG03-92-ER40701. Research of EW was partly supported by NSF Grant PHY-0503584.\n\n

Published - euclid.cdm.1223654541.pdf

Submitted - 0612073.pdf

", "abstract": "In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of \"surface operators,\" which are supported on two-dimensional surfaces somewhat as Wilson or 't Hooft operators are supported on curves. We describe the relevant surface operators in N=4 super Yang-Mills theory, and the parameters they depend on, and analyze how S-duality acts on these parameters. Then, after compactifying on a Riemann surface, we show that the hypothesis of S-duality for surface operators leads to a natural extension of the geometric Langlands program for the case of tame ramification. The construction involves an action of the affine Weyl group on the cohomology of the moduli space of Higgs bundles with ramification, and an action of the affine braid group on A-branes or B-branes on this space.", "date": "2008-10-10", "date_type": "published", "publication": "Current Developments in Mathematics", "volume": "2006", "publisher": "International Press", "pagerange": "35-180", "id_number": "CaltechAUTHORS:20160511-095533476", "issn": "1089-6384", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-095533476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0503584" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CDM.2006.v2006.n1.a2", "primary_object": { "basename": "0612073.pdf", "url": "https://authors.library.caltech.edu/records/js3z3-npm25/files/0612073.pdf" }, "related_objects": [ { "basename": "euclid.cdm.1223654541.pdf", "url": "https://authors.library.caltech.edu/records/js3z3-npm25/files/euclid.cdm.1223654541.pdf" } ], "pub_year": "2008", "author_list": "Gukov, Sergei and Witten, Edward" }, { "id": "https://authors.library.caltech.edu/records/zpzpy-0jz84", "eprint_id": 13146, "eprint_status": "archive", "datestamp": "2023-08-22 13:00:17", "lastmod": "2026-04-12 21:30:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Two extensions of Lubinsky's universality theorem", "ispublished": "pub", "full_text_status": "public", "keywords": "ORTHOGONAL POLYNOMIALS; UNIT-CIRCLE; PARAORTHOGONAL POLYNOMIALS; INTEGER COEFFICIENTS; ALGEBRAIC EQUATIONS; FINE-STRUCTURE; COMPLEX PLANE; ZEROS; BEHAVIOR; QUADRATURE", "note": "\u00a9 2008 Hebrew University Magnes Press. \n\nReceived: 11 June 2007. Published online: 5 September 2008. \n\nSupported in part by NSF grant DMS-0140592 and U.S.\u2013Israel Binational Science Foundation (BSF) Grant No. 2002068.\n\n

Accepted Version - p316.pdf

", "abstract": "We extend some remarkable recent results of Lubinsky and Levin\u2013Lubinsky from [\u22121, 1] to allow discrete eigenvalues outside \u03c3ess and to allow \u03c3ess first to be a finite union of closed intervals and then a fairly general compact set in\nR (one which is regular for the Dirichlet problem).", "date": "2008-09-05", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "105", "number": "1", "publisher": "Hebrew University Magnes Press", "pagerange": "345-362", "id_number": "CaltechAUTHORS:SIMjam08", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMjam08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s11854-008-0039-z", "primary_object": { "basename": "p316.pdf", "url": "https://authors.library.caltech.edu/records/zpzpy-0jz84/files/p316.pdf" }, "pub_year": "2008", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/d67wj-s0e37", "eprint_id": 11978, "eprint_status": "archive", "datestamp": "2023-08-22 12:42:07", "lastmod": "2026-04-13 04:47:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Rej-A", "name": { "family": "Rej", "given": "Abhijnan" } } ] }, "title": "Supermanifolds from Feynman graphs", "ispublished": "pub", "full_text_status": "public", "note": "Copyright \u00a9 Institute of Physics and IOP Publishing Limited 2008. \n\nReceived 4 April 2008, in final form 10 June 2008. Published 4 July 2008. \n\nThe first author is partially supported by NSF grant DMS-0651925. The second author is supported as a Marie Curie Early Stage Researcher at Durham University and by the Clay Mathematical Institute.\n\n

Submitted - 0806.1681.pdf

", "abstract": "We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying a condition generalizing the log divergence in this context. The analog in this setting of the graph hypersurfaces is a graph supermanifold given by the divisor of zeros and poles of the Berezinian of a matrix associated with the graph, inside a superprojective space. We introduce a Grothendieck group for supermanifolds and identify the subgroup generated by the graph supermanifolds. This can be seen as a general procedure for constructing interesting classes of supermanifolds with associated periods.", "date": "2008-08-08", "date_type": "published", "publication": "Journal of Physics A: Mathematical and Theoretical", "volume": "41", "number": "31", "publisher": "IOP", "pagerange": "315402", "id_number": "CaltechAUTHORS:MARjpa08", "issn": "1751-8113", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:MARjpa08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0651925" }, { "agency": "European Commission" }, { "agency": "Clay Mathematical Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1751-8113/41/31/315402", "primary_object": { "basename": "0806.1681.pdf", "url": "https://authors.library.caltech.edu/records/d67wj-s0e37/files/0806.1681.pdf" }, "pub_year": "2008", "author_list": "Marcolli, Matilde and Rej, Abhijnan" }, { "id": "https://authors.library.caltech.edu/records/m4gwj-46284", "eprint_id": 97848, "eprint_status": "archive", "datestamp": "2023-08-22 12:38:58", "lastmod": "2026-04-12 02:08:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "A new upper bound for the bipartite Ramsey problem", "ispublished": "pub", "full_text_status": "public", "keywords": "Bipartite Ramsey; Zarankiewicz problem", "note": "\u00a9 2008 Wiley. \n\nIssue online 17 June 2008; version of record online 28 May 2008; manuscript revised 21 March 2008; manuscript received 24 May 2007.", "abstract": "We consider the following question: how large does n have to be to guarantee that in any two\u2010coloring of the edges of the complete graph K_(n,n) there is a monochromatic K_(k,k)? In the late 1970s, Irving showed that it was sufficient, for k large, that n\u2009\u2265 2^(k\u2009\u2212 1) (k\u2009\u2212 1) \u2212 1. Here we improve upon this bound, showing that it is sufficient to take\n\nn \u2265 (1 + o(1))2^(k+1) log k,\n\nwhere the log is taken to the base 2.", "date": "2008-08", "date_type": "published", "publication": "Journal of Graph Theory", "volume": "58", "number": "4", "publisher": "Wiley", "pagerange": "351-356", "id_number": "CaltechAUTHORS:20190812-163001317", "issn": "0364-9024", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001317", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/jgt.20317", "pub_year": "2008", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/vyq2h-91d65", "eprint_id": 75999, "eprint_status": "archive", "datestamp": "2023-08-19 23:24:10", "lastmod": "2026-04-12 02:49:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Weidl-T", "name": { "family": "Weidl", "given": "Timo" } } ] }, "title": "Eigenvalue Bounds for Perturbations of Schr\u00f6dinger Operators and Jacobi Matrices With Regular Ground States", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag 2008. \n\nReceived: 28 June 2007 / Accepted: 19 July 2007\nPublished online: 14 March 2008. \n\nCommunicated by M. Aizenman. \n\nSupported in part by NSF Grant DMS-0140592 and U.S.\u2013Israel Binational Science Foundation (BSF) Grant No. 2002068. \n\nSupported in part by DFG grant WE-1964 2/1.\n\n

Submitted - 004635214ec13a61da000000.pdf

", "abstract": "We prove general comparison theorems for eigenvalues of perturbed Schr\u00f6dinger operators that allow proof of Lieb\u2013Thirring bounds for suitable non-free Schr\u00f6dinger operators and Jacobi matrices.", "date": "2008-08", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "282", "number": "1", "publisher": "Springer", "pagerange": "199-208", "id_number": "CaltechAUTHORS:20170408-144423477", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170408-144423477", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "WE-1964 2/1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-008-0453-1", "primary_object": { "basename": "004635214ec13a61da000000.pdf", "url": "https://authors.library.caltech.edu/records/vyq2h-91d65/files/004635214ec13a61da000000.pdf" }, "pub_year": "2008", "author_list": "Frank, Rupert L.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/8g1hg-hmz07", "eprint_id": 19084, "eprint_status": "archive", "datestamp": "2023-08-22 12:33:36", "lastmod": "2026-04-12 14:10:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Draganova-A", "name": { "family": "Draganova", "given": "Anna" } }, { "id": "Mutoh-Y", "name": { "family": "Mutoh", "given": "Yukiyasu" } }, { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "More on decompositions of edge-colored complete graphs", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Decomposition; Complete graph; Edge-colored", "note": "\u00a9 2008 Elsevier. \n\nReceived 30 August 2004; accepted 9 August 2007. Available online 3 December 2007. \n\nResearch supported by JSPS Research Fellow 09978. \n\nResearch supported by NSA Grant H98230-04-1-0037.", "abstract": "Let g be a family of graphs whose edges are colored with elements from a set R of r colors. We assume no two vertices of G are joined by more than one edge of color i for any i \u2208 R, for each G \u2208 g. K^((r))_n will denote the complete graph with r edges joining any pair of distinct vertices, one of each of the r colors. We describe necessary and asymptotically sufficient conditions on n for the existence of a family D of subgraphs of K^((r))_n, each of which is an isomorphic copy of some graph in g, so that each edge of K^((r))_n appears in exactly one of the subgraphs in D.", "date": "2008-07-28", "date_type": "published", "publication": "Discrete Mathematics", "volume": "308", "number": "14", "publisher": "Elsevier", "pagerange": "2926-2943", "id_number": "CaltechAUTHORS:20100715-120722042", "issn": "0012-365X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100715-120722042", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "09978" }, { "agency": "National Security Agency", "grant_number": "H98230-04-1-0037" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.disc.2007.08.044", "pub_year": "2008", "author_list": "Draganova, Anna; Mutoh, Yukiyasu; et al." }, { "id": "https://authors.library.caltech.edu/records/s19mn-5r963", "eprint_id": 88733, "eprint_status": "archive", "datestamp": "2023-08-19 23:05:26", "lastmod": "2026-04-13 00:25:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Normal subsystems of fusion systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 London Mathematical Society. \n\nIssue Online: 21 March 2008; Version of Record online: 21 March 2008; Manuscript revised: 16 August 2007; Manuscript received: 14 November 2006. \n\nThis work was partially supported by NSF\u20100504852.", "abstract": "The notion of a fusion system was first defined and explored by Puig in the context of modular representation theory. Later, Broto, Levi, and Oliver significantly extended the theory of fusion systems as a tool in homotopy theory. In this paper we begin a program to establish a local theory of fusion systems similar to the local theory of finite groups. In particular, we define the notion of a normal subsystem of a saturated fusion system, and prove some basic results about normal subsystems and factor systems.", "date": "2008-07", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "97", "number": "1", "publisher": "London Mathematical Society", "pagerange": "239-271", "id_number": "CaltechAUTHORS:20180810-075919663", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-075919663", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504852" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms/pdm057", "pub_year": "2008", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/f9z4h-qck67", "eprint_id": 13484, "eprint_status": "archive", "datestamp": "2023-08-22 11:38:10", "lastmod": "2026-04-13 05:24:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cornelissen-G", "name": { "family": "Cornelissen", "given": "Gunther" } }, { "id": "Lorscheid-O", "name": { "family": "Lorscheid", "given": "Oliver" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "On the K-Theory of Graph C^\u2217-Algebras", "ispublished": "pub", "full_text_status": "public", "keywords": "graph C^*-algebras; K-theory; edge incidence operator; Morita equivalence; strict isomorphism", "note": "\u00a9 2008 Springer Science. Received: 12 November 2007/ Accepted: 9 January 2008/Published online: 25 January 2008.\nWe thank Jakub Byszewski for his input in Sect. 2.8. The position of the unit in K0(OY) was guessed based on some example calculations by Jannis Visser in his SCI 291 Science Laboratory at Utrecht University College.\n\n

Submitted - 0606582.pdf

", "abstract": "We classify graph C^*-algebras, namely, Cuntz-Krieger algebras associated to the Bass-Hashimoto edge incidence operator of a finite graph, up to strict isomorphism. This is done by a purely graph theoretical calculation of the K-theory of the C^*-algebras and the method also provides an independent proof of the classification up to Morita equivalence and stable equivalence of such algebras, without using the boundary operator algebra. A direct relation is given between the K_1-group of the algebra and the cycle space of the graph.", "date": "2008-05", "date_type": "published", "publication": "Acta Applicandae Mathematicae", "volume": "102", "number": "1", "publisher": "Springer", "pagerange": "57-69", "id_number": "CaltechAUTHORS:CORaam08", "issn": "0167-8019", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORaam08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10440-008-9208-4", "primary_object": { "basename": "0606582.pdf", "url": "https://authors.library.caltech.edu/records/f9z4h-qck67/files/0606582.pdf" }, "pub_year": "2008", "author_list": "Cornelissen, Gunther; Lorscheid, Oliver; et al." }, { "id": "https://authors.library.caltech.edu/records/sfth9-7qg70", "eprint_id": 88710, "eprint_status": "archive", "datestamp": "2023-08-19 22:39:46", "lastmod": "2026-04-13 05:23:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "M." }, "orcid": "0000-0002-4523-9467" } ] }, "title": "Cohomology of topological groups with applications to the Weil group", "ispublished": "pub", "full_text_status": "restricted", "keywords": "cohomology, topological groups, Weil group", "note": "\u00a9 Foundation Compositio Mathematica 2008. \n\nReceived 7 October 2006, accepted in final form 1 October 2007. \n\nThe author is supported by grant DMS-0401403 from the National Science Foundation. \n\nI am very grateful to Steve Lichtenbaum for extremely stimulating discussions about Weil-\u00e9tale cohomology and for inviting me to speak at Brown University. I would also like to thank Thomas Geisser for many discussions related to topos theory, in particular concerning Proposition 7.1 above.", "abstract": "We establish various properties of the definition of cohomology of topological groups given by Grothendieck, Artin and Verdier in SGA4, including a Hochschild\u2013Serre spectral sequence and a continuity theorem for compact groups. We use these properties to compute the cohomology of the Weil group of a totally imaginary field, and of the Weil-\u00e9tale topology of a number ring recently introduced by Lichtenbaum (both with integer coefficients).", "date": "2008-05", "date_type": "published", "publication": "Compositio Mathematica", "volume": "144", "number": "03", "publisher": "Oxford University Press", "pagerange": "633-656", "id_number": "CaltechAUTHORS:20180809-133558024", "issn": "0010-437X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180809-133558024", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401403" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/s0010437x07003338", "pub_year": "2008", "author_list": "Flach, M." }, { "id": "https://authors.library.caltech.edu/records/4j82w-zbv21", "eprint_id": 13544, "eprint_status": "archive", "datestamp": "2023-08-22 11:38:18", "lastmod": "2026-04-12 05:24:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cornelissen-G", "name": { "family": "Cornelissen", "given": "Gunther" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Zeta functions that hear the shape of a Riemann surface", "ispublished": "pub", "full_text_status": "public", "keywords": "non-commutative geometry; spectral triples; Kleinian-groups; manifolds; algebras; rigidity; curves; set", "note": "\u00a9 2008 Elsevier Ltd.\n\n\nReceived 9 November 2007; \nrevised 17 December 2007; accepted 30 December 2007. \nAvailable online 6 January 2008.\n\n

Submitted - 0708.0500.pdf

", "abstract": "To a compact hyperbolic Riemann surface, we associate a finitely summable spectral triple whose underlying topological space is the limit set of a corresponding Schottky group, and whose \"Riemannian\" aspect (Hilbert space and Dirac operator) encode the boundary action through its Patterson-Sullivan measured. We prove that the ergodic rigidity theorem for this boundary action implies that the zeta functions of the spectral triple suffice to characterize the (anti-)complex isomorphism class of the corresponding Riemann surface. Thus, you can hear the complex analytic shape of a Riemann surface, by listening to a suitable spectral triple.", "date": "2008-05", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "58", "number": "5", "publisher": "Elsevier", "pagerange": "619-632", "id_number": "CaltechAUTHORS:CORjgp08", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORjgp08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2007.12.011", "primary_object": { "basename": "0708.0500.pdf", "url": "https://authors.library.caltech.edu/records/4j82w-zbv21/files/0708.0500.pdf" }, "pub_year": "2008", "author_list": "Cornelissen, Gunther and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/cvvx6-01q45", "eprint_id": 16346, "eprint_status": "archive", "datestamp": "2023-08-22 11:34:24", "lastmod": "2026-04-12 21:56:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "Dirk" }, "orcid": "0000-0002-0643-0138" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Eigenvalue bounds in the gaps of Schr\u00f6dinger operators and Jacobi matrices", "ispublished": "pub", "full_text_status": "public", "keywords": "Eigenvalue bounds; Jacobi matrices; Schr\u00f6dinger operators", "note": "\u00a9 2007 Elsevier. \n\nReceived 19 May 2007. Available online 22 September 2007. \n\nSubmitted by Goong Chen.\n\n

Submitted - 0705.3646

", "abstract": "We consider C = A + B where A is selfadjoint with a gap (a, b) in its spectrum and B is (relatively) compact. We prove\na general result allowing B of indefinite sign and apply it to obtain a (\u03b4V)^(d/2) bound for perturbations of suitable periodic Schr\u00f6dinger operators and a (not quite) Lieb\u2013Thirring bound for perturbations of algebro-geometric almost periodic Jacobi matrices.", "date": "2008-04-15", "date_type": "published", "publication": "Journal of Mathematical Analysis and Applictions", "volume": "340", "number": "2", "publisher": "Elsevier", "pagerange": "892-900", "id_number": "CaltechAUTHORS:20091014-110720129", "issn": "0022-247X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091014-110720129", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jmaa.2007.08.059", "primary_object": { "basename": "0705.3646", "url": "https://authors.library.caltech.edu/records/cvvx6-01q45/files/0705.3646" }, "pub_year": "2008", "author_list": "Hundertmark, Dirk and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/kk39t-qht03", "eprint_id": 16374, "eprint_status": "archive", "datestamp": "2023-08-19 22:26:38", "lastmod": "2026-04-12 14:11:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Fine structure of the zeros of orthogonal polynomials IV: A priori bounds and clock behavior", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Wiley Periodicals, Inc. \n\nReceived: May 2006; published online: 30 Apr 2007. \n\nSupported in part by The Israel Science Foundation (Grant No. 188/02). \n\nSupported in part by NSF grant DMS-0140592. \n\nResearch supported in part by Grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.\n\n

Submitted - 0606038

", "abstract": "We prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions (Jacobi parameters approach the free ones and are of bounded variation). We prove that for ergodic discrete Schr\u00f6dinger operators, Poisson behavior implies a positive Lyapunov exponent. Both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs.", "date": "2008-04", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "61", "number": "4", "publisher": "Wiley", "pagerange": "486-538", "id_number": "CaltechAUTHORS:20091016-144551584", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091016-144551584", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "188/02" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1002/cpa.20185", "primary_object": { "basename": "0606038", "url": "https://authors.library.caltech.edu/records/kk39t-qht03/files/0606038" }, "pub_year": "2008", "author_list": "Last, Yoram and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/d8zfe-0nc04", "eprint_id": 14253, "eprint_status": "archive", "datestamp": "2023-08-19 22:26:30", "lastmod": "2026-04-13 04:48:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Ookouchi-Yutaka", "name": { "family": "Ookouchi", "given": "Yutaka" } }, { "id": "Park-Chang-Soon", "name": { "family": "Park", "given": "Chang-Soon" } } ] }, "title": "Metastable vacua in perturbed Seiberg-Witten theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 International Press.\n\nH.O. thanks the hospitality of the high-energy theory group at the University of Tokyo at Hongo. This research is supported in part by DOE grant DEFG03-92-ER40701. The research of H.O. is also supported in part by the NSF grant OISE-0403366 and by the 21st Century COE Program at the University of Tokyo. Y.O. is also supported in part by the JSPS Fellowship for Research Abroad. C.P. is also supported in part by Samsung Scholarship. \n\nMathematical Reviews number (MathSciNet): MR2399315.\n\n

Published - OOGatmp08.pdf

Submitted - 0704.3613.pdf

", "abstract": "We show that, for a generic choice of a point on the Coulomb branch of any N = 2 supersymmetric gauge theory, it is possible to find a superpotential perturbation which generates a metastable vacuum at the point. For theories with SU(N) gauge group, such a superpotential can be expressed as a sum of single-trace terms for N = 2 and 3. If the metastable point is chosen at the origin of the moduli space, we can show that the superpotential can be a single-trace operator for any N. In both cases, the superpotential is a polynomial of degree 3N of the vector multiplet scalar field.", "date": "2008-04", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "12", "number": "2", "publisher": "International Press", "pagerange": "405-427", "id_number": "CaltechAUTHORS:20090518-095435229", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090518-095435229", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DEFG03-92-ER40701" }, { "agency": "NSF", "grant_number": "OISE-0403366" }, { "agency": "University of Tokyo" }, { "agency": "Japan Society for the Promotion of Science (JSPS)" }, { "agency": "Samsung Scholarship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2646", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0704.3613", "primary_object": { "basename": "0704.3613.pdf", "url": "https://authors.library.caltech.edu/records/d8zfe-0nc04/files/0704.3613.pdf" }, "related_objects": [ { "basename": "OOGatmp08.pdf", "url": "https://authors.library.caltech.edu/records/d8zfe-0nc04/files/OOGatmp08.pdf" } ], "pub_year": "2008", "author_list": "Ooguri, Hirosi; Ookouchi, Yutaka; et al." }, { "id": "https://authors.library.caltech.edu/records/cm5e5-ptt87", "eprint_id": 13447, "eprint_status": "archive", "datestamp": "2023-08-19 22:23:36", "lastmod": "2026-04-13 06:16:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "On intervals in subgroup lattices of finite groups", "ispublished": "pub", "full_text_status": "public", "keywords": "INTERMEDIATE SUBFACTORS.", "note": "\u00a9 2008 American Mathematical Society. Received by the editors June 28, 2006. Article electronically published on March 17, 2008. This work was partially supported by NSF-0504852. 20D30, 06B05, 46L37\n\n

Published - ASCjams08.pdf

", "abstract": "We investigate the question of which finite lattices L are isomorphic to the lattice [H,G] of all overgroups of a subgroup H in a finite group G. We show that the structure of G is highly restricted if [H,G] is disconnected. We define the notion of a \"signalizer lattice\" in H and show for suitable disconnected lattices L, if [H,G] is minimal subject to being isomorphic to L or its dual, then either G is almost simple or H admits a signalizer lattice isomorphic to L or its dual. We use this theory to answer a question in functional analysis raised by Watatani.", "date": "2008-03-17", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "21", "number": "3", "publisher": "American Mathematical Society", "pagerange": "809-830", "id_number": "CaltechAUTHORS:ASCjams08", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ASCjams08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0504852" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-08-00602-4", "primary_object": { "basename": "ASCjams08.pdf", "url": "https://authors.library.caltech.edu/records/cm5e5-ptt87/files/ASCjams08.pdf" }, "pub_year": "2008", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/avg45-kdv44", "eprint_id": 82859, "eprint_status": "archive", "datestamp": "2023-08-19 22:18:54", "lastmod": "2026-04-12 13:48:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "New Deformations of Group Algebras of Coxeter Groups, II", "ispublished": "pub", "full_text_status": "public", "keywords": "Coxeter groups, Hecke algebras, deformations", "note": "\u00a9 2008 Birkhaeuser. \n\nReceived: May 2006; Accepted: July 2007; First Online: 30 January 2008. \n\nIt is our pleasure to dedicate this paper to Joseph\nBernstein. His work, as well as style of doing and explaining mathematics, have been an inspiration for generations of mathematicians. The work of P.E. was partially supported by the NSF grant DMS-0504847 and the CRDF grant RM1-2545-MO-03. E.R. was supported in part by NSF grant DMS-0401387. The authors would also like to acknowledge that at many stages of this work they used the MAGMA package for algebraic computations [M].\n\n

Submitted - 0604519.pdf

", "abstract": "This paper is a sequel of [ER]. Specifically, let W be a Coxeter group, generated by s_i, i \u2208 I. Then, following [ER], one can define a new deformation A_+ = A_+(W) of the group algebra Z[W_+] of the group W_+ of even elements\nin W. This deformation is an algebra over the ring R = Z[t^(\u00b11)_(ijk)] = Z[T] of regular functions on a certain torus T of deformation parameters. The main result of [ER] implies that this deformation is flat (i.e. A_+ is a flat\nR-module) if and only if for every triple of indices \u0394 = {i, j, k} \u2282 I the corresponding rank 3 parabolic subgroup W\u0394 \u2282 W is infinite. (To be more precise, in [ER] we work over C, but the results routinely extend to the case of ground ring Z.)", "date": "2008-03", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "17", "number": "6", "publisher": "Springer", "pagerange": "1851-1871", "id_number": "CaltechAUTHORS:20171101-153438612", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171101-153438612", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504847" }, { "agency": "Civilian Research & Development Foundation (CRDF)", "grant_number": "RM1-2545-MO-03" }, { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-007-0642-7", "primary_object": { "basename": "0604519.pdf", "url": "https://authors.library.caltech.edu/records/avg45-kdv44/files/0604519.pdf" }, "pub_year": "2008", "author_list": "Etingof, Pavel and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/3cd3v-fdk54", "eprint_id": 77356, "eprint_status": "archive", "datestamp": "2023-08-19 22:18:20", "lastmod": "2026-04-12 14:38:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Siedentop-H", "name": { "family": "Siedentop", "given": "Heinz" } }, { "id": "Warzel-S", "name": { "family": "Warzel", "given": "Simone" } } ] }, "title": "The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction", "ispublished": "pub", "full_text_status": "public", "keywords": "Heavy atoms, ground state energy, relativistic Coulomb system, Scott correction", "note": "\u00a9 2007 The authors. Reproduction of this article for non-commercial purposes by any means is permitted.\n\nReceived: 16 February 2007; Accepted: 02 May 2007; First Online: 21 December 2007.\n\nWe thank Elliott Lieb and Robert Seiringer for various supportive discussions. R.F. and H.S. thank the Departments ofMathematics and Physics of Princeton University for hospitality while this work was done. The work has been partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (R.F.), the U.S. National Science Foundation, grant PHY 01 39984 (H.S.), and the Deutsche Forschungsgemeinschaft, grant SI 348/13-1 (H.S.).\n\n

Submitted - 0702056.pdf

", "abstract": "We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction, exists. It turns out to be lower than in the non-relativistic description of atoms. Our proof is valid up to and including the critical coupling constant. It is based on a renormalization of the energy whose zero level we adjust to be the ground-state energy of the corresponding non-relativistic problem. This allows us to roll the proof back to results for the Schr\u00f6dinger operator.", "date": "2008-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "278", "number": "2", "publisher": "Springer", "pagerange": "549-566", "id_number": "CaltechAUTHORS:20170510-160420593", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-160420593", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Foundation for International Cooperation in Research and Higher Education (STINT)" }, { "agency": "NSF", "grant_number": "PHY-0139984" }, { "agency": "Deutsche Forschungsgemeinschaft", "grant_number": "SI 348/13-1" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-007-0397-x", "primary_object": { "basename": "0702056.pdf", "url": "https://authors.library.caltech.edu/records/3cd3v-fdk54/files/0702056.pdf" }, "pub_year": "2008", "author_list": "Frank, Rupert L.; Siedentop, Heinz; et al." }, { "id": "https://authors.library.caltech.edu/records/v1sem-11x68", "eprint_id": 14541, "eprint_status": "archive", "datestamp": "2023-08-19 22:10:41", "lastmod": "2026-04-12 21:11:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henderson-A", "name": { "family": "Henderson", "given": "Anthony" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "The cohomology of real De Concini\u2013Procesi models of Coxeter type", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 The Author 2008. \n\nReceived July 19, 2007; Revised July 19, 2007; Accepted January 4, 2008. \n\nThis work was supported by Australian Research Council grant DP0344185\n\n

Submitted - 0612010.pdf

", "abstract": "We study the rational cohomology groups of the real De Concini\u2013Procesi model corresponding to a finite Coxeter group, generalizing the type-A case of the moduli space of stable genus 0 curves with marked points. We compute the Betti numbers in the exceptional types, and give formulae for them in types B and D. We give a generating-function formula for the characters of the representations of a Coxeter group of type B on the rational cohomology groups of the corresponding real De Concini\u2013Procesi model, and deduce the multiplicities of one-dimensional characters in the representations, and a formula for the Euler character. We also give a moduli space interpretation of this type-B variety, and hence show that the action of the Coxeter group extends to a slightly larger group.", "date": "2008-02-14", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2008", "publisher": "Oxford University Press", "pagerange": "Art. No. rnn001", "id_number": "CaltechAUTHORS:20090709-105804586", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090709-105804586", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council", "grant_number": "DP0344185" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1093/imrn/rnn001", "primary_object": { "basename": "0612010.pdf", "url": "https://authors.library.caltech.edu/records/v1sem-11x68/files/0612010.pdf" }, "pub_year": "2008", "author_list": "Henderson, Anthony and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/kexey-etw10", "eprint_id": 56960, "eprint_status": "archive", "datestamp": "2023-08-19 22:05:25", "lastmod": "2026-04-12 22:32:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "A compactification of Igusa varieties", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Springer. \n\nReceived: 28 October 2005 / Revised: 26 June 2007 / Published online: 28 August 2007. \n\nThe author is very grateful to Richard Taylor and Brian Conrad for their help with all the phases of this project, and to Ben Moonen for his useful comments on an early version of this paper. She is also indebted to the referee for her or his help.\n\n

Submitted - Igusa.pdf

", "abstract": "We investigate the notion of Igusa level structure for a one-dimensional Barsotti\u2013Tate group over a scheme X of positive characteristic and compare it to Drinfeld's notion of level structure. In particular, we show how the geometry of the Igusa covers of X is useful for studying the geometry of its Drinfeld covers (e.g. connected and smooth components, singularities). Our results apply in particular to the study of the Shimura varieties considered in Harris and Taylor (On the geometry and cohomology of some simple Shimura varieties. Princeton University Press, Princeton, 2001). In this context, they are higher dimensional analogues of the classical work of Igusa for modular curves and of the work of Carayol for Shimura curves. In the case when the Barsotti\u2013Tate group has constant p-rank, this approach was carried-out by Harris and Taylor (On the geometry and cohomology of some simple Shimura varieties. Princeton University Press, Princeton, 2001).", "date": "2008-02", "date_type": "published", "publication": "Mathematische Annalen", "volume": "340", "number": "2", "publisher": "Springer Verlag", "pagerange": "265-292", "id_number": "CaltechAUTHORS:20150424-125450008", "issn": "0025-5831", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150424-125450008", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00208-007-0149-4", "primary_object": { "basename": "Igusa.pdf", "url": "https://authors.library.caltech.edu/records/kexey-etw10/files/Igusa.pdf" }, "pub_year": "2008", "author_list": "Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/adn33-1yw32", "eprint_id": 104416, "eprint_status": "archive", "datestamp": "2023-08-19 22:04:29", "lastmod": "2026-04-12 14:01:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "David" }, "orcid": "0000-0001-5924-3849" }, { "id": "Pushnitski-A", "name": { "family": "Pushnitski", "given": "Alexander" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Analytic Theory of Matrix Orthogonal Polynomials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 Israel Institute of Technology. \n\nPublished: 30 January 2008. \n\nIt is a pleasure to thank Alexander Aptekarev, Christian Berg, Antonio Dur\u00e1n, Jeff Geronimo, Fritz Gesztesy, Alberto Gr\u00fcnbaum, Paco Marcell\u00e1n, Ken McLaughlin, Hermann Schulz-Baldes, and Walter Van Assche for useful correspondence. D.D. was supported in part by NSF grants DMS-0500910 and DMS-0653720. B.S. was supported in part by NSF grants DMS-0140592 and DMS-0652919 and U.S.\u2013Israel Binational Science Foundation (BSF) Grant No. 2002068.\n\n

Published - 11.pdf

Submitted - 0711.2703.pdf

", "abstract": "We survey the analytic theory of matrix orthogonal polynomials.", "date": "2008-01-30", "date_type": "published", "publication": "Surveys in Approximation Theory", "volume": "4", "publisher": "Israel Institute of Technology", "pagerange": "1-85", "id_number": "CaltechAUTHORS:20200716-153633045", "issn": "1555-578X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200716-153633045", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0500910" }, { "agency": "NSF", "grant_number": "DMS-0653720" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "NSF", "grant_number": "DMS-0652919" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.48550/arXiv.0711.2703", "primary_object": { "basename": "0711.2703.pdf", "url": "https://authors.library.caltech.edu/records/adn33-1yw32/files/0711.2703.pdf" }, "related_objects": [ { "basename": "11.pdf", "url": "https://authors.library.caltech.edu/records/adn33-1yw32/files/11.pdf" } ], "pub_year": "2008", "author_list": "Damanik, David; Pushnitski, Alexander; et al." }, { "id": "https://authors.library.caltech.edu/records/88p4a-x6g86", "eprint_id": 38559, "eprint_status": "archive", "datestamp": "2023-08-22 10:54:15", "lastmod": "2026-03-09 20:31:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Miller-B-D", "name": { "family": "Miller", "given": "Benjamin D." } } ] }, "title": "Means on equivalence relations", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Equivalence Class; Equivalence Relation; Polish Space; Countable Group; Partial Transversal", "note": "\u00a9 2008 Springer. Received December 17, 2004 and in revised form April 10, 2006. Research partially supported by NSF Grants DMS-9987437 and DMS-0455285. Research partially supported by NSF VIGRE Grant DMS-0502315. We would like to thank Vadim Kaimanovich for asking the question that led to this paper, Greg Hjorth for many interesting conversations along the way, and the anonymous referee for suggesting the current proof of Lemma 5.4 as a replacement for our original incorrect argument, and also for making several other useful suggestions.", "abstract": "Suppose that X is a Polish space and E is a countable Borel equivalence relation on X. We show that if there is a Borel assignment of means to the equivalence classes of E, then E is smooth. We also show that if there is a Baire measurable assignment of means to the equivalence classes of E, then E is generically smooth.", "date": "2008-01", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "163", "number": "1", "publisher": "Springer Verlag", "pagerange": "241-262", "id_number": "CaltechAUTHORS:20130517-111643755", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-111643755", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9987437" }, { "agency": "NSF", "grant_number": "DMS-0455285" }, { "agency": "NSF", "grant_number": "DMS-0502315" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11856-008-0011-8", "pub_year": "2008", "author_list": "Kechris, Alexander S. and Miller, Benjamin D." }, { "id": "https://authors.library.caltech.edu/records/kyyvh-g6728", "eprint_id": 81814, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:28", "lastmod": "2026-03-09 23:04:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "G\u00fcnther-A", "name": { "family": "G\u00fcnther", "given": "Annika" } }, { "id": "Nebe-G", "name": { "family": "Nebe", "given": "Gabriele" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Clifford-Weil groups of quotient representations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 AulonaPress.\n\n

Published - quotcliff.pdf

", "abstract": "This note gives an explicit proof that the scalar subgroup of the Clifford-Weil group remains unchanged when passing to the quotient representation filling a gap in [3]. For other current and future errata to [3] see\nhttp://www.research.att.com/~njas/doc/cliff2.html/.", "date": "2008", "date_type": "published", "publication": "Albanian Journal of Mathematics", "volume": "2", "number": "3", "publisher": "AulonaPress", "pagerange": "159-169", "id_number": "CaltechAUTHORS:20170925-133038865", "issn": "1930-1235", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-133038865", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "quotcliff.pdf", "url": "https://authors.library.caltech.edu/records/kyyvh-g6728/files/quotcliff.pdf" }, "pub_year": "2008", "author_list": "G\u00fcnther, Annika; Nebe, Gabriele; et al." }, { "id": "https://authors.library.caltech.edu/records/2zkan-3mb89", "eprint_id": 13824, "eprint_status": "archive", "datestamp": "2023-08-22 10:47:50", "lastmod": "2026-03-09 20:33:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Tsankov-T", "name": { "family": "Tsankov", "given": "Todor" } } ] }, "title": "Amenable actions and almost invariant sets", "ispublished": "pub", "full_text_status": "public", "keywords": "generalized Bernoulli shifts; amenable actions; almost invariant sets; E-0-ergodicity", "note": "\u00a9 2007 American Mathematical Society.\nReceived by editor(s): October 2, 2006. \nReceived by editor(s) in revised form: February 8, 2007. \nPosted: November 3, 2007. \nAdditional Notes: This research was partially supported by NSF grant DMS-0455285. \nCommunicated by: Jane M. Hawkins.\n\n

Published - KECpams08.pdf

", "abstract": "In this paper, we study the connections between properties of the action of a countable group \u0393 on a countable set X and the ergodic theoretic properties of the corresponding generalized Bernoulli shift, i.e., the corresponding shift action of \u0393 on M^X, where M is a measure space. In particular, we show that the action of \u0393 on X is amenable iff the shift \u0393 \u2192 M^X has almost invariant sets.", "date": "2008", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "136", "number": "2", "publisher": "American Mathematical Society", "pagerange": "687-697", "id_number": "CaltechAUTHORS:KECpams08", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KECpams08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0455285" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9939-07-09116-2", "primary_object": { "basename": "KECpams08.pdf", "url": "https://authors.library.caltech.edu/records/2zkan-3mb89/files/KECpams08.pdf" }, "pub_year": "2008", "author_list": "Kechris, Alexander S. and Tsankov, Todor" }, { "id": "https://authors.library.caltech.edu/records/ae8zd-vfk56", "eprint_id": 16348, "eprint_status": "archive", "datestamp": "2023-08-19 21:43:40", "lastmod": "2026-03-09 21:28:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "On Non-Basic Rapoport-Zink Spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "p-divisible groups, Rapoport-Zink spaces, Shimura varieties, Langlands correspondences", "note": "\u00a9 Soci\u00e9t\u00e9 Math\u00e9matique de France. \n\nReceived March 16 2007. Accepted with revisions March 6 2008.\n\n

Submitted - RZ.pdf

", "abstract": "In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents.\nThis aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz's prediction that thir l-adic cohomology groups provide a realization of certain cases of local Laglands correspondences and in particular to the question of whether they contain any supercuspidal representations. \nOur results are compatible with this prediction and identify many cases when no supercuspidal representations appear. In those cases we prove that the l-adic cohomology of some associated lower-dimensional (and in most favorable cases basic) Rapoport-Zink spaces. Such an equality was originally conjectured by Harris in [11](Conjecture 5.2, p.420).", "date": "2008", "date_type": "published", "publication": "Annales Scientifiques de l'\u00c9cole Normale Sup\u00e9rieure", "volume": "41", "number": "5", "publisher": "Soci\u00e9t\u00e9 Math\u00e9matique de France", "pagerange": "671-716", "id_number": "CaltechAUTHORS:20091014-113154943", "issn": "0012-9593", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20091014-113154943", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.24033/asens.2079", "primary_object": { "basename": "RZ.pdf", "url": "https://authors.library.caltech.edu/records/ae8zd-vfk56/files/RZ.pdf" }, "pub_year": "2008", "author_list": "Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/v88ga-mt387", "eprint_id": 11760, "eprint_status": "archive", "datestamp": "2023-08-22 10:46:56", "lastmod": "2026-03-18 00:07:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Geszetsy-F", "name": { "family": "Geszetsy", "given": "Fritz" } }, { "id": "Pushnitski-A", "name": { "family": "Pushnitski", "given": "Alexander" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On the Koplienko Spectral Shift Function. I. Basics", "ispublished": "pub", "full_text_status": "public", "keywords": "Krein's spectral shift function, Koplienko's spectral shift function, self-adjoint operators, trace class and Hilbert\u2013Schmidt perturbations, convexity properties, boundary values of (modified) Fredholm determinants", "note": "Published version. Copyright ILTPE. 2008. Preprint copyright 2007, The Authors. \n\nSubmitted [to arXiv] 24 May 2007. Submitted to the Marchenko and Pastur birthday issue of Journal of Mathematical Physics, Analysis and Geometry. \n\nWe are indebted to E. Lieb, K.A. Makarov, V.V. Peller, and M.B. Ruskai for useful discussions. F. G. and A.P. wish to thank Gary Lorden and Tom Tombrello for the hospitality of Caltech where some of this work was done. F.G. gratefully acknowledges a research leave for the academic year 2005/06 granted by the Research Council and the Office of Research of the University of Missouri-Columbia. A.P. gratefully acknowledges financial support by the Leverhulme Trust. \n\nIt is a great pleasure to dedicate this paper to the birthdays of two giants of spectral theory: Vladimir A. Marchenko and Leonid A. Pastur. \n\n[F.G. was] [s]upported in part by NSF Grant DMS-0405526. \n\n[A.P. was] [s]upported in part by the Leverhulme Trust. \n\n[B.S. was] [s]upported in part by NSF Grant DMS-0140592 and U.S.\u2013Israel Binational Science Foundation (BSF) Grant No. 2002068.\n\n

Submitted - GESjmpag08preprint.pdf

", "abstract": "We study the Koplienko Spectral Shift Function (KoSSF), which is distinct from the one of Krein (KrSSF). KoSSF is defined for pairs A,B with (A \u2212 B) \u2208 I2, the Hilbert\u2013Schmidt operators, while KrSSF is defined for pairs A,B with (A\u2212B) \u2208 I1, the trace class operators. We review various aspects of the construction of both KoSSF and KrSSF. Among our new results are: (i) that any positive Riemann integrable function of compact support occurs as a KoSSF; (ii) that there exist A,B with (A\u2212B) \u2208 I2 so det2((A \u2212 z)(B \u2212 z)^\u22121) does not have nontangential boundary values; (iii) an alternative definition of KoSSF in the unitary case; and (iv) a new proof of the invariance of the a.c. spectrum under I1-perturbations that uses the KrSSF.", "date": "2008", "date_type": "published", "publication": "Journal of Mathematical Physics, Analysis and Geometry", "volume": "4", "number": "1", "publisher": "ILTPE", "pagerange": "63-107", "id_number": "CaltechAUTHORS:GESjmpag08", "issn": "1812-9471", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GESjmpag08", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Leverhulme Trust" }, { "agency": "NSF", "grant_number": "DMS-0405526" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.48550/arXiv.0705.3629", "primary_object": { "basename": "GESjmpag08preprint.pdf", "url": "https://authors.library.caltech.edu/records/v88ga-mt387/files/GESjmpag08preprint.pdf" }, "pub_year": "2008", "author_list": "Geszetsy, Fritz; Pushnitski, Alexander; et al." }, { "id": "https://authors.library.caltech.edu/records/gwp8z-3y709", "eprint_id": 66685, "eprint_status": "archive", "datestamp": "2023-08-19 21:52:50", "lastmod": "2026-03-09 02:30:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gaberdiel-M-R", "name": { "family": "Gaberdiel", "given": "Matthias R." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Keller-C-A", "name": { "family": "Keller", "given": "Christoph A." }, "orcid": "0000-0003-2592-2012" }, { "id": "Moore-G-W", "name": { "family": "Moore", "given": "Gregory W." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Extremal N = (2, 2) 2D Conformal Field Theories and Constraints of Modularity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2008 International Press. \n\nReceived June 17, 2008. \n\nWe would like to thank C. Vafa for collaboration at an earlier stage of this project. GM would also like to thank M. Douglas for a past collaboration on closely related issues. We would like to thank F.Denef, T. Gannon, S. Kachru, J. Maldacena, J. Manschot, P. Sarnak, and D. Zagier for useful discussions. \n\nGM and HO thank the organizers of the 37th Paris Summer Institute on Black Holes, Black Rings and Modular Forms, which stimulated progress in this work. SG acknowledges the hospitality of Institut f\u00fcr Theoretische Physik, ETH Zurich, Institute for Advanced Study, Harvard University, Banff Center, the Aspen Center for Physics, the Simons Workshops in 2005, 2006, and 2007, where part of this work was carried out. HO also thanks the Aspen Center for Physics, the Kavli Institute for Theoretical Physics in Santa Barbara, Harvard University, the Simons Workshops in 2005 and 2006 in Stony Brook, the Banff International Research Station, the University of Tokyo, the Galileo Galilei Institute in Florence, the CERN theory institute, and the Ettore Majorana Centre for scientific Culture in Erice, where part of this work was carried out. \n\nThe work of MRG and CAK is supported by the Swiss National Science Foundation. GM is supported by DOE grant DE-FG02-96ER40949. The work of SG and HO is supported in part by DOE grant DE-FG03-92-ER40701. The work of SG is also supported in part by NSF Grant DMS-0635607 and by the Alfred P. Sloan Foundation. The work of HO is also supported in part by NSF grant OISE-0403366, by a Grant-in-Aid for Scientific Research (C) 20540256 from the Japan Society for the Promotion of Science, by the 21st Century COE Visiting Professorship at the University of Tokyo, by the World Premier International Research Center Initiative of MEXT of Japan, and by the Kavli Foundation. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.\n\n

Published - CNTP-2008-0002-0004-a003.pdf

Submitted - 0805.4216.pdf

", "abstract": "We explore the constraints on the spectrum of primary fields implied by modularity of the elliptic genus of N = (2, 2) 2D CFT's. We show that such constraints have nontrivial implications for the existence of \"extremal\" N = (2, 2) conformal field theories. Applications to AdS_3 supergravity and flux compactifications are addressed.", "date": "2008", "date_type": "published", "publication": "Communications in Number Theory and Physics", "volume": "2", "number": "4", "publisher": "International Press", "pagerange": "743-801", "id_number": "CaltechAUTHORS:20160505-104651886", "issn": "1931-4523", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-104651886", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swiss National Science Foundation (SNSF)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40949" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "DMS-0635607" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "OISE-0403366" }, { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "20540256" }, { "agency": "University of Tokyo" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" }, { "agency": "Kavli Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "68-2685", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CNTP.2008.v2.n4.a3", "primary_object": { "basename": "0805.4216.pdf", "url": "https://authors.library.caltech.edu/records/gwp8z-3y709/files/0805.4216.pdf" }, "related_objects": [ { "basename": "CNTP-2008-0002-0004-a003.pdf", "url": "https://authors.library.caltech.edu/records/gwp8z-3y709/files/CNTP-2008-0002-0004-a003.pdf" } ], "pub_year": "2008", "author_list": "Gaberdiel, Matthias R.; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/k0j6b-asr40", "eprint_id": 77867, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:19", "lastmod": "2026-03-08 19:57:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ekholm-T", "name": { "family": "Ekholm", "given": "Tomas" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert" }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Lieb\u2013Thirring inequalities on the half-line with critical exponent", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator, Lieb\u2013Thirring inequalities, Hardy inequality", "note": "\u00a9 2008 European Mathematical Society. \n\nReceived December 6, 2006 and in revised form January 22, 2007. \n\nThis work was partially supported by FCT Portugal, post-doc grant SFRH/BPD/23820/2005, (T.E.), by the Swedish Foundation for International Cooperation in Research\nand Higher Education (STINT) (R.F.), as well as through the ESF Scientific Programme in Spectral Theory and Partial Differential Equations (SPECT). The authors are grateful to the American Institute of Mathematics for the invitation to the workshop Low Eigenvalues of Laplace and Schr\u00f6dinger Operators where this problem was brought up. R.F. would like to thank E.H. Lieb and R. Seiringer for the hospitality at Princeton University and for helpful discussions. Remarks by A. Hansson and A. Laptev are gratefully acknowledged.\n\n

Submitted - 0611247.pdf

", "abstract": "We consider the operator -d^2/dr^2 - V in L_2(R_+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound tr (-d^2)/dr^2 -V)^y_- \u2264 Cy,\u0251\u0283_(R+) (v(r)-1/_(4r)^2)^(y+(1+\u0251)/2_(r^\u0251 dr) for any \u0251 \u0404 [0,1] and y \u2265 (1 - \u0251)/2. This includes a Lieb\u2013Thirring inequality in the critical endpoint case.", "date": "2008", "date_type": "published", "publication": "European Mathematical Society", "volume": "10", "number": "3", "publisher": "EMS Publishing House", "pagerange": "739-755", "id_number": "CaltechAUTHORS:20170531-151816388", "issn": "1435-9855", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170531-151816388", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia (FCT)", "grant_number": "SFRH/BPD/23820/2005" }, { "agency": "Swedish Foundation for International Cooperation in Research and Higher Education (STINT)" }, { "agency": "European Science Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/JEMS/128", "primary_object": { "basename": "0611247.pdf", "url": "https://authors.library.caltech.edu/records/k0j6b-asr40/files/0611247.pdf" }, "pub_year": "2008", "author_list": "Ekholm, Tomas and Frank, Rupert" }, { "id": "https://authors.library.caltech.edu/records/mdw3w-ahw89", "eprint_id": 82256, "eprint_status": "archive", "datestamp": "2023-08-19 21:36:35", "lastmod": "2026-04-14 04:06:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Vazirani-Monica-J", "name": { "family": "Vazirani", "given": "Monica" } } ] }, "title": "Vanishing Integrals of Macdonald and Koornwinder polynomials", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2007 Birkhauser Boston. \n\nReceived June 29, 2006. Accepted January 29, 2007. First Online: 28 November 2007. \n\nSupported in part by NSF grant DMS-0401387. \n\nSupported in part by NSF grant DMS-0301320, and the UC Davis Faculty Development Program.", "abstract": "When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form. A number of q,t-analogues of this fact were conjectured in [10]; the present paper proves most of those conjectures, as well as some new identities suggested by the proof technique. The proof involves showing that a nonsymmetric version of the relevant integral is annihilated by a suitable ideal of the affine Hecke algebra, and that any such annihilated functional satisfies the desired vanishing property. This does not, however, give rise to vanishing identities for the standard nonsymmetric Macdonald and Koornwinder polynomials; we discuss the required modification to these polynomials to support such results.", "date": "2007-12", "date_type": "published", "publication": "Transformation Groups", "volume": "12", "number": "4", "publisher": "Springer", "pagerange": "725-759", "id_number": "CaltechAUTHORS:20171010-113734662", "issn": "1083-4362", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171010-113734662", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" }, { "agency": "NSF", "grant_number": "DMS-0301320" }, { "agency": "University of California, Davis" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/S00031-007-0058-3", "pub_year": "2007", "author_list": "Rains, Eric M. and Vazirani, Monica" }, { "id": "https://authors.library.caltech.edu/records/409ge-22x52", "eprint_id": 56827, "eprint_status": "archive", "datestamp": "2023-08-19 21:34:52", "lastmod": "2026-04-13 21:38:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Knot Floer homology detects fibred knots", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Springer. \n\nPublished online: 20 September 2007. \n\nDedicated to Professor Boju Jiang on the occasion of his 70th birthday. \n\nThis paper has been submitted to Princeton University as the author's PhD thesis. We wish to thank David Gabai and Zolt\u00e1n Szab\u00f3 for their guidance. We would like to thank Paolo Ghiggini for many fruitful discussions during the course of this work. This paper benefits a lot from his work [5]. \n\nA version of Theorem 6.2 was also proved by Ian Agol via a different approach. We wish to thank him for some interesting discussions. \n\nWe are grateful to Matthew Hedden, Andr\u00e1s Juh\u00e1sz, Tao Li, Peter Ozsv\u00e1th, Jiajun Wang and Chenyang Xu for some helpful conversations and their interests in this work. We are particularly grateful to an anonymous referee for enormous suggestions and corrections. The author was partially supported by a Graduate School Centennial Fellowship at Princeton University. Parts of the work were carried out when the author visited UQAM and Peking University; he wishes to thank Steve Boyer, Olivier Collin and Shicheng Wang for their hospitality. The author extends his gratitude to the American Institute of Mathematics and the Clay Mathematics Institute for their subsequent support.\n\n

Accepted Version - 0607156.pdf

Erratum - 0808.0940.pdf

", "abstract": "Ozsv\u00e1th and Szab\u00f3 conjectured that knot Floer homology detects fibred knots in S^3. We will prove this conjecture for null-homologous knots in arbitrary closed 3-manifolds. Namely, if K is a knot in a closed 3-manifold Y, Y-K is irreducible, and \\hat{HFK}(Y,K) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsv\u00e1th\u2013Szab\u00f3, Ghiggini and the author. A corollary is that if a knot in S^3 admits a lens space surgery, then the knot is fibred.", "date": "2007-12", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "170", "number": "3", "publisher": "Springer", "pagerange": "577-608", "id_number": "CaltechAUTHORS:20150421-115906058", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115906058", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Princeton University Centennial Fellowship" }, { "agency": "AIM Five-Year Fellowship" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00222-007-0075-9", "primary_object": { "basename": "0607156.pdf", "url": "https://authors.library.caltech.edu/records/409ge-22x52/files/0607156.pdf" }, "related_objects": [ { "basename": "0808.0940.pdf", "url": "https://authors.library.caltech.edu/records/409ge-22x52/files/0808.0940.pdf" } ], "pub_year": "2007", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/80s5z-kmc69", "eprint_id": 77341, "eprint_status": "archive", "datestamp": "2023-08-19 21:36:03", "lastmod": "2026-04-14 03:47:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Hainzl-C", "name": { "family": "Hainzl", "given": "Christian" } }, { "id": "Naboko-S", "name": { "family": "Naboko", "given": "Serguei" } }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "The critical temperature for the BCS equation at weak coupling", "ispublished": "pub", "full_text_status": "public", "keywords": "Gap equation, critical temperature, Birman-Schwinger kernel, degenerate symbols", "note": "\u00a9 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived October 24, 2007. \n\nThe last author acknowledges partial support by U.S. NSF grant PHY-0353181 and by an A.P. Sloan Fellowship.\n\n

Submitted - 0704.3564.pdf

", "abstract": "For the BCS equation with local two-body interaction \u03bbV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as \u03b3\u00bb0. We derive necessary and sufficient conditions on V(x) for the existence of a nontrivial solution for all values of \u03bb>0.", "date": "2007-12", "date_type": "published", "publication": "Journal of Geometric Analysis", "volume": "17", "number": "4", "publisher": "Springer-Verlag", "pagerange": "559-567", "id_number": "CaltechAUTHORS:20170510-105303048", "issn": "1050-6926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-105303048", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0353181" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/BF02937429", "primary_object": { "basename": "0704.3564.pdf", "url": "https://authors.library.caltech.edu/records/80s5z-kmc69/files/0704.3564.pdf" }, "pub_year": "2007", "author_list": "Frank, Rupert L.; Hainzl, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/6b08h-ccy93", "eprint_id": 81984, "eprint_status": "archive", "datestamp": "2023-08-22 10:38:23", "lastmod": "2026-04-13 23:22:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Symmetrized Models of Last Passage Percolation and Non-Intersecting Lattice Paths", "ispublished": "pub", "full_text_status": "public", "keywords": "Hammersely process; Non-intersecting paths; Random matrices", "note": "\u00a9 2007 Springer Science+Business Media, LLC. \n\nReceived: 29 April 2007; Accepted: 21 August 2007; First Online: 21 September 2007. \n\nThe work of PJF has been supported by the Australian Research Council. EMR was supported in part by NSF Grant No. DMS-0403187.\n\n

Submitted - 0705.3925.pdf

", "abstract": "It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups U(l), Sp(2l) and O(l). We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.", "date": "2007-12", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "129", "number": "5-6", "publisher": "Springer", "pagerange": "833-855", "id_number": "CaltechAUTHORS:20171003-095341751", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-095341751", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" }, { "agency": "NSF", "grant_number": "DMS-0403187" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10955-007-9413-y", "primary_object": { "basename": "0705.3925.pdf", "url": "https://authors.library.caltech.edu/records/6b08h-ccy93/files/0705.3925.pdf" }, "pub_year": "2007", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/av1yj-y7j76", "eprint_id": 77336, "eprint_status": "archive", "datestamp": "2023-08-22 10:38:15", "lastmod": "2026-04-13 17:27:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Number of Bound States of Schr\u00f6edinger Operators with Matrix-Valued Potentials", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator; Lieb\u2013Thirring inequality; Cwikel\u2013Lieb\u2013Rozenblum inequality", "note": "\u00a9 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\n\nReceived: 09 October 2007; Revised: 15 November 2007; Accepted: 16 November 2007. \n\nDedicated to Jean-Claude Cortet, in appreciation of his contribution to Letters in Mathematical Physics. \n\nThis work was supported by DAAD grant D/06/49117 (R.F.), by U.S. National Science Foundation grants PHY 06 52854 (E.L.) and PHY 06 52356 (R.S.), and by an A.P. Sloan Fellowship (R.S.).\n\n

Published - Frank2007_Article_NumberOfBoundStatesOfSchr\u00f6ding.pdf

Submitted - 0710.1877.pdf

", "abstract": "We give a Cwikel\u2013Lieb\u2013Rozenblum type bound on the number of bound states of Schr\u00f6dinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly improves the constant in this inequality obtained earlier by Hundertmark.", "date": "2007-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "82", "number": "2-3", "publisher": "Springer", "pagerange": "107-116", "id_number": "CaltechAUTHORS:20170510-095237526", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-095237526", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutscher Akademischer Austauschdienst (DAAD)", "grant_number": "D/06/49117" }, { "agency": "NSF", "grant_number": "PHY-0652854" }, { "agency": "NSF", "grant_number": "PHY-0652356" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-007-0211-x", "primary_object": { "basename": "0710.1877.pdf", "url": "https://authors.library.caltech.edu/records/av1yj-y7j76/files/0710.1877.pdf" }, "related_objects": [ { "basename": "Frank2007_Article_NumberOfBoundStatesOfSchr\u00f6ding.pdf", "url": "https://authors.library.caltech.edu/records/av1yj-y7j76/files/Frank2007_Article_NumberOfBoundStatesOfSchr\u00f6ding.pdf" } ], "pub_year": "2007", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/3ykd4-8df69", "eprint_id": 77364, "eprint_status": "archive", "datestamp": "2023-08-19 21:36:08", "lastmod": "2026-04-13 18:24:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } }, { "id": "Molchanov-S", "name": { "family": "Molchanov", "given": "Stanislav" } } ] }, "title": "Eigenvalue estimates for magnetic Schr\u00f6dinger operators in domains", "ispublished": "pub", "full_text_status": "public", "keywords": "Eigenvalue bounds, semi-classical estimates, Laplace operator, magnetic Schr\u00f6dinger operator", "note": "\u00a9 2008 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived by the editors May 29, 2007. Published electronically: July 29, 2008. \n\nThe authors would like to thank Mark Ashbaugh for several helpful remarks. Partial financial support through the SPECT ESF programme for the first and second authors and the Gustafsson Foundation for the third author is gratefully acknowledged. The first two authors appreciate the hospitality of the Isaac Newton Institute Cambridge, where this work was completed.\n\n

Published - S0002-9939-08-09523-3.pdf

Submitted - 0705.3969.pdf

", "abstract": "Inequalities are derived for sums and quotients of eigenvalues of magnetic Schr\u00f6dinger operators with non-negative electric potentials in domains. The bounds reflect the correct order of growth in the semi-classical limit.", "date": "2007-12", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "136", "number": "12", "publisher": "American Mathematical Society", "pagerange": "4245-4255", "id_number": "CaltechAUTHORS:20170511-070749185", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170511-070749185", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Science Foundation" }, { "agency": "Gustafsson Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9939-08-09523-3", "primary_object": { "basename": "0705.3969.pdf", "url": "https://authors.library.caltech.edu/records/3ykd4-8df69/files/0705.3969.pdf" }, "related_objects": [ { "basename": "S0002-9939-08-09523-3.pdf", "url": "https://authors.library.caltech.edu/records/3ykd4-8df69/files/S0002-9939-08-09523-3.pdf" } ], "pub_year": "2007", "author_list": "Frank, Rupert L.; Laptev, Ari; et al." }, { "id": "https://authors.library.caltech.edu/records/fdxqc-dsf13", "eprint_id": 17460, "eprint_status": "archive", "datestamp": "2023-08-22 10:23:23", "lastmod": "2026-04-13 17:48:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "CMV matrices: Five years after", "ispublished": "pub", "full_text_status": "restricted", "keywords": "CMV matrix; Spectra", "note": "\u00a9 2006 Elsevier.\n\nReceived 20 February 2006; available online 28 November 2006. \n\nSupported in part by NSF grant DMS-0140592.\nSubmitted to the Proceedings of the W. D. Evans' 65th Birthday Conference.", "abstract": "CMV matrices are the unitary analog of Jacobi matrices; we review their general theory.", "date": "2007-11-01", "date_type": "published", "publication": "Journal of Computational and Applied Mathematics", "volume": "208", "number": "1", "publisher": "Elsevier", "pagerange": "120-154", "id_number": "CaltechAUTHORS:20100211-153106376", "issn": "0377-0427", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100211-153106376", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.cam.2006.10.033", "pub_year": "2007", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/73pyd-qjx23", "eprint_id": 9246, "eprint_status": "archive", "datestamp": "2023-08-22 10:18:37", "lastmod": "2026-04-13 23:37:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Tomasiello-A", "name": { "family": "Tomasiello", "given": "Alessandro" }, "orcid": "0000-0002-5772-5729" } ] }, "title": "The general (2, 2) gauged sigma model with three-form flux", "ispublished": "pub", "full_text_status": "public", "keywords": "Superstring Vacua; Extended Supersymmetry; Differential and Algebraic Geometry; Flux compactifications", "note": "\u00a9 2007 SISSA. \n\nReceived 14 September 2007, accepted for publication 7 November 2007. Published 19 November 2007. \n\nWe would like to thank Marco Gualtieri for useful correspondence. A.K. is supported in part by the DOE under contract DOE-FG03-92-ER40701. A.T. is supported by the DOE under contract DEAC03-76SF00515 and by the NSF under contract 9870115. \n\nE-print number: hep-th/0610210\n\n

Published - KAPjhep07.pdf

", "abstract": "We find the conditions under which a Riemannian manifold equipped with a closed three-form and a vector field define an on-shell Script N = (2, 2) supersymmetric gauged sigma model. The conditions are that the manifold admits a twisted generalized K\u00e4hler structure, that the vector field preserves this structure, and that a so-called generalized moment map exists for it. By a theorem in generalized complex geometry, these conditions imply that the quotient is again a twisted generalized K\u00e4hler manifold; this is in perfect agreement with expectations from the renormalization group flow. This method can produce new Script N = (2, 2) models with NS flux, extending the usual K\u00e4hler quotient construction based on K\u00e4hler gauged sigma models.", "date": "2007-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2007", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 053", "id_number": "CaltechAUTHORS:KAPjhep07", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00515" }, { "agency": "NSF", "grant_number": "9870115" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2007/11/053", "primary_object": { "basename": "KAPjhep07.pdf", "url": "https://authors.library.caltech.edu/records/73pyd-qjx23/files/KAPjhep07.pdf" }, "pub_year": "2007", "author_list": "Kapustin, Anton and Tomasiello, Alessandro" }, { "id": "https://authors.library.caltech.edu/records/b37ga-r5358", "eprint_id": 77817, "eprint_status": "archive", "datestamp": "2023-08-19 21:07:14", "lastmod": "2026-04-13 19:14:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Hardy-Lieb-Thirring inequalities for fractional Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Hardy inequality, relativistic Schr\u00a8odinger operator, Lieb-Thirring inequalities,\nSobolev inequalities, stability of matter, diamagnetic inequality.", "note": "\u00a9 2007 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived by the editors October 18, 2006. \n\nWe thank Heinz Siedentop for suggesting that we study inequalities of this type, and we thank him, Ari Laptev and Jan Philip Solovej for helpful discussions. We also thank Renming Song for valuable comments on a previous version of this manuscript. This work was partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (R.F.), by U.S. National Science Foundation grants PHY 01 39984 (E.L.) and PHY 03 53181 (R.S.), and by an A.P. Sloan Fellowship (R.S.).\n\n

Published - S0894-0347-07-00582-6.pdf

Submitted - 0610593.pdf

", "abstract": "We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schr\u00f6dinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C \u2502x\u2502^(-2) is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and, in particular, for relativistic Schr\u00f6dinger operators. We also allow for the inclusion of magnetic vector potentials. As an application, we extend, for the first time, the proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Z\u0251 = 2/\u03c0, for \u0251 less than some critical value.", "date": "2007-10-10", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "21", "number": "4", "publisher": "American Mathematical Society", "pagerange": "925-950", "id_number": "CaltechAUTHORS:20170526-134159102", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-134159102", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Foundation for International Cooperation in Research and Higher Education (STINT)" }, { "agency": "NSF", "grant_number": "PHY-0139984" }, { "agency": "NSF", "grant_number": "PHY-0353181" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-07-00582-6", "primary_object": { "basename": "0610593.pdf", "url": "https://authors.library.caltech.edu/records/b37ga-r5358/files/0610593.pdf" }, "related_objects": [ { "basename": "S0894-0347-07-00582-6.pdf", "url": "https://authors.library.caltech.edu/records/b37ga-r5358/files/S0894-0347-07-00582-6.pdf" } ], "pub_year": "2007", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/zrw1x-b5m79", "eprint_id": 13550, "eprint_status": "archive", "datestamp": "2023-08-19 21:04:29", "lastmod": "2026-04-14 04:15:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Consani-C", "name": { "family": "Consani", "given": "Caterina" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Noncommutative geometry and motives: the thermodynamics of endomotives", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Elsevier Inc.\n\nReceived 22 December 2005; accepted 22 March 2007.\nAvailable online 30 March 2007.\n\nThis research was partially supported by the third author's Sofya Kovalevskaya Award and\nby the second author's NSERC grant 7024520. Part of this work was done during a visit of the\nfirst and third authors to the Kavli Institute in Santa Barbara, supported in part by the National\nScience Foundation under Grant No. PHY99-07949, and during a visit of the first two authors to\nthe Max Planck Institute.\n\n

Submitted - 0512138.pdf

", "abstract": "We combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spectral realization of zeros of L-functions. The analogue in characteristic zero of the action of the Frobenius on \u2113-adic cohomology is the action of the scaling group on the cyclic homology of the cokernel (in a suitable category of motives) of a restriction map of noncommutative spaces. The latter is obtained through the thermodynamics of the quantum statistical system associated to an endomotive (a noncommutative generalization of Artin motives). Semigroups of endomorphisms of algebraic varieties give rise canonically to such endomotives, with an action of the absolute Galois group. The semigroup of endomorphisms of the multiplicative group yields the Bost\u2013Connes system, from which one obtains, through the above procedure, the desired cohomological interpretation of the zeros of the Riemann zeta function. In the last section we also give a Lefschetz formula for the archimedean local L-factors of arithmetic varieties.", "date": "2007-10-01", "date_type": "published", "publication": "Advances in Mathematics", "volume": "214", "number": "2", "publisher": "Elsevier", "pagerange": "761-831", "id_number": "CaltechAUTHORS:CONam07", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CONam07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Sofya Kovalevskaya Award" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "7024520" }, { "agency": "NSF", "grant_number": "PHY99-07949" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2007.03.006", "primary_object": { "basename": "0512138.pdf", "url": "https://authors.library.caltech.edu/records/zrw1x-b5m79/files/0512138.pdf" }, "pub_year": "2007", "author_list": "Connes, Alain; Consani, Caterina; et al." }, { "id": "https://authors.library.caltech.edu/records/ttnz8-1f951", "eprint_id": 77875, "eprint_status": "archive", "datestamp": "2023-08-19 21:03:29", "lastmod": "2026-04-13 18:02:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Stability of Relativistic Matter with Magnetic Fields for Nuclear Charges up to the Critical Value", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 R.L. Frank, E.H. Lieb, R. Seiringer. \n\nReceived: 20 October 2006. Accepted: 20 March 2007. Published online: 31 July 2007. \n\nWe thank Heinz Siedentop for helpful remarks. This work was partially supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (R.F.), by U.S. National Science Foundation grants PHY 01 39984 (E.L.) and PHY 01 39984 (R.S.), and by an A.P. Sloan Fellowship (R.S.).\n\n

Published - stability275.pdf

Submitted - 0610062.pdf

", "abstract": "We give a proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Z\u03b1 = 2/\u03c0.", "date": "2007-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "275", "number": "2", "publisher": "Springer", "pagerange": "479-489", "id_number": "CaltechAUTHORS:20170601-073744902", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170601-073744902", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Foundation for International Cooperation in Research and Higher Education (STINT)" }, { "agency": "NSF", "grant_number": "PHY-0139984" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-007-0307-2", "primary_object": { "basename": "0610062.pdf", "url": "https://authors.library.caltech.edu/records/ttnz8-1f951/files/0610062.pdf" }, "related_objects": [ { "basename": "stability275.pdf", "url": "https://authors.library.caltech.edu/records/ttnz8-1f951/files/stability275.pdf" } ], "pub_year": "2007", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/tm7fy-zvs51", "eprint_id": 81988, "eprint_status": "archive", "datestamp": "2023-08-19 21:03:42", "lastmod": "2026-04-13 17:32:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "van-de-Bult-F-J", "name": { "family": "van de Bult", "given": "F. J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Stokman-J-V", "name": { "family": "Stokman", "given": "J. V." } } ] }, "title": "Properties of Generalized Univariate Hypergeometric Functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Springer-Verlag. \n\nReceived: 4 August 2006; Accepted: 4 January 2007; Published online: 24 July 2007. \n\nRains was supported in part by NSF Grant No. DMS-0401387. Stokman was supported by the Netherlands Organization for Scientific Research (NWO) in the VIDI-project \"Symmetry and modularity in exactly solvable models\".\n\n

Submitted - 0607250.pdf

", "abstract": "Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E_7 (elliptic, hyperbolic) and of type E_6 (trigonometric) using the appropriate versions of the Nassrallah-Rahman beta integral, and we derive contiguous relations using fundamental addition formulas for theta and sine functions. The top level degenerations of the hyperbolic and trigonometric hypergeometric functions are identified with Ruijsenaars' relativistic hypergeometric function and the Askey-Wilson function, respectively. We show that the degeneration process yields various new and known identities for hyperbolic and trigonometric special functions. We also describe an intimate connection between the hyperbolic and trigonometric theory, which yields an expression of the hyperbolic hypergeometric function as an explicit bilinear sum in trigonometric hypergeometric functions.", "date": "2007-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "275", "number": "1", "publisher": "Springer", "pagerange": "37-95", "id_number": "CaltechAUTHORS:20171003-101141109", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-101141109", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0401387" }, { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-007-0289-0", "primary_object": { "basename": "0607250.pdf", "url": "https://authors.library.caltech.edu/records/tm7fy-zvs51/files/0607250.pdf" }, "pub_year": "2007", "author_list": "van de Bult, F. J.; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/esz6x-f6v37", "eprint_id": 19519, "eprint_status": "archive", "datestamp": "2023-08-19 20:49:22", "lastmod": "2026-04-14 02:17:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aganagic-M", "name": { "family": "Aganagic", "given": "Mina" } }, { "id": "Okuda-Takuya", "name": { "family": "Okuda", "given": "Takuya" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Quantum Entanglement of Baby Universes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Elsevier. \n\nReceived 21 February 2007; accepted 2 April 2007. Available online 18 April 2007. \n\nThis article is registered under preprint number hep-th/0612067.\n\n

Submitted - AGAnpb07preprint.pdf

", "abstract": "We study quantum entanglements of baby universes which appear in non-perturbative\ncorrections to the OSV formula for the entropy of extremal black holes in Type IIA string\ntheory compactified on the local Calabi-Yau manifold defined as a rank 2 vector bundle\nover an arbitrary genus G Riemann surface. This generalizes the result for G = 1 in\nhep-th/0504221. Non-perturbative terms can be organized into a sum over contributions\nfrom baby universes, and the total wave-function is their coherent superposition in the third\nquantized Hilbert space. We find that half of the universes preserve one set of supercharges\nwhile the other half preserve a different set, making the total universe stable but non-BPS.\nThe parent universe generates baby universes by brane/anti-brane pair creation, and baby\nuniverses are correlated by conservation of non-normalizable D-brane charges under the\nprocess. There are no other source of entanglement of baby universes, and all possible\nstates are superposed with the equal weight.", "date": "2007-08-27", "date_type": "published", "publication": "Nuclear Physics B", "volume": "778", "number": "1-2", "publisher": "Elsevier", "pagerange": "36-68", "id_number": "CaltechAUTHORS:20100819-114040490", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100819-114040490", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "68-2622", "name": "calt" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2007.04.006", "primary_object": { "basename": "AGAnpb07preprint.pdf", "url": "https://authors.library.caltech.edu/records/esz6x-f6v37/files/AGAnpb07preprint.pdf" }, "pub_year": "2007", "author_list": "Aganagic, Mina; Okuda, Takuya; et al." }, { "id": "https://authors.library.caltech.edu/records/q3za1-kbn12", "eprint_id": 20118, "eprint_status": "archive", "datestamp": "2023-08-19 20:46:35", "lastmod": "2026-04-13 15:07:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kawano-Teruhiko", "name": { "family": "Kawano", "given": "Teruhiko" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Ookouchi-Yutaka", "name": { "family": "Ookouchi", "given": "Yutaka" } } ] }, "title": "Gauge mediation in string theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Elsevier.\n\nReceived 14 June 2007; accepted 26 June 2007. Editor: M. Cveti\u010d. Available online 29 June 2007.\nWe thank D. Berenstein, M. Dine, R. Kitano, J. Marsano, C. S. Park, N. Seiberg,\nM. Shigemori, and T. Watari for discussions. H.O. thanks the hospitality of the high\nenergy theory group at the University of Tokyo at Hongo.\nH.O. and Y.O. are supported in part by the DOE grant DE-FG03-92-ER40701. The\nresearch of H.O. is also supported in part by the NSF grant OISE-0403366 and by the 21st\nCentury COE Program at the University of Tokyo. Y.O. is also supported in part by the\nJSPS Fellowship for Research Abroad. The research of T.K. was supported in part by the\nGrants-in-Aid (#16740133) and (#16081206) from the Ministry of Education, Culture,\nSports, Science, and Technology of Japan.\n\n

Submitted - KAWplb07preprint.pdf

", "abstract": "We show that a large class of phenomenologically viable models for gauge mediation of supersymmetry breaking based on meta-stable vacua can be realized in local Calabi\u2013Yau compactifications of string theory.", "date": "2007-08-16", "date_type": "published", "publication": "Physics Letters B", "volume": "652", "number": "1", "publisher": "Elsevier", "pagerange": "40-42", "id_number": "CaltechAUTHORS:20100924-082214141", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100924-082214141", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "OISE-0403366" }, { "agency": "University of Tokyo" }, { "agency": "Japan Society for the Promotion of Science (JSPS)" }, { "agency": "Ministry of Education, Culture, Sports, Science, and Technology (MEXT)", "grant_number": "16740133" }, { "agency": "Ministry of Education, Culture, Sports, Science, and Technology (MEXT)", "grant_number": "16081206" } ] }, "other_numbering_system": { "items": [ { "id": "68-2642", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.physletb.2007.06.056", "primary_object": { "basename": "KAWplb07preprint.pdf", "url": "https://authors.library.caltech.edu/records/q3za1-kbn12/files/KAWplb07preprint.pdf" }, "pub_year": "2007", "author_list": "Kawano, Teruhiko; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/3bkfa-pm216", "eprint_id": 8641, "eprint_status": "archive", "datestamp": "2023-08-22 09:45:21", "lastmod": "2026-04-16 01:39:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feldman-D-E", "name": { "family": "Feldman", "given": "D. E." } }, { "id": "Gefen-Y", "name": { "family": "Gefen", "given": "Yuval" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Law-K-T", "name": { "family": "Law", "given": "K. T." } }, { "id": "Stern-A", "name": { "family": "Stern", "given": "Ady" }, "orcid": "0000-0002-9493-268X" } ] }, "title": "Shot noise in an anyonic Mach-Zehnder interferometer", "ispublished": "pub", "full_text_status": "public", "keywords": "electron spin polarisation; Mach-Zehnder interferometers; quantum Hall effect; quasiparticles; shot noise", "note": "\u00a92007 The American Physical Society \n\n(Received 6 July 2007; published 21 August 2007) \n\nWe acknowledge the support by ARO under Grants Nos. W911NF-04-1-0236 (A.K.) and W911NF-05-1-0294) (A.K.), by NSF under Grants Nos. PHY99-07949 (D.E.F.), PHY-0456720 (A.K.), and DMR-0544116 (D.E.F. and K.T.L.), by the U.S.-Israel BSF (Y.G. and A.S.), the Minerva Foundation (A.S.), and the ISF of the Israel Academy of Sciences (Y.G.). D.E.F. acknowledges the hospitality of Microsoft Station Q and KITP in Santa Barbara.", "abstract": "We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise on the magnetic flux through the interferometer allows for a simple way to distinguish Abelian from non-Abelian quasiparticle statistics. In the Abelian case, the Fano factor (in units of the electron charge) is always lower than unity. In the non-Abelian case, the maximal Fano factor as a function of the magnetic flux exceeds 1.", "date": "2007-08-15", "date_type": "published", "publication": "Physical Review B", "volume": "76", "number": "8", "publisher": "Physical Review B", "pagerange": "Art. No. 085333", "id_number": "CaltechAUTHORS:FELprb07", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FELprb07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.76.085333", "primary_object": { "basename": "FELprb07.pdf", "url": "https://authors.library.caltech.edu/records/3bkfa-pm216/files/FELprb07.pdf" }, "pub_year": "2007", "author_list": "Feldman, D. E.; Gefen, Yuval; et al." }, { "id": "https://authors.library.caltech.edu/records/epnsv-kdn74", "eprint_id": 56805, "eprint_status": "archive", "datestamp": "2023-08-19 20:41:58", "lastmod": "2026-04-14 03:21:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Boileau-M", "name": { "family": "Boileau", "given": "Michel" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wang-Shicheng", "name": { "family": "Wang", "given": "Shicheng" } } ] }, "title": "Pseudo-Anosov extensions and degree one maps between hyperbolic surface bundles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Springer-Verlag.\n\nReceived: 9 August 2006; accepted: 15 November 2006; published online: 22 February 2007.\n\nWe are grateful to Dr. Hao Zheng for drawing the figures in this paper. Boileau and Wang wish to thank Prof. D. Gabai and Prof. G. Mess for helpful conversations. Y. Ni joined this project when he was a graduate student at Peking University. The paper was finished when Ni visited Peking University.\n\n

Submitted - 0509592v1.pdf

", "abstract": "Let F\u2032,F be any two closed orientable surfaces of genus g\u2032 > g\u2265 1, and f:F\u2192 F be any pseudo-Anosov map. Then we can \"extend\" f to be a pseudo- Anosov map f\u2032:F\u2032\u2192 F\u2032 so that there is a fiber preserving degree one map M(F\u2032,f\u2032)\u2192 M(F,f) between the hyperbolic surface bundles. Moreover the extension f\u2032 can be chosen so that the surface bundles M(F\u2032,f\u2032) and M(F,f) have the same first Betti numbers.", "date": "2007-08", "date_type": "published", "publication": "Mathematische Zeitschrift", "volume": "256", "number": "4", "publisher": "Springer Verlag", "pagerange": "913-923", "id_number": "CaltechAUTHORS:20150421-093641890", "issn": "0025-5874", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-093641890", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00209-007-0113-8", "primary_object": { "basename": "0509592v1.pdf", "url": "https://authors.library.caltech.edu/records/epnsv-kdn74/files/0509592v1.pdf" }, "pub_year": "2007", "author_list": "Boileau, Michel; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/b3ffe-r2346", "eprint_id": 8248, "eprint_status": "archive", "datestamp": "2023-08-22 09:34:24", "lastmod": "2026-04-14 04:21:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Green-Michael-B", "name": { "family": "Green", "given": "Michael B." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Schwarz-J-H", "name": { "family": "Schwarz", "given": "John H." }, "orcid": "0000-0001-9861-7559" } ] }, "title": "Nondecoupling of Maximal Supergravity from the Superstring", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 The American Physical Society \n\n(Received 9 May 2007; published 25 July 2007) \n\nWe thank Z. Bern, N. Dorey, C. Hull, J. Russo, N. Seiberg, A. Sen, M. Shigemori, Y. Tachikawa, D. Tong, P. Vanhove, and E. Witten for discussions. H.O. thanks the particle theory group of the University of Tokyo for hospitality. H.O. and J.H.S. are supported in part by DOE Grant No. DE-FG03-92-ER40701. The research of H.O. is also supported in part by NSF Grant No. OISE-0403366 and by the 21st Century COE Program at the University of Tokyo.\n\n

Published - GREprl07.pdf

Submitted - 0704.0777.pdf

", "abstract": "We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10-d) torus. For dimensions d=2 and d=3, it is possible to define a limit in which the only finite-mass states are the 256 massless states of maximal supergravity. However, in dimensions d>=4, there are infinite towers of additional massless and finite-mass states. These correspond to Kaluza-Klein charges, wound strings, Kaluza-Klein monopoles, or branes wrapping around cycles of the toroidal extra dimensions. We conclude that perturbative supergravity cannot be decoupled from string theory in dimensions >=4. In particular, we conjecture that pure [script N]=8 supergravity in four dimensions is in the Swampland.", "date": "2007-07-27", "date_type": "published", "publication": "Physical Review Letters", "volume": "99", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 041601", "id_number": "CaltechAUTHORS:GREprl07", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GREprl07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "OISE-0403366" }, { "agency": "University of Tokyo" } ] }, "other_numbering_system": { "items": [ { "id": "68-2636", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.99.041601", "primary_object": { "basename": "0704.0777.pdf", "url": "https://authors.library.caltech.edu/records/b3ffe-r2346/files/0704.0777.pdf" }, "related_objects": [ { "basename": "GREprl07.pdf", "url": "https://authors.library.caltech.edu/records/b3ffe-r2346/files/GREprl07.pdf" } ], "pub_year": "2007", "author_list": "Green, Michael B.; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/fghe7-rhg71", "eprint_id": 82471, "eprint_status": "archive", "datestamp": "2023-08-22 09:30:42", "lastmod": "2026-04-14 04:41:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Oblomkov-A", "name": { "family": "Oblomkov", "given": "Alexei" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Generalized double affine Hecke algebras of rank 1; Quantized del Pezzo surfaces", "note": "\u00a9 2006 Elsevier Inc. \n\nReceived 27 July 2006, Accepted 22 November 2006, Available online 16 January 2007. \n\nThe work of P.E. and A.O. was partially supported by the NSF grant DMS-9988796 and the CRDF grant RM1-2545-MO-03. P.E. is very grateful to M. Artin for many useful explanations about noncommutative algebraic geometry. We are also grateful to J. Starr for discussions about del Pezzo surfaces, and to W. Crawley-Boevey, A. Malkin and M. Vybornov for explanations about preprojective algebras of quivers.\n\n

Published - 1-s2.0-S0001870806003811-main.pdf

Submitted - 0406480.pdf

", "abstract": "Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D_4, E_6, E_7, E_8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z_\u2113\u22c9Z^2, where \u2113 is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t, q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t, q) for D4 is the Cherednik algebra of type C\u2228C_1, which was studied by Noumi, Sahi, and Stokman, and controls Askey\u2013Wilson polynomials. We prove that H(t, q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t, q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t, q)e provides a quantization of such surfaces. We also discuss connections of H(t, q)with preprojective algebras and Painlev\u00e9 VI.", "date": "2007-07-10", "date_type": "published", "publication": "Advances in Mathematics", "volume": "212", "number": "2", "publisher": "Elsevier", "pagerange": "749-796", "id_number": "CaltechAUTHORS:20171018-155901135", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171018-155901135", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9988796" }, { "agency": "Civilian Research & Development Foundation (CRDF)", "grant_number": "RM1-2545-MO-03" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.aim.2006.11.008", "primary_object": { "basename": "0406480.pdf", "url": "https://authors.library.caltech.edu/records/fghe7-rhg71/files/0406480.pdf" }, "related_objects": [ { "basename": "1-s2.0-S0001870806003811-main.pdf", "url": "https://authors.library.caltech.edu/records/fghe7-rhg71/files/1-s2.0-S0001870806003811-main.pdf" } ], "pub_year": "2007", "author_list": "Etingof, Pavel; Oblomkov, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/fmnzv-qbn32", "eprint_id": 82036, "eprint_status": "archive", "datestamp": "2023-08-22 09:29:01", "lastmod": "2026-04-13 20:00:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Latour-F", "name": { "family": "Latour", "given": "Fr\u00e9d\u00e9ric" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "On central extensions of preprojective algebras", "ispublished": "pub", "full_text_status": "public", "keywords": "Preprojective algebra; Simple Lie algebra; Quiver", "note": "\u00a9 2007 Elsevier Inc. \n\nReceived 16 June 2006, Available online 24 January 2007. \n\nP.E. thanks George Lusztig for a useful discussion. The work of P.E. was partially supported by the NSF grant DMS-0504847 and the CRDF grant RM1-2545-MO-03. F.L. thanks the IH\u00c9S in Bures-sur-Yvette, France. E.R. was supported in part by NSF grant DMS-0401387.\n\n

Submitted - 0606403.pdf

", "abstract": "We show that the Hilbert polynomial P(t) of the trace space A/[A,A] of the centrally extended preprojective algebra A of an ADE quiver is equal to the Hilbert series of the maximal nilpotent subalgebra of the corresponding simple Lie algebra under the principal gradation. This implies that the Hilbert polynomial of the center of A is t^(2h\u22124)P(1/t), where h is the Coxeter number.", "date": "2007-07-01", "date_type": "published", "publication": "Journal of Algebra", "volume": "313", "number": "1", "publisher": "Elsevier", "pagerange": "165-175", "id_number": "CaltechAUTHORS:20171004-092059005", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171004-092059005", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504847" }, { "agency": "Civilian Research & Development Foundation (CRDF)", "grant_number": "RM1-2545-MO-03" }, { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2006.11.040", "primary_object": { "basename": "0606403.pdf", "url": "https://authors.library.caltech.edu/records/fmnzv-qbn32/files/0606403.pdf" }, "pub_year": "2007", "author_list": "Etingof, Pavel; Latour, Fr\u00e9d\u00e9ric; et al." }, { "id": "https://authors.library.caltech.edu/records/ssj0x-a9q91", "eprint_id": 77879, "eprint_status": "archive", "datestamp": "2023-08-19 20:34:03", "lastmod": "2026-04-13 18:54:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "On the asymptotic number of edge states for magnetic Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 London Mathematical Society. \n\nReceived 17 March 2006; revised 4 July 2006; published online 31 January 2007. \n\nThe author wishes to thank Professor B. Helffer for the invitation to Orsay and numerous fruitful discussions. He is also grateful to S. Fournais and A. Hansson for useful remarks. Financial support through the ESF Scientific Programme in Spectral Theory and Partial Differential Equations (SPECT) as well as through the European Research Network 'Postdoctoral Training Program in Mathematical Analysis of Large Quantum Systems' (Contract Number HPRN-CT-2002-00277) is gratefully acknowledged.\n\n

Submitted - 0603046.pdf

", "abstract": "We consider a Schr\u00f6dinger operator ( hD \u2212 A )^2 with a positive magnetic field B = curlA in a domain \u03a9 \u2282 \u211d^2 . The imposing of Neumann boundary conditions leads to the existence of some spectrum below h \u2208 f B . This is a boundary effect and it is related to the existence of edge states of the system. We show that the number of these eigenvalues, in the semi-classical limit h \u2192 0, is governed by a Weyl-type law and that it involves a symbol on \u2202\u03a9. In the particular case of a constant magnetic field, the curvature plays a major role.", "date": "2007-07", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "95", "number": "1", "publisher": "London Mathematical Society", "pagerange": "1-19", "id_number": "CaltechAUTHORS:20170601-081138045", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170601-081138045", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Science Foundation" }, { "agency": "European Union Network Project", "grant_number": "HPRN-CT-2002-00277" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms/pdl024", "primary_object": { "basename": "0603046.pdf", "url": "https://authors.library.caltech.edu/records/ssj0x-a9q91/files/0603046.pdf" }, "pub_year": "2007", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/gn36h-40570", "eprint_id": 97818, "eprint_status": "archive", "datestamp": "2023-08-22 09:14:48", "lastmod": "2026-04-13 18:34:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Jungi\u0107-Veselin", "name": { "family": "Jungi\u0107", "given": "Veselin" } }, { "id": "Radoi\u010di\u0107-Rado\u0161", "name": { "family": "Radoi\u010di\u0107", "given": "Rado\u0161" } } ] }, "title": "On the Existence of Rainbow 4-Term Arithmetic Progressions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Arithmetic Progression; Distinct Color; Color Class; Acta Arith; Consecutive Integer", "note": "\u00a9 Springer-Verlag Tokyo 2007.\n\nReceived 31 August 2005; accepted 18 December 2006. \n\nThis research was supported by NSF grant DMS-0503184.", "abstract": "For infinitely many natural numbers n, we construct 4-colorings of [n] = {1, 2, . . ., n}, with equinumerous color classes, that contain no 4-term arithmetic progression whose elements are colored in distinct colors. This result solves an open problem of Jungi\u0107 et al. (Comb Probab Comput 12:599\u2013620, 2003) Axenovich and Fon-der-Flaass (Electron J Comb 11:R1, 2004).", "date": "2007-06", "date_type": "published", "publication": "Graphs and Combinatorics", "volume": "23", "number": "3", "publisher": "Springer", "pagerange": "249-254", "id_number": "CaltechAUTHORS:20190812-162958451", "issn": "0911-0119", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162958451", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0503184" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00373-007-0723-2", "pub_year": "2007", "author_list": "Conlon, David; Jungi\u0107, Veselin; et al." }, { "id": "https://authors.library.caltech.edu/records/t9fbw-et876", "eprint_id": 80011, "eprint_status": "archive", "datestamp": "2023-08-22 09:03:56", "lastmod": "2026-04-13 20:04:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Meromorphic Jost functions and asymptotic expansions for Jacobi parameters", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Jost function; Jacobi matrix exponential decay", "note": "\u00a9 by B. Simon, Original Russian Text Copyright. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 41, No. 2, pp. 78\u201392, 2007. \n\nReceived May 12, 2006. \n\nSupported in part by NSF grant DMS-0140592 and in part by grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.", "abstract": "We show that the parameters \u0251_n, b_n of a Jacobi matrix have a complete asymptotic expansion\n\u0251^2_n \u2212 1 = \u2211_(k=1)^(K(R)) pk(n)\u03bc^(\u22122n)_k + O(R^(\u22122n)),b_n = \u2211_(k=1)^(K(R)) pk (n)\u03bc^(\u22122n+1)_k + O(R^(\u22122n)), where 1 < |\u00b5_j| < R for j \u2a7d K(R) and all R, if and only if the Jost function, u, written in terms of z (where E = z + z\u22121) is an entire meromorphic function. We relate the poles of u to the \u00b5j's.", "date": "2007-05-12", "date_type": "published", "publication": "Functional Analysis and its Applications", "volume": "41", "number": "2", "publisher": "Springer", "pagerange": "143-153", "id_number": "CaltechAUTHORS:20170809-102314012", "issn": "0016-2663", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170809-102314012", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s10688-007-0013-z", "pub_year": "2007", "author_list": "Simon, B." }, { "id": "https://authors.library.caltech.edu/records/sz01y-81d62", "eprint_id": 77352, "eprint_status": "archive", "datestamp": "2023-08-22 09:01:55", "lastmod": "2026-04-13 18:19:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circle", "ispublished": "pub", "full_text_status": "public", "keywords": "Paraorthogonal polynomials; Rank one", "note": "\u00a9 2006 Elsevier Inc.\n\nReceived 10 May 2006, Available online 27 July 2006.\n\nSupported in part by NSF grant DMS-0140592.\n\n

Submitted - 0606037.pdf

", "abstract": "We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC.", "date": "2007-05-01", "date_type": "published", "publication": "Journal of Mathematical Analysis and Applictions", "volume": "329", "number": "1", "publisher": "Elsevier", "pagerange": "376-382", "id_number": "CaltechAUTHORS:20170510-141814909", "issn": "0022-247X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-141814909", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jmaa.2006.06.076", "primary_object": { "basename": "0606037.pdf", "url": "https://authors.library.caltech.edu/records/sz01y-81d62/files/0606037.pdf" }, "pub_year": "2007", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/w1fyp-hjm29", "eprint_id": 8566, "eprint_status": "archive", "datestamp": "2023-08-22 08:54:26", "lastmod": "2026-04-16 01:40:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feiguin-A", "name": { "family": "Feiguin", "given": "Adrian" } }, { "id": "Trebst-S", "name": { "family": "Trebst", "given": "Simon" } }, { "id": "Ludwig-A-W-W", "name": { "family": "Ludwig", "given": "Andreas W. W." } }, { "id": "Troyer-M", "name": { "family": "Troyer", "given": "Matthis" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" }, { "id": "Freedman-M-H", "name": { "family": "Freedman", "given": "Michael H." } } ] }, "title": "Interacting Anyons in Topological Quantum Liquids: The Golden Chain", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 The American Physical Society \n\n(Received 19 December 2006; published 20 April 2007) \n\nWe thank E. Ardonne, N. Bonesteel, P. Fendley, C. Nayak, G. Refael, S. H. Simon, and J. Slingerland for discussions.\n\n

Published - FEIprl07.pdf

", "abstract": "We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial (\"identity\") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=(7/10). An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.", "date": "2007-04-20", "date_type": "published", "publication": "Physical Review Letters", "volume": "98", "number": "16", "publisher": "American Physical Society", "pagerange": "Art. No. 160409", "id_number": "CaltechAUTHORS:FEIprl07", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FEIprl07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.98.160409", "primary_object": { "basename": "FEIprl07.pdf", "url": "https://authors.library.caltech.edu/records/w1fyp-hjm29/files/FEIprl07.pdf" }, "pub_year": "2007", "author_list": "Feiguin, Adrian; Trebst, Simon; et al." }, { "id": "https://authors.library.caltech.edu/records/5x592-8wn14", "eprint_id": 71903, "eprint_status": "archive", "datestamp": "2023-08-19 20:01:44", "lastmod": "2026-04-13 19:12:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Shporer-A", "name": { "family": "Shporer", "given": "A." }, "orcid": "0000-0002-1836-3120" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "O." }, "orcid": "0000-0002-0111-0418" }, { "id": "Zucker-S", "name": { "family": "Zucker", "given": "S." } }, { "id": "Mazeh-T", "name": { "family": "Mazeh", "given": "T." } } ] }, "title": "Photometric follow-up of the transiting planet WASP-1b", "ispublished": "pub", "full_text_status": "public", "keywords": "techniques: photometric stars: individual: WASP-1 planetary systems", "note": "\u00a9 2007 The Authors. Journal compilation \u00a9 2007 RAS. \n\nIn original form 2006 October 18. Received 2007 January 16. Accepted 2007 January 22. First published online April 11, 2007. \n\nWe would like to thank Efi Hoory for his dedicated work while observing WASP-1 on the night of 2006 October 9. We also wish to thank Elia Leibowitz and Liliana Formiggini for allowing us to use their telescope time on the night of 2006 October 4. We thank the anonymous referee for his thorough reading of the paper and his comments which allowed us to improve this paper. This work was supported by the Israeli Science Foundation through Grant No. 03/323. This research has made use of NASA's Astrophysics Data System Abstract Service and of the SIMBAD data base, operated at CDS, Strasbourg, France.\n\n

Published - 1296.full.pdf

Submitted - 0610556.pdf

Supplemental Material - mnras0376-1296-SD1.pdf

", "abstract": "We report on photometric follow-up of the recently discovered transiting planet WASP-1b. We observed two transits with the Wise Observatory 1-m telescope, and used a variant of the Eclipsing Binary Orbit Program (EBOP) code together with the Sys-Rem detrending approach to fit the light curve. Assuming a stellar mass of 1.15 M_\u2299, we derived a planetary radius of R_p= 1.40 \u00b1 0.06R_J and mass of M_p= 0.87 \u00b1 0.07M_J. An uncertainty of 15 per cent in the stellar mass results in an additional systematic uncertainty of 5 per cent in the planetary radius and of 10 per cent in planetary mass. Our observations yielded a slightly better ephemeris for the centre of the transit: T_c [HJD]= (245 4013.3127 \u00b1 0.0004) +N_(tr)(2.51996 \u00b1 0.00002). The new planet is an inflated, low-density planet, similar to HAT-P-1b and HD 209458b.", "date": "2007-04-11", "date_type": "published", "publication": "Monthly Notices of the Royal Astronomical Society", "volume": "376", "number": "3", "publisher": "Royal Astronomical Society", "pagerange": "1296-1300", "id_number": "CaltechAUTHORS:20161109-163957800", "issn": "0035-8711", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-163957800", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "03/323" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1111/j.1365-2966.2007.11537.x", "primary_object": { "basename": "0610556.pdf", "url": "https://authors.library.caltech.edu/records/5x592-8wn14/files/0610556.pdf" }, "related_objects": [ { "basename": "1296.full.pdf", "url": "https://authors.library.caltech.edu/records/5x592-8wn14/files/1296.full.pdf" }, { "basename": "mnras0376-1296-SD1.pdf", "url": "https://authors.library.caltech.edu/records/5x592-8wn14/files/mnras0376-1296-SD1.pdf" } ], "pub_year": "2007", "author_list": "Shporer, A.; Tamuz, O.; et al." }, { "id": "https://authors.library.caltech.edu/records/t7y0y-zdx71", "eprint_id": 77881, "eprint_status": "archive", "datestamp": "2023-08-19 19:58:50", "lastmod": "2026-04-13 23:25:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Exner-P", "name": { "family": "Exner", "given": "Pavel" } }, { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Absolute Continuity of the Spectrum for Periodically Modulated Leaky Wires in R^3", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 Birkh\u00e4user Verlag Basel/Switzerland. \n\nSubmitted: August 29, 2005. Accepted: June 9, 2006. \n\nCommunicated by Vincent Rivasseau. \n\nThe research was supported in part by ASCR and its Grant Agency within the projects IRP AV0Z10480505 and A100480501. The second author acknowledges gratefully a partial support through the ESF SPECT programme.\n\n

Submitted - 0508525.pdf

", "abstract": "We consider a model of leaky quantum wires in three dimensions. The Hamiltonian is a singular perturbation of the Laplacian supported by a line with the coupling which is bounded and periodically modulated along the line. We demonstrate that such a system has a purely absolutely continuous spectrum and its negative part has band structure with an at most finite number of gaps. This result is extended also to the situation when there is an infinite number of the lines supporting the perturbations arranged periodically in one direction.", "date": "2007-04", "date_type": "published", "publication": "Annales Henri Poincar\u00e9", "volume": "8", "number": "2", "publisher": "Springer", "pagerange": "241-263", "id_number": "CaltechAUTHORS:20170601-083108196", "issn": "1424-0637", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170601-083108196", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "\u00dastav d\u011bjin um\u011bn\u00ed Akademie v\u011bd \u010cR", "grant_number": "AV0Z10480505" }, { "agency": "\u00dastav d\u011bjin um\u011bn\u00ed Akademie v\u011bd \u010cR", "grant_number": "A100480501" }, { "agency": "European Science Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00023-006-0307-3", "primary_object": { "basename": "0508525.pdf", "url": "https://authors.library.caltech.edu/records/t7y0y-zdx71/files/0508525.pdf" }, "pub_year": "2007", "author_list": "Exner, Pavel and Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/6kna4-ffz46", "eprint_id": 13479, "eprint_status": "archive", "datestamp": "2023-08-19 19:55:14", "lastmod": "2026-04-14 03:51:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Consani-C", "name": { "family": "Consani", "given": "Caterina" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Quantum statistical mechanics over function fields", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Elsevier Inc.\n\n\nReceived 26 July 2006; revised 7 December 2006.\nAvailable online 17 December 2006.\nCommunicated by David Goss.\n\n\nPart of this work was completed during a visit of the first author to the Max-Planck Institute \nwhose hospitality is gratefully acknowledged. We thank David Goss and Benoit Jacob for reading \nan early draft of the manuscript and providing useful feedback. We thank the referees for many\nuseful comments.\n\n

Submitted - 0607363.pdf

", "abstract": "In this paper we construct a noncommutative space of \"pointed Drinfeld modules\" that generalizes to the case of function fields the noncommutative spaces of commensurability classes of Q-lattices. It extends the usual moduli spaces of Drinfeld modules to possibly degenerate level structures. In the second part of the paper we develop some notions of quantum statistical mechanics in positive characteristic and we show that, in the case of Drinfeld modules of rank one, there is a natural time evolution on the associated noncommutative space, which is closely related to the positive characteristic L-functions introduced by Goss. The points of the usual moduli space of Drinfeld modules define KMS functionals for this time evolution. We also show that the scaling action on the dual system is induced by a Frobenius action, up to a Wick rotation to imaginary time.", "date": "2007-04", "date_type": "published", "publication": "Journal of Number Theory", "volume": "123", "number": "2", "publisher": "Elsevier", "pagerange": "487-528", "id_number": "CaltechAUTHORS:CONjnt07", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CONjnt07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jnt.2006.12.002", "primary_object": { "basename": "0607363.pdf", "url": "https://authors.library.caltech.edu/records/6kna4-ffz46/files/0607363.pdf" }, "pub_year": "2007", "author_list": "Consani, Caterina and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/eb5rc-are19", "eprint_id": 66986, "eprint_status": "archive", "datestamp": "2023-08-19 19:56:52", "lastmod": "2026-04-13 18:45:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Motl-L", "name": { "family": "Motl", "given": "Lubo\u0161" } }, { "id": "Neitzke-A", "name": { "family": "Neitzke", "given": "Andrew" } } ] }, "title": "Equivalence of twistor prescriptions for super Yang-Mills", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 International Press. \n\nFirst available in Project Euclid: 24 July 2007. \n\nWe are grateful to Michal Fabinger, Peter Svr\u02c7cek, Cumrun Vafa, Anastasia Volovich, and Edward Witten for very useful discussions. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 01-02-17488. The work of L.M. was supported in part by Harvard DOE grant DE-FG01-91ER40654 and the Harvard Society of Fellows. The work of A.N. was supported by NSF grants PHY-0255841 and DMS-0244464.\n\n

Published - Gukov,A.et.al.pdf

Submitted - 0404085.pdf

", "abstract": "There is evidence that one can compute tree-level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We give a partial explanation of the equivalence between the two computations, by showing that they could both be reduced to the same integral over a moduli space of singular curves, subject to some assumptions about the choices of integration contours. We also formulate a class of new \"intermediate\" prescriptions to calculate the same amplitudes.", "date": "2007-04", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "11", "number": "2", "publisher": "International Press", "pagerange": "199-231", "id_number": "CaltechAUTHORS:20160511-104623256", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-104623256", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG01-91ER40654" }, { "agency": "Harvard Society of Fellows" }, { "agency": "NSF", "grant_number": "PHY-0255841" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2007.v11.n2.a1", "primary_object": { "basename": "0404085.pdf", "url": "https://authors.library.caltech.edu/records/eb5rc-are19/files/0404085.pdf" }, "related_objects": [ { "basename": "Gukov,A.et.al.pdf", "url": "https://authors.library.caltech.edu/records/eb5rc-are19/files/Gukov,A.et.al.pdf" } ], "pub_year": "2007", "author_list": "Gukov, Sergei; Motl, Lubo\u0161; et al." }, { "id": "https://authors.library.caltech.edu/records/ewzyq-wmm17", "eprint_id": 7533, "eprint_status": "archive", "datestamp": "2023-08-22 08:43:06", "lastmod": "2026-04-14 02:32:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitano-Ryuichiro", "name": { "family": "Kitano", "given": "Ryuichiro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Ookouchi-Yutaka", "name": { "family": "Ookouchi", "given": "Yutaka" } } ] }, "title": "Direct mediation of metastable supersymmetry breaking", "ispublished": "pub", "full_text_status": "public", "keywords": "Supersymmetric unified models", "note": "\u00a9 2007 The American Physical Society. \n\n(Received 20 December 2006; published 28 February 2007) \n\nWe would like to thank K. Intriligator, H. Murayama, E. Silverstein, T. Watari, and T. Yanagida for discussions. R.K. thanks the hospitality of the high energy theory group at Rutgers University. The work of R.K. was supported by the U.S. Department of Energy under Contract No. DEAC02-76SF00515. The work of H.O. and Y.O. is supported in part by the U.S. Department of Energy under Contract No. DE-FG03-92-ER40701. H.O. is also supported in part by the U.S. National Science Foundation under Contract No. OISE-0403366. Y.O. also acknowledges support by JSPS.\n\n

Published - KITprd07.pdf

Submitted - 0612139.pdf

", "abstract": "The supersymmetric SU(NC) Yang-Mills theory coupled to NF matter fields in the fundamental representation has metastable vacua with broken supersymmetry when NC", "date": "2007-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "75", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 045022", "id_number": "CaltechAUTHORS:KITprd07", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITprd07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC02-76SF00515" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "OISE-0403366" }, { "agency": "Japan Society for the Promotion of Science (JSPS)" } ] }, "other_numbering_system": { "items": [ { "id": "68-2621", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.75.045022", "primary_object": { "basename": "0612139.pdf", "url": "https://authors.library.caltech.edu/records/ewzyq-wmm17/files/0612139.pdf" }, "related_objects": [ { "basename": "KITprd07.pdf", "url": "https://authors.library.caltech.edu/records/ewzyq-wmm17/files/KITprd07.pdf" } ], "pub_year": "2007", "author_list": "Kitano, Ryuichiro; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/34s0v-by239", "eprint_id": 38626, "eprint_status": "archive", "datestamp": "2023-08-19 19:49:34", "lastmod": "2026-04-14 03:10:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Rosendal-C", "name": { "family": "Rosendal", "given": "Christian" } } ] }, "title": "Turbulence, amalgamation, and generic automorphisms of homogeneous structures", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 London Mathematical Society.\nReceived 29 November 2004; Revised 21 February 2006; Published online 27 November 2006.\nThe research of ASK was partially supported by NSF Grants DMS 9987437 and DMS 0455285, the Centre\nde Recerca Matem\u00e0tica, Bellatera, and a Guggenheim Fellowship.\n\n

Submitted - 0409567.pdf

", "abstract": "We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups\nof homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological\nRokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class\n(answering a question of Truss) and apply this to show that the homeomorphism group of the Cantor space has\na comeager conjugacy class (answering a question of Akin, Hurley and Kennedy). Finally, we study Polish groups\nthat admit comeager conjugacy classes in any dimension (in which case the groups are said to admit ample\ngenerics). We show that Polish groups with ample generics have the small index property (generalizing results\nof Hodges, Hodkinson, Lascar and Shelah) and arbitrary homomorphisms from such groups into separable\ngroups are automatically continuous. Moreover, in the case of oligomorphic permutation groups, they have\nuncountable cofinality and the Bergman property. These results in particular apply to automorphism groups of\nmany \u03c9-stable, \u21350-categorical structures and of the random graph. In this connection, we also show that the\ninfinite symmetric group S\u221e has a unique non-trivial separable group topology. For several interesting groups\nwe also establish Serre's properties (FH) and (FA).", "date": "2007-03-01", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "94", "number": "2", "publisher": "London Mathematical Society", "pagerange": "302-350", "id_number": "CaltechAUTHORS:20130522-084128445", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-084128445", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 9987437" }, { "agency": "NSF", "grant_number": "DMS 0455285" }, { "agency": "Guggenheim Fellowship" }, { "agency": "Centre de Recerca Matem\u00e0tica, Bellatera" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/plms/pdl007", "primary_object": { "basename": "0409567.pdf", "url": "https://authors.library.caltech.edu/records/34s0v-by239/files/0409567.pdf" }, "pub_year": "2007", "author_list": "Kechris, Alexander S. and Rosendal, Christian" }, { "id": "https://authors.library.caltech.edu/records/h0k3e-2fp33", "eprint_id": 98246, "eprint_status": "archive", "datestamp": "2023-08-19 19:48:41", "lastmod": "2026-04-13 22:26:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Childs-A-M", "name": { "family": "Childs", "given": "Andrew M." } }, { "id": "Wocjan-P", "name": { "family": "Wocjan", "given": "Pawe\u0142" } } ] }, "title": "The limitations of nice mutually unbiased bases", "ispublished": "pub", "full_text_status": "public", "keywords": "Quantum information theory . Mutually unbiased bases . Quantum designs", "note": "\u00a9 Springer Science + Business Media, LLC 2006. \n\nPublished online: 11 July 2006. \n\nMA is supported by the National Science Foundation under Grant No. DMS-0203417. AMC and PW are supported by the National Science Foundation under Grant No. EIA-0086038.\n\n

Submitted - 0412066.pdf

", "abstract": "Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets.", "date": "2007-03", "date_type": "published", "publication": "Journal of Algebraic Combinatorics", "volume": "25", "number": "2", "publisher": "Springer", "pagerange": "111-123", "id_number": "CaltechAUTHORS:20190826-124740760", "issn": "0925-9899", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190826-124740760", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0203417" }, { "agency": "NSF", "grant_number": "EIA-0086038" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10801-006-0002-y", "primary_object": { "basename": "0412066.pdf", "url": "https://authors.library.caltech.edu/records/h0k3e-2fp33/files/0412066.pdf" }, "pub_year": "2007", "author_list": "Aschbacher, Michael; Childs, Andrew M.; et al." }, { "id": "https://authors.library.caltech.edu/records/s7ryr-p5p27", "eprint_id": 79419, "eprint_status": "archive", "datestamp": "2023-08-19 19:37:05", "lastmod": "2026-04-13 23:24:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Zeros of OPUC and long time asymptotics of Schur and related flows", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Schur flows, orthogonal polynomials, Toda flows", "note": "\u00a9 2007 American Institute of Mathematical Sciences.\n\nReceived: September 2006; Revised: October 2006; Available Online: January 2007. \n\nSupported in part by NSF grant DMS-0140592 and U.S.\u2013Israel Binational Science Foundation (BSF) Grant No. 2002068. \n\nIt is a pleasure to thank Andrei Mart\u00ednez-Finkelshtein, Irina Nenciu, Paul Nevai, and Vilmos Totik, and especially Leonid Golinskii for useful discussions and correspondence.", "abstract": "We provide a complete analysis of the asymptotics for the semi-infinite Schur flow: \u03b1j (t) = (1 \u2212 |\u03b1j(t)|^2)(\u03b1j+1(t) \u2212 \u03b1j\u22121(t)) for \u03b1\u22121(t) = 1 boundary conditions and n = 0, 1, 2,..., with initial condition \u03b1j (0) 2 (\u22121, 1). \n\nWe also provide examples with \u03b1j (0) 2 D for which \u03b10(t) does not have a limit. The proofs depend on the solution via a direct/inverse spectral transform.", "date": "2007-02", "date_type": "published", "publication": "Inverse Problems and Imaging", "volume": "1", "number": "1", "publisher": "American Institute of Mathematical Sciences", "pagerange": "189-215", "id_number": "CaltechAUTHORS:20170726-115725562", "issn": "1930-8345", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170726-115725562", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.3934/ipi.2007.1.189", "pub_year": "2007", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/wwqtw-d9y58", "eprint_id": 38920, "eprint_status": "archive", "datestamp": "2023-08-19 19:26:54", "lastmod": "2026-04-13 19:04:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Unitary representations and modular actions", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2007 Springer. \n\nResearch partially supported by NSF Grant DMS-9987437 and a Guggenheim Fellowship. \n\nDedicated to Professor Anatoly Vershik on the occasion of his 70th birthday.", "abstract": "We call a measure-preserving action of a countable discrete group on a standard probability space tempered if the associated Koopman representation restricted to the orthogonal complement to the constant functions is weakly contained in the regular representation. Extending a result of Hjorth, we show that every tempered action is antimodular, i.e., in a precise sense \"orthogonal\" to any Borel action of a countable group by automorphisms on a countable rooted tree. We also study tempered actions of countable groups by automorphisms on compact metrizable groups, where it turns out that this notion has several ergodic theoretic reformulations and fits naturally in a hierarchy of strong ergodicity properties strictly between ergodicity and strong mixing.", "date": "2007-01", "date_type": "published", "publication": "Journal of Mathematical Sciences", "volume": "140", "number": "3", "publisher": "Springer Verlag", "pagerange": "398-425", "id_number": "CaltechAUTHORS:20130612-132700025", "issn": "1072-3374", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-132700025", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9987437" }, { "agency": "John Simon Guggenheim Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10958-007-0449-y", "pub_year": "2007", "author_list": "Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/kb2xz-vwr68", "eprint_id": 13602, "eprint_status": "archive", "datestamp": "2023-08-22 07:55:34", "lastmod": "2026-04-14 04:16:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chamseddine-A-H", "name": { "family": "Chamseddine", "given": "Ali H." } }, { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Gravity and the standard model with neutrino mixing", "ispublished": "pub", "full_text_status": "public", "keywords": "noncommutative geometry; renormalization-group; spectral action; gauge-theories; unification; relativity", "note": "\u00a9 2007 International Press. \n\nIt is a pleasure to acknowledge the independent preprint by John Barrett [4] with a solution of the fermion doubling problem. The first author is supported by NSF Grant Phys-0601213. The second author thanks G. Landi and T. Schucker, the third author thanks Laura Reina and Don Zagier for useful conversations. We thank the Newton Institute where part of this work was done.\n\n

Published - CHAatmp07.pdf

Submitted - 0610241.pdf

", "abstract": "We present an effective unified theory based on noncommutative geometry for the standard model with neutrino mixing, minimally coupled to gravity. The unification is based on the symplectic unitary group in Hilbert space and on the spectral action. It yields all the detailed structure of the standard model with several predictions at unification scale. Besides the familiar predictions for the gauge couplings as for GUT theories, it predicts the Higgs scattering parameter and the sum of the squares of Yukawa couplings. From these relations, one can extract predictions at low energy, giving in particular a Higgs mass around 170 GeV and a top mass compatible with present experimental value. The geometric picture that emerges is that space-time is the product of an ordinary spin manifold (for which the theory would deliver Einstein gravity) by a finite noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8 and of metric dimension 0, and accounts for all the intricacies of the standard model with its spontaneous symmetry breaking Higgs sector.", "date": "2007", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "11", "number": "6", "publisher": "International Press", "pagerange": "991-1089", "id_number": "CaltechAUTHORS:CHAatmp07", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHAatmp07", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHYS-0601213" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2007.v11.n6.a3", "primary_object": { "basename": "0610241.pdf", "url": "https://authors.library.caltech.edu/records/kb2xz-vwr68/files/0610241.pdf" }, "related_objects": [ { "basename": "CHAatmp07.pdf", "url": "https://authors.library.caltech.edu/records/kb2xz-vwr68/files/CHAatmp07.pdf" } ], "pub_year": "2007", "author_list": "Chamseddine, Ali H.; Connes, Alain; et al." }, { "id": "https://authors.library.caltech.edu/records/6ajw8-3xf04", "eprint_id": 66694, "eprint_status": "archive", "datestamp": "2023-08-19 19:21:59", "lastmod": "2026-03-09 02:37:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Li-Y", "name": { "family": "Li", "given": "Yi" } } ] }, "title": "Topological sigma-models with H-flux and twisted generalized complex manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2007 International Press.\n\nA.K. is grateful to Andrew Frey, Marco Gualtieri, and Misha Verbitsky for\nadvice. Y.L. would like to thank Vadim Borokhov, Takuya Okuda, and\nXinkai Wu for helpful discussions. This work was supported in part by the\nDOE grant DE-FG03-92-ER40701.\n\n

Submitted - 0407249.pdf

", "abstract": "We study the topological sector of N = 2 sigma-models with HH-flux. It has been known for a long time that the target-space geometry of these theories is not K\u00e4hler and can be described in terms of a pair of complex structures, which do not commute, in general, and are parallel with respect to two different connections with torsion. Recently an alternative description of this geometry was found, which involves a pair of commuting twisted generalized complex structures on the target space. In this paper, we define and study the analogs of A and B-models for N = 2 sigma-models with HH-flux and show that the results are naturally expressed in the language of twisted generalized complex geometry. For example, the space of topological observables is given by the cohomology of a Lie algebroid associated to one of the two twisted generalized complex structures. We determine the topological scalar product, which endows the algebra of observables with the structure of a Frobenius algebra. We also discuss mirror symmetry for twisted generalized Calabi-Yau manifolds.", "date": "2007", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "11", "number": "2", "publisher": "International Press", "pagerange": "269-290", "id_number": "CaltechAUTHORS:20160505-115113631", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-115113631", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2007.v11.n2.a3", "primary_object": { "basename": "0407249.pdf", "url": "https://authors.library.caltech.edu/records/6ajw8-3xf04/files/0407249.pdf" }, "pub_year": "2007", "author_list": "Kapustin, Anton and Li, Yi" }, { "id": "https://authors.library.caltech.edu/records/47bvp-rpt47", "eprint_id": 18097, "eprint_status": "archive", "datestamp": "2023-08-22 07:55:47", "lastmod": "2026-04-14 03:18:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Guralnick-R", "name": { "family": "Guralnick", "given": "Robert" } }, { "id": "Segev-Y", "name": { "family": "Segev", "given": "Yoav" } } ] }, "title": "Elementary abelian 2-subgroups of Sidki-type in finite groups", "ispublished": "pub", "full_text_status": "restricted", "keywords": "finite simple groups; involutions; parabolic subgroups; fundamental subgroups; saturation", "note": "\u00a9 2007 European Mathematical Society.\nReceived November 3, 2006; revised March 6, 2007.\nPartially supported by NSF-0504852.\nPartially supported by NSF-0140578.\nPartially supported by BSF grant no. 2004-083.\nThe referee report consisted of six pages of detailed, useful comments.\nWe thank and applaud the referee for this work.", "abstract": "Let G be a finite group. We say that a nontrivial elementary abelian 2-subgroup V of\nG is of Sidki-type in G, if for each involution i in G, C_V(i) \u2260 1. A conjecture due to S. Sidki\n(J. Algebra 39, 1976) asserts that if V is of Sidki-type in G, then V \u2229 0_2(G) \u2260 1. In this paper\nwe prove a stronger version of Sidki's conjecture. As part of the proof, we also establish weak\nversions of the saturation results of G. Seitz (Invent. Math. 141, 2000) for involutions in finite\ngroups of Lie type in characteristic 2. Seitz's results apply to elements of order p in groups\nof Lie type in characteristic p, but only when p is a good prime, and 2 is usually not a good\nprime.", "date": "2007", "date_type": "published", "publication": "Groups, Geometry, and Dynamics", "volume": "1", "number": "4", "publisher": "European Mathematical Society", "pagerange": "347-400", "id_number": "CaltechAUTHORS:20100503-094555816", "issn": "1661-7207", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100503-094555816", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0504852" }, { "agency": "NSF", "grant_number": "0140578." }, { "agency": "United States-Israel Binational Science Foundation (BSF)", "grant_number": "2004-083" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4171/GGD/18", "pub_year": "2007", "author_list": "Aschbacher, Michael; Guralnick, Robert; et al." }, { "id": "https://authors.library.caltech.edu/records/yvdee-4xc88", "eprint_id": 7484, "eprint_status": "archive", "datestamp": "2023-08-22 07:51:21", "lastmod": "2026-04-14 04:57:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Keevash-P", "name": { "family": "Keevash", "given": "Peter" } }, { "id": "Mubayi-D", "name": { "family": "Mubayi", "given": "Dhruv" } }, { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "Set Systems with No Singleton Intersection", "ispublished": "pub", "full_text_status": "public", "keywords": "extremal set theory, restricted intersections", "note": "\u00a92006 Society for Industrial and Applied Mathematics. \n\nReceived by the editors December 12, 2005; accepted for publication (in revised form) June 5, 2006; published electronically December 15, 2006. \n\nThe first author's [PK] research was supported in part by NSF grant DMS-0555755. \n\nThis author's [D.M.] research was supported in part by NSF grant DMS-0400812 and by an Alfred P. Sloan fellowship.", "abstract": "Let $\\mathcal{F}$ be a $k$-uniform set system defined on a ground set of size $n$ with no singleton intersection; i.e., no pair $A,B\\in\\mathcal{F}$ has $|A\\cap B|=1$. Frankl showed that $|\\mathcal{F}|\\leq\\binom{n-2}{k-2}$ for $k\\geq4$ and $n$ sufficiently large, confirming a conjecture of Erd\u0151s and S\u00f3s. We determine the maximum size of $\\mathcal{F}$ for $k=4$ and all $n$, and also establish a stability result for general $k$, showing that any $\\mathcal{F}$ with size asymptotic to that of the best construction must be structurally similar to it.", "date": "2006-12-15", "date_type": "published", "publication": "SIAM Journal on Discrete Mathematics", "volume": "20", "number": "4", "publisher": "SIAM Journal on Discrete Mathematics", "pagerange": "1031-1041", "id_number": "CaltechAUTHORS:KEEsiamjd06", "issn": "0895-4801", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KEEsiamjd06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/050647372", "primary_object": { "basename": "KEEsiamjdm06.pdf", "url": "https://authors.library.caltech.edu/records/yvdee-4xc88/files/KEEsiamjdm06.pdf" }, "pub_year": "2006", "author_list": "Keevash, Peter; Mubayi, Dhruv; et al." }, { "id": "https://authors.library.caltech.edu/records/541xy-9cc71", "eprint_id": 24480, "eprint_status": "archive", "datestamp": "2023-08-22 07:48:08", "lastmod": "2026-04-13 17:43:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "A lemma on polynomials modulo p^m and applications to coding theory", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Polynomials; Codes; Coding theory; Weights; McEliece; Ax-Katz", "note": "\u00a9 2006 Elsevier B.V.\n\nReceived 8 January 2004; revised 22 September 2004; accepted 24 October 2004. Available online 24 July 2006.", "abstract": "An integer-valued function f(x) on the integers that is periodic of period p^e, p prime, can be matched, modulo p^m, by a polynomial function w(x); we show that w(x) may be taken to have degree at most (m(p-1)+1)p^(e-1)-1. Applications include a short proof of the theorem of McEliece on the divisibility of weights of codewords in p-ary cyclic codes by powers of p, an elementary proof of the Ax\u2013Katz theorem on solutions of congruences modulo p, and results on the numbers of codewords in p-ary linear codes with weights in a given congruence class modulo p^e.", "date": "2006-12-06", "date_type": "published", "publication": "Discrete Mathematics", "volume": "306", "number": "23", "publisher": "Elsevier", "pagerange": "3154-3165", "id_number": "CaltechAUTHORS:20110720-095319774", "issn": "0012-365X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110720-095319774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.disc.2004.10.030", "pub_year": "2006", "author_list": "Wilson, Richard M." }, { "id": "https://authors.library.caltech.edu/records/hc5m3-t6626", "eprint_id": 79420, "eprint_status": "archive", "datestamp": "2023-08-19 19:01:25", "lastmod": "2026-04-14 04:48:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Essential Spectrum of Schr\u00f6dinger, Jacobi, and CMV Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 The Hebrew University Magnes Press 2006. \n\nReceived March 8, 2005 and in revised form April 28, 2005. \n\nSupported in part by The Israel Science Foundation (grant No. 188/02). Supported in part by NSF grant DMS-0140592. \n\nResearch supported in part by grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.", "abstract": "We provide a very general result which identifies the essential spectrum of broad classes of operators as exactly equal to the closure of the union of the spectra of suitable limits at infinity. Included is a new result on the essential spectra when potentials are asymptotic to isospectral tori. We also recover within a unified framework the HVZ Theorem and Krein's results on orthogonal polynomials with finite essential spectra.", "date": "2006-12", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "98", "number": "1", "publisher": "Hebrew University Magnes Press", "pagerange": "183-220", "id_number": "CaltechAUTHORS:20170726-123106726", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170726-123106726", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "188/02" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02790275", "pub_year": "2006", "author_list": "Last, Yoram and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/2n3pg-94803", "eprint_id": 81974, "eprint_status": "archive", "datestamp": "2023-08-19 18:53:54", "lastmod": "2026-04-13 18:47:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bartholdi-L", "name": { "family": "Bartholdi", "given": "Laurent" } }, { "id": "Enriquez-B", "name": { "family": "Enriquez", "given": "Benjamin" } }, { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Groups and Lie algebras corresponding to the Yang\u2013Baxter equations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Elsevier Inc. \n\nReceived 28 September 2005, Available online 17 February 2006. \n\nThe authors are very grateful to: Richard Stanley for help with the statement and proof of Proposition 5.1\u2014this allowed us to significantly strengthen the main results of the paper; Andr\u00e9 Henriques for contributing a proof of Theorem 8.1; and Leonid Bokut for pointing out an error in the previous version and for giving useful references. P.E. and B.E. thank the Mathematics Department of ETH (Z\u00fcrich) for hospitality. The work of P.E. was partially supported by the NSF grant DMS-0504847 and the CRDF grant RM1-2545-MO-03. E.R. was supported in part by NSF Grant No. DMS-0401387. Throughout the work, we used the \"Magma\" program for algebraic computations [Ma].\n\n

Submitted - 0509661.pdf

", "abstract": "For a positive integer n we introduce quadratic Lie algebras tr_n, qtr_n and finitely discrete groups Tr_n, QTr_n naturally associated with the classical and quantum Yang\u2013Baxter equation, respectively.\nWe prove that the universal enveloping algebras of the Lie algebras tr_n, qtr_n are Koszul, and compute their Hilbert series. We also compute the cohomology rings for these Lie algebras (which by Koszulity are the quadratic duals of the enveloping algebras). Finally, we construct a basis of U(tr_n).\nWe construct cell complexes which are classifying spaces of the groups Tr_n and QTr_n, and show that the boundary maps in them are zero, which allows us to compute the integral cohomology of these groups.\nWe show that the Lie algebras tr_n, qtr_n map onto the associated graded algebras of the Malcev Lie algebras of the groups Tr_n, QTr_n, respectively. In the case of Tr_n, we use quantization theory of Lie bialgebras to show that this map is actually an isomorphism. At the same time, we show that the groups Tr_n and QTr_n are not formal for n\u2a7e4.", "date": "2006-11-15", "date_type": "published", "publication": "Journal of Algebra", "volume": "305", "number": "2", "publisher": "Elsevier", "pagerange": "742-764", "id_number": "CaltechAUTHORS:20171002-155152258", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-155152258", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0504847" }, { "agency": "Civilian Research & Development Foundation (CRDF)", "grant_number": "RM1-2545-MO-03" }, { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2005.12.006", "primary_object": { "basename": "0509661.pdf", "url": "https://authors.library.caltech.edu/records/2n3pg-94803/files/0509661.pdf" }, "pub_year": "2006", "author_list": "Bartholdi, Laurent; Enriquez, Benjamin; et al." }, { "id": "https://authors.library.caltech.edu/records/7hjm9-2r617", "eprint_id": 6188, "eprint_status": "archive", "datestamp": "2023-08-22 07:11:29", "lastmod": "2026-04-16 01:39:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Feldman-D-E", "name": { "family": "Feldman", "given": "D. E." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Detecting Non-Abelian Statistics with an Electronic Mach-Zehnder Interferometer", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92006 The American Physical Society \n\n(Received 21 July 2006; published 3 November 2006) \n\nWe thank K.T. Law for the help with figures. A.K. acknowledges support by ARO under Grants No. W911NF-04-1-0236 and No. W911NF-05-1-0294 and by NSF under Grant No. PHY-0456720. D.E.F. acknowledges support by NSF under Grant No. DMR-0544116.", "abstract": "Fractionally charged quasiparticles in the quantum Hall state with a filling factor nu=5/2 are expected to obey non-Abelian statistics. We demonstrate that their statistics can be probed by transport measurements in an electronic Mach-Zehnder interferometer. The tunneling current through the interferometer exhibits a characteristic dependence on the magnetic flux and a nonanalytic dependence on the tunneling amplitudes which can be controlled by gate voltages.", "date": "2006-11-03", "date_type": "published", "publication": "Physical Review Letters", "volume": "97", "number": "18", "publisher": "American Physical Society", "pagerange": "Art. No. 186803", "id_number": "CaltechAUTHORS:FELprl06", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FELprl06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "FELprl06.pdf", "url": "https://authors.library.caltech.edu/records/7hjm9-2r617/files/FELprl06.pdf" }, "pub_year": "2006", "author_list": "Feldman, D. E. and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/m6t3x-mns90", "eprint_id": 82726, "eprint_status": "archive", "datestamp": "2023-08-22 07:08:11", "lastmod": "2026-04-13 19:26:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Heninger-N", "name": { "family": "Heninger", "given": "Nadia" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "On the integrality of nth roots of generating functions", "ispublished": "pub", "full_text_status": "public", "keywords": "Formal power series; Square roots of series; Fractional powers; Integer sequences; Theta series; Barnes\u2013Wall lattices; E8 lattice; Leech lattice; Weight enumerators; BCH codes; Kerdock codes; Preparata codes; Reed\u2013Muller codes", "note": "\u00a9 2006 Elsevier Inc. \n\nReceived 13 September 2005, Available online 12 June 2006. \n\nSupported by the AT&T Labs Fellowship Program.\n\n

Submitted - 0509316.pdf

", "abstract": "Motivated by the discovery that the eighth root of the theta series of the E_8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f\u2208R (where R=1+xZ\u301ax\u301b) can be written as f=g^n for g\u2208R, n\u2a7e2. Let P_n:={g^n|g\u2208R} and let \u03bc_n:=n\u220f_p|_np. We show among other things that (i) for f\u2208R, f\u2208P_n\u21d4f(mod \u03bc_n)\u2208P_n, and (ii) if f\u2208P_n, there is a unique g\u2208P_n with coefficients mod \u03bc_n/n such that f\u2261g^n(mod \u03bc_n). In particular, if f\u22611(mod \u03bc_n) then f\u2208P_n. The latter assertion implies that the theta series of any extremal even unimodular lattice in R^n (e.g. E_8 in R^8) is in P_n if n is of the form 2^i3^j5^k (i\u2a7e3). There do not seem to be any exact analogues for codes, although we show that the weight enumerator of the rth order Reed\u2013Muller code of length 2^m is in P_2r(and similarly that the theta series of the Barnes\u2013Wall lattice BW_2m is in P_2m). We give a number of other results and conjectures, and establish a conjecture of Paul D. Hanna that there is a unique element f\u2208P_n (n\u2a7e2) with coefficients restricted to the set {1,2,\u2026,n}.", "date": "2006-11", "date_type": "published", "publication": "Journal of Combinatorial Theory. Series A", "volume": "113", "number": "8", "publisher": "Elsevier", "pagerange": "1732-1745", "id_number": "CaltechAUTHORS:20171027-091207506", "issn": "0097-3165", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171027-091207506", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AT&T Labs" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jcta.2006.03.018", "primary_object": { "basename": "0509316.pdf", "url": "https://authors.library.caltech.edu/records/m6t3x-mns90/files/0509316.pdf" }, "pub_year": "2006", "author_list": "Heninger, Nadia; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/ax6xf-zdw63", "eprint_id": 23048, "eprint_status": "archive", "datestamp": "2023-08-22 06:53:56", "lastmod": "2026-04-14 02:02:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Gopakumar-R", "name": { "family": "Gopakumar", "given": "Rajesh" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Baby universes and string theory", "ispublished": "pub", "full_text_status": "restricted", "keywords": "baby universes; Hartle-Hawking; 2D Yang-Mills; topological string", "note": "\u00a9 2006 World Scientific Publishing Company. \n\nR. Gopakumar would like to thank the organizers of the conference on \"Einstein's Legacy in the New Millenium\" (Puri, 2005) for inviting him to speak. He would also like to thank them for their hospitality and for organizing a very stimulating conference.", "abstract": "The description of 4D BPS black holes in terms of branes wrapped on various cycles in\na Calabi-Yau space gives us the opportunity to study various issues in quantum gravity\nin a definite way by means of the worldvolume theory of the branes. In the particular\nexample discussed here, there is a simple worldvolume description in terms of 2D Yang-Mills\ntheory. The latter is an exactly solvable system of free fermions in one dimension.\nThe exact answer for the free energy of this system can be written in a way that suggests\nan interpretation in terms of contributions from multiple (baby) universes.", "date": "2006-10", "date_type": "published", "publication": "International Journal of Modern Physics D", "volume": "15", "number": "10", "publisher": "World Scientific Publishing", "pagerange": "1581-1586", "id_number": "CaltechAUTHORS:20110322-100922722", "issn": "0218-2718", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110322-100922722", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0218271806008978", "pub_year": "2006", "author_list": "Dijkgraaf, Robbert; Gopakumar, Rajesh; et al." }, { "id": "https://authors.library.caltech.edu/records/dgwdk-sq532", "eprint_id": 97806, "eprint_status": "archive", "datestamp": "2023-08-22 06:29:07", "lastmod": "2026-04-13 18:39:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Rainbow solutions of linear equations over \u2124_p", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Rainbow Ramsey theory; Inverse theorem", "note": "\u00a9 2006 Elsevier B.V. All rights reserved. \n\nReceived 12 September 2005; received in revised form 12 February 2006; accepted 28 March 2006; available online 17 July 2006. \n\nThe author is kindly supported by a grant from St. John's College, Cambridge. \n\nI would like to thank both Tim Gowers and Imre Leader for their comments and observations.", "abstract": "We prove that if the group \u2124_p, with p a prime, is coloured with k \u2265 4 different colours such that each colour appears at least k times, then for any a_1, . . . a_k, b in \u2124_p with not all the a_i being equal, we may solve the equation A_(1)x_(1) + \u2022 \u2022 \u2022 + a_(k)x_(k) = b so that each of the variables is chosen in a different colour class. This generalises a similar result concerning three colour classes due to Jungi\u0107, Licht, Mahdian, Ne\u0161et\u0159il and Radoi\u010di\u0107.\n\nIn the course of our proof we classify, with some size caveats, the sets in \u2124_p which satisfy the inequality | A_1 + \u2022 \u2022 \u2022 + A_n | \u2264 | A_1 | + \u2022 \u2022 \u2022 + | A_1 |. This is a generalisation of an inverse theorem due to Hamidoune and R\u00f8dseth concerning the case n = 2.", "date": "2006-09-06", "date_type": "published", "publication": "Discrete Mathematics", "volume": "306", "number": "17", "publisher": "Elsevier", "pagerange": "2056-2063", "id_number": "CaltechAUTHORS:20190812-162957077", "issn": "0012-365X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162957077", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "St. John's College, Cambridge" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.disc.2006.03.070", "pub_year": "2006", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/p2ay3-jrf87", "eprint_id": 77877, "eprint_status": "archive", "datestamp": "2023-08-19 18:32:16", "lastmod": "2026-04-13 21:35:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "Lieb\u2013Thirring Inequalities for Schr\u00f6dinger Operators with Complex-valued Potentials", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator, Lieb\u2013Thirring inequalities, complex potential", "note": "\u00a9 By the Authors 2006. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nReceived: 5 May 2006. Published online: 29 July 2006. \n\nThe work of Rupert L. Frank and Ari Laptev was supported by the Swedish Foundation for International Cooperation in Research and Higher Education (STINT). The work of Elliott H. Lieb was supported by U.S. National Science Foundation grant PHY 01 39984. The work of Robert Seiringer was supported by U.S. National Science Foundation grant PHY 03 53181, and by an A.P. Sloan Fellowship.\n\n

Published - FrankRupert309-.pdf

Submitted - 0605017.pdf

", "abstract": "Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schr\u00f6dinger operator with a complex-valued potential.", "date": "2006-09", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "77", "number": "3", "publisher": "Springer", "pagerange": "309-316", "id_number": "CaltechAUTHORS:20170601-075251570", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170601-075251570", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swedish Foundation for International Cooperation in Research and Higher Education (STINT)" }, { "agency": "NSF", "grant_number": "PHY-0139984" }, { "agency": "NSF", "grant_number": "PHY-0353181" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-006-0095-1", "primary_object": { "basename": "0605017.pdf", "url": "https://authors.library.caltech.edu/records/p2ay3-jrf87/files/0605017.pdf" }, "related_objects": [ { "basename": "FrankRupert309-.pdf", "url": "https://authors.library.caltech.edu/records/p2ay3-jrf87/files/FrankRupert309-.pdf" } ], "pub_year": "2006", "author_list": "Frank, Rupert L.; Laptev, Ari; et al." }, { "id": "https://authors.library.caltech.edu/records/4m9zp-td458", "eprint_id": 77387, "eprint_status": "archive", "datestamp": "2023-08-19 18:22:54", "lastmod": "2026-04-13 17:11:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Davies-E-B", "name": { "family": "Davies", "given": "E. B." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Eigenvalue estimates for non-normal matrices and the zeros of random orthogonal polynomials on the unit circle", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Elsevier Inc. \n\nReceived 30 August 2005, Accepted 3 March 2006, Available online 15 May 2006. \n\nCommunicated by Paul Nevai \n\nSupported in part by EPSRC grant GR/R81756. Supported in part by NSF grant DMS-0140592. \n\nThis work was done while B. Simon was a visitor at King's College London. He would like to thank A.N. Pressley and E.B. Davies for the hospitality of King's College, and the London Mathematical Society for partial support. The calculations of M. Stoiciu [20,21] were an inspiration for our pursuing the estimate we found. We appreciate useful correspondence/discussions with M. Haase, N. Higham, R. Nagel, N.K. Nikolski, V. Totik, and L.N. Trefethen.\n\n

Submitted - 0603098.pdf

", "abstract": "We prove that for any n\u00d7n matrix, A, and z with |z|\u2a7e\u2225A\u2225, we have that \u2225(z-A)^(-1) \u2225\u2a7dcot(^\u03c0_(4n))dist(z,spec(A))^(-1). We apply this result to the study of random orthogonal polynomials on the unit circle.", "date": "2006-08", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "141", "number": "2", "publisher": "Elsevier", "pagerange": "189-213", "id_number": "CaltechAUTHORS:20170512-073744225", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744225", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Engineering and Physical Sciences Research Council (EPSRC)", "grant_number": "GR/R81756" }, { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2006.03.006", "primary_object": { "basename": "0603098.pdf", "url": "https://authors.library.caltech.edu/records/4m9zp-td458/files/0603098.pdf" }, "pub_year": "2006", "author_list": "Davies, E. B. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/m3n1c-gz984", "eprint_id": 3909, "eprint_status": "archive", "datestamp": "2023-08-22 06:05:00", "lastmod": "2026-04-13 20:29:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Wilson-'t Hooft operators in four-dimensional gauge theories and S-duality", "ispublished": "pub", "full_text_status": "public", "keywords": "Gauge field theories", "note": "\u00a9 2006 The American Physical Society. \n\n(Received 14 May 2006; published 7 July 2006) \n\nI would like to thank Andrei Mikhailov for helpful discussions. This work was supported in part by the DOE grant No. DE-FG03-92-ER40701.\n\n

Published - KAPprd06.pdf

", "abstract": "We study operators in four-dimensional gauge theories which are localized on a straight line, create electric and magnetic flux, and in the UV limit break the conformal invariance in the minimal possible way. We call them Wilson-'t Hooft operators, since in the purely electric case they reduce to the well-known Wilson loops, while in general they may carry 't Hooft magnetic flux. We show that to any such operator one can associate a maximally symmetric boundary condition for gauge fields on AdSE2\u00d7S2. We show that Wilson-'t Hooft operators are classified by a pair of weights (electric and magnetic) for the gauge group and its magnetic dual, modulo the action of the Weyl group. If the magnetic weight does not belong to the coroot lattice of the gauge group, the corresponding operator is topologically nontrivial (carries nonvanishing 't Hooft magnetic flux). We explain how the spectrum of Wilson-'t Hooft operators transforms under the shift of the \u03b8-angle by 2\u03c0. We show that, depending on the gauge group, either SL(2,[openface Z]) or one of its congruence subgroups acts in a natural way on the set of Wilson-'t Hooft operators. This can be regarded as evidence for the S-duality of N=4 super-Yang-Mills theory. We also compute the one-point function of the stress-energy tensor in the presence of a Wilson-'t Hooft operator at weak coupling.", "date": "2006-07-15", "date_type": "published", "publication": "Physical Review D", "volume": "74", "number": "2", "publisher": "American Physical Society", "pagerange": "Art. No. 025005", "id_number": "CaltechAUTHORS:KAPprd06", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPprd06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.74.025005", "primary_object": { "basename": "KAPprd06.pdf", "url": "https://authors.library.caltech.edu/records/m3n1c-gz984/files/KAPprd06.pdf" }, "pub_year": "2006", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/h1xzj-kdm60", "eprint_id": 79350, "eprint_status": "archive", "datestamp": "2023-08-19 18:13:14", "lastmod": "2026-04-13 19:34:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "David" }, "orcid": "0000-0001-5924-3849" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Jost functions and Jost solutions for Jacobi matrices, I. A necessary and sufficient condition for Szeg\u0151 asymptotics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Springer-Verlag. \n\nReceived: 22 February 2005; Accepted: 10 October 2005; First Online: 09 January 2006. \n\nSupported in part by NSF grant DMS-0227089. \n\nSupported in part by NSF grant DMS-0140592 and in part by Grant No. 2002068 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.\n\n

Submitted - 0502486.pdf

", "abstract": "We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szeg\u0151 asymptotics off the real axis. A key idea is to prove the equivalence of Szeg\u0151 asymptotics and of Jost asymptotics for the Weyl solution. We also prove L^2 convergence of Szeg\u0151 asymptotics on the spectrum.", "date": "2006-07", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "165", "number": "1", "publisher": "Springer", "pagerange": "1-50", "id_number": "CaltechAUTHORS:20170725-145819291", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170725-145819291", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0227089" }, { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00222-005-0485-5", "primary_object": { "basename": "0502486.pdf", "url": "https://authors.library.caltech.edu/records/h1xzj-kdm60/files/0502486.pdf" }, "pub_year": "2006", "author_list": "Damanik, David and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/6n7v2-esa70", "eprint_id": 78927, "eprint_status": "archive", "datestamp": "2023-08-19 18:13:06", "lastmod": "2026-04-13 23:38:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Wiley Periodicals, Inc. \n\nIssue online: 25 Apr 2006. Version of Record online: 5 Oct 2005. Manuscript Received: Dec 2004. \n\nThis work was partially supported by NSF Grant DMS-0140592. It is a pleasure to thank Chuck Newman and Percy Deift for the hospitality of the Courant Institute, where some of this work was done.\n\n

Submitted - 0412336.pdf

", "abstract": "We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to the density of zeros. Zeros away from the a.c. spectrum have limit points mod p and only finitely many of them.", "date": "2006-07", "date_type": "published", "publication": "Communications on Pure and Applied Mathematics", "volume": "59", "number": "7", "publisher": "Wiley", "pagerange": "1042-1062", "id_number": "CaltechAUTHORS:20170711-080502782", "issn": "0010-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170711-080502782", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Courant Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1002/cpa.20106", "primary_object": { "basename": "0412336.pdf", "url": "https://authors.library.caltech.edu/records/6n7v2-esa70/files/0412336.pdf" }, "pub_year": "2006", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/c4adw-9py07", "eprint_id": 22090, "eprint_status": "archive", "datestamp": "2023-08-19 18:08:05", "lastmod": "2026-04-13 23:19:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Kinyon-M-K", "name": { "family": "Kinyon", "given": "Michael K." } }, { "id": "Phillips-J-D", "name": { "family": "Phillips", "given": "J. D." } } ] }, "title": "Finite Bruck loops", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 American Mathematical Society. \n\nReceived by the editors December 15, 2003 and, in revised form, June 29, 2004. Article electronically published on September 22, 2005. \n\nThe first author was partially supported by NSF-0203417.\n\n

Published - ASCtams06.pdf

Submitted - 0401193.pdf

", "abstract": "Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops X, showing that X is essentially the direct product of a Bruck loop of odd order with a 2-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 2-element Bruck loops are 2-loops, leaving open the question of whether such obstructions actually exist.", "date": "2006-07", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "358", "number": "7", "publisher": "American Mathematical Society", "pagerange": "3061-3075", "id_number": "CaltechAUTHORS:20110209-094820472", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110209-094820472", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0203417" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9947-05-03778-5", "primary_object": { "basename": "0401193.pdf", "url": "https://authors.library.caltech.edu/records/c4adw-9py07/files/0401193.pdf" }, "related_objects": [ { "basename": "ASCtams06.pdf", "url": "https://authors.library.caltech.edu/records/c4adw-9py07/files/ASCtams06.pdf" } ], "pub_year": "2006", "author_list": "Aschbacher, Michael; Kinyon, Michael K.; et al." }, { "id": "https://authors.library.caltech.edu/records/ffcrf-5m029", "eprint_id": 56831, "eprint_status": "archive", "datestamp": "2023-08-22 05:59:23", "lastmod": "2026-04-13 18:15:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jiang-Boju", "name": { "family": "Jiang", "given": "Boju" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wang-Shicheng", "name": { "family": "Wang", "given": "Shicheng" } }, { "id": "Zhou-Qing", "name": { "family": "Zhou", "given": "Qing" } } ] }, "title": "Embedding infinite cyclic covers of knot spaces into 3-space", "ispublished": "pub", "full_text_status": "public", "keywords": "Embedding; Non-fibre knots; Infinite cyclic coverings; Alexander polynomial", "note": "\u00a9 2006 Elsevier Ltd. \n\nReceived 5 December 2004. \n\nDedicated to the memory of Professor Shiing-shen Chern. \n\nWe are grateful to Dr. Hao Zheng for drawing the pictures, to Professor William Browder for a helpful conversation with the second author, to Professor Robert D. Edwards for bringing the third author to this simply stated intuitive question, and to Professor David Gabai for a comment on alternating knots. All authors are partially supported by a MOSTC grant and a MOEC grant. The second author is partially supported by the Centennial fellowship of Princeton University. Part of the paper is revised from the Master thesis of the second named author submitted to Peking University.\n\n

Submitted - 0505206.pdf

", "abstract": "We say a knot k in the 3-sphere S^3 has Property IE if the infinite cyclic cover of the knot exterior embeds into S^3. Clearly all fibred knots have Property IE.\n\nThere are infinitely many non-fibred knots with Property IE and infinitely many non-fibred knots without property IE. Both kinds of examples are established here for the first time. Indeed we show that if a genus 1 non-fibred knot has Property IE, then its Alexander polynomial \u0394k(t) must be either 1 or 2t^2\u22125t+2, and we give two infinite families of non-fibred genus 1 knots with Property IE and having _(\u0394k)(t)=1 and 2t^2\u22125t+2 respectively.\n\nHence among genus 1 non-fibred knots, no alternating knot has Property IE, and there is only one knot with Property IE up to ten crossings.\n\nWe also give an obstruction to embedding infinite cyclic covers of a compact 3-manifold into any compact 3-manifold.", "date": "2006-07", "date_type": "published", "publication": "Topology", "volume": "45", "number": "4", "publisher": "Elsevier", "pagerange": "691-705", "id_number": "CaltechAUTHORS:20150421-115920260", "issn": "0040-9383", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115920260", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "MOSTC" }, { "agency": "MOEC" }, { "agency": "Princeton University Centennial Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.top.2006.01.005", "primary_object": { "basename": "0505206.pdf", "url": "https://authors.library.caltech.edu/records/ffcrf-5m029/files/0505206.pdf" }, "pub_year": "2006", "author_list": "Jiang, Boju; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/ng7m7-2qq61", "eprint_id": 56830, "eprint_status": "archive", "datestamp": "2023-08-19 18:03:03", "lastmod": "2026-03-09 21:53:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "A note on knot Floer homology of links", "ispublished": "pub", "full_text_status": "public", "keywords": "knot Floer homology, links, homology 3\u2013sphere, maximal Euler characteristic, taut foliations, alternative links", "note": "\u00a9 2006 Mathematical Science Publishers. \n\nReceived: 11 June 2005. Revised: 6 January 2006. \n\nWe are grateful to David Gabai, Peter Kronheimer and Zolt\u00e1n Szab\u00f3 for some helpful conversations. The author is partially supported by the Centennial fellowship of the Graduate School at Princeton University\n\n

Published - gt-v10-n2-p03-p.pdf

Submitted - 0506208v4.pdf

", "abstract": "Ozsv\u00e1th and Szab\u00f3 proved that knot Floer homology determines the genera of\nknots in S^3. We will generalize this deep result to links in homology\n3-spheres, by adapting their method. Our proof relies on a result of Gabai and some constructions related to foliations. We also interpret a theorem of\nKauffman in the world of knot Floer homology, hence we can compute the top\nfiltration term of the knot Floer homology for alternative links.", "date": "2006-06-21", "date_type": "published", "publication": "Geometry and Topology", "volume": "10", "number": "2", "publisher": "Geometry & Topology Publications", "pagerange": "695-713", "id_number": "CaltechAUTHORS:20150421-115916774", "issn": "1465-3060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115916774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Princeton University Centennial Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/gt.2006.10.695", "primary_object": { "basename": "0506208v4.pdf", "url": "https://authors.library.caltech.edu/records/ng7m7-2qq61/files/0506208v4.pdf" }, "related_objects": [ { "basename": "gt-v10-n2-p03-p.pdf", "url": "https://authors.library.caltech.edu/records/ng7m7-2qq61/files/gt-v10-n2-p03-p.pdf" } ], "pub_year": "2006", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/ffgjt-zke89", "eprint_id": 5039, "eprint_status": "archive", "datestamp": "2023-08-22 05:46:56", "lastmod": "2026-04-13 23:18:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Argyres-P-C", "name": { "family": "Argyres", "given": "Philip C." } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Seiberg-N", "name": { "family": "Seiberg", "given": "Nathan" }, "orcid": "0000-0003-3897-046X" } ] }, "title": "On S-duality for non-simply-laced gauge groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Duality in Gauge Field Theories, Supersymmetric gauge theory", "note": "\u00a9 2006 SISSA.\n\nReceived 31 March 2006, accepted for publication 15 May 2006. Published 20 June 2006.\n\nP.C.A. and A.K. would like to thank Institute for Advanced Study, Princeton, NJ, for hospitality while this work was being performed. P.C.A. is supported in part by DOE grant DOE-FG02-84-ER40153. A.K. is supported in part by DOE grant DOE-FG03-92-ER40701. N.S. is supported in part by DOE grant DOE-FG02-90-ER40542. \n\nE-print number: hep-th/0603048\n\n

Published - ARGjhep06.pdf

", "abstract": "We point out that for Script N = 4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality groups of these theories are the Hecke groups with elliptic elements of order 6 and 4, respectively. These groups extend the \u0393_0(3) and \u0393_0(2) subgroups of SL(2,\u2124) by elements with a non-trivial action on the moduli space. We show that under a certain embedding of these gauge theories into string theory, the Hecke duality groups are represented by T-duality transformations.", "date": "2006-06", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2006", "number": "6", "publisher": "Springer", "pagerange": "Art. No. 043", "id_number": "CaltechAUTHORS:ARGjhep06", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ARGjhep06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-84-ER40153" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2006/06/043", "primary_object": { "basename": "ARGjhep06.pdf", "url": "https://authors.library.caltech.edu/records/ffgjt-zke89/files/ARGjhep06.pdf" }, "pub_year": "2006", "author_list": "Argyres, Philip C.; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/433yf-nrz48", "eprint_id": 81972, "eprint_status": "archive", "datestamp": "2023-08-19 17:51:21", "lastmod": "2026-04-13 17:29:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Elsevier Inc.\n\nReceived 21 March 2005, Available online 24 January 2006.\n\nThe work of the author was partially supported by the NSF Grant DMS-9988796 and the CRDF Grant RM1-2545-MO-03.\n\nThe author was supported in part by NSF Grant No. DMS-0401387.\n\nP.E. is grateful to W. Crawley-Boevey for the references [Ru,CB2], and to M. Artin, J. de Jong, V. Ostrik, D. Rogalski, and R. Rouquier for useful discussions.\n\n

Submitted - 0503393.pdf

", "abstract": "Preprojective algebras of quivers were introduced in 1979 by Gelfand and Ponomarev [GP], because for quivers of finite ADE type, they are models for indecomposable\nrepresentations (they contain each indecomposable exactly once). Twenty years later, these algebras and their deformed versions introduced in [CBH] (for arbitrary quivers) became a subject of intense interest, since their representation varieties, called quiver varieties,\nplayed an important role in geometric representation theory. Ironically, it is exactly for quivers of finite ADE type that preprojective algebras fail to have good properties\u2014they are not Koszul and their deformed versions are not flat.", "date": "2006-05-15", "date_type": "published", "publication": "Journal of Algebra", "volume": "299", "number": "2", "publisher": "Elsevier", "pagerange": "570-588", "id_number": "CaltechAUTHORS:20171002-152707569", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-152707569", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9988796" }, { "agency": "Civilian Research & Development Foundation (CRDF)", "grant_number": "RM1-2545-MO-03" }, { "agency": "NSF", "grant_number": "DMS-0401387" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.jalgebra.2006.01.005", "primary_object": { "basename": "0503393.pdf", "url": "https://authors.library.caltech.edu/records/433yf-nrz48/files/0503393.pdf" }, "pub_year": "2006", "author_list": "Etingof, Pavel and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/2fj5e-fqq81", "eprint_id": 71901, "eprint_status": "archive", "datestamp": "2023-08-19 17:43:12", "lastmod": "2026-04-14 02:49:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "O." }, "orcid": "0000-0002-0111-0418" }, { "id": "Mazeh-T", "name": { "family": "Mazeh", "given": "T." } }, { "id": "North-P", "name": { "family": "North", "given": "P." } } ] }, "title": "Automated analysis of eclipsing binary light curves - I. EBAS - a new Eclipsing Binary Automated Solver with EBOP", "ispublished": "pub", "full_text_status": "public", "keywords": "methods: data analysis binaries: eclipsing", "note": "\u00a9 2006 The Authors. Journal compilation \u00a9 2006 RAS. \n\nIn original form 2005 May 13. Received 2005 November 30. Accepted 2006 January 9. First published online April 21, 2006. \n\nWe are grateful to the OGLE team, and to L. Wyrzykowski in particular, for the excellent photometric data set and the eclipsing binary analysis that was made available to us. We thank J. Devor, G. Torres and I. Ribas for very useful comments. The remarks and suggestions of the referee, T. Zwitter, helped us to substantially improve the algorithm and this paper. This work was supported by the Israeli Science Foundation through grant no. 03/233.\n\n

Published - 1521.full.pdf

Submitted - 0601199.pdf

", "abstract": "We present a new algorithm, Eclipsing Binary Automated Solver (EBAS), to analyse light curves of eclipsing binaries. The algorithm is designed to analyse large numbers of light curves, and is therefore based on the relatively fast EBOP code. To facilitate the search for the best solution, EBAS uses two parameter transformations. Instead of the radii of the two stellar components, EBAS uses the sum of radii and their ratio, while the inclination is transformed into the impact parameter. To replace human visual assessment, we introduce a new 'alarm' goodness-of-fit statistic that takes into account correlation between neighbouring residuals. We perform extensive tests and simulations that show that our algorithm converges well, finds a good set of parameters and provides reasonable error estimation.", "date": "2006-04-21", "date_type": "published", "publication": "Monthly Notices of the Royal Astronomical Society", "volume": "367", "number": "4", "publisher": "Royal Astronomical Society", "pagerange": "1521-1530", "id_number": "CaltechAUTHORS:20161109-162833455", "issn": "0035-8711", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-162833455", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "03/233" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1111/j.1365-2966.2006.10049.x", "primary_object": { "basename": "0601199.pdf", "url": "https://authors.library.caltech.edu/records/2fj5e-fqq81/files/0601199.pdf" }, "related_objects": [ { "basename": "1521.full.pdf", "url": "https://authors.library.caltech.edu/records/2fj5e-fqq81/files/1521.full.pdf" } ], "pub_year": "2006", "author_list": "Tamuz, O.; Mazeh, T.; et al." }, { "id": "https://authors.library.caltech.edu/records/s5ddn-sc375", "eprint_id": 71902, "eprint_status": "archive", "datestamp": "2023-08-19 17:43:21", "lastmod": "2026-04-13 19:40:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mazeh-T", "name": { "family": "Mazeh", "given": "T." } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "O." }, "orcid": "0000-0002-0111-0418" }, { "id": "North-P", "name": { "family": "North", "given": "P." } } ] }, "title": "Automated analysis of eclipsing binary light curves - II. Statistical analysis of OGLE LMC eclipsing binaries", "ispublished": "pub", "full_text_status": "public", "keywords": "methods: data analysis binaries: eclipsing Magellanic Clouds", "note": "\u00a9 2006 The Authors. Journal compilation \u00a9 2006 RAS. \n\nIn original form 2005 September 26. Received 2005 November 30. Accepted 2006 January 9. First published online April 21, 2006. \n\nWe are grateful to the OGLE team, and to L. Wyrzykowski in particular, for the excellent photometric data set and the eclipsing binary analysis that was available to us. We thank J. Devor, G. Torres and I. Ribas for very useful comments. The remarks and suggestions of the referee, T. Zwitter, helped us to substantially improve the algorithm and this paper. This work was supported by the Israeli Science Foundation through grant no. 03/233.\n\n

Published - MNRAS-2006-Mazeh-1531-42.pdf

Submitted - 0601201.pdf

Supplemental Material - mnras0367-1531-SD1.pdf

Supplemental Material - mnras0367-1531-SD2.pdf

", "abstract": "In the first paper of this series, we presented EBAS \u2013 Eclipsing Binary Automated Solver, a new fully automated algorithm to analyse the light curves of eclipsing binaries, based on the EBOP code. Here, we apply the new algorithm to the whole sample of 2580 binaries found in the Optical Gravitational Lensing Experiment (OGLE) Large Magellanic Cloud (LMC) photometric survey and derive the orbital elements for 1931 systems. To obtain the statistical properties of the short-period binaries of the LMC, we construct a well-defined subsample of 938 eclipsing binaries with main-sequence B-type primaries. Correcting for observational selection effects, we derive the distributions of the fractional radii of the two components and their sum, the brightness ratios and the periods of the short-period binaries. Somewhat surprisingly, the results are consistent with a flat distribution in log P between 2 and 10 d. We also estimate the total number of binaries in the LMC with the same characteristics, and not only the eclipsing binaries, to be about 5000. This figure leads us to suggest that (0.7 \u00b1 0.4) per cent of the main-sequence B-type stars in the LMC are found in binaries with periods shorter than 10 d. This frequency is substantially smaller than the fraction of binaries found by small Galactic radial-velocity surveys of B stars. On the other hand, the binary frequency found by Hubble Space Telescope (HST) photometric searches within the late main-sequence stars of 47 Tuc is only slightly higher and still consistent with the frequency we deduced for the B stars in the LMC.", "date": "2006-04-21", "date_type": "published", "publication": "Monthly Notices of the Royal Astronomical Society", "volume": "367", "number": "4", "publisher": "Royal Astronomical Society", "pagerange": "1531-1542", "id_number": "CaltechAUTHORS:20161109-163450950", "issn": "0035-8711", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-163450950", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "03/233" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1111/j.1365-2966.2006.10050.x", "primary_object": { "basename": "0601201.pdf", "url": "https://authors.library.caltech.edu/records/s5ddn-sc375/files/0601201.pdf" }, "related_objects": [ { "basename": "mnras0367-1531-SD1.pdf", "url": "https://authors.library.caltech.edu/records/s5ddn-sc375/files/mnras0367-1531-SD1.pdf" }, { "basename": "mnras0367-1531-SD2.pdf", "url": "https://authors.library.caltech.edu/records/s5ddn-sc375/files/mnras0367-1531-SD2.pdf" }, { "basename": "MNRAS-2006-Mazeh-1531-42.pdf", "url": "https://authors.library.caltech.edu/records/s5ddn-sc375/files/MNRAS-2006-Mazeh-1531-42.pdf" } ], "pub_year": "2006", "author_list": "Mazeh, T.; Tamuz, O.; et al." }, { "id": "https://authors.library.caltech.edu/records/z9zv5-xan08", "eprint_id": 56829, "eprint_status": "archive", "datestamp": "2023-08-19 17:39:55", "lastmod": "2026-03-09 21:51:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Sutured Heegaard diagrams for knots", "ispublished": "pub", "full_text_status": "public", "keywords": "knot Floer homology, sutured Heegaard diagram, Murasugi sum, semifibred satellite knot", "note": "\u00a9 2006 Mathematical Sciences Publishers. \n\nReceived: 22 July 2005. Revised: 13 January 2006. Accepted: 12 March 2006. Published: 2 April 2006. \n\nWe are grateful to David Gabai, Jacob Rasmussen and Zolt\u00e1n Szab\u00f3 for many stimulating discussions and encouragements. We are especially grateful to the referee for a detailed list of corrections and suggestions. \n\nThe author is partially supported by the Centennial fellowship of the Graduate School at Princeton University. Part of this work was carried out during a visit to Peking University; the author wishes to thank Shicheng Wang for his hospitality during the visit.\n\n

Published - agt-v6-n2-p01-p.pdf

", "abstract": "We define sutured Heegaard diagrams for null-homologous knots in 3\u2013manifolds. These diagrams are useful for computing the knot Floer homology at the top filtration level. As an application, we give a formula for the knot Floer homology of a Murasugi sum. Our result echoes Gabai's earlier works. We also show that for so-called \"semifibred\" satellite knots, the top filtration term of the knot Floer homology is isomorphic to the counterpart of the companion.", "date": "2006-04-02", "date_type": "published", "publication": "Algebraic and Geometric Topology", "volume": "6", "number": "2", "publisher": "Geometry & Topology Publications", "pagerange": "513-537", "id_number": "CaltechAUTHORS:20150421-115913176", "issn": "1472-2747", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115913176", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Princeton University" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2140/agt.2006.6.513", "primary_object": { "basename": "agt-v6-n2-p01-p.pdf", "url": "https://authors.library.caltech.edu/records/z9zv5-xan08/files/agt-v6-n2-p01-p.pdf" }, "pub_year": "2006", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/6ap12-1wh22", "eprint_id": 24746, "eprint_status": "archive", "datestamp": "2023-08-22 05:26:29", "lastmod": "2026-04-13 18:19:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Ramachandran-N", "name": { "family": "Ramachandran", "given": "Niranjan" } } ] }, "title": "KMS states and complex multiplication", "ispublished": "pub", "full_text_status": "public", "keywords": "KMS states; K-lattices; complex multiplication; explicit class field theory; quantum statistical mechanics", "note": "\u00a9 2005 Birkha\u00fcser Verlag Basel/Switzerland.\nPublished online December 28, 2005.\n\n

Submitted - 0501424.pdf

", "abstract": "We construct a quantum statistical mechanical system which generalizes the Bost\u2013Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the explicit class field theory for such fields. This system admits the Dedekind zeta function as partition function and the id\u00e8le class group as group of symmetries. The extremal KMS states at zero temperature intertwine this symmetry with the Galois action on the values of the states on the arithmetic subalgebra. The geometric notion underlying the construction is that of commensurability of K-lattices.", "date": "2006-04", "date_type": "published", "publication": "Selecta Mathematica - New Series", "volume": "11", "number": "3-4", "publisher": "Springer", "pagerange": "325-347", "id_number": "CaltechAUTHORS:20110808-140919868", "issn": "1022-1824", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110808-140919868", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00029-005-0013-x", "primary_object": { "basename": "0501424.pdf", "url": "https://authors.library.caltech.edu/records/6ap12-1wh22/files/0501424.pdf" }, "pub_year": "2006", "author_list": "Connes, Alain; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/najt2-z6t81", "eprint_id": 2323, "eprint_status": "archive", "datestamp": "2023-08-22 13:31:30", "lastmod": "2026-04-14 03:51:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Berkooz-M", "name": { "family": "Berkooz", "given": "Micha" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "New IR dualities in supersymmetric gauge theory in three dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "field theories in lower dimensions; duality in gauge field theories; M-theory, orientifolds", "note": "Copyright \u00a9 Institute of Physics and IOP Publishing Limited 1999. \n\nReceived 14 December 1998, accepted for publication 10 February 1999. Published 6 April 1999. \n\nWe would like to thank J. Park, N. Seiberg, S. Sethi, and E. Witten for helpful discussions. We are especially grateful to K. Intriligator for patient explanations of his work. The work of M.B. is supported by NSF grant PHY-9513835; that of A.K. by DOE grant DE-FG02-90ER40542.\n\n

Published - BERjhep99.pdf

", "abstract": "We present nontrivial examples of d = 3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the gauge theories of interest using D2-branes and orientifolds and then consider their lift to M-theory. We also discuss the strong coupling limit of orientifold two-planes and orbifolds of orientifold six-planes.", "date": "2006-03-27", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1999", "number": "2", "publisher": "Springer", "pagerange": "Art. No. 009", "id_number": "CaltechAUTHORS:BERjhep99", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BERjhep99", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1999/02/009", "primary_object": { "basename": "BERjhep99.pdf", "url": "https://authors.library.caltech.edu/records/najt2-z6t81/files/BERjhep99.pdf" }, "pub_year": "2006", "author_list": "Berkooz, Micha and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/bs5y2-6qt49", "eprint_id": 3504, "eprint_status": "archive", "datestamp": "2023-08-22 05:24:02", "lastmod": "2026-04-16 01:40:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Topological Entanglement Entropy", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum entanglement; quantum field theory; ground states; entropy; many-body problems; fermion systems", "note": "\u00a92006 The American Physical Society \n\n(Received 13 October 2005; published 24 March 2006) \n\nWe thank Anton Kapustin for discussions. This work has been supported in part by: the Department of Energy under Grant No. DE-FG03-92-ER40701, the National Science Foundation under Grant No. PHY-0456720, the Army Research Office under Grants No. W911NF-04-1-0236 and No. W911NF-05-1-0294, and the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374.", "abstract": "We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho)=alphaL-gamma+[centered ellipsis], where the ellipsis represents terms that vanish in the limit L-->[infinity]. We show that -gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.", "date": "2006-03-24", "date_type": "published", "publication": "Physical Review Letters", "volume": "96", "number": "11", "publisher": "American Physical Society", "pagerange": "Art. No. 110404", "id_number": "CaltechAUTHORS:KITprl06", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITprl06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.96.110404", "primary_object": { "basename": "KITprl06.pdf", "url": "https://authors.library.caltech.edu/records/bs5y2-6qt49/files/KITprl06.pdf" }, "pub_year": "2006", "author_list": "Kitaev, Alexei and Preskill, John" }, { "id": "https://authors.library.caltech.edu/records/wh2az-ps992", "eprint_id": 66975, "eprint_status": "archive", "datestamp": "2023-08-19 17:31:04", "lastmod": "2026-04-14 03:52:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Saraikin-K", "name": { "family": "Saraikin", "given": "Kirill" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Stringy wave function for an S^3 cosmology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 The American Physical Society. \n\nReceived 20 January 2006; published 21 March 2006. \n\nWe would like to thank N. Arkani-Hamed, R.Dijkgraaf, A. Neitzke, and H. Ooguri for valuable discussions. This research was supported in part by NSF Grants No. PHY-0244821 and No. DMS-0244464. K. S. and S. G. are also supported in part by RFBR Grant No. 04-02-16880.\n\n

Published - PhysRevD.73.066009.pdf

Submitted - 0505204.pdf

", "abstract": "Using the recent observations of the relation between the Hartle-Hawking wave function and the topological string partition function, we propose a wave function for scalar metric fluctuations on S^3 embedded in a Calabi-Yau manifold. This problem maps to a study of noncritical bosonic string propagating on a circle at the self-dual radius. This can be viewed as a stringy toy model for a quantum cosmology.", "date": "2006-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "73", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066009", "id_number": "CaltechAUTHORS:20160511-085455539", "issn": "1550-7998", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-085455539", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.73.066009", "primary_object": { "basename": "0505204.pdf", "url": "https://authors.library.caltech.edu/records/wh2az-ps992/files/0505204.pdf" }, "related_objects": [ { "basename": "PhysRevD.73.066009.pdf", "url": "https://authors.library.caltech.edu/records/wh2az-ps992/files/PhysRevD.73.066009.pdf" } ], "pub_year": "2006", "author_list": "Gukov, Sergei; Saraikin, Kirill; et al." }, { "id": "https://authors.library.caltech.edu/records/011h4-5f284", "eprint_id": 3166, "eprint_status": "archive", "datestamp": "2023-08-22 05:21:30", "lastmod": "2026-04-14 04:01:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Saraikin-K", "name": { "family": "Saraikin", "given": "Kirill" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Entropic principle and asymptotic freedom", "ispublished": "pub", "full_text_status": "public", "keywords": "entropy; black holes; wave functions; string theory", "note": "\u00a9 2006 The American Physical Society. \n\n(Received 20 January 2006; published 21 March 2006) \n\nWe would like to thank R. Dijkgraaf, S. Katz, A. Klemm, M. Ro\u010dek, T. Oliker and H. Ooguri for valuable discussions. We also thank B. Fiol for pointing out a sign error in the large complex structure limit example, that appeared in the first version of the paper. This research was supported in part by NSF Grant Nos. PHY-0244821 and DMS-0244464. K. S. and S. G. are also supported in part by RFBR grant 04-02-16880. We would like to thank the 2005 Simons Workshop on Mathematics and Physics for providing a stimulating environment where part of this work was done. S. G. would also like to thank the KITP at Santa Barbara for hospitality during the completion of this work. While at KITP, the research of S. G. was supported in part by the NSF under grant PHY99-07949.\n\n

Published - GUKprd06.pdf

", "abstract": "Motivated by the recent developments about the Hartle-Hawking wave function associated to black holes, we formulate an entropy functional on the moduli space of Calabi-Yau compactifications. We find that the maximization of the entropy is correlated with the appearance of asymptotic freedom in the effective field theory. The points where the entropy is maximized correspond to points on the moduli which are maximal intersection points of walls of marginal stability for Bogomolnyi-Prasad-Sommerfield states. We also find an intriguing link between extremizing the entropy functional and the points on the moduli space of Calabi-Yau three folds which admit a \"quantum deformed\" complex multiplication.", "date": "2006-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "73", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066010", "id_number": "CaltechAUTHORS:GUKprd06", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKprd06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-024446" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY99-07949" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.73.066010", "primary_object": { "basename": "GUKprd06.pdf", "url": "https://authors.library.caltech.edu/records/011h4-5f284/files/GUKprd06.pdf" }, "pub_year": "2006", "author_list": "Gukov, Sergei; Saraikin, Kirill; et al." }, { "id": "https://authors.library.caltech.edu/records/ayxmf-hpf58", "eprint_id": 5000, "eprint_status": "archive", "datestamp": "2023-08-22 05:21:49", "lastmod": "2026-04-14 03:57:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Gopakumar-R", "name": { "family": "Gopakumar", "given": "Rajesh" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Baby universes in string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "string theory; black holes; cosmology; Yang-Mills theory; space-time configurations; wave functions", "note": "\u00a9 2006 The American Physical Society \n\n(Received 7 October 2005; published 10 March 2006) \n\nWe would like to thank A. Adams, M. Aganagic, F. Denef, D. Gaiotto, D. Gross, G. Horowitz, R. Kallosh, M. Kardar, A. Linde, A. Maloney, J. Maldacena, G. Moore, L. Motl, J. Polchinski, J. Preskill, E. Silverstein, A. Strominger, and E. Verlinde for useful discussions. R.D. and H.O. want to thank the Harvard Physics Department for kind hospitality. H.O. also thanks the Institute for Theoretical Physics at the University of Amsterdam for kind hospitality. The research of R.D. was supported by a NWO Spinoza grant and the FOM program String Theory and Quantum Gravity. R.G.'s research has been generously supported by the citizens of India. The research of H.O. was supported in part by DOE Grant No. DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF Grants No. PHY-0244821 and No. DMS-0244464.\n\n

Published - DIJprd06.pdf

Submitted - 0504221.pdf

", "abstract": "We argue that the holographic description of four-dimensional Bogomol'nyi-Prasad-Sommerfield black holes naturally includes multicenter solutions. This suggests that the holographic dual to the gauge theory is not a single AdS2\u00d7S2 but a coherent ensemble of them. We verify this in a particular class of examples, where the two-dimensional Yang-Mills theory gives a holographic description of the black holes obtained by branes wrapping Calabi-Yau cycles. Using the free fermionic formulation, we show that O(e-N) nonperturbative effects entangle the two Fermi surfaces. In an Euclidean description, the wave function of the multicenter black holes gets mapped to the Hartle-Hawking wave function of baby universes. This provides a concrete realization, within string theory, of effects that can be interpreted as the creation of baby universes. We find that, at least in the case we study, the baby universes do not lead to a loss of quantum coherence, in accord with general arguments.", "date": "2006-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "73", "number": "6", "publisher": "American Physical Society", "pagerange": "Art. No. 066002", "id_number": "CaltechAUTHORS:DIJprd06", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:DIJprd06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" }, { "agency": "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "other_numbering_system": { "items": [ { "id": "68-2557", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.73.066002", "primary_object": { "basename": "0504221.pdf", "url": "https://authors.library.caltech.edu/records/ayxmf-hpf58/files/0504221.pdf" }, "related_objects": [ { "basename": "DIJprd06.pdf", "url": "https://authors.library.caltech.edu/records/ayxmf-hpf58/files/DIJprd06.pdf" } ], "pub_year": "2006", "author_list": "Dijkgraaf, Robbert; Gopakumar, Rajesh; et al." }, { "id": "https://authors.library.caltech.edu/records/cw614-xfy70", "eprint_id": 3919, "eprint_status": "archive", "datestamp": "2023-08-22 05:19:53", "lastmod": "2026-04-16 01:40:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kempe-J", "name": { "family": "Kempe", "given": "Julia" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Regev-O", "name": { "family": "Regev", "given": "Oded" } } ] }, "title": "The Complexity of the Local Hamiltonian Problem", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum computation, local Hamiltonian problem, complete problems, adiabatic computation", "note": "\u00a9 2006 SIAM \n\nReceived by the editors July 20, 2004; accepted for publication (in revised form) June 23, 2005; published electronically March 3, 2006. A preliminary version of this paper appeared in Proceedings of the 24th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS), 2004. \n\nThis author's [JK] work was supported by ACI S\u00e9curit\u00e9 Informatique, 2003-n24; projet \"R\u00e9seaux Quantiques,\" ACI-CR 2002-40 and EU 5th framework program RESQ IST-2001-37559; by DARPA and Air Force Laboratory, Air Force Materiel Command, USAF, under agreement F30602-01-2-0524; by DARPA and the Office of Naval Research under grant FDN-00014-01-1-0826; and during a visit supported in part by the National Science Foundation under grant EIA-0086038 through the Institute for Quantum Information at the California Institute of Technology. \n\nThis author's [AK] work was supported in part by the National Science Foundation under grant EIA-0086038. \n\nThis author's [OR] work was supported by an Alon Fellowship, the Binational Science Foundation, the Israel Science Foundation, and the Army Research Office grant DAAD19-03-1-0082 and partly supported by ACI S\u00e9curit\u00e9 Informatique, 2003-n24, projet \"R\u00e9seaux Quantiques.\" Part of this author's work was carried out during a visit at LRI, Universit\u00e9 de Paris-Sud, and he thanks his hosts for their hospitality. \n\nDiscussions with Sergey Bravyi and Frank Verstraete are gratefully acknowledged.\n\n

Published - KEMsiamjc06.pdf

Submitted - 0406180.pdf

", "abstract": "The k-LOCAL Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analogue of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k >= 2. It was known that the problem is QMA-complete for any k >= 3. On the other hand, 1-LOCAL Hamiltonian is in P and hence not believed to be QMA-complete. The complexity of the 2-LOCAL Hamiltonian problem has long been outstanding. Here we settle the question and show that it is QMA-complete. We provide two independent proofs; our first proof uses only elementary linear algebra. Our second proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. Using our techniques we also show that adiabatic computation with 2-local interactions on qubits is equivalent to standard quantum computation.", "date": "2006-03-03", "date_type": "published", "publication": "SIAM Journal on Computing", "volume": "35", "number": "5", "publisher": "SIAM", "pagerange": "1070-1097", "id_number": "CaltechAUTHORS:KEMsiamjc06", "issn": "0097-5397", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KEMsiamjc06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1137/S0097539704445226", "primary_object": { "basename": "0406180.pdf", "url": "https://authors.library.caltech.edu/records/cw614-xfy70/files/0406180.pdf" }, "related_objects": [ { "basename": "KEMsiamjc06.pdf", "url": "https://authors.library.caltech.edu/records/cw614-xfy70/files/KEMsiamjc06.pdf" } ], "pub_year": "2006", "author_list": "Kempe, Julia; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/3y99p-gqe61", "eprint_id": 3140, "eprint_status": "archive", "datestamp": "2023-08-22 05:08:44", "lastmod": "2026-04-16 01:40:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aharonov-D", "name": { "family": "Aharonov", "given": "Dorit" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Fault-Tolerant Quantum Computation with Long-Range Correlated Noise", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum computing; quantum noise; fault tolerant computing", "note": "\u00a92006 The American Physical Society \n\n(Received 31 October 2005; published 7 February 2006) \n\nWe thank Daniel Gottesman for helpful comments. This work has been supported in part by DOE under Grant No. DE-FG03-92-ER40701, NSF under Grant No. PHY-0456720, ARO under Grants No. W911NF-04-1-0236, No. W911NF-05-1-0294, and No. DAAD19-00-1-0374, ISF under Grants No. 032-9739 and No. 039-7549, the U.S. Army under Grant No. 030-7657, and the Council of Higher Education in Israel under Grant No. 033-7233.", "abstract": "We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r^D.", "date": "2006-02-10", "date_type": "published", "publication": "Physical Review Letters", "volume": "96", "number": "5", "publisher": "American Physical Society", "pagerange": "Art. No. 050504", "id_number": "CaltechAUTHORS:AHAprl06", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:AHAprl06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.96.050504", "primary_object": { "basename": "AHAprl06.pdf", "url": "https://authors.library.caltech.edu/records/3y99p-gqe61/files/AHAprl06.pdf" }, "pub_year": "2006", "author_list": "Aharonov, Dorit; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/wg6v4-ht550", "eprint_id": 2160, "eprint_status": "archive", "datestamp": "2023-08-22 04:58:49", "lastmod": "2026-04-16 01:40:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bonderson-P", "name": { "family": "Bonderson", "given": "Parsa" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Shtengel-K", "name": { "family": "Shtengel", "given": "Kirill" } } ] }, "title": "Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum Hall effect; interferometry; quasiparticles", "note": "\u00a92006 The American Physical Society \n\n(Received 30 August 2005; published 6 January 2006) \n\nThe authors would like to thank W. Bishara, N. Bonesteel, C. Chamon, J. Eisenstein, E. Fradkin, F. D. M. Haldane, S. Simon, N.-C. Yeh, and especially C. Nayak for many illuminating discussions. This work was supported in part by the NSF under Grant No. EIA-0086038 and the ARO under Grant No. W911NF-04-1-0236. K. S. would also like to acknowledge the hospitality of the Aspen Center for Physics.", "abstract": "In this Letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics\u2014one of the hallmark characteristics of the Moore-Read state expected to describe the observed fractional quantum Hall effect plateau at nu=5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et al. are also addressed.", "date": "2006-01-13", "date_type": "published", "publication": "Physical Review Letters", "volume": "96", "number": "1", "publisher": "American Physical Society", "pagerange": "Art. No. 016803", "id_number": "CaltechAUTHORS:BONprl06.799", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BONprl06.799", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.96.016803", "primary_object": { "basename": "BONprl06.pdf", "url": "https://authors.library.caltech.edu/records/wg6v4-ht550/files/BONprl06.pdf" }, "pub_year": "2006", "author_list": "Bonderson, Parsa; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/zg25p-56b04", "eprint_id": 78930, "eprint_status": "archive", "datestamp": "2023-08-19 17:12:05", "lastmod": "2026-04-13 18:10:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "D." }, "orcid": "0000-0001-5924-3849" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Jost functions and Jost solutions for Jacobi matrices, II. Decay and analyticity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Oxford University Press. \n\nReceived 24 October 2005; Revised 8 March 2006; Accepted 9 March 2006. \n\nThe first author is supported in part by NSF Grant DMS-0227089. The second author is supported in part by NSF Grant DMS-0140592.\n\n

Submitted - 0502487.pdf

", "abstract": "We present necessary and sufficient conditions on the Jost function for the corresponding Jacobi parameters an \u2212 1 and bn to have a given degree of exponential decay.", "date": "2006-01-01", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2006", "publisher": "Oxford University Press", "pagerange": "Art. No. 19396", "id_number": "CaltechAUTHORS:20170711-081744987", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170711-081744987", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0227089" }, { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1155/IMRN/2006/19396", "primary_object": { "basename": "0502487.pdf", "url": "https://authors.library.caltech.edu/records/zg25p-56b04/files/0502487.pdf" }, "pub_year": "2006", "author_list": "Damanik, D. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/80402-gxn02", "eprint_id": 83003, "eprint_status": "archive", "datestamp": "2023-08-19 17:10:59", "lastmod": "2026-03-09 23:07:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Nagao-Taro", "name": { "family": "Nagao", "given": "Taro" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Correlation functions for random involutions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Hindawi Publishing Corporation.\n\nReceived: 31 August 2005; Revision Received: 15 March 2006;\nAccepted: 30 May 2006; Published: 01 January 2006.\n\nOne of the authors (T.N.) is grateful to Dr. Tomohiro Sasamoto for valuable discussions. The referee is to be thanked for some useful suggestions. The work of PJF was supported by the Australian Research Council.\n\n

Submitted - 0503074.pdf

", "abstract": "Our interest is in the scaled joint distribution associated with k-increasing subsequences for random involutions with a prescribed number of fixed points. We proceed by specifying in terms of correlation functions the same distribution for a Poissonized model in which both the number of symbols in the involution and the number of fixed points are random variables. From this, a de-Poissonization argument yields the scaled correlations and distribution function for the random involutions. These are found to coincide with the same quantities known in random matrix theory from the study of ensembles interpolating between the orthogonal and symplectic universality classes at the soft edge, the interpolation being due to a rank 1 perturbation.", "date": "2006-01", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2006", "publisher": "Oxford University Press", "pagerange": "Art. No. 89796", "id_number": "CaltechAUTHORS:20171106-151415738", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-151415738", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1155/IMRN/2006/89796", "primary_object": { "basename": "0503074.pdf", "url": "https://authors.library.caltech.edu/records/80402-gxn02/files/0503074.pdf" }, "pub_year": "2006", "author_list": "Forrester, Peter J.; Nagao, Taro; et al." }, { "id": "https://authors.library.caltech.edu/records/aw0e1-bab18", "eprint_id": 22468, "eprint_status": "archive", "datestamp": "2023-08-22 04:52:44", "lastmod": "2026-03-09 21:43:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Quantum fields and motives", "ispublished": "pub", "full_text_status": "public", "keywords": "perturbative renormalization; Hopf algebras and affine group schemes; equisingular connections; irregular Riemann-Hilbert correspondence; motives; motivic Galois groups", "note": "\u00a9 2005 Elsevier B.V. Received 22 March 2005; accepted 13 April 2005; Available online 25 May 2005.\n\n

Submitted - 0504085.pdf

", "abstract": "This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field theories share a common universal symmetry realized as a motivic Galois group, whose action is dictated by the divergences and generalizes that of the renormalization group. The existence of such a group was conjectured by P. Cartier based on number theoretic evidence and on the Connes-Kreimer theory of perturbative renormalization. The group provides a universal formula for counterterms and is obtained via a Riemann-Hilbert correspondence classifying equivalence classes of flat equisingular bundles, where the equisingularity condition corresponds to the independence of the counterterms on the mass scale.", "date": "2006-01", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "56", "number": "1", "publisher": "Elsevier", "pagerange": "55-85", "id_number": "CaltechAUTHORS:20110224-082841783", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110224-082841783", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2005.04.004", "primary_object": { "basename": "0504085.pdf", "url": "https://authors.library.caltech.edu/records/aw0e1-bab18/files/0504085.pdf" }, "pub_year": "2006", "author_list": "Connes, Alain and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/63zzg-arw72", "eprint_id": 22467, "eprint_status": "archive", "datestamp": "2023-08-22 04:52:35", "lastmod": "2026-03-09 21:37:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Q-lattices: Quantum statistical mechanics and Galois theory", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Q-lattices; quantum statistical mechanics; KMS states; class field theory; modular field; Shimura varieties", "note": "\u00a9 2005 Elsevier B.V. Received 22 March 2005; accepted 13 April 2005; Available online 4 June 2005.", "abstract": "We review our recent results on the noncommutative geometry of Q-lattices modulo commensurability. We discuss the cases of 1-dimensional and 2-dimensional Q-lattices. In the first case, we show that, by considering commensurability classes of 1-dimensional Q-lattices up to scaling, one recovers the Bost-Connes quantum statistical mechanical system, whose zero temperature KMS states intertwine the symmetries of the system with the Galois action of Gal(Q/Q). In the 2-dimensional case, commensurability classes of Q-lattices up to scaling give rise to another quantum statistical mechanical system, whose symmetries are the automorphisms of the modular field, and whose (generic) zero temperature KMS states intertwine the action of these symmetries with the Galois action on an embedding in C of the modular field. Following our joint work with Ramachandran, we then show how the noncommutative spaces associated to commensurability classes of Q-lattices up to scale have a natural geometric interpretation as noncommutative versions of the Shimura varieties Sh(GL_1,{\u00b11}) in the Bost-Connes case and Sh(GL_2, H^\u00b1) in the case of the GL_2 system. We also show how this leads naturally to the construction of a system generalizing the Bost-Connes system that fully recovers the explicit class field theory of imaginary quadratic fields.", "date": "2006-01", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "56", "number": "1", "publisher": "Elsevier", "pagerange": "2-23", "id_number": "CaltechAUTHORS:20110224-082841614", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110224-082841614", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.geomphys.2005.04.010", "pub_year": "2006", "author_list": "Connes, Alain and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/rjsfj-tjw47", "eprint_id": 83004, "eprint_status": "archive", "datestamp": "2023-08-19 17:11:04", "lastmod": "2026-03-09 23:05:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Jacobians and rank 1 perturbations relating to unitary Hessenberg matrices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Hindawi Publishing Corporation. \n\nReceived: 27 May 2005; Revision Received: 06 January 2006; Accepted: 08 February 2006; Published: 01 January 2006. \n\nSupported by the Australian Research Council.\n\n

Submitted - 0505552.pdf

", "abstract": "Killip and Nenciu gave random recurrences for the characteristic polynomials of certain unitary and real orthogonal upper Hessenberg matrices. The corresponding eigenvalue probability density functions (p.d.f's) are \u03b2-generalizations of the classical groups. Left open was the direct calculation of certain Jacobians. We provide the sought direct calculation. Furthermore, we show how a multiplicative rank 1 perturbation of the unitary Hessenberg matrices provides a joint eigenvalue p.d.f. generalizing the circular \u03b2-ensemble, and we show how this joint density is related to known interrelations between circular ensembles. Projecting the joint density onto the real line leads to the derivation of a random three-term recurrence for polynomials with zeros distributed according to the circular Jacobi \u03b2-ensemble.", "date": "2006-01", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2006", "publisher": "Oxford University Press", "pagerange": "Art. No. 48306", "id_number": "CaltechAUTHORS:20171106-151903451", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-151903451", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1155/IMRN/2006/48306", "primary_object": { "basename": "0505552.pdf", "url": "https://authors.library.caltech.edu/records/rjsfj-tjw47/files/0505552.pdf" }, "pub_year": "2006", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/zxskn-0rq20", "eprint_id": 2444, "eprint_status": "archive", "datestamp": "2023-08-22 04:51:20", "lastmod": "2026-04-16 01:40:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Anyons in an exactly solved model and beyond", "ispublished": "pub", "full_text_status": "public", "note": "Author preprint; arXiv.org/abs/cond-mat/0506438 \n\nDuring the years this work was in progress I received genuine interest and words of encouragement from John Preskill, Michael Freedman, Mikhail Feigelman, Grigory Volovik, and many other people. I thank Andreas Ludwig for having convinced me in the importance of the chiral central charge in the study of topological order. A conversation with Dmitri Ivanov was essential for understanding the difference between non-Abelian anyons and Majorana vortices in two-dimensional p-wave superconductors. I also thank Matthew Fisher, Nicholas Read, and Xiao-Gang Wen for helpful discussions. I am especially grateful to Jean Bellissard who read a preliminary version of the manuscript and made some valuable comments; in particular, he directed me to Ref. [50]. This work was supported in part by the National Science Foundation under Grant No. EIA-0086038 and by the Army Research Office under grant No. W911NF-04-1-0236. \n\nPublished article: \n\nAlexei Kitaev (2006) Anyons in an exactly solved model and beyond. Annals of Physics 321:2-111\n\n

Submitted - KITaop06.pdf

", "abstract": "A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z2 source gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number \u03bd. The Abelian and non-Abelian phases of the original model correspond to \u03bd = 0 and \u03bd = \u00b11, respectively. The anyonic properties of excitation depend on \u03bd mod 16, whereas \u03bd itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.", "date": "2006-01", "date_type": "published", "publication": "Annals of Physics", "volume": "321", "number": "1", "publisher": "Elsevier", "pagerange": "2-111", "id_number": "CaltechAUTHORS:KITaop06", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITaop06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.aop.2005.10.005", "primary_object": { "basename": "KITaop06.pdf", "url": "https://authors.library.caltech.edu/records/zxskn-0rq20/files/KITaop06.pdf" }, "pub_year": "2006", "author_list": "Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/2g55t-2j491", "eprint_id": 79429, "eprint_status": "archive", "datestamp": "2023-08-19 17:10:34", "lastmod": "2026-03-18 00:09:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Aizenman's Theorem for Orthogonal Polynomials on the Unit Circle", "ispublished": "pub", "full_text_status": "public", "keywords": "OPUC, Random Verblunsky coefficients, Localization", "note": "\u00a9 Springer 2005. \n\nDate received: September 27, 2004. Date accepted: February 8, 2005. Online publication: June 3, 2005. \n\nCommunicated by Percy A. Deift. \n\nSupported in part by NSF grant DMS-0140592. I would like to thank Mihai Stoiciu for useful discussions.\n\n

Submitted - 0411388.pdf

", "abstract": "For suitable classes of random Verblunsky coefficients, including independent, identically distributed, rotationally invariant ones, we prove that if E(\u23b0d\u03b8\\2\u03c0\u2502(C+e^(i\u03b8) C-e^(i\u03b8)_(k\u2113)\u2502^p)\u2264 C_(le)^kl\u2223k-\u2113\u2223 for some k_l > 0 and p < 1, then for suitable C_2 and k_2 > 0, E(sup_n\u2223(C^n)_k\u2113\u2223) \u2264C_2e^(-k_2\u2223k-\u2113\u2223. Here C is the CMV matrix.", "date": "2006-01", "date_type": "published", "publication": "Constructive Approximation", "volume": "23", "number": "2", "publisher": "Springer", "pagerange": "229-240", "id_number": "CaltechAUTHORS:20170726-134636444", "issn": "0176-4276", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170726-134636444", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00365-005-0599-4", "primary_object": { "basename": "0411388.pdf", "url": "https://authors.library.caltech.edu/records/2g55t-2j491/files/0411388.pdf" }, "pub_year": "2006", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/68y9k-a6z05", "eprint_id": 82015, "eprint_status": "archive", "datestamp": "2023-08-19 17:07:09", "lastmod": "2026-03-09 23:05:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "BC_n-symmetric abelian functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Duke University Press. \n\nReceived 21 April 2005. Revision received 7 February 2006. \n\nAuthor's work supported in part by National Science Foundation grant DMS-0403187. \n\nWe thank R. Gustafson, A. Okounkov, H. Rosengren, S. Sahi, and V. Spiridonov for enlightening conversations related to this work.\n\n

Submitted - 0402113.pdf

", "abstract": "We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials (see [10]) and prove a number of their properties, most notably analogues of Macdonald's conjectures. The construction is based on a direct construction for a special case generalizing Okounkov's interpolation polynomials (see [13]). We show that these interpolation functions satisfy a collection of generalized hypergeometric identities, including new multivariate elliptic analogues of Jackson's summation and Bailey's transformation.", "date": "2006", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "135", "number": "1", "publisher": "Duke University Press", "pagerange": "99-180", "id_number": "CaltechAUTHORS:20171003-154931716", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-154931716", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0403187" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0402113", "primary_object": { "basename": "0402113.pdf", "url": "https://authors.library.caltech.edu/records/68y9k-a6z05/files/0402113.pdf" }, "pub_year": "2006", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/bsa63-djf41", "eprint_id": 8433, "eprint_status": "archive", "datestamp": "2023-08-22 04:45:45", "lastmod": "2026-03-18 00:01:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Fine structure of the zeros of orthogonal polynomials, I. A tale of two pictures", "ispublished": "pub", "full_text_status": "public", "keywords": "OPUC, clock behavior, Poisson zeros, orthogonal polynomials", "note": "\u00a9 2006, Kent State University \n\nReceived April 20, 2005. Accepted for publication August 23, 2005. Recommended by I. Pritsker. \n\nSupported in part by NSF grant DMS-0140592. \n\nElectronic Transactions on Numerical Analysis, Volume 25 (2006) - Special Volume on Constructive Function Theory. Dedicated to Ed Saff on the occasion of his 60th birthday. \n\nThis special volume of ETNA contains selected papers presented at Constructive Functions Tech-04, a conference held at the Georgia Institute of Technology, Atlanta, November 7\u20139, 2004. The conference honored the sixtieth birthday of Edward B. Saff, and the twentieth anniversary of the international journal Constructive Approximation, which he founded together with Ronald DeVore. \n\n[This paper is based on the plenary talk given by Professor Barry Simon.]\n\n

Published - SIMetna06.pdf

", "abstract": "Mhaskar-Saff found a kind of universal behavior for the bulk structure of the zeros of orthogonal polynomials for large n. Motivated by two plots, we look at the finer structure for the case of the Verblunsky coefficients and for what we call the BLS condition: \u03b1n = Cb^n + O ((b\u0394)^n). In the former case, we describe the results of Stoiciu. In the latter case, we prove asymptotically equal spacing for the bulk of zeros.", "date": "2006", "date_type": "published", "publication": "Electronic Transactions on Numerical Analysis", "volume": "25", "publisher": "Kent State University", "pagerange": "328-368", "id_number": "CaltechAUTHORS:SIMetna06", "issn": "1068-9613", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMetna06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "SIMetna06.pdf", "url": "https://authors.library.caltech.edu/records/bsa63-djf41/files/SIMetna06.pdf" }, "pub_year": "2006", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/3vjj3-nfq28", "eprint_id": 24001, "eprint_status": "archive", "datestamp": "2023-08-19 16:57:31", "lastmod": "2026-03-09 21:54:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Entropy of Small Black Holes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Publication Office of Progress of Theoretical Physics. \n\nWe would like to thank the organizers of YKIS2005 for giving me the opportunity to present this talk. The research of H. O. was supported in part by DOE grant DEEG03-92.\n\n

Published - Ooguri2006p9464Prog_Theor_Phys_Supp.pdf

", "abstract": "I will describe the relation between the entropy of extremal black holes and the topological string partition function.", "date": "2006", "date_type": "published", "publication": "Progress of Theoretical Physics Supplement", "number": "163", "publisher": "Publication Office of Progress of Theoretical Physics", "pagerange": "355-357", "id_number": "CaltechAUTHORS:20110614-104609810", "issn": "0375-9687", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110614-104609810", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1143/PTPS.163.355", "primary_object": { "basename": "Ooguri2006p9464Prog_Theor_Phys_Supp.pdf", "url": "https://authors.library.caltech.edu/records/3vjj3-nfq28/files/Ooguri2006p9464Prog_Theor_Phys_Supp.pdf" }, "pub_year": "2006", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/v8f4x-j9911", "eprint_id": 66977, "eprint_status": "archive", "datestamp": "2023-08-19 17:06:17", "lastmod": "2026-03-09 02:20:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dunfield-N-M", "name": { "family": "Dunfield", "given": "Nathan M." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Rasmussen-J", "name": { "family": "Rasmussen", "given": "Jacob" } } ] }, "title": "The Superpolynomial for Knot Homologies", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Taylor & Francis. \n\nWe are grateful to P. Etingof, B. Gornik, V. Kac, M. Khovanov, C. Manolescu, P. Ozsv\u00e1th, A. Schwarz, C. Taubes, C. Vafa, and Z. Szab\u00f3 for valuable discussions. N.D. was partially supported by NSF grant #DMS-0405491 and a Sloan Fellowship. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. J.R. was partially supported by an NSF Postdoctoral Fellowship.\n\n

Submitted - 0505662.pdf

", "abstract": "We propose a framework for unifying the sl(N) Khovanov\u2013 Rozansky homology (for all N) with the knot Floer homology. We argue that this unification should be accomplished by a triply graded homology theory that categorifies the HOMFLY polynomial. Moreover, this theory should have an additional formal structure of a family of differentials. Roughly speaking, the triply graded theory by itself captures the large-N behavior of the sl(N) homology, and differentials capture nonstable behavior for small N, including knot Floer homology. The differentials themselves should come from another variant of sl(N) homology, namely the deformations of it studied by Gornik, building on work of Lee.\n\nWhile we do not give a mathematical definition of the triply graded theory, the rich formal structure we propose is powerful enough to make many nontrivial predictions about the existing knot homologies that can then be checked directly. We include many examples in which we can exhibit a likely candidate for the triply graded theory, and these demonstrate the internal consistency of our axioms. We conclude with a detailed study of torus knots, developing a picture that gives new predictions even for the original sl(2) Khovanov homology.", "date": "2006", "date_type": "published", "publication": "Experimental Mathematics", "volume": "15", "number": "2", "publisher": "Taylor & Francis", "pagerange": "129-159", "id_number": "CaltechAUTHORS:20160511-091653426", "issn": "1058-6458", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-091653426", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0405491" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Clay Mathematics Institute" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1080/10586458.2006.10128956", "primary_object": { "basename": "0505662.pdf", "url": "https://authors.library.caltech.edu/records/v8f4x-j9911/files/0505662.pdf" }, "pub_year": "2006", "author_list": "Dunfield, Nathan M.; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/mmnvj-c4k12", "eprint_id": 11197, "eprint_status": "archive", "datestamp": "2023-08-22 04:45:50", "lastmod": "2026-03-08 18:14:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Burns-D", "name": { "family": "Burns", "given": "David" } }, { "id": "Flach-M", "name": { "family": "Flach", "given": "Matthias" }, "orcid": "0000-0002-4523-9467" } ] }, "title": "On the Equivariant Tamagawa Number Conjecture for Tate Motives, Part II", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 Documenta Mathematica. \n\nReceived: October 26, 2005. Revised: May 1, 2006. \n\nExtra Volume: John H. Coates' Sixtieth Birthday (2006).\n\n

Published - BURdm06.pdf

", "abstract": "Let K be any finite abelian extension of Q, k any subfield of K and r any integer. We complete the proof of the equivariant Tamagawa Number Conjecture for the pair (h\u2070(Spec(K))(r),Z[Gal(K/k)]).", "date": "2006", "date_type": "published", "publication": "Documenta Mathematica", "volume": "Extra", "publisher": "Documenta Mathematica", "pagerange": "133-163", "id_number": "CaltechAUTHORS:BURdm06", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BURdm06", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "BURdm06.pdf", "url": "https://authors.library.caltech.edu/records/mmnvj-c4k12/files/BURdm06.pdf" }, "pub_year": "2006", "author_list": "Burns, David and Flach, Matthias" }, { "id": "https://authors.library.caltech.edu/records/bmnrq-bc072", "eprint_id": 1172, "eprint_status": "archive", "datestamp": "2023-08-22 04:36:12", "lastmod": "2026-04-16 01:40:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Freedman-M-H", "name": { "family": "Freedman", "given": "Michael H." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Nayak-C", "name": { "family": "Nayak", "given": "Chetan" } }, { "id": "Slingerland-J-K", "name": { "family": "Slingerland", "given": "Johannes K." } }, { "id": "Walker-K", "name": { "family": "Walker", "given": "Kevin" } }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Universal manifold pairings and positivity", "ispublished": "pub", "full_text_status": "public", "keywords": "Manifold pairing, unitary, positivity, TQFT, s-cobordism", "note": "\u00a9 2005 Geometry & Topology Publications.\n\nSubmitted to G&T on 25 May 2005. (Revised 2 December 2005.) Paper accepted 3 December 2005. Paper published 10 December 2005.\n\n

Published - FREgt05.pdf

Submitted - 0503054v1.pdf

", "abstract": "Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p onto a finite dimensional quotient pairing q with values in C which in physically motivated cases is positive definite. To see if such a \"unitary\" TQFT can potentially detect any nontrivial x, we ask if is non-zero whenever x is non-zero. If this is the case, we call the pairing p positive. The question arises for each dimension d=0,1,2,.... We find p(d) positive for d=0,1, and 2 and not positive for d=4. We conjecture that p(3) is also positive. Similar questions may be phrased for (manifold, submanifold) pairs and manifolds with other additional structure. The results in dimension 4 imply that unitary TQFTs cannot distinguish homotopy equivalent simply connected 4-manifolds, nor can they distinguish smoothly s-cobordant 4-manifolds. This may illuminate the difficulties that have been met by several authors in their attempts to formulate unitary TQFTs for d=3+1. There is a further physical implication of this paper. Whereas 3-dimensional Chern-Simons theory appears to be well-encoded within 2-dimensional quantum physics, eg in the fractional quantum Hall effect, Donaldson-Seiberg-Witten theory cannot be captured by a 3-dimensional quantum system. The positivity of the physical Hilbert spaces means they cannot see null vectors of the universal pairing; such vectors must map to zero.", "date": "2005-12-10", "date_type": "published", "publication": "Geometry and Topology", "volume": "9", "number": "53", "publisher": "Geometry & Topology Publications", "pagerange": "2303-2317", "id_number": "CaltechAUTHORS:FREgt05", "issn": "1465-3060", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FREgt05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.2140/gt.2005.9.2303", "primary_object": { "basename": "0503054v1.pdf", "url": "https://authors.library.caltech.edu/records/bmnrq-bc072/files/0503054v1.pdf" }, "related_objects": [ { "basename": "FREgt05.pdf", "url": "https://authors.library.caltech.edu/records/bmnrq-bc072/files/FREgt05.pdf" } ], "pub_year": "2005", "author_list": "Freedman, Michael H.; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/t97ew-cbs38", "eprint_id": 98909, "eprint_status": "archive", "datestamp": "2023-08-19 16:47:56", "lastmod": "2026-04-14 21:51:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } }, { "id": "Verlinde-E-P", "name": { "family": "Verlinde", "given": "Erik" } } ] }, "title": "Hartle-Hawking Wave-Function for Flux Compactifications: the Entropic Principle", "ispublished": "pub", "full_text_status": "public", "keywords": "topological string, mini-superspace, black hole, BPS state", "note": "\u00a9 Springer 2005. \n\n(Received: 21 March 2005) \n\nWe would like to thank F. Denef, R. Dijkgraaf, G. Gibbons, R. Gopakumar, S. Gukov, G. Mandal, S. Minwalla, L. Motl, A. Neitzke, J. Preskill, A. Strominger, and L. Susskind for useful discussions. \n\nThe research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\n

Accepted Version - 0502211.pdf

", "abstract": "We argue that the topological string partition function, which has been known to correspond to a wave-function, can be interpreted as an exact \"wave-function of the universe\" in the mini-superspace sector of physical superstring theory. This realizes the idea of Hartle and Hawking in the context of string theory, including all loop quantum corrections. The mini-superspace approximation is justified as an exact description of BPS quantities. Moreover this proposal leads to a conceptual explanation of the recent observation that the black hole entropy is the square of the topological string wave-function. This wave-function can be interpreted in the context of flux compactification of all spatial dimensions as providing a physical probability distribution on the moduli space of string compactification. Euclidean time is realized holographically in this setup.", "date": "2005-12", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "74", "number": "3", "publisher": "Springer", "pagerange": "311-342", "id_number": "CaltechAUTHORS:20190927-133504041", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190927-133504041", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "other_numbering_system": { "items": [ { "id": "68-2543", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-005-0022-x", "primary_object": { "basename": "0502211.pdf", "url": "https://authors.library.caltech.edu/records/t97ew-cbs38/files/0502211.pdf" }, "pub_year": "2005", "author_list": "Ooguri, Hirosi; Vafa, Cumrun; et al." }, { "id": "https://authors.library.caltech.edu/records/caxzk-qqg81", "eprint_id": 81990, "eprint_status": "archive", "datestamp": "2023-08-22 04:23:52", "lastmod": "2026-04-14 18:55:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borodin-A", "name": { "family": "Borodin", "given": "Alexei" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Eynard\u2013Mehta Theorem, Schur Process, and their Pfaffian Analogs", "ispublished": "pub", "full_text_status": "public", "keywords": "Eynard\u2013Mehta theorem; Schur process; determinantal and pfaffian point processes", "note": "\u00a9 2005 Springer Science+Business Media, Inc. \n\nReceived February 11, 2005; accepted June 17, 2005. \n\nThis research was partially conducted during the period one of the authors (A.B.) served as a Clay Mathematics Institute Research Fellow. He was also partially supported by the NSF grant DMS-0402047. E. R. would like to thank J. Stembridge for introducing him to the elementary\nproof of the Cauchy\u2013Binet identity generalized by the present arguments.\n\n

Submitted - 0409059.pdf

", "abstract": "We give simple linear algebraic proofs of the Eynard\u2013Mehta theorem, the Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set.", "date": "2005-11", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "121", "number": "3-4", "publisher": "Springer", "pagerange": "291-317", "id_number": "CaltechAUTHORS:20171003-102643862", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-102643862", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "NSF", "grant_number": "DMS-0402047" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s10955-005-7583-z", "primary_object": { "basename": "0409059.pdf", "url": "https://authors.library.caltech.edu/records/caxzk-qqg81/files/0409059.pdf" }, "pub_year": "2005", "author_list": "Borodin, Alexei and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/38qww-ejv63", "eprint_id": 105400, "eprint_status": "archive", "datestamp": "2023-08-22 04:19:10", "lastmod": "2026-04-14 21:03:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Highly complex proofs and implications of such proofs", "ispublished": "pub", "full_text_status": "restricted", "keywords": "complex; proof; simple group; classification", "note": "\u00a9 2005 The Royal Society. \n\nDiscussion Meeting Issue 'The nature of mathematical proof' organized by A. Bundy, M. Atiyah, A. Macintyre and D. Mackenzie.\n\nThis work was partially supported by NSF-0203417.", "abstract": "Conventional wisdom says the ideal proof should be short, simple, and elegant. However there are now examples of very long, complicated proofs, and as mathematics continues to mature, more examples are likely to appear. Such proofs raise various issues. For example it is impossible to write out a very long and complicated argument without error, so is such a 'proof' really a proof? What conditions make complex proofs necessary, possible, and of interest? Is the mathematics involved in dealing with information rich problems qualitatively different from more traditional mathematics?", "date": "2005-10-15", "date_type": "published", "publication": "Philosophical Transactions A: Mathematical, Physical and Engineering Sciences", "volume": "363", "number": "1835", "publisher": "Royal Society of London", "pagerange": "2401-2406", "id_number": "CaltechAUTHORS:20200916-090615838", "issn": "1364-503X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200916-090615838", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0203417" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1098/rsta.2005.1655", "pub_year": "2005", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/80mzw-v9z82", "eprint_id": 66974, "eprint_status": "archive", "datestamp": "2023-08-19 16:27:34", "lastmod": "2026-04-14 22:15:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Schwarz-A", "name": { "family": "Schwarz", "given": "Albert" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Khovanov-Rozansky Homology and Topological Strings", "ispublished": "pub", "full_text_status": "public", "keywords": "knots, quantum group invariants, knot homology, topological strings, BPS states", "note": "\u00a9 Springer 2005. \n\nReceived: 21 March 2005. \n\nDedicated to the memory of F.A. Berezin. \n\nWe would like to thank D. Bar-Natan, R. Dijkgraaf, M. Gross, K. Intriligator, A. Kapustin, M. Khovanov, A. Klemm, M. Mari\u00f1o, H. Ooguri, J. Roberts and D. Thurston for useful discussions. S.G. would also like to thank the Caltech Particle Theory Group for kind hospitality. The work of A.S. is supported by NSF grant DMS-0204927. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 04-02-16880. The work of C.V. is supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\n

Submitted - 0412243.pdf

", "abstract": "We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot homology groups and suggests that they can be interpreted directly in topological string theory. We use this approach in various examples to predict the sl(N) knot homology groups for all values of N. We verify that our predictions pass some non-trivial checks.", "date": "2005-10", "date_type": "published", "publication": "Letters in Mathematical Physics", "volume": "74", "number": "1", "publisher": "Springer", "pagerange": "53-74", "id_number": "CaltechAUTHORS:20160511-085302183", "issn": "0377-9017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-085302183", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0204927" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s11005-005-0008-8", "primary_object": { "basename": "0412243.pdf", "url": "https://authors.library.caltech.edu/records/80mzw-v9z82/files/0412243.pdf" }, "pub_year": "2005", "author_list": "Gukov, Sergei; Schwarz, Albert; et al." }, { "id": "https://authors.library.caltech.edu/records/sjzw9-jjm37", "eprint_id": 75867, "eprint_status": "archive", "datestamp": "2023-08-19 16:28:12", "lastmod": "2026-04-14 18:34:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Totik-V", "name": { "family": "Totik", "given": "Vilmos" } } ] }, "title": "Limits of zeros of orthogonal polynomials on the circle", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials, unit circle, zeros, density of zeros, universal measure, degree theory", "note": "\u00a9 2005 WILEY-VCH. \n\nReceived 8 April 2004, accepted 9 August 2004. Published online 8 September 2005. \n\nDedicated to the memory of F. V. Atkinson. \n\nAcknowledgements The first named author was supported in part by NSF grant DMS-0140592 and the second named author was supported by NSF grant DMS-0097484 and by OTKA T/034323, TS44782.\n\n

Submitted - 0404535.pdf

", "abstract": "We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials. This follows from an extension of a result of Alfaro and Vigil (which answered a question of P. Tur\u00e1n): namely, for n < N , one can freely prescribe the n -th polynomial and N \u2013 n zeros of the N -th one. We shall also describe all possible limit sets of zeros within the unit disk.", "date": "2005-10", "date_type": "published", "publication": "Mathematische Nachrichten", "volume": "278", "number": "12-13", "publisher": "Wiley", "pagerange": "1615-1620", "id_number": "CaltechAUTHORS:20170408-133653793", "issn": "1522-2616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170408-133653793", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "NSF", "grant_number": "DMS-0097484" }, { "agency": "Hungarian Scientific Research Fund (OTKA)", "grant_number": "T/034323" }, { "agency": "Hungarian Scientific Research Fund (OTKA)", "grant_number": "TS44782" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1002/mana.200410326", "primary_object": { "basename": "0404535.pdf", "url": "https://authors.library.caltech.edu/records/sjzw9-jjm37/files/0404535.pdf" }, "pub_year": "2005", "author_list": "Simon, Barry and Totik, Vilmos" }, { "id": "https://authors.library.caltech.edu/records/vk61j-8s282", "eprint_id": 56962, "eprint_status": "archive", "datestamp": "2023-08-19 16:23:50", "lastmod": "2026-04-14 18:28:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "On the cohomology of certain PEL-type Shimura varieties", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Duke University Press. \n\nReceived 26 November 2003. Revision received 9 November 2004. \n\nThe author thanks Frans Oort and Richard Taylor for their continuous interest and suggestions.\n\n

Submitted - PEL.pdf

", "abstract": "In this article we study the local geometry at a prime p of PEL-type Shimura varieties for which there is a hyperspecial level subgroup. We consider the Newton polygon stratification of the special fiber at p of Shimura varieties and show that each Newton polygon stratum can be described in terms of the products of the reduced fibers of the corresponding PEL-type Rapoport-Zink spaces with certain smooth varieties (which we call Igusa varieties) and of the action on them of a p-adic group that depends on the stratum. We then extend our construction to characteristic zero and, in the case of bad reduction at p, use it to compare the vanishing cycle sheaves of the Shimura varieties to those of the Rapoport-Zink spaces. As a result of this analysis, in the case of proper Shimura varieties we obtain a description of the l-adic cohomology of the Shimura varieties in terms of the l-adic cohomology with compact supports of the Igusa varieties and of the Rapoport-Zink spaces for any prime l\u2260p.", "date": "2005-09-15", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "129", "number": "3", "publisher": "Duke University Press", "pagerange": "573-610", "id_number": "CaltechAUTHORS:20150424-130425079", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150424-130425079", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/S0012-7094-05-12935-0", "primary_object": { "basename": "PEL.pdf", "url": "https://authors.library.caltech.edu/records/vk61j-8s282/files/PEL.pdf" }, "pub_year": "2005", "author_list": "Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/zxgzx-62712", "eprint_id": 79425, "eprint_status": "archive", "datestamp": "2023-08-19 16:19:34", "lastmod": "2026-04-14 18:18:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "David" }, "orcid": "0000-0001-5924-3849" }, { "id": "Killip-R", "name": { "family": "Killip", "given": "Rowan" }, "orcid": "0000-0002-4272-7916" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Schr\u00f6dinger Operators with Few Bound States", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag 2005. \n\nReceived: 16 August 2004. Accepted: 28 January 2005. Published online: 2 June 2005. \n\nD. D. was supported in part by NSF grant DMS\u20130227289. \n\nR. K. was supported in part by NSF grant DMS\u20130401277. \n\nB. S. was supported in part by NSF grant DMS\u20130140592. \n\nIt is our pleasure to thank Y. Pinchover and A. V. Sobolev for useful comments.\n\n

Submitted - 0409074.pdf

", "abstract": "We show that whole-line Schr\u00f6dinger operators with finitely many bound states have no embedded singular spectrum. In contradistinction, we show that embedded singular spectrum is possible even when the bound states approach the essential spectrum exponentially fast. We also prove the following result for one- and two-dimensional Schr\u00f6dinger operators, H, with bounded positive ground states: Given a potential V, if both H\u00b1V are bounded from below by the ground-state energy of H, then V\u22610.", "date": "2005-09", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "258", "number": "3", "publisher": "Springer", "pagerange": "741-750", "id_number": "CaltechAUTHORS:20170726-130636631", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170726-130636631", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS\u20130227289" }, { "agency": "NSF", "grant_number": "DMS\u20130401277" }, { "agency": "NSF", "grant_number": "DMS\u20130140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-005-1366-x", "primary_object": { "basename": "0409074.pdf", "url": "https://authors.library.caltech.edu/records/zxgzx-62712/files/0409074.pdf" }, "pub_year": "2005", "author_list": "Damanik, David; Killip, Rowan; et al." }, { "id": "https://authors.library.caltech.edu/records/9ty3g-btm02", "eprint_id": 79658, "eprint_status": "archive", "datestamp": "2023-08-19 16:19:41", "lastmod": "2026-04-14 18:44:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Meromorphic Szeg\u0151 functions and asymptotic series for Verblunsky coefficients", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2005 Institut Mittag-Leffler. \n\nReceived March 7, 2005. \n\nSupported in part by NSF Grant DMS-0140592 and in part by Grant No. 2002068 from the United States Israel Binational Science Foundation (BSF), Jerusalem, Israel.", "abstract": "[No abstract]", "date": "2005-09", "date_type": "published", "publication": "Acta Mathematica", "volume": "195", "number": "2", "publisher": "Springer", "pagerange": "267-285", "id_number": "CaltechAUTHORS:20170801-082824529", "issn": "0001-5962", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170801-082824529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2002068" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02588083", "pub_year": "2005", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/0xfe3-hcw27", "eprint_id": 38882, "eprint_status": "archive", "datestamp": "2023-08-19 16:17:44", "lastmod": "2026-03-09 20:39:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "Greg" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Rigidity theorems for actions of product groups and countable Borel equivalence relations", "ispublished": "pub", "full_text_status": "public", "keywords": "Borel equivalence relations, ergodic theory of nonamenable groups,\nproduct group actions, rigidity, Borel reducibility", "note": "\u00a9 2005 American Mathematical Society.\nReceived by the editor December 2, 2002.\nThe first author was supported in part by NSF Grant DMS-9970403, DMS-0140503.\nThe second author was supported in part by NSF Grant DMS-9987437.\n\n

Published - Kechris_2005p109.pdf

", "abstract": "This Memoir is both a contribution to the theory of Borel equivalence relations,\nconsidered up to Borel reducibility, and measure preserving group actions\nconsidered up to orbit equivalence. Here E is said to be Borel reducible to F if\nthere is a Borel function f with xEy if and only if f(x)Ff(y). Moreover, E is orbit\nequivalent to F if the respective measure spaces equipped with the extra structure\nprovided by the equivalence relations are almost everywhere isomorphic.\nWe consider product groups acting ergodically and by measure preserving transformations\non standard Borel probability spaces. In general terms, the basic parts\nof the monograph show that if the groups involved have a suitable notion of \"boundary\" (we make this precise with the definition of near hyperbolic), then one orbit\nequivalence relation can only be Borel reduced to another if there is some kind of\nalgebraic resemblance between the product groups and coupling of the action. This\nalso has consequence for orbit equivalence. In the case that the original equivalence\nrelations do not have non-trivial almost invariant sets, the techniques lead to relative\nergodicity results. An equivalence relation E is said to be relatively ergodic to\nF if any f with xEy\u21d2 f(x)Ff(y) has [f(x)]F constant almost everywhere.\nThis underlying collection of lemmas and structural theorems is employed in a\nnumber of different ways.\nOne of the most pressing concerns was to give completely self-contained proofs\nof results which had previously only been obtained using Zimmer's superrigidity\ntheory. We present \"elementary proofs\" that there are incomparable countable\nBorel equivalence relations (Adams-Kechris), inclusion does not imply reducibility\n(Adams), and (n + 1)E is not necessarily reducible to nE (Thomas).\nIn the later parts of the paper we give applications of the theory to specific\ncases of product groups. In particular, we catalog the actions of products of the\nfree group and obtain additional rigidity theorems and relative ergodicity results in\nthis context.\nThere is a rather long series of appendices, whose primary goal is to give the\nreader a comprehensive account of the basic techniques. But included here are also\nsome new results. For instance, we show that the Furstenberg-Zimmer lemma on\ncocycles from amenable groups fails with respect to Baire category, and use this\nto answer a question of Weiss. We also present a different proof that F_2 has the\nHaagerup approximation property.", "date": "2005-09", "date_type": "published", "publication": "Memoirs of the American Mathematical Society", "volume": "177", "number": "833", "publisher": "American Mathematical Society", "pagerange": "1-109", "id_number": "CaltechAUTHORS:20130610-145818965", "issn": "0065-9266", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130610-145818965", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9970403" }, { "agency": "NSF", "grant_number": "DMS-0140503" }, { "agency": "NSF", "grant_number": "DMS-9987437" } ] }, "other_numbering_system": { "items": [ { "id": "MR2155451", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "Kechris_2005p109.pdf", "url": "https://authors.library.caltech.edu/records/0xfe3-hcw27/files/Kechris_2005p109.pdf" }, "pub_year": "2005", "author_list": "Hjorth, Greg and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/8cdgw-ptn76", "eprint_id": 76782, "eprint_status": "archive", "datestamp": "2023-08-19 16:15:06", "lastmod": "2026-04-14 20:39:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Rebecca M." } }, { "id": "Jen-Wendy-S", "name": { "family": "Jen", "given": "Wendy S." } }, { "id": "MacMillan-D-W-C", "name": { "family": "MacMillan", "given": "David W. C." } } ] }, "title": "Enantioselective Organocatalytic Intramolecular Diels\u2212Alder Reactions. The Asymmetric Synthesis of Solanapyrone D", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 American Chemical Society. \n\nReceived June 16, 2005. Publication Date (Web): July 28, 2005. \n\nFinancial support was provided by the NIHGMS (R01 GM66142-01) and kind gifts from Amgen, Merck, and Astellas USA Foundation. W.S.J. and R.M.W. are grateful for NSF Predoctoral Fellowships.\n\n

Supplemental Material - ja054008qsi20050720_022414.pdf

", "abstract": "The first direct enantioselective organocatalytic intramolecular Diels\u2212Alder reaction has been accomplished. The use of iminium catalysis has provided a new catalytic strategy for the enantioselective [4 + 2] cycloisomerization of a wide variety of tethered diene-enal systems. The use of imidazolidinones 1 and 2 as the asymmetric catalysts has been found to mediate the enantioselective construction of [4.4.0] and [4.3.0] ring systems. Application of this methodology to the highly efficient asymmetric synthesis of the marine metabolite solanpyrone D has also been accomplished. A diverse spectrum of aldehyde substrates can also be accommodated in this new organocatalytic transformation. Importantly, this technology has been utilized to execute the first enantioselective, catalytic Type II IMDA reaction.", "date": "2005-08-24", "date_type": "published", "publication": "Journal of the American Chemical Society", "volume": "127", "number": "33", "publisher": "American Chemical Society", "pagerange": "11616-11617", "id_number": "CaltechAUTHORS:20170420-133643860", "issn": "0002-7863", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170420-133643860", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NIH", "grant_number": "R01 GM66142-01" }, { "agency": "Amgen" }, { "agency": "Merck" }, { "agency": "Astellas USA Foundation" }, { "agency": "NSF Predoctoral Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1021/ja054008q", "primary_object": { "basename": "ja054008qsi20050720_022414.pdf", "url": "https://authors.library.caltech.edu/records/8cdgw-ptn76/files/ja054008qsi20050720_022414.pdf" }, "pub_year": "2005", "author_list": "Wilson, Rebecca M.; Jen, Wendy S.; et al." }, { "id": "https://authors.library.caltech.edu/records/mdwaz-1gg66", "eprint_id": 66978, "eprint_status": "archive", "datestamp": "2023-08-19 16:10:00", "lastmod": "2026-04-14 21:44:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Neitzke-A", "name": { "family": "Neitzke", "given": "Andrew" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Topological M-theory as Unification of Form Theories of Gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 International Press. \n\nFirst available in Project Euclid: 3 April 2006. \n\nWe are grateful to M. Atiyah, J. de Boer, R. Bryant, C. LeBrun, J. Louis, H. Ooguri, M. Ro\u010dek, L. Smolin, C. Taubes, E. Verlinde, and S.-T. Yau for valuable discussions. We would like to thank the 2004 Simons Workshop on Mathematics and Physics and the Aspen Workshop \"Strings, Branes and Superpotentials,\" which led to the development of many of the ideas in this paper. We also thank the organizers of the Strings 2004 conference in Paris for providing a stimulating environment where part of this work was done. S.G. and A.N. would like to thank Caltech Particle Theory Group, where part of this work was done, for kind hospitality. This work was conducted during the period S.G. served as a Clay Mathematics Institute\nLong-Term Prize Fellow. S.G. was also supported in part by RFBR grant 04-02-16880. The research of A.N. and C.V. was supported in part by NSF grants PHY-0244821 and DMS-0244464. The research of R.D. was partly supported by FOM and the NWO Spinoza premium.\n\n

Published - euclid.atmp.1144070454.pdf

Submitted - 0411073.pdf

", "abstract": "We introduce a notion of topological M-theory and argue that it provides a unification of form theories of gravity in various dimensions. Its classical solutions involve G_2 holonomy metrics on 7-manifolds, obtained from a topological action for a 3-form gauge field introduced by Hitchin. We show that by reductions of this 7-dimensional theory, one can classically obtain 6-dimensional topological A and B models, the self-dual sector of loop quantum gravity in four dimensions, and Chern\u2013Simons gravity in 3 dimensions. We also find that the 7-dimensional M-theory perspective sheds some light on the fact that the topological string partition function is a wavefunction, as well as on S-duality between the A and B models. The degrees of freedom of the A and B models appear as conjugate variables in the 7-dimensional theory. Finally, from the topological M-theory perspective, we find hints of an intriguing holographic link between non-supersymmetric Yang\u2013Mills in four dimensions and A model topological strings on twistor space.", "date": "2005-08", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "9", "number": "4", "publisher": "International Press", "pagerange": "603-665", "id_number": "CaltechAUTHORS:20160511-091820774", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-091820774", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "04-02-16880" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" }, { "agency": "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" }, { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2005.v9.n4.a5", "primary_object": { "basename": "0411073.pdf", "url": "https://authors.library.caltech.edu/records/mdwaz-1gg66/files/0411073.pdf" }, "related_objects": [ { "basename": "euclid.atmp.1144070454.pdf", "url": "https://authors.library.caltech.edu/records/mdwaz-1gg66/files/euclid.atmp.1144070454.pdf" } ], "pub_year": "2005", "author_list": "Dijkgraaf, Robbert; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/ngfkh-k6x12", "eprint_id": 12229, "eprint_status": "archive", "datestamp": "2023-08-22 03:59:46", "lastmod": "2026-03-09 02:38:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Li-Yi", "name": { "family": "Li", "given": "Yi" } } ] }, "title": "Open-string BRST cohomology for generalized complex branes", "ispublished": "pub", "full_text_status": "public", "note": "2005 \u00a9 International Press of Boston. \n\nA.K. would like to thank Alexey Bondal, Andrei C\u0103ld\u0103raru, Tony Pantev, and Marco Gualtieri for helpful discussions. Y.L. would like to thank Yong-Geun Oh for an interesting discussion. We are also grateful to the organizers of the Workshop on Mirror Symmetry at the Perimeter Institute, Waterloo, for providing a stimulating atmosphere. This work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - KAPatmp05.pdf

", "abstract": "It has been shown recently that the geometry of D-branes in general topologically twisted (2,2) sigma-models can be described in the language of generalized complex (GC) structures. On general grounds, such D-branes (called GC branes) must form a category. We compute the BRST cohomology of open strings with both ends on the same GC brane. In mathematical terms, we determine spaces of endomorphisms in the category of GC branes. We find that the BRST cohomology can be expressed as the cohomology of a Lie algebroid canonically associated to any GC brane. In the special case of B-branes, this leads to an apparently new way to compute Ext groups of holomorphic line bundles supported on complex submanifolds: while the usual method leads to a spectral sequence converging to the Ext, our approach expresses the Ext group as the cohomology of a certain differential acting on the space of smooth sections of a graded vector bundle on the submanifold. In the case of coisotropic A-branes, our computation confirms a proposal of Orlov and one of the authors (A.K.).", "date": "2005-08", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "9", "number": "4", "publisher": "International Press", "pagerange": "559-574", "id_number": "CaltechAUTHORS:KAPatmp05", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPatmp05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2005.v9.n4.a2", "primary_object": { "basename": "KAPatmp05.pdf", "url": "https://authors.library.caltech.edu/records/ngfkh-k6x12/files/KAPatmp05.pdf" }, "pub_year": "2005", "author_list": "Kapustin, Anton and Li, Yi" }, { "id": "https://authors.library.caltech.edu/records/mdpc8-dtf22", "eprint_id": 77391, "eprint_status": "archive", "datestamp": "2023-08-22 03:51:44", "lastmod": "2026-04-14 20:41:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Fine structure of the zeros of orthogonal polynomials, II. OPUC with competing exponential decay", "ispublished": "pub", "full_text_status": "public", "keywords": "Zeros; OPUC", "note": "\u00a9 2005 Elsevier Inc. \n\nReceived 19 November 2004, Revised 6 March 2005, Accepted 13 April 2005, Available online 16 June 2005. \n\nCommunicated by Leonid Golinskii \n\nSupported in part by NSF grant DMS-0140592. \n\nI thank Percy Deift and Chuck Newman for the hospitality of the Courant Institute where some of this work was done.\n\n

Submitted - 0411392.pdf

", "abstract": "We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients \u03b1_n = \u2211_(\u2113=1)^L C_\u2113b_\u2113^n + O((b\u0394)^n) where \u0394 <1 and |b_\u2113|= b <1.", "date": "2005-07", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "135", "number": "1", "publisher": "Elsevier", "pagerange": "125-139", "id_number": "CaltechAUTHORS:20170512-073745361", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-073745361", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2005.04.003", "primary_object": { "basename": "0411392.pdf", "url": "https://authors.library.caltech.edu/records/mdpc8-dtf22/files/0411392.pdf" }, "pub_year": "2005", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/wbqqw-qjw93", "eprint_id": 77348, "eprint_status": "archive", "datestamp": "2023-08-22 03:45:24", "lastmod": "2026-04-14 21:20:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On a theorem of Kac and Gilbert", "ispublished": "pub", "full_text_status": "public", "keywords": "Spectral theory; Singular spectrum; Kac\u2013Gilbert", "note": "\u00a9 2005 Elsevier Inc. \n\nSupported in part by NSF Grant DMS-0140592.\n\n

Submitted - 0405110.pdf

", "abstract": "We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum.", "date": "2005-06-01", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "223", "number": "1", "publisher": "Elsevier", "pagerange": "109-115", "id_number": "CaltechAUTHORS:20170510-131903213", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-131903213", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jfa.2004.08.015", "primary_object": { "basename": "0405110.pdf", "url": "https://authors.library.caltech.edu/records/wbqqw-qjw93/files/0405110.pdf" }, "pub_year": "2005", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/c2y2w-4c831", "eprint_id": 66714, "eprint_status": "archive", "datestamp": "2023-08-19 15:53:43", "lastmod": "2026-04-14 21:18:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Martinec-E", "name": { "family": "Martinec", "given": "Emil" } }, { "id": "Moore-G", "name": { "family": "Moore", "given": "Gregory" } }, { "id": "Strominger-A", "name": { "family": "Strominger", "given": "Andrew" } } ] }, "title": "Search for a holographic dual to AdS_3 x S^3 x S^3 x S^1", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 International Press.\n\nWe would like to thank J. de Boer, R. Dijkgraaf, J. Maldacena, B. Mazur, H. Ooguri, and K. Skenderis for useful conversations. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term\nPrize Fellow. G.M. thanks the LPTHE theory group at Jussieu, and the KITP at Santa Barbara for hospitality during the course of part of this work. E.M. was supported in part by DOE grant DE-FG02-90ER40560, G.M. by DOE grant DE-FG02-96ER40949, and A.S. by DE-FG02-90ER40654.\n\n

Published - ATMP-2005-0009-0003-a003.pdf

Submitted - 0403090.pdf

", "abstract": "The problem of finding a holographic dual to string theory on AdS_3\u00d7\u00a7^3\u00d7\u00a7^3\u00d7\u00a7^1 is examined in depth. This background supports a large \\CN=4 superconformal symmetry. While in some respects similar to the familiar small \\CN=4 systems on AdS_3\u00d7\u00a7^3\u00d7K^3 and AdS_3\u00d7\u00a7^3\u00d7T^4, there are important qualitative differences. Using an analogue of the elliptic genus for large CN=4 theories we rule out all extant proposals--in their simplest form--for a holographic duality to supergravity at generic values of the background fluxes. Modifications of these extant proposals and other possible duals are discussed.", "date": "2005-06", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "9", "number": "3", "publisher": "International Press", "pagerange": "435-525", "id_number": "CaltechAUTHORS:20160506-120757475", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-120757475", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40560" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40949" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40654" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2005.v9.n3.a3", "primary_object": { "basename": "0403090.pdf", "url": "https://authors.library.caltech.edu/records/c2y2w-4c831/files/0403090.pdf" }, "related_objects": [ { "basename": "ATMP-2005-0009-0003-a003.pdf", "url": "https://authors.library.caltech.edu/records/c2y2w-4c831/files/ATMP-2005-0009-0003-a003.pdf" } ], "pub_year": "2005", "author_list": "Gukov, Sergei; Martinec, Emil; et al." }, { "id": "https://authors.library.caltech.edu/records/fnd0f-pn515", "eprint_id": 23658, "eprint_status": "archive", "datestamp": "2023-08-19 15:48:33", "lastmod": "2026-04-14 22:05:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aganagic-M", "name": { "family": "Aganagic", "given": "Mina" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Saulina-N", "name": { "family": "Saulina", "given": "Natalia" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Elsevier B.V. \n\nReceived 28 January 2005; accepted 23 February 2005. Available online 17 March 2005. \n\nThis article is registered under preprint number hep-th/0411280. \n\nWe are grateful to C. Beasley, J. Bryan, M. Marino, A. Neitzke and R. Pandharipande W. Taylor and E. Witten for valuable discussions. H.O. and C.V. thank the 2004 Simons Workshop on mathematics and physics, for stimulating talks. H.O. in addition thanks the Aspen Center for Physics and the High Energy Theory Group at Harvard University for their hospitalities. The research of M.A. was supported in part by a DOE OJI Award, and an Alfred P. Sloan Foundation fellowship. The research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of N.S. and C.V. was supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\n

Submitted - 0411280.pdf

", "abstract": "We count the number of bound states of BPS black holes on local Calabi\u2013Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang\u2013Mills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of O(e^(\u2212N)), ZBH is given as a sum of a square of chiral blocks, each of which corresponds to a specific D-brane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The subleading chiral blocks involve topological string amplitudes with D-brane insertions at (2g\u22122) points on the Riemann surface analogous to the \u03a9 points in the large N 2d Yang\u2013Mills theory. The finite N amplitude provides a non-perturbative definition of topological strings in these backgrounds. This also leads to a novel non-perturbative formulation of c=1 non-critical string at the self-dual radius.", "date": "2005-05-23", "date_type": "published", "publication": "Nuclear Physics B", "volume": "715", "number": "1-2", "publisher": "Elsevier", "pagerange": "304-348", "id_number": "CaltechAUTHORS:20110513-093141123", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110513-093141123", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "other_numbering_system": { "items": [ { "id": "68-2529", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2005.02.035", "primary_object": { "basename": "0411280.pdf", "url": "https://authors.library.caltech.edu/records/fnd0f-pn515/files/0411280.pdf" }, "pub_year": "2005", "author_list": "Aganagic, Mina; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/vm3na-09h20", "eprint_id": 77390, "eprint_status": "archive", "datestamp": "2023-08-22 03:35:20", "lastmod": "2026-04-14 19:07:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zlato\u0161-A", "name": { "family": "Zlato\u0161", "given": "Andrej" } } ] }, "title": "Higher-order Szeg\u0151 theorems with two singular points", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials on the unit circle; Szeg\u0151 theorem", "note": "\u00a9 2005 Elsevier Inc. \n\nReceived 16 September 2004, Accepted 9 February 2005, Available online 7 April 2005. \n\nCommunicated by Leonid Golinskii \n\nWe thank S. Denisovand S. Kupin for telling us of their joint work [3].\n\n

Submitted - 0409065.pdf

", "abstract": "We consider probability measures, d\u03bc = w(\u03b8)^(d\u03b8)_(2\u03c0) + d\u03bc_s, on the unit circle, \u2202D, with Verblunsky coefficients, {\u03b1j}_(j=0)^\u221e. We prove for \u03b8_1 \u2260 \u03b8_2 in [0,2\u03c0) that \u222b[1-cos(\u03b8-\u03b8_1)][1-cos(\u03b8-\u03b8_2)]log w(\u03b8)^(d\u03b8)_(2\u03c0 > -\u221eif and only if \u2211_(j=0)^\u221e \u2502{(\u03b4-e^(-i\u03b82))(\u03b4-e^(-i\u03b81))\u03b1}_j^2 +|\u03b1_j|^4 < \u221e,where \u03b4 is the left shift operator (\u03b4\u03b2)_j = \u03b2_(j+1). We also prove that \u222b(1-cos\u03b8)^2 log w (\u03b8)^(d\u03b8)_(2\u03c0) > - \u221e if and only if \u2211_(j=0)^\u221e|\u03b1_(j+2) - 2\u03b1_(j+1) + \u03b1_j|^2 + |\u03b1j|^ 6 <\u221e.", "date": "2005-05", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "134", "number": "1", "publisher": "Elsevier", "pagerange": "114-129", "id_number": "CaltechAUTHORS:20170512-073745126", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-073745126", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jat.2005.02.003", "primary_object": { "basename": "0409065.pdf", "url": "https://authors.library.caltech.edu/records/vm3na-09h20/files/0409065.pdf" }, "pub_year": "2005", "author_list": "Simon, Barry and Zlato\u0161, Andrej" }, { "id": "https://authors.library.caltech.edu/records/4z911-yts05", "eprint_id": 66723, "eprint_status": "archive", "datestamp": "2023-08-19 15:35:31", "lastmod": "2026-04-14 21:31:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Springer-Verlag. \n\nReceived: 15 July 2003. Accepted: 5 October 2004. Published online: 2 March 2005. \n\nIt is a pleasure to thank D. Bar-Natan, R. Dijkgraaf, N. Dunfield, S. Garoufalidis, R. Gopakumar, G. Horowitz, D. Long, M. Mari\u00f1o, S. Minwalla, H. Ooguri, F. Rodriguez-Villegas, L. Rozansky, C. Vafa, E. Witten, S.-T. Yau, and especially K. Krasnov, G. Moore, A. Strominger, and D. Thurston for valuable and stimulating discussions. This research was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. This work is also supported in part by RFBR grant 01-01-00549 and RFBR grant for Young Scientists 02-01-06322. I would also like to thank the University of California at Santa Barbara, Stanford University, California Institute of Technology, and Rutgers University for kind hospitality while this work was in progress. \n\nCommunicated by G.W. Gibbons\n\n

Submitted - 0306165.pdf

", "abstract": "We study three-dimensional Chern-Simons theory with complex gauge group SL(2,\u2102), which has many interesting connections with three-dimensional quantum gravity and geometry of hyperbolic 3-manifolds. We show that, in the presence of a single knotted Wilson loop in an infinite-dimensional representation of the gauge group, the classical and quantum properties of such theory are described by an algebraic curve called the A-polynomial of a knot. Using this approach, we find some new and rather surprising relations between the A-polynomial, the colored Jones polynomial, and other invariants of hyperbolic 3-manifolds. These relations generalize the volume conjecture and the Melvin-Morton-Rozansky conjecture, and suggest an intriguing connection between the SL(2,\u2102) partition function and the colored Jones polynomial.", "date": "2005-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "255", "number": "3", "publisher": "Springer", "pagerange": "577-627", "id_number": "CaltechAUTHORS:20160509-071118060", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160509-071118060", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-005-1312-y", "primary_object": { "basename": "0306165.pdf", "url": "https://authors.library.caltech.edu/records/4z911-yts05/files/0306165.pdf" }, "pub_year": "2005", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/q2h4h-2j234", "eprint_id": 81978, "eprint_status": "archive", "datestamp": "2023-08-19 15:26:47", "lastmod": "2026-04-14 19:21:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "BC_n-symmetric polynomials", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Birkhauser Boston. \n\nReceived: 03 October 2003; Accepted: 07 October 2004.\n\n

Submitted - 0112035.pdf

", "abstract": "We consider two important families of BC_n-symmetric polynomials, namely Okounkov's interpolation polynomials and Koornwinder's orthogonal polynomials. We give a family of difference equations satisfied by the former as well as generalizations of the branching rule and Pieri identity, leading to a number of multivariate q-analogues of classical hypergeometric transformations. For the latter, we give new proofs of Macdonald's conjectures, as well as new identities, including an inverse binomial formula and several branching rule and connection coefficient identities. We also derive families of ordinary symmetric functions that reduce to the interpolation and Koornwinder polynomials upon appropriate specialization. As an application, we consider a number of new integral conjectures associated to classical symmetric spaces.", "date": "2005-03", "date_type": "published", "publication": "Transformation Groups", "volume": "10", "number": "1", "publisher": "Springer", "pagerange": "63-132", "id_number": "CaltechAUTHORS:20171002-161044221", "issn": "1083-4362", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-161044221", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00031-005-1003-y", "primary_object": { "basename": "0112035.pdf", "url": "https://authors.library.caltech.edu/records/q2h4h-2j234/files/0112035.pdf" }, "pub_year": "2005", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/9r886-m4x65", "eprint_id": 38566, "eprint_status": "archive", "datestamp": "2023-08-19 15:20:08", "lastmod": "2026-04-14 21:33:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Pestov-P-G", "name": { "family": "Pestov", "given": "V. G." } }, { "id": "Todorcevic-S", "name": { "family": "Todorcevic", "given": "S." } } ] }, "title": "Fra\u00efss\u00e9 Limits, Ramsey Theory, and topological dynamics of automorphism groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Birkh\u00e4user Verlag, Basel. Submitted: May 2003 Revision: January 2004 Revision: June 2004.\n\n

Submitted - 0305241.pdf

", "abstract": "(A) In this paper we study some connections between the Fra\u00efss\u00e9 theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. A prime concern of topological dynamics is the study of continuous actions of (Hausdorff) topological groups G on (Hausdorff) compact spaces X.", "date": "2005-02-01", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "15", "number": "1", "publisher": "Springer", "pagerange": "106-189", "id_number": "CaltechAUTHORS:20130517-135759630", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-135759630", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00039-005-0503-1", "primary_object": { "basename": "0305241.pdf", "url": "https://authors.library.caltech.edu/records/9r886-m4x65/files/0305241.pdf" }, "pub_year": "2005", "author_list": "Kechris, A. S.; Pestov, V. G.; et al." }, { "id": "https://authors.library.caltech.edu/records/7w19k-px130", "eprint_id": 1053, "eprint_status": "archive", "datestamp": "2023-08-22 03:09:14", "lastmod": "2026-04-16 01:40:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bravyi-S", "name": { "family": "Bravyi", "given": "Sergey" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Universal quantum computation with ideal Clifford gates and noisy ancillas", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92005 The American Physical Society \n\n(Received 6 May 2004; published 22 February 2005) \n\nWe thank Mikhail Vyalyi for bringing to our attention many useful facts about the Clifford group. This work has been supported in part by the National Science Foundation under Grant No. EIA-0086038.", "abstract": "We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state rho, which should be regarded as a parameter of the model. Our goal is to determine for which rho universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of rho and produce a single output qubit with higher polarization. The protocols allow one to increase the polarization only along certain \"magic\" directions. If the polarization of rho along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, which we call a magic state. We show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of our results with the Gottesman-Knill theorem is discussed.", "date": "2005-02-01", "date_type": "published", "publication": "Physical Review A", "volume": "71", "number": "Art no", "publisher": "Physical Review A", "pagerange": "1-14", "id_number": "CaltechAUTHORS:BRApra05", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BRApra05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevA.71.022316", "primary_object": { "basename": "BRApra05.pdf", "url": "https://authors.library.caltech.edu/records/7w19k-px130/files/BRApra05.pdf" }, "pub_year": "2005", "author_list": "Bravyi, Sergey and Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/6t7fq-5s958", "eprint_id": 71900, "eprint_status": "archive", "datestamp": "2023-08-19 15:20:22", "lastmod": "2026-04-14 21:32:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "O." }, "orcid": "0000-0002-0111-0418" }, { "id": "Mazeh-T", "name": { "family": "Mazeh", "given": "T." } }, { "id": "Zucker-S", "name": { "family": "Zucker", "given": "S." } } ] }, "title": "Correcting systematic effects in a large set of photometric light curves", "ispublished": "pub", "full_text_status": "public", "keywords": "atmospheric effects \u2013 methods: data analysis \u2013 methods: statistical \u2013 techniques: photometric \u2013 surveys \u2013 planetary systems", "note": "\u00a9 2004 RAS. \n\nIn original form 2004 August 16. Received 2004 October 13. Accepted 2004 November 1. First published online February 1, 2005. \n\nThis work was supported by the Israeli Science Foundation through grant no. 03/233. SZ wishes to acknowledge support by the European RTN 'The Origin of Planetary Systems' (PLANETS, contract number HPRN-CT-2002-00308) in the form of a fellowship.\n\n

Published - 1466.full.pdf

Submitted - 0502056.pdf

", "abstract": "We suggest a new algorithm to remove systematic effects in a large set of lightcurves obtained by a photometric survey. The algorithm can remove systematic effects, like the ones associated with atmospheric extinction, detector efficiency, or PSF changes over the detector. The algorithm works without any prior knowledge of the effects, as long as they linearly appear in many stars of the sample. The approach, which was originally developed to remove atmospheric extinction effects, is based on a lower rank approximation of matrices, an approach which was already suggested and used in chemometrics, for example. The proposed algorithm is specially useful in cases where the uncertainties of the measurements are unequal. For equal uncertainties the algorithm reduces to the Principal Components Analysis (PCA) algorithm. We present a simulation to demonstrate the effectiveness of the proposed algorithm and point out its potential, in search for transit candidates in particular.", "date": "2005-02-01", "date_type": "published", "publication": "Monthly Notices of the Royal Astronomical Society", "volume": "356", "number": "4", "publisher": "Royal Astronomical Society", "pagerange": "1466-1470", "id_number": "CaltechAUTHORS:20161109-161950022", "issn": "0035-8711", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161109-161950022", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Israel Science Foundation", "grant_number": "03/233" }, { "agency": "European Research Training Network", "grant_number": "HPRN-CT-2002-00308" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1111/j.1365-2966.2004.08585.x", "primary_object": { "basename": "0502056.pdf", "url": "https://authors.library.caltech.edu/records/6t7fq-5s958/files/0502056.pdf" }, "related_objects": [ { "basename": "1466.full.pdf", "url": "https://authors.library.caltech.edu/records/6t7fq-5s958/files/1466.full.pdf" } ], "pub_year": "2005", "author_list": "Tamuz, O.; Mazeh, T.; et al." }, { "id": "https://authors.library.caltech.edu/records/yt7da-nr625", "eprint_id": 83002, "eprint_status": "archive", "datestamp": "2023-08-19 15:13:53", "lastmod": "2026-03-09 22:46:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Etingof-P", "name": { "family": "Etingof", "given": "Pavel" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "New deformations of group algebras of Coxeter groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2005 Hindawi Publishing Corporation. \n\nReceived: 15 September 2004; Accepted: 03 March 2005; Published: 01 January 2005.\n\n

Submitted - 0409261.pdf

", "abstract": "We define new deformations of group algebras of Coxeter groups W and of subgroups of even elements in them by deforming the braid relations. We show that these deformations are algebraically flat if and only if they are formally flat, and that this happens if and only if the group W has no finite parabolic subgroups of rank 3. We explain the connection of our deformations with the Hecke algebras of orbifolds defined by the first author and with generalized double affine Hecke algebras defined by the authors and A. Oblomkov.", "date": "2005-01-01", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2005", "number": "10", "publisher": "Oxford University Press", "pagerange": "635-646", "id_number": "CaltechAUTHORS:20171106-145535121", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-145535121", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1155/IMRN.2005.635", "primary_object": { "basename": "0409261.pdf", "url": "https://authors.library.caltech.edu/records/yt7da-nr625/files/0409261.pdf" }, "pub_year": "2005", "author_list": "Etingof, Pavel and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/2295s-pjs84", "eprint_id": 82017, "eprint_status": "archive", "datestamp": "2023-08-19 15:12:53", "lastmod": "2026-03-09 23:03:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Interpretations of some parameter dependent generalizations of classical matrix ensembles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag Berlin Heidelberg. \n\nReceived: 26 November 2002; Revised: 07 May 2004; First Online: 20 August 2004. \n\nSupported by the Australian Research Council.\n\n

Submitted - 0211042.pdf

", "abstract": "Two types of parameter dependent generalizations of classical matrix ensembles are defined by their probability density functions (PDFs). As the parameter is varied, one interpolates between the eigenvalue PDF for the superposition of two classical ensembles with orthogonal symmetry and the eigenvalue PDF for a single classical ensemble with unitary symmetry, while the other interpolates between a classical ensemble with orthogonal symmetry and a classical ensemble with symplectic symmetry. We give interpretations of these PDFs in terms of probabilities associated to the continuous Robinson-Schensted-Knuth correspondence between matrices, with entries chosen from certain exponential distributions, and non-intersecting lattice paths, and in the course of this probability measures on partitions and pairs of partitions are identified. The latter are generalized by using Macdonald polynomial theory, and a particular continuum limit \u2013 the Jacobi limit \u2013 of the resulting measures is shown to give PDFs related to those appearing in the work of Anderson on the Selberg integral, and also in some classical work of Dixon. By interpreting Anderson's and Dixon's work as giving the PDF for the zeros of a certain rational function, it is then possible to identify random matrices whose eigenvalue PDFs realize the original parameter dependent PDFs. This line of theory allows sampling of the original parameter dependent PDFs, their Dixon-Anderson-type generalizations and associated marginal distributions, from the zeros of certain polynomials defined in terms of random three term recurrences.", "date": "2005-01", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "131", "number": "1", "publisher": "Springer", "pagerange": "1-61", "id_number": "CaltechAUTHORS:20171003-160005064", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-160005064", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-004-0375-6", "primary_object": { "basename": "0211042.pdf", "url": "https://authors.library.caltech.edu/records/2295s-pjs84/files/0211042.pdf" }, "pub_year": "2005", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/ketag-p8z22", "eprint_id": 81890, "eprint_status": "archive", "datestamp": "2023-08-19 15:09:48", "lastmod": "2026-03-09 23:05:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "Jeffrey C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Dynamics of a family of piecewise-linear area-preserving plane maps I. Rational rotation numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "area preserving map, iterated map, discrete Schr\u00f6dinger operator", "note": "\u00a9 2005 Taylor & Francis. \n\nWe did most of the work on this paper while employed at AT&T Labs-Research, whom we thank for support; most of the results in parts I and II were obtained in the summer of 1993. We thank T. Spencer for helpful comments on the relation of (1.7) to nonlinear Schr\u00f6dinger operators, and M. Kontsevich for bringing the work of Bedford, Bullett\nand Rippon [2] to our attention.\n\n

Submitted - 0301294.pdf

", "abstract": "This paper studies the behavior under iteration of the maps T_(ab)(x,y) = (F_(ab)(x)\u2212y,x) of the plane \u211d^2 in which F_(ab)(x) = ax if x \u2265 0 and bx if x < 0. The orbits under iteration correspond to solutions of the nonlinear difference equation x_(n+2) = 1/2(a\u2212b)|x_(n+1)|+1/2(a+b)x_(n+1)\u2013x_n. This family of piecewise-linear maps has the parameter space(a,b)\u2208 \u211d^2. These maps are area-preserving homeomorphisms of \u211d^2 that map rays from the origin into rays from the origin. The action on rays gives an auxiliary map S_(ab) : S^1 \u2192 S^1 of the circle, which has a well-defined rotation number. This paper characterizes the possible dynamics under iteration of T_(ab) when the auxiliary map S_(ab) has rational rotation number. It characterizes cases where the map T_(ab) is a periodic map.", "date": "2005", "date_type": "published", "publication": "Journal of Difference Equations and Applications", "volume": "11", "number": "12", "publisher": "Taylor & Francis", "pagerange": "1089-1108", "id_number": "CaltechAUTHORS:20170927-154918316", "issn": "1023-6198", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170927-154918316", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AT&T Labs Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1080/10236190500273069", "primary_object": { "basename": "0301294.pdf", "url": "https://authors.library.caltech.edu/records/ketag-p8z22/files/0301294.pdf" }, "pub_year": "2005", "author_list": "Lagarias, Jeffrey C. and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/4gtf5-m5d87", "eprint_id": 81941, "eprint_status": "archive", "datestamp": "2023-08-19 15:09:56", "lastmod": "2026-03-09 22:12:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "Jeffrey C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles", "ispublished": "pub", "full_text_status": "public", "keywords": "Area preserving map, Iterated map, Symbolic dynamics, Plane maps", "note": "\u00a9 2005 Taylor & Francis. \n\nReceived 25 May 2005, Accepted 05 Jul 2005, Published online: 21 Aug 2006.\n\n

Submitted - 0303007.pdf

", "abstract": "This paper studies the behavior under iteration of the maps T_(ab) (x, y) = (F_(ab) (x) \u2212 y, x) of the plane \u211d^2, in which F_(ab) (x) = ax if x \u2265 0 and bx if x < 0. The orbits under iteration correspond to solutions of the difference equation x_(n+2) = \u00bd(a-b)|x_(n+1)| + \u00bd(a+b)x_(n+1) \u2013 x_n. This family of piecewise-linear maps of the plane has the parameter space (a,b) \u03f5 \u211d^2. These maps are area-preserving homeomorphisms of \u211d^2 that map rays from the origin into rays from the origin. We show the existence of special parameter values where T_(ab) has every nonzero orbit contained in an invariant circle with an irrational rotation number, with invariant circles that are piecewise unions of arcs of conic sections. Numerical experiments indicate the possible existence of invariant circles for many other parameter values.", "date": "2005", "date_type": "published", "publication": "Journal of Difference Equations and Applications", "volume": "11", "number": "13", "publisher": "Taylor & Francis", "pagerange": "1137-1163", "id_number": "CaltechAUTHORS:20171002-100946430", "issn": "1023-6198", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-100946430", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1080/10236190500273127", "primary_object": { "basename": "0303007.pdf", "url": "https://authors.library.caltech.edu/records/4gtf5-m5d87/files/0303007.pdf" }, "pub_year": "2005", "author_list": "Lagarias, Jeffrey C. and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/jjxm8-8bk45", "eprint_id": 25136, "eprint_status": "archive", "datestamp": "2023-08-19 15:03:13", "lastmod": "2026-03-09 23:12:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" }, { "id": "Rogawski-J", "name": { "family": "Rogawski", "given": "Jonathan" } } ] }, "title": "Average values of modular L-series via the relative trace formula", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2005 International Press. Received August 17, 2005.", "abstract": "N/A", "date": "2005", "date_type": "published", "publication": "Pure and Applied Mathematics Quarterly", "volume": "1", "number": "4", "publisher": "International Press", "pagerange": "701-735", "id_number": "CaltechAUTHORS:20110829-082741960", "issn": "1558-8602", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110829-082741960", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0510113", "pub_year": "2005", "author_list": "Ramakrishnan, Dinakar and Rogawski, Jonathan" }, { "id": "https://authors.library.caltech.edu/records/kyy39-4h743", "eprint_id": 81940, "eprint_status": "archive", "datestamp": "2023-08-19 15:09:52", "lastmod": "2026-03-09 23:04:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "Jeffrey C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra", "ispublished": "pub", "full_text_status": "public", "keywords": "Area preserving map, Discrete Schr\u00f6dinger operator, Symbolic dynamics, Tight binding model", "note": "\u00a9 2005 Taylor & Francis. \n\nReceived 25 May 2005, Accepted 05 Jun 2005, Published online: 19 Aug 2006.\n\n

Submitted - 0505103.pdf

", "abstract": "This paper studies the behavior under iteration of the maps T_(ab) (x,y) = (F_(ab) (x) \u2212 y, x) of the plane \u211d^2, in which F_(ab) (x) = ax if x \u2265 0 and bx if x < 0. These maps are area-preserving homeomorphisms of \u211d^2 that map rays from the origin to rays from the origin. Orbits of the map correspond to solutions of the nonlinear difference equation x_(n+2) = 1/2(a \u2212 b)|x_(n+1)|+1/2(a+b)x_(n+1) \u2013 x_n . This difference equation can be rewritten in an eigenvalue form for a nonlinear difference operator of Schr\u00f6dinger type \u2013 x_(n+2)+2x_(n+1) \u2013 x_n +V_\u03bc(x_(n+1))x_(n+1) = Ex_(n+1), in which \u03bc = (1/2)(a \u2212 b) is fixed, and V_\u03bc(x) = \u03bc(sgn(x)) is an antisymmetric step function potential, and the energy E = 2 \u2212 1/2(a+b). We study the set \u03a9_(SB) of parameter values where the map T_(ab) has at least one bounded orbit, which correspond to l\u221e-eigenfunctions of this difference operator. The paper shows that for transcendental \u03bc the set Spec\u221e[\u03bc] of energy values E having a bounded solution is a Cantor set. Numerical simulations suggest the possibility that these Cantor sets have positive (one-dimensional) measure for all real values of \u03bc.", "date": "2005", "date_type": "published", "publication": "Journal of Difference Equations and Applications", "volume": "11", "number": "14", "publisher": "Taylor & Francis", "pagerange": "1205-1224", "id_number": "CaltechAUTHORS:20171002-100214237", "issn": "1023-6198", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-100214237", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1080/10236190500273184", "primary_object": { "basename": "0505103.pdf", "url": "https://authors.library.caltech.edu/records/kyy39-4h743/files/0505103.pdf" }, "pub_year": "2005", "author_list": "Lagarias, Jeffrey C. and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/5v93r-0wy85", "eprint_id": 25128, "eprint_status": "archive", "datestamp": "2023-08-19 15:03:06", "lastmod": "2026-03-18 00:03:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "OPUC on one foot", "ispublished": "pub", "full_text_status": "public", "keywords": "Orthogonal polynomials, Verblunsky coefficients, Szego's theorem", "note": "\u00a9 2005 Barry Simon. Received by the editors February 2, 2005, and, in revised form, April 19, 2005. Posted: June 23, 2005. Supported in part by NSF grant DMS-0140592.\n\n

Published - SIMbams05.pdf

", "abstract": "We present an expository introduction to orthogonal polynomials on the unit circle (OPUC).", "date": "2005", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "42", "number": "4", "publisher": "American Mathematical Society", "pagerange": "431-460", "id_number": "CaltechAUTHORS:20110826-133837209", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110826-133837209", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "other_numbering_system": { "items": [ { "id": "2163705", "name": "MathSciNet review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0273-0979-05-01075-X", "primary_object": { "basename": "SIMbams05.pdf", "url": "https://authors.library.caltech.edu/records/5v93r-0wy85/files/SIMbams05.pdf" }, "pub_year": "2005", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/ewtr8-an419", "eprint_id": 24901, "eprint_status": "archive", "datestamp": "2023-08-19 14:44:12", "lastmod": "2026-04-15 17:49:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Berkovits-N", "name": { "family": "Berkovits", "given": "Nathan" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "On the Worldsheet Derivation of Large N Dualities for the Superstring", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag. \n\nReceived: 20 October 2003; Accepted: 12 May 2004; Published online: 7 October 2004. \n\nCommunicated by M.R. Douglas. \n\nC.V. thanks the theory group at Caltech for hospitality of, when he was a Gordon Moore Distinguished Scholar. N.B., H.O., and C.V. thank the Simons Workshop on Mathematics and Physics and the YITP at Stony Brook for their hospitality during the completion of this work. H.O. also thanks KITP, Santa Barbara and N.B. thanks Caltech for their hospitality. The research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329. The research of N.B. was supported in part by FAPESP grant 99/12763-0, CNPq grant 300256/94-9 and Pronex grant 66.2002/1998-9.\n\n

Submitted - BERcmp04preprint.pdf

", "abstract": "Large N topological string dualities have led to a class of proposed open/closed dualities for superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional superstring dualities by showing how the dualities arise on the superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the superstring is equivalent to a \u0109=5 topological string in ten-dimensional spacetime. Using the \u0109=5 description, we then show that the D brane boundary state for the ten-dimensional open superstring naturally emerges on the worldsheet of the closed superstring dual.", "date": "2004-12", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "252", "number": "1-3", "publisher": "Springer", "pagerange": "259-274", "id_number": "CaltechAUTHORS:20110817-084105266", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110817-084105266", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo (FAPESP)", "grant_number": "99/12763-0" }, { "agency": "Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)", "grant_number": "300256/94-9" }, { "agency": "Pronex", "grant_number": "66.2002/1998-9" }, { "agency": "Gordon and Betty Moore Foundation" } ] }, "other_numbering_system": { "items": [ { "id": "68-2455", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-004-1181-9", "primary_object": { "basename": "BERcmp04preprint.pdf", "url": "https://authors.library.caltech.edu/records/ewtr8-an419/files/BERcmp04preprint.pdf" }, "pub_year": "2004", "author_list": "Berkovits, Nathan; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/29zaw-44244", "eprint_id": 66971, "eprint_status": "archive", "datestamp": "2023-08-19 14:46:19", "lastmod": "2026-04-15 19:45:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Rozansky-L", "name": { "family": "Rozansky", "given": "Lev" } } ] }, "title": "On the Relation Between Open and Closed Topological Strings", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Springer-Verlag 2004. \n\nReceived: 4 June 2004. Accepted: 24 September 2004. \n\nCommunicated by M.R. Douglas. \n\nA.K. would like to thank Volodya Baranovsky, Ezra Getzler, Kentaro Hori, Dima Orlov, and SashaVoronov for help at various stages. A.K. is also grateful to the Department of Mathematics of Northwestern University and the Erwin Schr\u00f6dinger Institute for hospitality while this work was being completed. L. R. is very grateful to Mikhail Khovanov for numerous discussions of the category of matrix factorizations. This work was supported in part by the DOE grant DE-FG03-92-ER40701 and by the NSF grant DMS-0196131.\n\n

Submitted - 0405232.pdf

", "abstract": "We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.", "date": "2004-12", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "252", "number": "1-3", "publisher": "Springer", "pagerange": "393-414", "id_number": "CaltechAUTHORS:20160511-080711343", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-080711343", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "DMS-0196131" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-004-1227-z", "primary_object": { "basename": "0405232.pdf", "url": "https://authors.library.caltech.edu/records/29zaw-44244/files/0405232.pdf" }, "pub_year": "2004", "author_list": "Kapustin, Anton and Rozansky, Lev" }, { "id": "https://authors.library.caltech.edu/records/0wh7m-k9b33", "eprint_id": 81989, "eprint_status": "archive", "datestamp": "2023-08-19 14:46:55", "lastmod": "2026-04-15 17:12:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Forrester-P-J", "name": { "family": "Forrester", "given": "Peter J." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag Berlin Heidelberg. \n\nReceived: 26 November 2002; Revised version: 23 March 2004; Published online: 5 July 2004. \n\nWe thank J. Baik for encouraging us to take up the problem of calculating the correlation functions for (1.4), and the referee for a careful reading. The work of PJF was supported by the Australian Research Council.\n\n

Submitted - 0211041v1.pdf

", "abstract": "A superposition of a matrix ensemble refers to the ensemble constructed from two independent copies of the original, while a decimation refers to the formation of a new ensemble by observing only every second eigenvalue. In the cases of the classical matrix ensembles with orthogonal symmetry, it is known that forming superpositions and decimations gives rise to classical matrix ensembles with unitary and symplectic symmetry. The basic identities expressing these facts can be extended to include a parameter, which in turn provides us with probability density functions which we take as the definition of special parameter dependent matrix ensembles. The parameter dependent ensembles relating to superpositions interpolate between superimposed orthogonal ensembles and a unitary ensemble, while the parameter dependent ensembles relating to decimations interpolate between an orthogonal ensemble with an even number of eigenvalues and a symplectic ensemble of half the number of eigenvalues. By the construction of new families of biorthogonal and skew orthogonal polynomials, we are able to compute the corresponding correlation functions, both in the finite system and in various scaled limits. Specializing back to the cases of orthogonal and symplectic symmetry, we find that our results imply different functional forms to those known previously.", "date": "2004-12", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "130", "number": "4", "publisher": "Springer", "pagerange": "518-576", "id_number": "CaltechAUTHORS:20171003-102014270", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-102014270", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-004-0374-7", "primary_object": { "basename": "0211041v1.pdf", "url": "https://authors.library.caltech.edu/records/0wh7m-k9b33/files/0211041v1.pdf" }, "pub_year": "2004", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/t17et-sr644", "eprint_id": 3931, "eprint_status": "archive", "datestamp": "2023-08-22 02:41:57", "lastmod": "2026-04-15 19:16:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Strominger-A", "name": { "family": "Strominger", "given": "Andrew" } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Black hole attractors and the topological string", "ispublished": "pub", "full_text_status": "public", "keywords": "black holes; superstrings; Wigner distribution; wave functions; topology; supergravity", "note": "\u00a9 2004 The American Physical Society. \n\nReceived 15 July 2004; published 19 November 2004. \n\nWe would like to thank M. Aganagic, F. Denef, R. Dijkgraaf, M. Douglas, G. Moore, A. Neitzke, M. Rocek, A. van Proeyen and E. Witten for valuable discussions. The work of H.O. was supported in part by DOE Grant No. DE-FG03-92-ER40701, that of A. S. was supported in part by DOE Grant No. DE-FG02-96ER, and that of C.V. was supported in part by NSF Grants No. PHY-0244821 and No. DMS-0244464.\n\n

Published - OOGprd04.pdf

Submitted - 0405146.pdf

", "abstract": "A simple relationship of the form ZBH = |Ztop|2 is conjectured, where ZBH is a supersymmetric partition function for a four-dimensional BPS black hole in a Calabi-Yau compactification of Type II superstring theory and Ztop is a second-quantized topological string partition function evaluated at the attractor point in moduli space associated to the black hole charges. Evidence for the conjecture in a perturbation expansion about large graviphoton charge is given. The microcanonical ensemble of BPS black holes can be viewed as the Wigner function associated to the wave function defined by the topological string partition function.", "date": "2004-11-15", "date_type": "published", "publication": "Physical Review D", "volume": "70", "number": "10", "publisher": "American Physical Society", "pagerange": "Art. No. 106007", "id_number": "CaltechAUTHORS:OOGprd04.931", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGprd04.931", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0244821" }, { "agency": "NSF", "grant_number": "DMS-0244464" } ] }, "other_numbering_system": { "items": [ { "id": "68-2501", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.70.106007", "primary_object": { "basename": "0405146.pdf", "url": "https://authors.library.caltech.edu/records/t17et-sr644/files/0405146.pdf" }, "related_objects": [ { "basename": "OOGprd04.pdf", "url": "https://authors.library.caltech.edu/records/t17et-sr644/files/OOGprd04.pdf" } ], "pub_year": "2004", "author_list": "Ooguri, Hirosi; Strominger, Andrew; et al." }, { "id": "https://authors.library.caltech.edu/records/ftew9-hgv19", "eprint_id": 3733, "eprint_status": "archive", "datestamp": "2023-08-22 02:40:20", "lastmod": "2026-04-15 20:26:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Okuda-Takuya", "name": { "family": "Okuda", "given": "Takuya" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "D-branes and phases on string worldsheet", "ispublished": "pub", "full_text_status": "public", "keywords": "TOPOLOGICAL STRINGS; INVARIANTS; CONIFOLD", "note": "\u00a9 2004 Elsevier B.V. \n\nReceived 3 May 2004; accepted 18 August 2004. Available online 11 September 2004. \n\nWe would like to thank Mina Aganagic, Jaume Gomis, Nick Halmagyi, Kentaro Hori, Amir Kashani-Poor, Yi Li, Marcos Mari\u00f1o, Donal O'Connell, Christian Roemelsberger, and Cumrun Vafa for useful discussions. This research is supported in part by DOE grant DE-FG03-92-ER40701. \n\narXiv:hep-th/0404101; CALT-68-2491\n\n

Submitted - OKUnpb04.pdf

", "abstract": "We generalize the worldsheet derivation of the topological open/closed string duality given in hep-th/0205297 to cases when there are different types of D-branes on the open string side. We use the mirror Landau\u2013Ginzburg description to clarify the correspondence between D-branes on the open string side and C phases on the closed string side. We also discuss the duality from the point of view of the B-model.", "date": "2004-11-01", "date_type": "published", "publication": "Nuclear Physics B", "volume": "699", "number": "1-2", "publisher": "Elsevier", "pagerange": "135-150", "id_number": "CaltechAUTHORS:OKUnpb04", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OKUnpb04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "other_numbering_system": { "items": [ { "id": "68-2491", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.nuclphysb.2004.08.036", "primary_object": { "basename": "OKUnpb04.pdf", "url": "https://authors.library.caltech.edu/records/ftew9-hgv19/files/OKUnpb04.pdf" }, "pub_year": "2004", "author_list": "Okuda, Takuya and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/ek0j1-gm202", "eprint_id": 56832, "eprint_status": "archive", "datestamp": "2023-08-19 14:37:04", "lastmod": "2026-03-09 21:53:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jiang-Boju", "name": { "family": "Jiang", "given": "Boju" } }, { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } }, { "id": "Wang-Shicheng", "name": { "family": "Wang", "given": "Shicheng" } } ] }, "title": "3-manifolds that admit knotted solenoids as attractors", "ispublished": "pub", "full_text_status": "public", "keywords": "3-manifolds, homeomorphisms, attractors, solenoids, lens spaces", "note": "\u00a9 2004 American Mathematical Society. \n\nReceived by the editors February 20, 2003 and, in revised form, April 18, 2003. \n\nThis work was partially supported by a MOSTC grant and a MOEC grant.\n\nWe would like to thank the referee for his suggestions which enhanced the paper.\nWe also thank Professors H. Duan, S. Gan and L. Wen for helpful conversations.\n\n

Published - S0002-9947-04-03503-2.pdf

Submitted - 0403427v1.pdf

", "abstract": "Motivated by the study in Morse theory and Smale's work in dynamics, the following questions are studied and answered: (1) When does a 3-manifold admit an automorphism having a knotted Smale solenoid as an attractor? (2) When does a 3-manifold admit an automorphism whose non-wandering set consists of Smale solenoids? The result presents some intrinsic symmetries for a class of 3-manifolds.", "date": "2004-11", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "356", "number": "11", "publisher": "American Mathematical Society", "pagerange": "4371-4382", "id_number": "CaltechAUTHORS:20150421-115923758", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150421-115923758", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "MOSTC" }, { "agency": "MOEC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0403427", "primary_object": { "basename": "0403427v1.pdf", "url": "https://authors.library.caltech.edu/records/ek0j1-gm202/files/0403427v1.pdf" }, "related_objects": [ { "basename": "S0002-9947-04-03503-2.pdf", "url": "https://authors.library.caltech.edu/records/ek0j1-gm202/files/S0002-9947-04-03503-2.pdf" } ], "pub_year": "2004", "author_list": "Jiang, Boju; Ni, Yi; et al." }, { "id": "https://authors.library.caltech.edu/records/450q7-kdg78", "eprint_id": 2992, "eprint_status": "archive", "datestamp": "2023-08-22 02:28:32", "lastmod": "2026-04-15 23:50:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nekrasov-N", "name": { "family": "Nekrasov", "given": "Nikita" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "S-duality and topological strings", "ispublished": "pub", "full_text_status": "public", "keywords": "D-branes; topological strings", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2004. \n\nReceived 4 October 2004, accepted for publication 5 October 2004. Published 20 October 2004. \n\nWe would like to thank M. Aganagic, S. Gukov, A. Kapustin, S. Katz, L. Motl, A. Neitzke, A. Okounkov, A. Strominger and C. Taubes for valuable discussions. In addition NN would like to thank A. Losev for interesting discussions. \n\nThe research of NN is partly supported by RFFI grant 03-02-17554 and by the grant NX-1999.2003.2 for scientific schools. The research of HO is supported in part by DOE grant DE-FG03-92-ER40701. The research of CV is supported in part by NSF grants PHY-0244821 and DMS-0244464.\n\n

Published - NEKjhep04.pdf

Submitted - 0403167.pdf

", "abstract": "In this paper we show how S-duality of type-IIB superstrings leads to an S-duality relating A- and B-model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.", "date": "2004-10", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "10", "publisher": "Springer", "pagerange": "Art. No. 009", "id_number": "CaltechAUTHORS:NEKjhep04", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:NEKjhep04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "03-02-17554" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "NX-1999.2003.2" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-0244821" } ] }, "other_numbering_system": { "items": [ { "id": "68-2479", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/10/009", "primary_object": { "basename": "0403167.pdf", "url": "https://authors.library.caltech.edu/records/450q7-kdg78/files/0403167.pdf" }, "related_objects": [ { "basename": "NEKjhep04.pdf", "url": "https://authors.library.caltech.edu/records/450q7-kdg78/files/NEKjhep04.pdf" } ], "pub_year": "2004", "author_list": "Nekrasov, Nikita; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/5ged8-vc322", "eprint_id": 82035, "eprint_status": "archive", "datestamp": "2023-08-22 02:30:39", "lastmod": "2026-04-15 23:36:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nebe-G", "name": { "family": "Nebe", "given": "G." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "Codes and invariant theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Self-dual codes; weight enumerators; invariant ring; Clifford groups", "note": "\u00a9 2004 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. \n\nIssue online: 9 September 2004; Version of record online: 9 September 2004; Manuscript Accepted: 24 February 2004; Manuscript Received: 4 November 2003.\n\n

Submitted - 0311046.pdf

", "abstract": "The main theorem in this paper is a far-reaching generalization of Gleason's theorem on the weight enumerators of codes which applies to arbitrary-genus weight enumerators of self-dual codes defined over a large class of finite rings and modules. The proof of the theorem uses a categorical approach, and will be the subject of a forthcoming book. However, the theorem can be stated and applied without using category theory, and we illustrate it here by applying it to generalized doubly-even codes over fields of characteristic 2, doubly-even codes over \u2124/2f\u2124, and self-dual codes over the noncommutative ring F_q + F_qu, where u^2 = 0.", "date": "2004-10", "date_type": "published", "publication": "Mathematische Nachrichten", "volume": "274-275", "number": "1", "publisher": "Wiley", "pagerange": "104-116", "id_number": "CaltechAUTHORS:20171004-091341996", "issn": "0025-584X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171004-091341996", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/mana.200310204", "primary_object": { "basename": "0311046.pdf", "url": "https://authors.library.caltech.edu/records/5ged8-vc322/files/0311046.pdf" }, "pub_year": "2004", "author_list": "Nebe, G.; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/aeg2c-xmq47", "eprint_id": 82034, "eprint_status": "archive", "datestamp": "2023-08-22 02:30:30", "lastmod": "2026-04-15 19:10:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nebe-G", "name": { "family": "Nebe", "given": "Gabriele" } }, { "id": "Quebbemann-H-G", "name": { "family": "Quebbemann", "given": "H.-G." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "Complete weight enumerators of generalized doubly-even self-dual codes", "ispublished": "pub", "full_text_status": "public", "keywords": "Even self-dual codes; Weight enumerators; Invariant ring; Clifford group", "note": "\u00a9 2003 Elsevier Inc. \n\nReceived 6 July 2002, Revised 17 November 2003, Available online 6 January 2004. \n\nWe thank O. Jahn for computations in connection with Theorem 13 at an early stage of this work. We also thank the referees for their comments.\n\n

Submitted - 0311289.pdf

", "abstract": "For any q which is a power of 2 we describe a finite subgroup of GL_q(\u2102) under which the complete weight enumerators of generalized doubly-even self-dual codes over F_q are invariant. An explicit description of the invariant ring and some applications to extremality of such codes are obtained in the case q=4.", "date": "2004-10", "date_type": "published", "publication": "Finite Fields and Their Applications", "volume": "10", "number": "4", "publisher": "Elsevier", "pagerange": "540-550", "id_number": "CaltechAUTHORS:20171004-090734197", "issn": "1071-5797", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171004-090734197", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.ffa.2003.12.001", "primary_object": { "basename": "0311289.pdf", "url": "https://authors.library.caltech.edu/records/aeg2c-xmq47/files/0311289.pdf" }, "pub_year": "2004", "author_list": "Nebe, Gabriele; Quebbemann, H.-G.; et al." }, { "id": "https://authors.library.caltech.edu/records/b3wee-kah45", "eprint_id": 77349, "eprint_status": "archive", "datestamp": "2023-08-22 02:27:16", "lastmod": "2026-04-15 19:44:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A canonical factorization for meromorphic Herglotz functions on the unit disk and sum rules for Jacobi matrices", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Herglotz; Sum rules; Jacobi matrices", "note": "\u00a9 2003 Elsevier Inc. \n\nReceived 8 July 2003, Revised 12 November 2003, Accepted 13 November 2003, Available online 23 January 2004. \n\nSupported in part by NSF Grant DMS-0140592.", "abstract": "We prove a general canonical factorization for meromorphic Herglotz functions on the unit disk whose notable elements are that there is no restriction (other than interlacing) on the zeros and poles for their Blaschke product to converge and there is no singular inner function. We use this result to provide a significant simplification in the proof of Killip\u2013Simon (Ann. Math. 158 (2003) 253) of their result characterizing the spectral measures of Jacobi matrices, J, with J\u2212J_0 Hilbert-Schmidt. We prove a nonlocal version of Case and step-by-step sum rules.", "date": "2004-09-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "214", "number": "2", "publisher": "Elsevier", "pagerange": "396-409", "id_number": "CaltechAUTHORS:20170510-134147546", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-134147546", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/j.jfa.2003.11.006", "pub_year": "2004", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/a98vg-9tg35", "eprint_id": 612, "eprint_status": "archive", "datestamp": "2023-08-22 02:19:51", "lastmod": "2026-04-15 21:11:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Gauge theory, topological strings, and S-duality", "ispublished": "pub", "full_text_status": "public", "keywords": "D-branes, string duality, amplitudes", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2004. \n\nReceived 4 August 2004, accepted for publication 16 September 2004. Published 1 October 2004. \n\nI am grateful to Andrei Mikhailov and Hiroshi Ooguri for discussions. I also would like to thank Jaume Gomis for pointing out an inaccuracy in the first version of the paper. This work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - KAPjhep04.pdf

", "abstract": "We offer a derivation of the duality between the topological U(1) gauge theory on a Calabi-Yau 3-fold and the topological A-model on the same manifold. This duality was conjectured recently by Iqbal, Nekrasov, Okounkov, and Vafa. We deduce it from the S-duality of the IIB superstring. We also argue that the mirror version of this duality relates the topological B-model on a Calabi-Yau 3-fold and a topological sector of the Type IIA Little String Theory on the same manifold.", "date": "2004-09", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "9", "publisher": "Springer", "pagerange": "Art. No.-034", "id_number": "CaltechAUTHORS:KAPjhep04", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/09/034", "primary_object": { "basename": "KAPjhep04.pdf", "url": "https://authors.library.caltech.edu/records/a98vg-9tg35/files/KAPjhep04.pdf" }, "pub_year": "2004", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/qj7rd-agf66", "eprint_id": 79657, "eprint_status": "archive", "datestamp": "2023-08-22 02:15:35", "lastmod": "2026-04-15 21:40:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Isospectral sets of potentials; half-line Schr\u00f6dinger operators; inverse problems.", "note": "\u00a9 2004 Plenum Publishing Corporation.\n\nReceived June 27, 2003; accepted August 20, 2003.\n\nB.S. is supported in part by NSF Grant DMS-0140592.\n\n

Submitted - 0307007.pdf

", "abstract": "Let V_0 be a real-valued function on [0,\u221e) and V \u2208 L^1 ([0,R]) for all R > 0 so that H(V_0)=\u2212 d^2/dx^2+V_0 in L^2([0,\u221e)) with u(0)=0 boundary conditions has discrete spectrum bounded from below. Let M(V_0) be the set of V so that H(V) and H(V_0) have the same spectrum. We prove that MM (V_0) is connected.", "date": "2004-08", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "116", "number": "1-4", "publisher": "Springer", "pagerange": "361-365", "id_number": "CaltechAUTHORS:20170801-075355675", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170801-075355675", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1023/B:JOSS.0000037217.89500.b3", "primary_object": { "basename": "0307007.pdf", "url": "https://authors.library.caltech.edu/records/qj7rd-agf66/files/0307007.pdf" }, "pub_year": "2004", "author_list": "Gesztesy, Fritz and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/5b4mm-frv50", "eprint_id": 24909, "eprint_status": "archive", "datestamp": "2023-08-19 13:59:50", "lastmod": "2026-03-07 16:32:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "The Status of the Classification of the Finite Simple Groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 American Mathematical Society.\nThis work was partially supported by NSF-0203417.\n\n

Published - ASCnams04.pdf

", "abstract": "The classification of the finite simple groups is one of the great theorems of recent mathematics. One of its principal participants reviews the result and current progress on understanding it.", "date": "2004-08", "date_type": "published", "publication": "Notices of the American Mathematical Society", "volume": "51", "number": "7", "publisher": "American Mathematical Society", "pagerange": "736-740", "id_number": "CaltechAUTHORS:20110817-103540228", "issn": "0002-9920", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110817-103540228", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0203417" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "ASCnams04.pdf", "url": "https://authors.library.caltech.edu/records/5b4mm-frv50/files/ASCnams04.pdf" }, "pub_year": "2004", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/q1ztd-2z012", "eprint_id": 77724, "eprint_status": "archive", "datestamp": "2023-08-19 13:50:55", "lastmod": "2026-04-16 00:07:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "Dirk" }, "orcid": "0000-0002-0643-0138" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A diamagnetic inequality for semigroup differences", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Walter de Gruyter Berlin; New York.\n\nSupported in part by NSF grants DMS-9707661 and DMS-0140592. \n\nIt is a pleasure to thank Alexander Elgart for discussions\nand Hendrik Vogt for pointing us to [30]. D.H. also thanks Ari Laptev and Kjell-Ove Widman for their hospitality at the Mittag-Leffler institute.\n\n

Published - 286.pdf

Submitted - p286.pdf

", "abstract": "The diamagnetic inequality for the magnetic Schr\u00f6dinger semigroup is extended to the difference of the semigroups of magnetic Schr\u00f6dinger operators with Neumann and Dirichlet boundary conditions on arbitrary open domains and rather general magnetic vector potentials A and potentials V. In particular, this bound renders moot all the technical issues in the recent proofs of the independence of the boundary conditions for the integrated density of states for magnetic Schr\u00f6dinger operators: Independence of the boundary conditions for the free case, that is, for vanishing potentials and vector potentials, immediately implies independence of the boundary conditions of the\nintegrated density of states for a large class of magnetic Schr\u00f6dinger operators.", "date": "2004-07", "date_type": "published", "publication": "Journal f\u00fcr die reine und angewandte Mathematik (Crelles Journal)", "volume": "2004", "number": "571", "publisher": "De Gruyter", "pagerange": "107-130", "id_number": "CaltechAUTHORS:20170524-141635977", "issn": "0075-4102", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170524-141635977", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" }, { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1515/crll.2004.036", "primary_object": { "basename": "286.pdf", "url": "https://authors.library.caltech.edu/records/q1ztd-2z012/files/286.pdf" }, "related_objects": [ { "basename": "p286.pdf", "url": "https://authors.library.caltech.edu/records/q1ztd-2z012/files/p286.pdf" } ], "pub_year": "2004", "author_list": "Hundertmark, Dirk and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/ameg1-qmx34", "eprint_id": 614, "eprint_status": "archive", "datestamp": "2023-08-22 02:06:15", "lastmod": "2026-04-15 19:52:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Li-Yi", "name": { "family": "Li", "given": "Yi" } } ] }, "title": "D-branes in topological minimal models: the Landau-Ginzburg approach", "ispublished": "pub", "full_text_status": "public", "keywords": "topological field theories, D-branes", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2004. \n\nReceived 1 June 2004, accepted for publication 19 July 2004. Published 25 August 2004. \n\nWe are grateful to Vladimir Baranovsky, Kentaro Hori, and Dmitri Orlov for useful conversations. This work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - KAPjhep04b.pdf

", "abstract": "We study D-branes in topologically twisted N = 2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.", "date": "2004-07", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "7", "publisher": "Springer", "pagerange": "Art. No.-045", "id_number": "CaltechAUTHORS:KAPjhep04b", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep04b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/07/045", "primary_object": { "basename": "KAPjhep04b.pdf", "url": "https://authors.library.caltech.edu/records/ameg1-qmx34/files/KAPjhep04b.pdf" }, "pub_year": "2004", "author_list": "Kapustin, Anton and Li, Yi" }, { "id": "https://authors.library.caltech.edu/records/sh9ar-8f681", "eprint_id": 24932, "eprint_status": "archive", "datestamp": "2023-08-19 13:48:20", "lastmod": "2026-04-15 16:59:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Orthogonal polynomials on the unit circle: New results", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2004 Hindawi Publishing Corporation.\nReceived 5 May 2004.\nAccepted July 26, 2004.\nCommunicated by Percy Deift.\nI would like to thank P. Deift, S. Denisov, L. Golinskii, S. Khruschchev, R. Killip, I. Nenciu, P. Nevai, F. Peherstorfer, V. Totik, and A. Zlato\u0161 for useful discussions. This work was supported in part by National Scientific Foundation (NSF) Grant DMS-0140592.", "abstract": "We announce numerous new results in the theory of orthogonal polynomials on the unit circle, most of which involve the connection between a measure on the unit circle in the complex plane and the coefficients in the recursion relations for the polynomials known as Verblunsky coefficients. Included are several applications of the recently discovered matrix realization of Cantero, Moral, and Vel\u00e1zquez. In analogy with the spectral theory of Jacobi matrices, several classes of exotic Verblunsky coefficients are studied. A version of Rahkmanov's theorem is proven with a single gap with eigenvalues allowed in the gap. Analogs of Borg's theorem and the Birman-Schwinger principle are found.", "date": "2004-07", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2004", "number": "53", "publisher": "Oxford University Press", "pagerange": "2837-2880", "id_number": "CaltechAUTHORS:20110818-105014767", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110818-105014767", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1155/S1073792804141664", "pub_year": "2004", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/bgtfe-pd042", "eprint_id": 616, "eprint_status": "archive", "datestamp": "2023-08-22 01:59:13", "lastmod": "2026-04-15 20:24:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gomis-J", "name": { "family": "Gomis", "given": "Jaume" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Two-dimensional unoriented strings and matrix models", "ispublished": "pub", "full_text_status": "public", "keywords": "string duality, tachyon condensation, SUPER-LIOUVILLE THEORY, FRACTIONAL-STATISTICS, CRITICAL-BEHAVIOR, SCALE-INVARIANCE, DILATON TADPOLES, QUANTUM-GRAVITY, RANDOM SURFACES, FIELD-THEORY, D-BRANES, C=1", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2004. \n\nReceived 27 May 2004, accepted for publication 1 June 2004. Published 6 July 2004. \n\nWe would like to thank Juan Maldacena for useful discussions. J. G. was supported by the Sherman Fairchild Prize Fellowship. This research was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - GOMjhep04.pdf

", "abstract": "We investigate unoriented strings and superstrings in two dimensions and their dual matrix quantum mechanics. Most of the models we study have a tachyon tadpole coming from the RP2 worldsheet which needs to be cancelled by a renormalization of the worldsheet theory. We find evidence that the dual matrix models describe the renormalized theory. The singlet sector of the matrix models is integrable and can be formulated in terms of fermions moving in an external potential and interacting via the Calogero-Moser potential. We show that in the double-scaling limit the latter system exhibits particle-hole duality and interpret it in terms of the dual string theory. We also show that oriented string theories in two dimensions can be continuously deformed into unoriented ones by turning on non-local interactions on the worldsheet. We find two unoriented superstring models for which only oriented worldsheets contribute to the S-matrix. A simple explanation for this is found in the dual matrix model.", "date": "2004-06", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "6", "publisher": "Springer", "pagerange": "Art. No.-002", "id_number": "CaltechAUTHORS:GOMjhep04", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GOMjhep04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Sherman Fairchild Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/06/002", "primary_object": { "basename": "GOMjhep04.pdf", "url": "https://authors.library.caltech.edu/records/bgtfe-pd042/files/GOMjhep04.pdf" }, "pub_year": "2004", "author_list": "Gomis, Jaume and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/v34nw-yyv43", "eprint_id": 615, "eprint_status": "archive", "datestamp": "2023-08-22 01:59:08", "lastmod": "2026-04-15 19:02:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Noncritical superstrings in a Ramond-Ramond background", "ispublished": "pub", "full_text_status": "public", "keywords": "superstrings and heterotic strings, matrix models, DEFORMED MATRIX MODEL, 2-DIMENSIONAL STRING THEORY, EXACT S-MATRIX, BLACK-HOLE", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2004. \n\nReceived 1 June 2004, accepted for publication 15 June 2004. Published 28 June 2004. \n\nI am grateful to Jaume Gomis for useful discussions. This work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - KAPjhep04c.pdf

", "abstract": "We use the recently found matrix description of noncritical superstring theory of type-0A to compute tachyon scattering amplitudes in a background with a RR flux. We find that after the string coupling is multiplicatively renormalized, the amplitudes in any genus become polynomial in the RR flux. We propose that in the limit where both the string coupling and the RR flux go to infinity, the theory has a weakly-coupled description in terms of another superstring theory with a vanishingly small RR flux. This duality exchanges the inverse string coupling and the 0-brane charge. The dual superstring theory must have a peculiar property that its only field-theoretic degree of freedom is a massless RR scalar.", "date": "2004-06", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "6", "publisher": "Springer", "pagerange": "Art. No.-024", "id_number": "CaltechAUTHORS:KAPjhep04c", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep04c", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/06/024", "primary_object": { "basename": "KAPjhep04c.pdf", "url": "https://authors.library.caltech.edu/records/v34nw-yyv43/files/KAPjhep04c.pdf" }, "pub_year": "2004", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/ym8rj-ydt09", "eprint_id": 3505, "eprint_status": "archive", "datestamp": "2023-08-22 01:54:18", "lastmod": "2026-04-16 01:41:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Mayers-D", "name": { "family": "Mayers", "given": "Dominic" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Superselection rules and quantum protocols", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum cryptography; information theory; security of data; protocols; quantum computing", "note": "\u00a92004 The American Physical Society \n\n(Received 19 October 2003; published 21 May 2004) \n\nWe thank Stephen Bartlett, Michael Ben-Or, and Sandu Popescu for discussions. This work has been supported in part by the Department of Energy under Grant No. DEFG03-92-ER40701, by the National Science Foundation under Grant No. EIA-0086038, and by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374.", "abstract": "We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system\u2014in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an n-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applies only to a limited class of superselection rules, those in which the superselection sectors are labeled by unitary irreducible representations of a compact symmetry group. The second method uses the concept of the format of a message sent between parties\u2014by verifying the format, the recipient of a message can check whether the message could have been sent by a party who performed charge-conserving operations. By this method, we prove that protocols subject to general superselection rules (including those pertaining to non-Abelian anyons in two dimensions) are no more secure than protocols in the unrestricted world. However, the proof applies only to two-party protocols. Our results show in particular that, if no assumptions are made about the computational power of the cheater, then secure quantum bit commitment and strong quantum coin flipping with arbitrarily small bias are impossible in a world subject to superselection rules.", "date": "2004-05-01", "date_type": "published", "publication": "Physical Review A", "volume": "69", "number": "5", "publisher": "Physical Review A", "pagerange": "Art2. No. 052326", "id_number": "CaltechAUTHORS:KITpra04", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KITpra04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevA.69.052326", "primary_object": { "basename": "KITpra04.pdf", "url": "https://authors.library.caltech.edu/records/ym8rj-ydt09/files/KITpra04.pdf" }, "pub_year": "2004", "author_list": "Kitaev, Alexei; Mayers, Dominic; et al." }, { "id": "https://authors.library.caltech.edu/records/w8twr-7zc39", "eprint_id": 588, "eprint_status": "archive", "datestamp": "2023-08-22 01:51:01", "lastmod": "2026-04-15 22:31:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Grisaru-M-T", "name": { "family": "Grisaru", "given": "Marc T." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } }, { "id": "Zanon-D", "name": { "family": "Zanon", "given": "Daniela" } } ] }, "title": "Planar gravitational corrections for supersymmetric\n gauge theories", "ispublished": "pub", "full_text_status": "public", "keywords": "gauge symmetry, supersymmetric effective theories, \nTOPOLOGICAL STRINGS, COVARIANT SUPERGRAPHS, MATRIX MODELS, LARGE N, AMPLITUDES, DUALITY", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2004. \n\nReceived 11 February 2004, accepted for publication 13 April 2004. Published 26 April 2004. \n\nC.V. thanks the hospitality of the theory group at Caltech, where he was a Gordon Moore Distinguished Scholar. R.D., H.O., and C.V. thank the Simons Workshop on Mathematics and Physics and the YITP at Stony Brook for their hospitality during the completion of this work. \n\nThe research of R.D. was partly supported by FOM and the CMPA grant of the University of Amsterdam. The research of M.T.G. was supported by NSF grant PHY-0070475 and NSERC grant 204540. The research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329. The research of D.Z. was supported in part by INFN, MURST, and the European Commission RTN program HPRN-CT-2000-00113 in which the author is associated to the University of Torino.\n\n

Published - DIJjhep04.pdf

Submitted - 0310061.pdf

", "abstract": "In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N = 1 supersymmetric gauge theories admitting large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.", "date": "2004-04-26", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "4", "publisher": "Springer", "pagerange": "Art. No.-028", "id_number": "CaltechAUTHORS:DIJjhep04", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:DIJjhep04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" }, { "agency": "University of Amsterdam" }, { "agency": "NSF", "grant_number": "PHY-0070475" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "204540" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "Istituto Nazionale di Fisica Nucleare (INFN)" }, { "agency": "Ministero dell'Istruzione, dell'Universit\u00e0 e della Ricerca (MIUR)" }, { "agency": "European Commission", "grant_number": "HPRN-CT-2000-00113" } ] }, "other_numbering_system": { "items": [ { "id": "68-2454", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/04/028", "primary_object": { "basename": "0310061.pdf", "url": "https://authors.library.caltech.edu/records/w8twr-7zc39/files/0310061.pdf" }, "related_objects": [ { "basename": "DIJjhep04.pdf", "url": "https://authors.library.caltech.edu/records/w8twr-7zc39/files/DIJjhep04.pdf" } ], "pub_year": "2004", "author_list": "Dijkgraaf, Robbert; Grisaru, Marc T.; et al." }, { "id": "https://authors.library.caltech.edu/records/p9dxd-0p698", "eprint_id": 3167, "eprint_status": "archive", "datestamp": "2023-08-22 01:49:38", "lastmod": "2026-04-15 22:34:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kachru-S", "name": { "family": "Kachru", "given": "Shamit" } }, { "id": "Liu-Xiao", "name": { "family": "Liu", "given": "Xiao" } }, { "id": "McAllister-L", "name": { "family": "McAllister", "given": "Liam" } } ] }, "title": "Heterotic moduli stabilization with fractional Chern-Simons invariants", "ispublished": "pub", "full_text_status": "public", "keywords": "superstrings; membrane theory; grand unified theory; Chern-Simons theory; spontaneous symmetry breaking", "note": "\u00a92004 The American Physical Society \n\n(Received 11 November 2003; published 29 April 2004) \n\nWe would like to thank B. Acharya, N. Arkani-Hamed, P. Aspinwall, M. Becker, K. Dasgupta, M. Dine, M. Douglas, R. Kallosh, A. Krause, E. Silverstein, S. Thomas, S. Trivedi, and E. Witten for interesting discussions on related subjects. S.G. is supported in part by the RFBR Grant No. 01-01-00549 and the RFBR grant for Young Scientists 02-01-06322. The work of S.K. is supported in part by the David and Lucile Packard Foundation, National Science Foundation Grant No. PHY-0097915, and the DOE under Contract No. DE-AC03-76SF00515. The work of L.M. is supported by the National Science Foundation.\n\n

Published - GUKprd04.pdf

", "abstract": "We show that fractional flux from Wilson lines can stabilize the moduli of heterotic string compactifications on Calabi-Yau threefolds. We observe that the Wilson lines used in GUT symmetry breaking naturally induce a fractional flux. When combined with a hidden-sector gaugino condensate, this generates a potential for the complex structure moduli, K\u00e4hler moduli, and dilaton. This potential has a supersymmetric AdS minimum at moderately weak coupling and large volume. Notably, the necessary ingredients for this construction are often present in realistic models. We explore the type IIA dual phenomenon, which involves Wilson lines in D6-branes wrapping a three-cycle in a Calabi-Yau threefold, and comment on the nature of the fractional instantons that change the Chern-Simons invariant.", "date": "2004-04-15", "date_type": "published", "publication": "Physical Review D", "volume": "69", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 086008", "id_number": "CaltechAUTHORS:GUKprd04", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKprd04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "PHY-0097915" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00515" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.69.086008", "primary_object": { "basename": "GUKprd04.pdf", "url": "https://authors.library.caltech.edu/records/p9dxd-0p698/files/GUKprd04.pdf" }, "pub_year": "2004", "author_list": "Gukov, Sergei; Kachru, Shamit; et al." }, { "id": "https://authors.library.caltech.edu/records/766s2-30b74", "eprint_id": 66684, "eprint_status": "archive", "datestamp": "2023-08-22 01:46:09", "lastmod": "2026-04-15 19:32:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Topological strings on noncommutative manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Topological sigma-models; topological D-branes; noncommutative geometry", "note": "\u00a9 2004 World Scientific Publishing. \n\nReceived: 29 October 2003; Revised: 24 November 2003. \n\nI would like to thank Marco Gualtieri, Nigel Hitchin, and Dmitri Orlov for discussions. I also would like to thank the organizers of the workshop \"Geometry and Topology of Strings\" at KITP, UC Santa Barbara, July-August 2004, for a very stimulating meeting. This research was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Submitted - 0310057.pdf

", "abstract": "We identify a deformation of the N=2 supersymmetric sigma model on a Calabi\u2013Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperk\u00e4hler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.", "date": "2004-04", "date_type": "published", "publication": "International Journal of Geometric Methods in Modern Physics", "volume": "1", "number": "2", "publisher": "World Scientific", "pagerange": "49-81", "id_number": "CaltechAUTHORS:20160505-104335472", "issn": "0219-8878", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-104335472", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219887804000034", "primary_object": { "basename": "0310057.pdf", "url": "https://authors.library.caltech.edu/records/766s2-30b74/files/0310057.pdf" }, "pub_year": "2004", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/2ha7d-ah715", "eprint_id": 2018, "eprint_status": "archive", "datestamp": "2023-08-22 01:35:09", "lastmod": "2026-04-15 23:21:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Takanayagi-Tadashi", "name": { "family": "Takayanagi", "given": "Tadashi" } }, { "id": "Toumbas-N", "name": { "family": "Toumbas", "given": "Nicolaos" } } ] }, "title": "Flux backgrounds in 2D string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Superstrings and Heterotic Strings, D-branes, Black Holes in String Theory, Matrix Models", "note": "\u00a9 Institute of Physics 2004 \n\nReceived 20 January 2004, accepted for publication 4 March 2004, Published 19 March 2004 \n\nWe would like to thank V. Balasubramanian, J. de Boer, R. Dijkgraaf, T. Eguchi, J. Gomis, P.M. Ho, A. Kapustin, J. Karczmarek, Y. Matsuo, J. Mcgreevy, S. Murthy, S. Terashima, C. Vafa, H. Verlinde, X. Yi and especially I. Klebanov, J. Maldacena, S. Minwalla, N. Seiberg and A. Strominger for valuable discussions. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. S.G. is also supported in part by RFBR grant 01-02-17488. T.T. would like to thank Institute for Advanced Study for its hospitality. The work of T.T. was supported in part by DOE grant DE-FG03-91ER40654. \n\nE-print number: hep-th/0312208\n\n

Published - GUKjhep04.pdf

", "abstract": "We study RR flux backgrounds in two dimensional type 0 string theories. In particular, we study the relation between the 0A matrix model and the extremal black hole in two dimensions. Using T-duality we find a dual flux background in type 0B theory and propose its matrix model description. When the Fermi level \u03bc is set to zero this system remains weakly coupled and exhibits a larger symmetry related to the structure of flux vacua. Finally, we construct a two dimensional type-IIB background as an orbifold of the 0B background.", "date": "2004-03", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2004", "number": "3", "publisher": "Springer", "pagerange": "Art. No. 017", "id_number": "CaltechAUTHORS:GUKjhep04", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKjhep04", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-91ER40654" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2004/03/017", "primary_object": { "basename": "GUKjhep04.pdf", "url": "https://authors.library.caltech.edu/records/2ha7d-ah715/files/GUKjhep04.pdf" }, "pub_year": "2004", "author_list": "Gukov, Sergei; Takayanagi, Tadashi; et al." }, { "id": "https://authors.library.caltech.edu/records/v7gfx-sd755", "eprint_id": 66710, "eprint_status": "archive", "datestamp": "2023-08-19 13:11:14", "lastmod": "2026-04-15 23:38:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Rational Conformal Field Theories and Complex Multiplication", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag. \n\nReceived: 18 July 2003. Accepted: 26 August 2003. Published online: 23 January 2004.\n\nWe would like to thank D. Kazhdan and B. Mazur for many illuminating discussions on complex multiplication. We are also grateful to J. de Jong, J. Maldacena, K. Oguiso, H. Ooguri, F. Oort, A. Recknagel, S. Shenker, F. Rodriguez-Villegas, and E. Witten for valuable discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize\nFellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. The work of C.V. is supported in part by NSF grants PHY-9802709 and DMS 0074329. \n\nCommunicated by Y. Kawahigashi.\n\n

Submitted - 0203213.pdf

", "abstract": "We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFT's corresponding to the T ^2 target and identify the Cardy branes with geometric branes. The T ^2 's leading to RCFT's admit \"complex multiplication\" which characterizes Cardy branes as specific D0-branes. We propose a condition for the conformal sigma model to be RCFT for arbitrary Calabi-Yau n-folds, which agrees with the known cases. Together with recent conjectures by mathematicians it appears that rational conformal theories are not dense in the space of all conformal theories, and sometimes appear to be finite in number for Calabi-Yau n-folds for n>2. RCFT's on K3 may be dense. We speculate about the meaning of these special points in the moduli spaces of Calabi-Yau n-folds in connection with freezing geometric moduli.", "date": "2004-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "246", "number": "1", "publisher": "Springer", "pagerange": "181-210", "id_number": "CaltechAUTHORS:20160506-080721343", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-080721343", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-003-1032-0", "primary_object": { "basename": "0203213.pdf", "url": "https://authors.library.caltech.edu/records/v7gfx-sd755/files/0203213.pdf" }, "pub_year": "2004", "author_list": "Gukov, Sergei and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/4bgvm-3at53", "eprint_id": 66990, "eprint_status": "archive", "datestamp": "2023-08-19 13:11:22", "lastmod": "2026-04-15 20:24:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Acharya-B-S", "name": { "family": "Acharya", "given": "Bobby S." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "M theory and singularities of exceptional holonomy manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Elsevier B.V. \n\nAccepted 28 October 2003. editor: A. Schwimmer. \n\nVarious topics covered in this review are based on the work done together with A. Brandhuber, J. Gomis, S. Gubser, X. de la Ossa, D. Tong, J. Sparks, C. Vafa, E. Witten, S.-T. Yau, and E. Zaslow, whom we wish to thank for many useful discussions and collaboration. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by RFBR grant 01-01-00549 and RFBR grant for Young Scientists 02-01-06322.\n\n

Submitted - 0409191.pdf

", "abstract": "M theory compactifications on G_2 holonomy manifolds, whilst supersymmetric, require singularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a simple explanation in M theory.", "date": "2004-03", "date_type": "published", "publication": "Physics Reports", "volume": "392", "number": "3", "publisher": "Elsevier", "pagerange": "121-189", "id_number": "CaltechAUTHORS:20160511-110724676", "issn": "0370-1573", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-110724676", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/j.physrep.2003.10.017", "primary_object": { "basename": "0409191.pdf", "url": "https://authors.library.caltech.edu/records/4bgvm-3at53/files/0409191.pdf" }, "pub_year": "2004", "author_list": "Acharya, Bobby S. and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/2jqee-tcd23", "eprint_id": 56963, "eprint_status": "archive", "datestamp": "2023-08-19 12:47:17", "lastmod": "2026-03-09 21:28:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "On certain unitary group Shimura varieties. Vari\u00e9t\u00e9s de Shimura, espaces de Rapoport-Zink et correspondances de Langlands locales", "ispublished": "pub", "full_text_status": "public", "keywords": "Shimura varieties, Barsotti-Tate groups, Rapoport-Zink spaces, Langlands correspondences", "note": "\u00a9 2004 Soci\u00e9t\u00e9 Math\u00e9matique de France. \n\nPartially supported under a I.N.d.A.M. Fellowship. \n\nThe author will like to thank R. Taylor suggesting the topic of this paper, and for his inestimable help with all the phases of its realization. She is also very grateful to B. Conrad, J. de Jong, L. Fargues, T. Graber and F. Oort for many enlighting mathematical discussions and for carefully reading early drafts of this paper.\n\n

Submitted - Ast.pdf

", "abstract": "In this paper, we study the local geometry at a prime p of a certain class of (PEL) type Shimura varieties. We begin by studying the Newton polygon stratification of the special fiber of a Shimura variety with good reduction at p. Each stratum can be described in terms of the products of the reduced fiber of the corresponding Rapoport-Zink space with some smooth varieties (we call the Igusa varieties), and of the action on them of a certain p-adic group T_\u03b1, which depends on the stratum. (The definition of the Igusa varieties in this context is based upon a result of Zink on the slope filtration of a Barsotti-Tate group and on the notion of Oort's foliation.) In particular, we show that it is possible to compute the \u00e9tale cohomology with compact supports of the Newton polygon strata, in terms of the \u00e9tale cohomology with compact supports of the Igusa varieties and the Rapoport-Zink spaces, and of the group homology of T_\u03b1. Further more, we are able to extend Zariski locally the above constructions to characteristic zero and obtain an analoguous description for the \u00e9tale cohomology of the Shimura varieties in both the cases of good and bad reduction at p. As a result of this analysis, we obtain a description of the l-adic cohomology of the Shimura varieties, in terms of the l-adic cohomology with compact supports of the Igusa varieties and of the Rapoport-Zink spaces.", "date": "2004", "date_type": "published", "publication": "Ast\u00e9risque", "volume": "291", "publisher": "Societe Mathematique de France", "pagerange": "201-331", "id_number": "CaltechAUTHORS:20150424-131722811", "issn": "0303-1179", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150424-131722811", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Istituto Nazionale di Alta Matematica (INdAM)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "Ast.pdf", "url": "https://authors.library.caltech.edu/records/2jqee-tcd23/files/Ast.pdf" }, "pub_year": "2004", "author_list": "Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/fd2v8-vwd20", "eprint_id": 24916, "eprint_status": "archive", "datestamp": "2023-08-19 12:43:24", "lastmod": "2026-04-15 19:03:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Renormalization and motivic galois theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Hindawi Publishing Corporation. Received September 12, 2004. Accepted November 2, 2004. Communicated by Yuri I. Manin.\n\n

Submitted - 0409306.pdf

", "abstract": "We investigate the nature of divergences in quantum field theory, showing that they are organized in the structure of a certain \"motivic Galois group\" U*, which is uniquely determined and universal with respect to the set of physical theories. The renormalization group can be identified canonically with a one-parameter subgroup of U*. The group U* arises through a Riemann-Hilbert correspondence. Its representations classify equisingular flat vector bundles, where the equisingularity condition is a geometric formulation of the fact that in quantum field theory the counterterms are independent of the choice of a unit of mass. As an algebraic group scheme, U* is a semidirect product by the multiplicative group G_m of a prounipotent group scheme whose Lie algebra is freely generated by one generator in each positive integer degree. There is a universal singular frame in which all divergences disappear. When computed as iterated integrals, its coefficients are certain rational numbers that appear in the local index formula of Connes-Moscovici. When working with formal Laurent series over \u211a, the data of equisingular flat vector bundles define a Tannakian category whose properties are reminiscent of a category of mixed Tate motives.", "date": "2004", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "76", "publisher": "Oxford University Press", "pagerange": "4073-4091", "id_number": "CaltechAUTHORS:20110817-140437615", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110817-140437615", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1155/S1073792804143122", "primary_object": { "basename": "0409306.pdf", "url": "https://authors.library.caltech.edu/records/fd2v8-vwd20/files/0409306.pdf" }, "pub_year": "2004", "author_list": "Connes, Alain and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/9z6dh-x1s64", "eprint_id": 25365, "eprint_status": "archive", "datestamp": "2023-08-19 12:44:18", "lastmod": "2026-04-15 19:55:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "David" }, "orcid": "0000-0001-5924-3849" }, { "id": "Killip-R", "name": { "family": "Killip", "given": "Rowan" }, "orcid": "0000-0002-4272-7916" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Necessary and Sufficient Conditions in the Spectral Theory\n of Jacobi Matrices and Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2004 Hindawi Publishing Corporation. Received September 11, 2003. Revision received December 3, 2003. Accepted January 29, 2004. We would like to thank Roman Romanov for drawing our attention to [9]. David Damanik was supported in part by National Science Foundation (NSF) Grant DMS-0227289, and Barry Simon was supported in part by NSF Grant DMS-0140592.", "abstract": "We announce three results in the theory of Jacobi matrices and Schr\u00f6dinger operators. First, we give necessary and sufficient conditions for a measure to be the spectral measure of a Schr\u00f6dinger operator \u2212d^2/dx^2+V(x) on L^2 (0,\u221e) with V \u2208 L2(0,\u221e) and the boundary condition u(0) = 0. Second, we give necessary and sufficient conditions on the Jacobi parameters for the associated orthogonal polynomials to have Szeg\u0151 asymptotics. Finally, we provide necessary and sufficient conditions on a measure to be the spectral measure of a Jacobi matrix with exponential decay at a given rate.", "date": "2004", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2004", "number": "22", "publisher": "Oxford University Press", "pagerange": "1087-1097", "id_number": "CaltechAUTHORS:20110920-104550878", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110920-104550878", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0227289" }, { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1155/S1073792804132790", "pub_year": "2004", "author_list": "Damanik, David; Killip, Rowan; et al." }, { "id": "https://authors.library.caltech.edu/records/dxn8p-p4989", "eprint_id": 27291, "eprint_status": "archive", "datestamp": "2023-08-19 12:45:03", "lastmod": "2026-03-09 23:12:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" }, { "id": "Wang-Song", "name": { "family": "Wang", "given": "Song" }, "orcid": "0000-0003-3116-5038" } ] }, "title": "A Cuspidality Criterion for the Functorial Product\n on GL(2) \u00d7 GL(3) with a Cohomological Application", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2004 Hindawi Publishing Corporation. Received 17 September 2003. Revision received 14 January 2004. Accepted March 22, 2004. Communicated by Freydoon Shahidi. The first author would like to thank Avner Ash for his question and for making comments on an earlier version of this paper, Freydoon Shahidi for his interest, Mahdi Asgari for initially tweaking his curiosity (at Park City, UT) about the problem of establishing a precise cuspidality criterion for the\nKim-Shahidi product, David Rohrlich for his comments on Hecke characters, and the National Science Foundation for financial support through Grant DMS-0100372. The second author would like to thank James Cogdell and Henry Kim for their interest in his lecture on this work at the Fields Institute Workshop on Automorphic L-functions in May 2003.Both authors thank the referee for a careful reading of the paper.", "abstract": "For all cusp forms \u03c0 on GL(3) and \u03c0\u2032 on GL(2) over a number field F, H. Kim and F. Shahidi have functorially associated an automorphic form Formula on GL(6) such that L(s, \u03a0) agrees with the Rankin-Selberg L-function of the pair (\u03c0, \u03c0\u2032). First we establish a criterion as to when \u03a0 is cuspidal. Then we apply it to construct non-self-dual, nonmonomial cuspidal cohomology classes for suitable congruence subgroups of SL(3, \u2124). We also analyze the Galois image of certain related \u2113-adic representations.", "date": "2004", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2004", "number": "27", "publisher": "Oxford University Press", "pagerange": "1355-1394", "id_number": "CaltechAUTHORS:20111019-072552735", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111019-072552735", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0100372" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1155/S1073792804132856", "pub_year": "2004", "author_list": "Ramakrishnan, Dinakar and Wang, Song" }, { "id": "https://authors.library.caltech.edu/records/zsaxt-79888", "eprint_id": 66717, "eprint_status": "archive", "datestamp": "2023-08-19 12:48:15", "lastmod": "2026-04-15 17:13:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Orlov-D", "name": { "family": "Orlov", "given": "Dmitri" }, "orcid": "0000-0002-2230-457X" } ] }, "title": "Lectures on mirror symmetry, derived categories, and D-branes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2004 Turpion Ltd. \n\nThe first author was supported in part by the DOE grant DE-FG03-92-ER40701. The second author was supported in part by the grant of the President of RF for young scientists D-2731.2004.1, by Civic Research Development Foundation (CRDF Award No RM1-2405-MO-02), and by the Russian Science Support Foundation.\n\n

Submitted - 0308173.pdf

", "abstract": "This paper, mainly intended for a mathematical audience, is an introduction to homological mirror symmetry, derived categories, and topological D-branes. Mirror symmetry from the point of view of physics is explained, along with the relationship between symmetry and derived categories, and the reason why the Fukaya category must be extended by using co-isotropic A-branes. There is also a discussion of how to extend the definition of the Floer homology to these objects and a description of mirror symmetry for flat tori. The paper consists of four lectures given at the Institute of Pure and Applied Mathematics (Los Angeles) in March 2003, as a part of the programme \"Symplectic Geometry and Physics\".", "date": "2004", "date_type": "published", "publication": "Russian Mathematical Surveys", "volume": "59", "number": "5", "publisher": "Turpion", "pagerange": "907-940", "id_number": "CaltechAUTHORS:20160506-151404465", "issn": "0036-0279", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-151404465", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "President of of the Russian Federation", "grant_number": "D-2731.2004.1" }, { "agency": "Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF)", "grant_number": "RM1-2405-MO-02" }, { "agency": "Russian Science Support Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1070/RM2004v059n05ABEH000772", "primary_object": { "basename": "0308173.pdf", "url": "https://authors.library.caltech.edu/records/zsaxt-79888/files/0308173.pdf" }, "pub_year": "2004", "author_list": "Kapustin, Anton and Orlov, Dmitri" }, { "id": "https://authors.library.caltech.edu/records/ph8hr-s1495", "eprint_id": 77926, "eprint_status": "archive", "datestamp": "2023-08-19 12:40:14", "lastmod": "2026-04-15 17:06:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "David" }, "orcid": "0000-0001-5924-3849" }, { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "Dirk" }, "orcid": "0000-0002-0643-0138" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Bound states and the Szeg\u0151 condition for Jacobi matrices and Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Elsevier Inc. \n\nReceived 22 August 2002, Accepted 2 January 2003, Available online 29 April 2003. \n\nCommunicated by L. Gross \n\nWe thank Rowan Killip, Paul Nevai, Mihai Stoiciu, and Andrej Zlato\u0161 for valuable communications. \n\nSupported in part by NSF Grant DMS-0227289. \nSupported in part by NSF Grants DMS-9707661 and DMS-0140592.\n\n

Submitted - 0208035.pdf

", "abstract": "For Jacobi matrices with a_n=1+(\u22121)^n\u03b1n\u2212\u03b3, b_n=(\u22121)^n\u03b2n\u2212\u03b3, we study bound states and the Szeg\u0151 condition. We provide a new proof of Nevai's result that if \u03b3>12, the Szeg\u0151 condition holds, which works also if one replaces (\u22121)^n by cos(\u03bcn). We show that if \u03b1=0, \u03b2\u22600, and \u03b3<12, the Szeg\u0151 condition fails. We also show that if \u03b3=1, \u03b1 and \u03b2 are small enough (\u03b2^2+8\u03b1^2<1/24 will do), then the Jacobi matrix has finitely many bound states (for \u03b1=0, \u03b2 large, it has infinitely many).", "date": "2003-12-20", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "205", "number": "2", "publisher": "Elsevier", "pagerange": "357-379", "id_number": "CaltechAUTHORS:20170602-143616540", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170602-143616540", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0227289" }, { "agency": "NSF", "grant_number": "DMS-9707661" }, { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/S0022-1236(03)00070-3", "primary_object": { "basename": "0208035.pdf", "url": "https://authors.library.caltech.edu/records/ph8hr-s1495/files/0208035.pdf" }, "pub_year": "2003", "author_list": "Damanik, David; Hundertmark, Dirk; et al." }, { "id": "https://authors.library.caltech.edu/records/mjp58-gps06", "eprint_id": 3081, "eprint_status": "archive", "datestamp": "2023-08-22 01:09:43", "lastmod": "2026-04-15 22:35:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Li-Yi", "name": { "family": "Li", "given": "Yi" } } ] }, "title": "D-branes in Landau-Ginzburg models and algebraic geometry", "ispublished": "pub", "full_text_status": "public", "keywords": "topological field theories; D-branes; differential and algebraic geometry", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2003. \n\nReceived 20 August 2003, accepted for publication 3 December 2003. Published 2 February 2004. \n\nWe are deeply grateful to Maxim Kontsevich for sharing with us his ideas about B-branes in Landau-Ginzburg models, and to Alexander Polishchuk for pointing out the relevance of non-homogeneous Koszul duality. We also thank Kentaro Hori and Dmitri Orlov for reading a preliminary draft of the paper and making a number of valuable comments. The first author would like to thank Institut des Hautes Etudes Scientifiques for hospitality during the writing of this paper. This work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - KAPjhep03.pdf

", "abstract": "We study topological D-branes of type B in N = 2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N = 2 sigma-model with a Calabi-Yau target space are described by the derived category of coherent sheaves on this space. M. Kontsevich previously proposed a candidate category for B-branes in N = 2 Landau-Ginzburg models, and our computations confirm this proposal. We also give a heuristic physical derivation of the proposal. Assuming its validity, we can completely describe the category of B-branes in an arbitrary massive Landau-Ginzburg model in terms of modules over a Clifford algebra. Assuming in addition Homological Mirror Symmetry, our results enable one to compute the Fukaya category for a large class of Fano varieties. We also provide a (somewhat trivial) counter-example to the hypothesis that given a closed string background there is a unique set of D-branes consistent with it.", "date": "2003-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2003", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 005", "id_number": "CaltechAUTHORS:KAPjhep03", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2003/12/005", "primary_object": { "basename": "KAPjhep03.pdf", "url": "https://authors.library.caltech.edu/records/mjp58-gps06/files/KAPjhep03.pdf" }, "pub_year": "2003", "author_list": "Kapustin, Anton and Li, Yi" }, { "id": "https://authors.library.caltech.edu/records/0xwde-yf153", "eprint_id": 77453, "eprint_status": "archive", "datestamp": "2023-08-19 12:28:49", "lastmod": "2026-04-15 18:25:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zlato\u0161-A", "name": { "family": "Zlato\u0161", "given": "Andrej" } } ] }, "title": "Sum Rules and the Szeg\u0151 Condition for Orthogonal Polynomials on the Real Line", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Springer-Verlag Berlin Heidelberg.\n\nReceived: 27 January 2003; Accepted: 25 March 2003; First Online: 10 October 2003.\n\nSupported in part by NSF grant DMS-9707661.\n\n

Submitted - 0206023.pdf

", "abstract": "We study the Case sum rules, especially C_0, for general Jacobi matrices. We establish situations where the sum rule is valid. Applications include an extension of Shohat's theorem to cases with an infinite point spectrum and a proof that if lim n(a_n\u22121)=\u03b1 and lim nb_n=\u03b2 exist and 2\u03b1<|\u03b2|, then the Szeg\u0151 condition fails.", "date": "2003-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "242", "number": "3", "publisher": "Springer", "pagerange": "393-423", "id_number": "CaltechAUTHORS:20170515-111325638", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170515-111325638", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-003-0906-5", "primary_object": { "basename": "0206023.pdf", "url": "https://authors.library.caltech.edu/records/0xwde-yf153/files/0206023.pdf" }, "pub_year": "2003", "author_list": "Simon, Barry and Zlato\u0161, Andrej" }, { "id": "https://authors.library.caltech.edu/records/cjmxf-76417", "eprint_id": 66713, "eprint_status": "archive", "datestamp": "2023-09-22 22:52:51", "lastmod": "2026-04-15 19:24:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Orlov-D", "name": { "family": "Orlov", "given": "Dmitri" }, "orcid": "0000-0002-2230-457X" } ] }, "title": "Remarks on A-branes, mirror symmetry, and the Fukaya category", "ispublished": "pub", "full_text_status": "public", "keywords": "A-branes; Mirror symmetry; The Fukaya category", "note": "\u00a9 2003 Elsevier Science B.V. \n\nReceived 31 May 2002, Accepted 28 January 2003, Available online 2 April 2003. \n\nWe are grateful to Dan Freed for useful suggestions and to Ezra Getzler for pointing out the relevance of bihamiltonian geometry. Some preliminary results have been presented by AK at the Duality Workshop, ITP, Santa Barbara, 18 June\u201313 July, 2001. AK would like to thank Ron Donagi, Dan Freed, Ezra Getzler, Tony Pantev, and other participants for stimulating discussions, and the organizers for making this workshop possible. AK was supported in part by DOE grants DE-FG02-90ER40542 and DE-FG03-92-ER40701. DO was supported in part by RFFI grant 99-01-01144 and a grant for support of leading scientific groups N 00-15-96085. The research described in this publication was made possible in part by Award No RMl-2089 of the US. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF).\n\n

Submitted - 0109098.pdf

", "abstract": "We discuss D-branes of the topological A-model (A-branes), which are believed to be closely related to the Fukaya category. We give string theory arguments which show that A-branes are not necessarily Lagrangian submanifolds in the Calabi\u2013Yau: more general coisotropic branes are also allowed, if the line bundle on the brane is not flat. We show that a coisotropic A-brane has a natural structure of a foliated manifold with a transverse holomorphic structure. We argue that the Fukaya category must be enlarged with such objects for the Homological Mirror Symmetry Conjecture to be true.", "date": "2003-10", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "48", "number": "1", "publisher": "Elsevier", "pagerange": "84-99", "id_number": "CaltechAUTHORS:20160506-093522683", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-093522683", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Russian Foundation for Fundamental Investigations (RFFI)", "grant_number": "99-01-01144" }, { "agency": "Russian Foundation for Fundamental Investigations (RFFI)", "grant_number": "N 00-15-96085" }, { "agency": "Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF)", "grant_number": "RM1-2089" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0393-0440(03)00026-3", "primary_object": { "basename": "0109098.pdf", "url": "https://authors.library.caltech.edu/records/cjmxf-76417/files/0109098.pdf" }, "pub_year": "2003", "author_list": "Kapustin, Anton and Orlov, Dmitri" }, { "id": "https://authors.library.caltech.edu/records/kr7zj-3pg39", "eprint_id": 3766, "eprint_status": "archive", "datestamp": "2023-08-22 00:49:29", "lastmod": "2026-04-15 20:03:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kazakov-V-A", "name": { "family": "Kazakov", "given": "Vladimir A." } }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Perturbative analysis of gauged matrix models", "ispublished": "pub", "full_text_status": "public", "keywords": "M-theory; gauge field theory; spontaneous symmetry breaking; perturbation theory", "note": "\u00a92003 The American Physical Society. \n\nReceived 5 May 2003; published 18 August 2003. \n\nWe would like to thank M. Aganagic, R. Bousso, F. Cachazo, S. J. Gates, Jr., M. Marino, A. Marshakov, H. Ooguri, S. Theisen, and K. Zarembo for valuable discussions. The research of R.D. is partly supported by FOM and the CMPA grant of the University of Amsterdam. S.G. is supported by the Clay Mathematics Institute, RFBR grants 01-01-00549 and 02-01-06322. V.A.K. is partly supported by European Union under the RTN contracts HPRN-CT-2000-00122 and -00131. C.V. is partly supported by NSF grants PHY-9802709 and DMS-0074329. We would like to thank the Max Planck Institute in Potsdam (V.A.K.), Ecole Normale Superieure (S.G.), and Harvard University (R.D.) for kind hospitality during part of this work.\n\n

Published - DIJprd03.pdf

", "abstract": "We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that nonperturbative aspects of [script N] = 1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for [script N] = 2 gauge theory, the Montonen-Olive modular invariance for [script N] = 1*, and the superpotential for the Leigh-Strassler deformation of [script N] = 4 can be systematically computed in perturbation theory of the matrix model or gauge theory (even though in some of these cases an exact answer can also be obtained by summing up planar diagrams of matrix models).", "date": "2003-08-15", "date_type": "published", "publication": "Physical Review D", "volume": "68", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. No. 045007", "id_number": "CaltechAUTHORS:DIJprd03", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:DIJprd03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Stichting voor Fundamenteel Onderzoek der Materie (FOM)" }, { "agency": "University of Amsterdam" }, { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "02-01-06322" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00122" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00131" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.68.045007", "primary_object": { "basename": "DIJprd03.pdf", "url": "https://authors.library.caltech.edu/records/kr7zj-3pg39/files/DIJprd03.pdf" }, "pub_year": "2003", "author_list": "Dijkgraaf, Robbert; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/p2kv5-y2516", "eprint_id": 27150, "eprint_status": "archive", "datestamp": "2023-08-19 11:46:57", "lastmod": "2026-04-15 23:38:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kaminsky-K", "name": { "family": "Kaminsky", "given": "Kirk" } }, { "id": "Okawa-Yuji", "name": { "family": "Okawa", "given": "Yuji" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Quantum aspects of the Seiberg\u2013Witten map in noncommutative Chern\u2013Simons theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Elsevier B.V. \n\nReceived 4 February 2003; Accepted 2 May 2003. Available online 27 May 2003. \n\nThis article is registered under preprint number hep-th/0301133. \n\nY.O. and H.O. would like to thank the Aspen Center for Physics, where part of this work was done. This work was supported in part by the DOE grant DE-FG03-92ER40701. The work of K.K. was supported in part by the Natural Sciences and Engineering Research Council of Canada. The work of Y.O. was supported in part by a John A. McCone Fellowship in Theoretical Physics from California Institute of Technology.\n\n

Submitted - KAMnpb03preprint.pdf

", "abstract": "Noncommutative Chern\u2013Simons theory can be classically mapped to commutative Chern\u2013Simons theory by the Seiberg\u2013Witten map. We provide evidence that the equivalence persists at the quantum level by computing two and three-point functions of field strengths on the commutative side and their Seiberg\u2013Witten transforms on the noncommutative side to the first nontrivial order in perturbation theory.", "date": "2003-07-21", "date_type": "published", "publication": "Nuclear Physics B", "volume": "663", "number": "1-2", "publisher": "Elsevier", "pagerange": "33-59", "id_number": "CaltechAUTHORS:20111011-075425541", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111011-075425541", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "John A. McCone Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2420", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(03)00383-3", "primary_object": { "basename": "KAMnpb03preprint.pdf", "url": "https://authors.library.caltech.edu/records/p2kv5-y2516/files/KAMnpb03preprint.pdf" }, "pub_year": "2003", "author_list": "Kaminsky, Kirk; Okawa, Yuji; et al." }, { "id": "https://authors.library.caltech.edu/records/nqfrn-c7g37", "eprint_id": 79427, "eprint_status": "archive", "datestamp": "2023-08-19 11:42:46", "lastmod": "2026-04-15 20:18:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Damanik-D", "name": { "family": "Damanik", "given": "D." }, "orcid": "0000-0001-5924-3849" }, { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "D." }, "orcid": "0000-0002-0643-0138" }, { "id": "Killip-R", "name": { "family": "Killip", "given": "R." }, "orcid": "0000-0002-4272-7916" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Variational Estimates for Discrete Schr\u00f6dinger Operators with Potentials of Indefinite Sign", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Springer-Verlag.\n\nReceived: 5 November 2002. Accepted: 31 January 2003\nPublished online: 3 June 2003.\n\nSupported in part by NSF grant DMS-0227289. \n\nSupported in part by NSF grant DMS-0140592.\n\n

Submitted - 0211015.pdf

", "abstract": "Let H be a one-dimensional discrete Schr\u00f6dinger operator. We prove that if \u03a3_(ess)(H)\u2282[\u22122,2], then H\u2212H_0 is compact and \u03a3_(ess)(H)=[\u22122,2]. We also prove that if H_0 + 1/4 V^2 has at least one bound state, then the same is true for H_0 + V. Further, if H_0 + 1/4 V^2 has infinitely many bound states, then so does H_0 + V. Consequences include the fact that for decaying potential V with lim\u2006inf_(|n|\u2192 \u221e|nV(n)|> 1 lim\u2006inf_(|n|\u2192\u221e)|nV(n)|>1, H_0 + V has infinitely many bound states; the signs of V are irrelevant. Higher-dimensional analogues are also discussed.", "date": "2003-07", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "238", "number": "3", "publisher": "Springer", "pagerange": "545-562", "id_number": "CaltechAUTHORS:20170726-131903680", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170726-131903680", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0227289" }, { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s00220-003-0868-7", "primary_object": { "basename": "0211015.pdf", "url": "https://authors.library.caltech.edu/records/nqfrn-c7g37/files/0211015.pdf" }, "pub_year": "2003", "author_list": "Damanik, D.; Hundertmark, D.; et al." }, { "id": "https://authors.library.caltech.edu/records/4rhar-vez51", "eprint_id": 81815, "eprint_status": "archive", "datestamp": "2023-08-22 00:41:04", "lastmod": "2026-04-15 18:12:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Quebbemann-H-G", "name": { "family": "Quebbemann", "given": "H.-G." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "On the involutions fixing the class of a lattice", "ispublished": "pub", "full_text_status": "public", "keywords": "Lattices; Modular; Iso-dual; Involutions; 2-Groups", "note": "\u00a9 2003 Elsevier Science (USA). \n\nReceived 23 October 2002, Revised 15 November 2002, Available online 16 April 2003.\n\n

Submitted - 0301308.pdf

", "abstract": "With any integral lattice \u039b in n-dimensional Euclidean space we associate an elementary abelian 2-group I(\u039b) whose elements represent parts of the dual lattice that are similar to \u039b. There are corresponding involutions on modular forms for which the theta series of \u039bis an eigenform; previous work has focused on this connection. In the present paper I(\u039b) is considered as a quotient of some finite 2-subgroup of O_n(\u211d). We establish upper bounds, depending only on n, for the order of I(\u039b), and we study the occurrence of similarities of specific types.", "date": "2003-07", "date_type": "published", "publication": "Journal of Number Theory", "volume": "101", "number": "1", "publisher": "Elsevier", "pagerange": "185-194", "id_number": "CaltechAUTHORS:20170925-135839254", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-135839254", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0022-314X(03)00022-2", "primary_object": { "basename": "0301308.pdf", "url": "https://authors.library.caltech.edu/records/4rhar-vez51/files/0301308.pdf" }, "pub_year": "2003", "author_list": "Quebbemann, H.-G. and Rains, E. M." }, { "id": "https://authors.library.caltech.edu/records/csfjn-qpd26", "eprint_id": 12224, "eprint_status": "archive", "datestamp": "2023-08-22 00:39:26", "lastmod": "2026-03-09 02:39:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Li-Yi", "name": { "family": "Li", "given": "Yi" } } ] }, "title": "Topological Correlators in Landau-Ginzburg Models with Boundaries", "ispublished": "pub", "full_text_status": "public", "note": "2003 \u00a9 International Press of Boston. \n\nWe are grateful to Vladimir Baranovsky and Dmitri Orlov for useful conversations. This work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Published - KAPatmp03.pdf

", "abstract": "We compute topological correlators in Landau-Ginzburg models on a Riemann surface with arbitrary number of handles and boundaries. The boundaries may correspond to arbitrary topological D-branes of type B. We also allow arbitrary operator insertions on the boundary and in the bulk. The answer is given by an explicit formula which can be regarded as an open-string generalization of C. Vafa's formula for closed-string topological correlators. We discuss how to extend our results to the case of Landau-Ginzburg orbifolds.", "date": "2003-07", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "7", "number": "4", "publisher": "International Press", "pagerange": "727-749", "id_number": "CaltechAUTHORS:KAPatmp03", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPatmp03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2003.v7.n4.a5", "primary_object": { "basename": "KAPatmp03.pdf", "url": "https://authors.library.caltech.edu/records/csfjn-qpd26/files/KAPatmp03.pdf" }, "pub_year": "2003", "author_list": "Kapustin, Anton and Li, Yi" }, { "id": "https://authors.library.caltech.edu/records/xrh02-11280", "eprint_id": 1653, "eprint_status": "archive", "datestamp": "2023-08-22 00:38:56", "lastmod": "2026-03-18 00:06:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Killip-R", "name": { "family": "Killip", "given": "Rowan" }, "orcid": "0000-0002-4272-7916" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Sum rules for Jacobi matrices and their applications to spectral theory", "ispublished": "pub", "full_text_status": "public", "keywords": "ABSOLUTELY CONTINUOUS-SPECTRUM; DIMENSIONAL SCHRODINGER-OPERATORS; ORTHOGONAL POLYNOMIALS; DECAYING POTENTIALS; SCATTERING-THEORY; TODA LATTICE; BOUND-STATES; FINITE; INTEGRALS; NUMBER", "note": "\u00a9 2005 Princeton University. \n\nReceived December 13, 2001. \n\nThe first named author was supported in part by NSF grant DMS-9729992. The second named author was supported in part by NSF grant DMS-9707661.\n\n

Published - KILam05.pdf

", "abstract": "We discuss the proof of and systematic application of Case's sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classification of the spectral measures of all Jacobi matrices J for which J - J(0) is Hilbert-Schmidt, and a proof of Nevai's conjecture that the Szego condition holds if J - J(0) is trace class.", "date": "2003-07", "date_type": "published", "publication": "Annals of Mathematics", "volume": "158", "number": "1", "publisher": "Annals of Mathematics", "pagerange": "253-321", "id_number": "CaltechAUTHORS:KILam05", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KILam05", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9729992" }, { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "KILam05.pdf", "url": "https://authors.library.caltech.edu/records/xrh02-11280/files/KILam05.pdf" }, "pub_year": "2003", "author_list": "Killip, Rowan and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/294z7-hvy83", "eprint_id": 3095, "eprint_status": "archive", "datestamp": "2023-08-22 00:36:56", "lastmod": "2026-04-15 20:54:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kraus-P", "name": { "family": "Kraus", "given": "Per" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Shenker-S-H", "name": { "family": "Shenker", "given": "Stephen" } } ] }, "title": "Inside the horizon with AdS/CFT", "ispublished": "pub", "full_text_status": "public", "keywords": "complementarity; black holes; conformal field theory; string theory", "note": "\u00a9 2003 The American Physical Society. \n\nReceived 23 February 2003; published 20 June 2003. \n\nP.K. was supported in part by NSF Grant No. PHY-0099590, H.O. was supported in part by Grant No. DEFG03-92ER40701, and S.S. was supported in part by NSF Grant No. PHY-9870115. We thank Micha Berkooz, Ben Craps, Robbert Dijkgraaf, David Kutasov, Juan Maldacena, Don Marolf, Emil Martinec, Will McElgin, Greg Moore, Rob Myers, and Lenny Susskind for discussions, and the Aspen Center for Physics for hospitality during the initial stages of this work.\n\n

Published - KRAprd03.pdf

Submitted - 0212277.pdf

", "abstract": "Using the eternal BTZ black hole as a concrete example, we show how spacelike singularities and horizons can be described in terms of AdS/CFT amplitudes. Our approach is based on analytically continuing amplitudes defined in a Euclidean signature. This procedure yields finite Lorentzian amplitudes. The naive divergences associated with the Milne type singularity of BTZ black holes are regulated by an iepsilon prescription inherent in the analytic continuation and a cancellation between future and past singularities. The boundary description corresponds to a tensor product of two CFTs in an entangled state, as in previous work. We give two bulk descriptions corresponding to two different analytic continuations. In the first, only regions outside the horizon appear explicitly, and so amplitudes are manifestly finite. In the second, regions behind the horizon and on both sides of the singularity appear, thus yielding finite amplitudes for virtual particles propagating through the black hole singularity. This equivalence between descriptions only outside and both inside and outside the horizon is reminiscent of the ideas of black hole complementarity.", "date": "2003-06-15", "date_type": "published", "publication": "Physical Review D", "volume": "67", "number": "12", "publisher": "American Physical Society", "pagerange": "Art. No. 124022", "id_number": "CaltechAUTHORS:KRAprd03", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KRAprd03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0099590" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "NSF", "grant_number": "PHY-9870115" } ] }, "other_numbering_system": { "items": [ { "id": "68-2421", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.67.124022", "primary_object": { "basename": "0212277.pdf", "url": "https://authors.library.caltech.edu/records/294z7-hvy83/files/0212277.pdf" }, "related_objects": [ { "basename": "KRAprd03.pdf", "url": "https://authors.library.caltech.edu/records/294z7-hvy83/files/KRAprd03.pdf" } ], "pub_year": "2003", "author_list": "Kraus, Per; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/26c0z-18p29", "eprint_id": 2021, "eprint_status": "archive", "datestamp": "2023-08-22 00:36:04", "lastmod": "2026-04-16 01:40:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Vidal-G", "name": { "family": "Vidal", "given": "G." } }, { "id": "Latorre-J-I", "name": { "family": "Latorre", "given": "J. I." } }, { "id": "Rico-E", "name": { "family": "Rico", "given": "E." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A." }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Entanglement in Quantum Critical Phenomena", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum entanglement; critical points; conformal field theory; spin systems; long-range order; magnetic transitions", "note": "\u00a92003 The American Physical Society \n\n(Received 5 December 2002; published 2 June 2003) \n\nThis work was supported by the Spanish Grants No. GC2001SGR-00065 and No. MCYT FPA2001-3598, by the National Science Foundation of USA under Grant No. EIA\u20130086038, and by the European Union under Grant No. ISF1999-11053.", "abstract": "Entanglement, one of the most intriguing features of quantum theory and a main resource in quantum information science, is expected to play a crucial role also in the study of quantum phase transitions, where it is responsible for the appearance of long-range correlations. We investigate, through a microscopic calculation, the scaling properties of entanglement in spin chain systems, both near and at a quantum critical point. Our results establish a precise connection between concepts of quantum information, condensed matter physics, and quantum field theory, by showing that the behavior of critical entanglement in spin systems is analogous to that of entropy in conformal field theories. We explore some of the implications of this connection.", "date": "2003-06-06", "date_type": "published", "publication": "Physical Review Letters", "volume": "90", "number": "22", "publisher": "American Physical Society", "pagerange": "Art. No. 227902", "id_number": "CaltechAUTHORS:VIDprl03", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:VIDprl03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.90.227902", "primary_object": { "basename": "VIDprl03.pdf", "url": "https://authors.library.caltech.edu/records/26c0z-18p29/files/VIDprl03.pdf" }, "pub_year": "2003", "author_list": "Vidal, G.; Latorre, J. I.; et al." }, { "id": "https://authors.library.caltech.edu/records/d2yky-epj69", "eprint_id": 81817, "eprint_status": "archive", "datestamp": "2023-08-19 11:24:31", "lastmod": "2026-03-09 23:07:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "New asymptotic bounds for self-dual codes and lattices", "ispublished": "pub", "full_text_status": "public", "keywords": "Asymptotic bounds, linear programming, modular lattices, saddle-point method, self-dual codes", "note": "\u00a9 2003 IEEE. \n\nManuscript received October 2, 2001; revised December 2, 2002. \n\nThe author would like to thank H. Landau, A. M. Odlyzko, and N. J. A. Sloane for helpful discussions regarding Section II, especially Lemma 2.3, as well as I. Duursma for pointing out that I. Krasikov and S. Litsyn had improved their earlier bound to the one stated above.\n\n

Published - 01197853.pdf

Submitted - 0104145.pdf

", "abstract": "We give an independent proof of the Krasikov-Litsyn bound d/n \u227e (1-5/^(-1/4))/2 on doubly-even self-dual binary codes. The technique used (a refinement of the Mallows-Odlyzko-Sloane approach) extends easily to other families of self-dual codes, modular lattices, and quantum codes; in particular, we show that the Krasikov-Litsyn bound applies to singly-even binary codes, and obtain an analogous bound for unimodular lattices. We also show that in each case, our bound differs from the true optimum by an amount growing faster than O(\u221an).", "date": "2003-05", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "49", "number": "5", "publisher": "IEEE", "pagerange": "1261-1274", "id_number": "CaltechAUTHORS:20170925-142327910", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-142327910", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/TIT.2003.810623", "primary_object": { "basename": "0104145.pdf", "url": "https://authors.library.caltech.edu/records/d2yky-epj69/files/0104145.pdf" }, "related_objects": [ { "basename": "01197853.pdf", "url": "https://authors.library.caltech.edu/records/d2yky-epj69/files/01197853.pdf" } ], "pub_year": "2003", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/yxx9g-gxz26", "eprint_id": 5433, "eprint_status": "archive", "datestamp": "2023-08-22 00:26:21", "lastmod": "2026-03-09 21:56:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Gravity Induced C-Deformation", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 International Press of Boston \n\nWe thank R. Dijkgraaf, M. Grisaru, and D. Zanon, whose insights have contributed significantly to this paper. We are also grateful to N. Berkovits for valuable discussion. \n\nC.V. thanks the hospitality of the theory group at Caltech, where he is a Gordon Moore Distinguished Scholar. \n\nThe research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329. \n\ne-print archive: http://lanl.arXiv.org/abs/hep-th/0303063 \n\nTechnical report nos.: CALT-68-2433; HUTP-03/A020\n\n

Published - OOGatmp03b.pdf

Submitted - OOGatmp03bpreprint.pdf

", "abstract": "We study F-terms describing coupling of the supergravity to N = 1 supersymmetric gauge theories which admit large N expansions. We show that these F-terms are given by summing over genus one non-planar diagrams of the large N expansion of the associated matrix model (or more generally bosonic gauge theory). The key ingredient in this derivation is the observation that the chiral ring of the gluino fields is deformed by the supergravity fields, generalizing the C-deformation which was recently introduced. The gravity induced part of the C-deformation can be derived from the Bianchi identities of the supergravity, but understanding gravitational corrections to the F-terms requires a non-traditional interpretation of these identities.", "date": "2003-05", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "7", "number": "3", "publisher": "International Press", "pagerange": "407-419", "id_number": "CaltechAUTHORS:OOGatmp03b", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGatmp03b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" } ] }, "other_numbering_system": { "items": [ { "id": "68-2433", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0303063", "primary_object": { "basename": "OOGatmp03b.pdf", "url": "https://authors.library.caltech.edu/records/yxx9g-gxz26/files/OOGatmp03b.pdf" }, "related_objects": [ { "basename": "OOGatmp03bpreprint.pdf", "url": "https://authors.library.caltech.edu/records/yxx9g-gxz26/files/OOGatmp03bpreprint.pdf" } ], "pub_year": "2003", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/nrj7q-4r664", "eprint_id": 82296, "eprint_status": "archive", "datestamp": "2023-08-22 00:25:04", "lastmod": "2026-04-15 19:33:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Applegate-D", "name": { "family": "Applegate", "given": "David" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "On asymmetric coverings and covering numbers", "ispublished": "pub", "full_text_status": "public", "keywords": "covering designs; covering numbers; Tur\u00e1n problem", "note": "\u00a9 2003 Wiley Periodicals, Inc. \n\nIssue online: 18 April 2003; Version of record online: 18 April 2003; Manuscript Revised: 29 May 2002; Manuscript Received: 5 February 2002.\n\n

Submitted - 0205303.pdf

", "abstract": "An asymmetric covering D(n,R) is a collection of special subsets S of an n-set such that every subset T of the n-set is contained in at least one special S with |S| - |T| \u2264 R. In this paper we compute the smallest size of any D(n,1) for n \u2264 8. We also investigate \"continuous\" and \"banded\" versions of the problem. The latter involves the classical covering numbers C(n, k, k-1), and we determine the following new values: C(10, 5, 4) = 51, C(11, 7, 6) = 84, C(12, 8, 7) = 126, C(13, 9, 8) = 185 and C(14, 10, 9) = 259. We also find the number of non-isomorphic minimal covering designs in several cases.", "date": "2003-04-18", "date_type": "published", "publication": "Journal of Combinatorial Designs", "volume": "11", "number": "3", "publisher": "Wiley", "pagerange": "218-228", "id_number": "CaltechAUTHORS:20171011-152858004", "issn": "1063-8539", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171011-152858004", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1002/jcd.10022", "primary_object": { "basename": "0205303.pdf", "url": "https://authors.library.caltech.edu/records/nrj7q-4r664/files/0205303.pdf" }, "pub_year": "2003", "author_list": "Applegate, David; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/4a30f-30843", "eprint_id": 82994, "eprint_status": "archive", "datestamp": "2023-08-19 11:16:07", "lastmod": "2026-04-15 23:34:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Images of eigenvalue distributions under power maps", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Springer-Verlag Berlin Heidelberg. \n\nReceived: 19 December 2000; Revised version: 7 August 2002; Published online: 21 February 2003.\n\n

Submitted - 0008079.pdf

", "abstract": "In [9], it was shown that if U is a random n\u00d7n unitary matrix, then for any p\u2265n, the eigenvalues of U^p are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens when p", "date": "2003-04", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "125", "number": "4", "publisher": "Springer", "pagerange": "522-538", "id_number": "CaltechAUTHORS:20171106-141427328", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-141427328", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00440-002-0250-2", "primary_object": { "basename": "0008079.pdf", "url": "https://authors.library.caltech.edu/records/4a30f-30843/files/0008079.pdf" }, "pub_year": "2003", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/rkv6c-tes94", "eprint_id": 66697, "eprint_status": "archive", "datestamp": "2023-08-19 11:07:03", "lastmod": "2026-04-15 23:25:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cherkis-S-A", "name": { "family": "Cherkis", "given": "Sergey A." }, "orcid": "0000-0002-0785-0126" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Periodic Monopoles With Singularities And N = 2 Super-QCD", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Springer-Verlag. \n\nReceived: 9 March 2001. Accepted: 15 January 2002.\n\nIt is our pleasure to thank Nigel Hitchin, Marcos Jardim, and Tony Pantev for discussions. S.Ch. is grateful to the Institute for Advanced Study, Princeton, for hospitality during the final stage of this work. S.Ch. was supported in\npart by NSF grant PHY9819686. A.K. was supported in part by DOE grant DE-FG02-90ER40542.\n\n

Submitted - 0011081.pdf

", "abstract": "We study solutions of the Bogomolny equation on R^2 \u00d7 S^1 with prescribed singularities. We show that Nahm transform establishes a one-to-one correspondence between such solutions and solutions of the Hitchin equations on a punctured cylinder with the eigenvalues of the Higgs field growing at infinity in a particular manner. The moduli spaces of solutions have natural hyperk\u00e4hler metrics of a novel kind. We show that these metrics describe the quantum Coulomb branch of certain N = 2 d = 4 supersymmetric gauge theories on R^3 \u00d7S^1. The Coulomb branches of the corresponding uncompactified theories have been previously determined by E. Witten using the M-theory fivebrane. We show that the Seiberg-Witten curves of these theories are identical to the spectral curves associated to solutions of\nthe Bogomolny equation on R^2 \u00d7 S^1. In particular, this allows us to rederive Witten's results without recourse to the M-theory fivebrane.", "date": "2003-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "234", "number": "1", "publisher": "Springer", "pagerange": "1-35", "id_number": "CaltechAUTHORS:20160505-144258782", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-144258782", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY9819686" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-002-0786-0", "primary_object": { "basename": "0011081.pdf", "url": "https://authors.library.caltech.edu/records/rkv6c-tes94/files/0011081.pdf" }, "pub_year": "2003", "author_list": "Cherkis, Sergey A. and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/hj1j4-bk116", "eprint_id": 2015, "eprint_status": "archive", "datestamp": "2023-08-22 00:14:57", "lastmod": "2026-04-16 00:10:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sparks-J", "name": { "family": "Sparks", "given": "James" } }, { "id": "Tong-David", "name": { "family": "Tong", "given": "David" } } ] }, "title": "Conifold transitions and five-brane condensation in M-theory on Spin(7) manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Institute of Physics 2003 \n\nReceived 23 September 2002, in final form 6 January 2003, Published 28 January 2003, Print publication: Issue 4 (21 February 2003) \n\nWe wish to thank Roman Jackiw, Neil Lambert, Igor Polyubin, Ashoke Sen, Andrew Strominger, Jan Troost, Cumrun Vafa,Ashvin Vishwanath, Eric Zaslow and especially Bobby Acharya and Edward Witten for useful discussions. SG and DT would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, and SG would further like to thank the New High Energy Theory Center at Rutgers University for kind hospitality during the course of this work. This research was conducted during the period SG served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of SG is also supported in part by grant RFBR no 01-02-17488, and the Russian President's grant no 00-15-99296. DT is a Pappalardo fellow and is grateful to the Pappalardo family for their kind support. The work of DT is also supported in part by funds provided by the US Department of Energy (DOE) under cooperative research agreement no DF-FC02-94ER40818.\n\n

Published - GUKcqg03.pdf

Submitted - 0207244v2.pdf

", "abstract": "We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a Bbb CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond\u2013Ramond flux. This is the first non-trivial example of a topology-changing transition with only 1/16 supersymmetry.", "date": "2003-02-21", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "20", "number": "4", "publisher": "IOP", "pagerange": "665-705", "id_number": "CaltechAUTHORS:GUKcqg03", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKcqg03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Pappalardo Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FC02-94ER40818" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/0264-9381/20/4/306", "primary_object": { "basename": "0207244v2.pdf", "url": "https://authors.library.caltech.edu/records/hj1j4-bk116/files/0207244v2.pdf" }, "related_objects": [ { "basename": "GUKcqg03.pdf", "url": "https://authors.library.caltech.edu/records/hj1j4-bk116/files/GUKcqg03.pdf" } ], "pub_year": "2003", "author_list": "Gukov, Sergei; Sparks, James; et al." }, { "id": "https://authors.library.caltech.edu/records/mnm5v-da011", "eprint_id": 77350, "eprint_status": "archive", "datestamp": "2023-08-19 11:02:32", "lastmod": "2026-04-15 23:04:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kiselev-A", "name": { "family": "Kiselev", "given": "Alexander" } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Stability of singular spectral types under decaying perturbations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science. \n\nReceived 15 October 2001, Revised 27 June 2002, Accepted 3 July 2002, Available online 7 January 2003. \n\nSupported in part by NSF Grant DMS-0102554 and by an Alfred P. Sloan fellowship. \n\nSupported in part by The Israel Science Foundation Grant 447/99 and by an Allon fellowship. \n\nSupported in part by NSF Grant DMS-9707661.\n\n

Submitted - 0110139.pdf

", "abstract": "We look at invariance of a.e. boundary condition spectral behavior under perturbations, W, of half-line, continuum or discrete Schr\u00f6dinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported W's to suitable short-range W. We also discuss invariance of the local Hausdorff dimension of spectral measures under such perturbations.", "date": "2003-02-20", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "198", "number": "1", "publisher": "Elsevier", "pagerange": "1-27", "id_number": "CaltechAUTHORS:20170510-134955944", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-134955944", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0102554" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Israel Science Foundation", "grant_number": "447/99" }, { "agency": "Council for Higher Education (Israel)" }, { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/S0022-1236(02)00053-8", "primary_object": { "basename": "0110139.pdf", "url": "https://authors.library.caltech.edu/records/mnm5v-da011/files/0110139.pdf" }, "pub_year": "2003", "author_list": "Kiselev, Alexander; Last, Yoram; et al." }, { "id": "https://authors.library.caltech.edu/records/9ebra-b7512", "eprint_id": 5431, "eprint_status": "archive", "datestamp": "2023-08-22 00:10:56", "lastmod": "2026-03-09 22:03:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "The C-deformation of gluino and non-planar diagrams", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2006 International Press of Boston.\n\nWe are grateful to N. Berkovits for valuable discussion about the covariant quantization of superstring. We would also like to thank R. Dijkgraaf, M. Grisaru, S. Minwalla, Y. Okawa, J. Schwarz, P. van Nieuwenhuizen, N. Warner, E. Witten, and S.-T. Yau for useful discussions. \n\nH.O. thanks the theory group at Harvard University for the hospitality. C.V. thanks the hospitality of the theory group at Caltech, where he is a Gordon Moore Distinguished Scholar. \n\nThe research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329. \n\ne-print archive: http://lanl.arXiv.org/abs/hep-th/0302109. Date (v1): Fri, 14 Feb 2003; Date (revised v2): Thu, 27 Feb 2003. \n\nTechnical report nos.: CALT-68-2428; HUTP-03/A014 \n\nEuclid Identifier: euclid.atmp/1112627974 \n\nMathmatical Reviews number (MathSciNet): MR2014958\n\n

Published - OOGatmp03a.pdf

Submitted - OOGatmp03apreprint.pdf

", "abstract": "We consider a deformation of N = 1 supersymmetric gauge theories in four dimensions, which we call the C-deformation, where the gluino field satisfies a Clifford-like algebra dictated by a self-dual two-form, instead of the standard Grassmannian algebra. The superpotential of the deformed gauge theory is computed by the full partition function of an associated matrix model (or more generally a bosonic gauge theory), including non-planar diagrams. In this identification, the strength of the two-form controls the genus expansion of the matrix model partition function. For the case of pure N = 1 Yang-Mills this deformation leads to the identification of the all genus partition function of c non-critical bosonic string at self-dual radius as the glueball superpotential. Though the C-deformation violates Lorentz invariance, the deformed F-terms are Lorentz invariant and the Lorentz violation is screened in the IR.", "date": "2003-02", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "7", "number": "1", "publisher": "International Press", "pagerange": "53-85", "id_number": "CaltechAUTHORS:OOGatmp03a", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGatmp03a", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Gordon and Betty Moore Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" } ] }, "other_numbering_system": { "items": [ { "id": "68-2428", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0302109", "primary_object": { "basename": "OOGatmp03a.pdf", "url": "https://authors.library.caltech.edu/records/9ebra-b7512/files/OOGatmp03a.pdf" }, "related_objects": [ { "basename": "OOGatmp03apreprint.pdf", "url": "https://authors.library.caltech.edu/records/9ebra-b7512/files/OOGatmp03apreprint.pdf" } ], "pub_year": "2003", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/0pby9-bs443", "eprint_id": 66708, "eprint_status": "archive", "datestamp": "2023-08-19 10:55:13", "lastmod": "2026-04-15 20:51:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Orlov-D", "name": { "family": "Orlov", "given": "Dmitri" }, "orcid": "0000-0002-2230-457X" } ] }, "title": "Vertex Algebras, Mirror Symmetry, and D-Branes: The Case of Complex Tori", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 Springer-Verlag. \n\nReceived: 3 May 2001. Accepted: 17 August 2002. Published online: 8 January 2003. \n\nWe are grateful to Maxim Kontsevich for valuable comments and to Markus Rosellen for pointing out a gap in the reasoning of Appendix B in the first version of the paper. We also wish to thank the Institute for Advanced Study, Princeton, NJ, for a very stimulating atmosphere. The first author was supported by DOE grant DE-FG02-90ER40542. The second author was supported in part by RFFI grant 99-01-01144 and a grant for support of leading scientific groups N 00-15-96085. The research described in this publication was made possible in part by Award No RM1-2089 of the U.S. Civilian Research and Development Foundation for the Independent States of the Former Soviet Union\n(CRDF). Communicated by R.H. Dijkgraaf.\n\n

Submitted - 0010293.pdf

", "abstract": "A vertex algebra is an algebraic counterpart of a two-dimensional conformal field theory. We give a new definition of a vertex algebra which includes chiral algebras as a special case, but allows for fields which are neither meromorphic nor anti-meromorphic. To any complex torus equipped with a flat K\u00e4hler metric and a closed 2-form we associate an N=2 superconformal vertex algebra (N=2 SCVA) in the sense of our definition. We find a criterion for two different tori to produce isomorphic N=2 SCVA's. We show that for algebraic tori the isomorphism of N=2 SCVA's implies the equivalence of the derived categories of coherent sheaves corresponding to the tori or their noncommutative generalizations (Azumaya algebras over tori). We also find a criterion for two different tori to produce N=2 SCVA's related by a mirror morphism. If the 2-form is of type (1,1), this condition is identical to the one proposed by Golyshev, Lunts, and Orlov, who used an entirely different approach inspired by the Homological Mirror Symmetry Conjecture of Kontsevich. Our results suggest that Kontsevich's conjecture must be modified: coherent sheaves must be replaced with modules over Azumaya algebras, and the Fukaya category must be ``twisted'' by a closed 2-form. We also describe the implications of our results for BPS D-branes on Calabi-Yau manifolds.", "date": "2003-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "233", "number": "1", "publisher": "Springer", "pagerange": "79-136", "id_number": "CaltechAUTHORS:20160506-073753322", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-073753322", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" }, { "agency": "Russian Foundation for Fundamental Investigations (RFFI)", "grant_number": "99-01-01144" }, { "agency": "Russian Foundation for Fundamental Investigations (RFFI)", "grant_number": "N 00-15-96085" }, { "agency": "Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (CRDF)", "grant_number": "RM1-2089" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s00220-002-0755-7", "primary_object": { "basename": "0010293.pdf", "url": "https://authors.library.caltech.edu/records/0pby9-bs443/files/0010293.pdf" }, "pub_year": "2003", "author_list": "Kapustin, Anton and Orlov, Dmitri" }, { "id": "https://authors.library.caltech.edu/records/ay5x0-y5c29", "eprint_id": 27214, "eprint_status": "archive", "datestamp": "2023-08-19 10:54:23", "lastmod": "2026-04-15 19:21:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Limiting modular symbols and the Lyapunov spectrum", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science. Received 1 December 2001; revised 22 May 2002; Communicated by D. Goss. Available online 25 December 2002. Partially supported by Humboldt Foundation Sofja Kovalevskaja Award. Conversations with Yuri Manin were a great source of inspiration. I thank Dieter\nMayer for useful comments.\n\n

Submitted - 0111093.pdf

", "abstract": "This paper consists of variations upon a theme, that of limiting modular symbols introduced in [17]. We show that, on level sets of the Lyapunov exponent for the shift map T of the continued fraction expansion, the limiting modular symbol can be computed as a Birkhoff average. We show that the limiting modular symbols vanish almost everywhere on T-invariant subsets for which a corresponding transfer operator has a good spectral theory, thus improving the weak convergence result proved in [17]. We also show that, even when the limiting modular symbol vanishes, it is possible to construct interesting non-trivial homology classes on modular curves that are associated to non-closed geodesics. These classes are related to \"automorphic series\", defined in terms of successive denominators of continued fraction expansion, and their integral averages are related to certain Mellin transforms of modular forms of weight two considered in [17]. We discuss some variants of the Selberg zeta function that sum over certain classes of closed geodesics, and their relation to Fredholm determinants of transfer operators. Finally, we argue that one can use T-invariant subsets to enrich the picture of non-commutative geometry at the boundary of modular curves presented in [17].", "date": "2003-02", "date_type": "published", "publication": "Journal of Number Theory", "volume": "98", "number": "2", "publisher": "Elsevier", "pagerange": "348-376", "id_number": "CaltechAUTHORS:20111013-134118921", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111013-134118921", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Humboldt Foundation Sofja Kovalevskaja Award" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0022-314X(02)00044-6", "primary_object": { "basename": "0111093.pdf", "url": "https://authors.library.caltech.edu/records/ay5x0-y5c29/files/0111093.pdf" }, "pub_year": "2003", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/00940-v9565", "eprint_id": 27458, "eprint_status": "archive", "datestamp": "2023-08-22 00:06:07", "lastmod": "2026-03-09 23:14:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" }, { "id": "Wang-Song", "name": { "family": "Wang", "given": "Song" }, "orcid": "0000-0003-3116-5038" } ] }, "title": "On the Exceptional Zeros of Rankin\u2013Selberg L-Functions", "ispublished": "pub", "full_text_status": "public", "keywords": "factorizations; GL(n); holomorphic forms; Landau\u2013Siegel zeros; lower bound; Maass forms; Petersson norm; positive Dirichlet series; Rankin\u2013Selberg L-functions; selfdual forms; spectral normalization; symmetric power liftings; symmetric space.", "note": "\u00a9 2003 Kluwer Academic Publishers. Received 7 August 2001; accepted in final form: 29 November 2001. We would like to thank D. Bump, W. Duke, H. Jacquet, H. Kim, W. Luo, S. Miller, F. Shahidi and E. Stade for useful conversations and/or correspondence. Clearly this paper depends on the ideas and results of the articles [HL94], [GHLL94], [HRa95],\n[Ra2000], [KSh2000,1] and [K2000]. The first author would like to thank the NSF for support through the grants DMS-9801328 and DMS-0100372. The subject matter of this paper formed a portion of the first author's Schur Lecture at the University of Tel Aviv in March 2001, and he would like to thank J. Bernstein and S. Gelbart for inviting him and for their interest.\n\n

Published - RAMcm03.pdf

", "abstract": "The main objects of study in this article are two classes of Rankin\u2013Selberg L-functions, namely L(s,\u0192\u00d7g) and L(s, sym^2(g)\u00d7 sym^2(g)), where \u0192, g are newforms, holomorphic or of Maass type, on the upper half plane, and sym^2(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound on the norm of sym^2(g).", "date": "2003-01", "date_type": "published", "publication": "Compositio Mathematica", "volume": "135", "number": "2", "publisher": "Cambridge University Press", "pagerange": "211-244", "id_number": "CaltechAUTHORS:20111026-134851953", "issn": "0010-437X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111026-134851953", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9801328" }, { "agency": "NSF", "grant_number": "DMS-0100372" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/A:1021761421232", "primary_object": { "basename": "RAMcm03.pdf", "url": "https://authors.library.caltech.edu/records/00940-v9565/files/RAMcm03.pdf" }, "pub_year": "2003", "author_list": "Ramakrishnan, Dinakar and Wang, Song" }, { "id": "https://authors.library.caltech.edu/records/b6es1-vp247", "eprint_id": 26604, "eprint_status": "archive", "datestamp": "2023-08-19 10:43:40", "lastmod": "2026-04-16 01:39:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "A. Yu." }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Fault-tolerant quantum computation by anyons", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science. Received 20 May 2002; Available online 24 December 2002. I am grateful to J. Preskill, D.P. DiVincenzo and C.H. Bennett for interesting discussions\nand questions which helped me to clarify some points in my constructions. This work was supported, in part, by the Russian Foundation for Fundamental Research, Grant No. 96-01-01113. Part of this work was completed during the 1997\nElsag-Bailey\u2014I.S.I. Foundation research meeting on quantum computation.\n\n

Submitted - KITaop03preprint.pdf

", "abstract": "A two-dimensional quantum system with anyonic excitations can be considered as a quantum\ncomputer. Unitary transformations can be performed by moving the excitations around\neach other. Measurements can be performed by joining excitations in pairs and observing the\nresult of fusion. Such computation is fault-tolerant by its physical nature.", "date": "2003-01", "date_type": "published", "publication": "Annals of Physics", "volume": "303", "number": "1", "publisher": "Elsevier", "pagerange": "2-30", "id_number": "CaltechAUTHORS:20111005-144725727", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111005-144725727", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Fundamental Research", "grant_number": "96-01-01113" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/S0003-4916(02)00018-0", "primary_object": { "basename": "KITaop03preprint.pdf", "url": "https://authors.library.caltech.edu/records/b6es1-vp247/files/KITaop03preprint.pdf" }, "pub_year": "2003", "author_list": "Kitaev, A. Yu." }, { "id": "https://authors.library.caltech.edu/records/cgh0x-enw90", "eprint_id": 38548, "eprint_status": "archive", "datestamp": "2023-08-19 10:44:09", "lastmod": "2026-03-09 21:25:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gao-Su", "name": { "family": "Gao", "given": "Su" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On the classification of Polish metric spaces up to isometry", "ispublished": "pub", "full_text_status": "public", "keywords": "Polish group, the Urysohn space, Borel (bi)reducible, isometry", "note": "\u00a9 2003 American Mathematical Society. \n\nReceived by the editor August, 14, 2000. \n\nAlexander S. Kechris' research was partially supported by NSF Grant DMS-9987437.\n\n

Published - Kechris_2003p78.pdf

Draft - iso.pdf

", "abstract": "We study the classification problem of Polish metric spaces up to isometry and\nthe isometry groups of Polish metric spaces. In the framework of the descriptive\nset theory of definable equivalence relations, we determine the exact complexity of\nvarious classification problems concerning Polish metric spaces. We start with the\nclass of all Polish metric spaces and prove that it is Borel bireducible to the universal\norbit equivalence relation induced by Borel actions of Polish groups. We then turn\nto special classes of Polish metric spaces, including locally compact, ultrametric,\nzero-dimensional, homogeneous, and ultrahomogeneous spaces. In the investigation\nof the classification problems we also obtain characterizations for isometry groups\nof various classes of Polish metric spaces.", "date": "2003-01", "date_type": "published", "publication": "Memoirs of the American Mathematical Society", "volume": "161", "number": "766", "publisher": "American Mathematical Society", "pagerange": "1-78", "id_number": "CaltechAUTHORS:20130516-152757565", "issn": "0065-9266", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130516-152757565", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9987437" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "iso.pdf", "url": "https://authors.library.caltech.edu/records/cgh0x-enw90/files/iso.pdf" }, "related_objects": [ { "basename": "Kechris_2003p78.pdf", "url": "https://authors.library.caltech.edu/records/cgh0x-enw90/files/Kechris_2003p78.pdf" } ], "pub_year": "2003", "author_list": "Gao, Su and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/f9056-g4d25", "eprint_id": 38690, "eprint_status": "archive", "datestamp": "2023-08-22 00:00:18", "lastmod": "2026-03-09 21:10:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Pestov-V", "name": { "family": "Pestov", "given": "V." } }, { "id": "Todor\u010devi\u0107-S", "name": { "family": "Todor\u010devi\u0107", "given": "S." } } ] }, "title": "Universal minimal flows of automorphism groups", "ispublished": "pub", "full_text_status": "public", "keywords": "group actions; universal minimal flows; Fra\u00efss\u00e9 theory; structural Ramsey theory", "note": "\u00a9 2003 Srpska akademija nauka i umetnosti, Beograd. \n\nPresented at the 3rd Meeting, held on May 9, 2003. \n\nPartially supported by NSF Grant DMS-9987437, the Fields Institute, Toronto, and a Guggenheim Fellowship. Partially supported by the Marsden Fund of the Royal Society of New Zeeland, and the NSERC of Canada. Partially supported by CNRS, Paris and the Fields Institute, Toronto.\n\n

Published - Kechris_2003p93.pdf

", "abstract": "We investigate some connections between the Fra\u00efss\u00e9 theory of amalgamation classes and ultrahomogeneous structures, Ramsey theory, and topological dynamics of automorphism groups of countable structures. We show, in particular, that results from the structural Ramsey theory can be quite useful in recognizing the universal minimal flows of this kind of groups. As a result we compute the universal minimal flows of several well known topological groups such as, for example, the automorphism group of the random graph, the automorphism group of the random triangle-free graph, the automorphism group of the \u221e-dimensional vector space over a finite field, the automorphism group of the countable atomless Boolean algebra, etc. So we have here a reversal in the traditional relationship between topological dynamics and Ramsey theory: the Ramsey-theoretic results are used in proving theorems of topological dynamics rather than vice versa.", "date": "2003", "date_type": "published", "publication": "Bulletin Classe des Sciences Math\u00e9matiques et Naturelles, Sciences math\u00e9matiques", "volume": "28", "publisher": "Srpska akademija nauka i umetnosti, Beograd", "pagerange": "93-106", "id_number": "CaltechAUTHORS:20130528-105759569", "issn": "0561-7332", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-105759569", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9987437" }, { "agency": "Fields Institute for Research in the Mathematical Sciences" }, { "agency": "John Simon Guggenheim Foundation" }, { "agency": "Royal Society of New Zealand Marsden Fund" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Centre National de la Recherche Scientifique (CNRS)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "Kechris_2003p93.pdf", "url": "https://authors.library.caltech.edu/records/f9056-g4d25/files/Kechris_2003p93.pdf" }, "pub_year": "2003", "author_list": "Kechris, A. S.; Pestov, V.; et al." }, { "id": "https://authors.library.caltech.edu/records/m3wrn-5w840", "eprint_id": 3654, "eprint_status": "archive", "datestamp": "2023-08-21 23:59:31", "lastmod": "2026-03-07 04:15:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "A 2-local characterization of M(12)", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92003 University of Illinois. \n\nReceived August 16, 2002.\nDedicated to Reinhold Baer on the 100th anniversary of his birth. This work was partially supported by NSF DMS-0203417.", "abstract": "A characterization of the Mathieu group M(12) is established; the characterization is used by Aschbacher and Smith in their classification of the quasithin finite simple groups.", "date": "2003", "date_type": "published", "publication": "Illinois Journal of Mathematics", "volume": "47", "number": "1-2", "publisher": "Illinois Journal of Mathematics", "pagerange": "31-47", "id_number": "CaltechAUTHORS:ASCijm03", "issn": "0019-2082", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ASCijm03", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "aschbacher.ps", "url": "https://authors.library.caltech.edu/records/m3wrn-5w840/files/aschbacher.ps" }, "related_objects": [ { "basename": "ASCijm03.pdf", "url": "https://authors.library.caltech.edu/records/m3wrn-5w840/files/ASCijm03.pdf" } ], "pub_year": "2003", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/2xk03-s5993", "eprint_id": 66715, "eprint_status": "archive", "datestamp": "2023-08-19 10:37:16", "lastmod": "2026-03-09 02:33:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Yau-Shing-Tung", "name": { "family": "Yau", "given": "Shing-Tung" } }, { "id": "Zaslow-E", "name": { "family": "Zaslow", "given": "Eric" } } ] }, "title": "Duality and Fibrations on G_2 Manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2003 T\u00fcrkiye Bilimsel ve Teknolojik Ara\u015ft\u0131rma Kurumu (T\u00dcB\u0130TAK). \n\nWe would like to thank A. Strominger, R. Thomas, C. Vafa, and E. Witten for instructive discussions. This research was conducted during the period S.G. served as a Clay\nMathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. The work of S.T.Y. is supported in part by grants DMS-0074329 and DMS-9803347. The work of E.Z. is supported in part by NSF grant DMS-0072504 and by an Alfred P. Sloan Foundation Fellowship.\n\n

Submitted - 0203217.pdf

", "abstract": "We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M-five-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G_2 manifolds may be incorporated into this framework. To give some examples, we construct two non-compact manifolds with G_2 structures: one with a K3 fibration, and one with a torus fibration and a metric of G_2 holonomy. Kaluza-Klein reduction of the latter solution gives abelian BPS monopoles in 3 + 1 dimensions.", "date": "2003", "date_type": "published", "publication": "Turkish Journal of Mathematics", "volume": "27", "number": "1", "publisher": "Scientific and Technical Research Council of Turkey", "pagerange": "61-97", "id_number": "CaltechAUTHORS:20160506-122921323", "issn": "1303-6149", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-122921323", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "NSF", "grant_number": "DMS-9803347" }, { "agency": "NSF", "grant_number": "DMS-0072504" }, { "agency": "Alfred P. Sloan Foundation Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0203217v1", "primary_object": { "basename": "0203217.pdf", "url": "https://authors.library.caltech.edu/records/2xk03-s5993/files/0203217.pdf" }, "pub_year": "2003", "author_list": "Gukov, Sergei; Yau, Shing-Tung; et al." }, { "id": "https://authors.library.caltech.edu/records/jhpxc-43271", "eprint_id": 82725, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:28", "lastmod": "2026-03-09 22:10:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "Jeffrey C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "On a two-variable zeta function for number fields", "ispublished": "pub", "full_text_status": "public", "keywords": "Arakelov divisors, functional equation, infinitely divisible distributions, zeta functions", "note": "\u00a9 2003 Association des Annales de l'Institut Fourier. \n\nReceived September 24, 2001; accepted April 25, 2002. \n\nWork done in part during a visit to the Institute of Advanced Study.\n\n

Published - AIF_2003__53_1_1_0.pdf

", "abstract": "Recently van der Geer and Schoof [11, Prop. 1] formulated an \"exact\" analogue of the Riemann-Roch theorem for an algebraic number field K, based on Arakelov divisors. They used this result to formally express the completed zeta function \u03b6_K(s) of K as an integral over the Arakelov divisor class group Pic(K) of K. They introduced a two-variable zeta function attached to a number field K, also given as an integral over the Arkelov class group, which we call either the Arakelov zeta function or the two-variable zeta function. This zeta function was modelled after a two-variable zeta function attached to a function field over a finite filed, introduced in 1996 by Pellikaan [18]. For convenience we review the Arakelov divisor interpretation of the two-variable zeta function and the Riemann-Roch theorem for number fields in an appendix.", "date": "2003", "date_type": "published", "publication": "Annales de l'Institut Fourier", "volume": "53", "number": "1", "publisher": "Association des Annales de l'Institut Fourier", "pagerange": "1-68", "id_number": "CaltechAUTHORS:20171027-085620532", "issn": "1777-5310", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171027-085620532", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "AIF_2003__53_1_1_0.pdf", "url": "https://authors.library.caltech.edu/records/jhpxc-43271/files/AIF_2003__53_1_1_0.pdf" }, "pub_year": "2003", "author_list": "Lagarias, Jeffrey C. and Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/wq9z7-7ns50", "eprint_id": 27472, "eprint_status": "archive", "datestamp": "2023-08-19 10:31:32", "lastmod": "2026-03-18 00:05:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Golinskii-Ibragimov Method and a Theorem of Damanik and Killip", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2003 Hindawi Publishing Corporation. Received March 13, 2003. Accepted June 8, 2003. Communicated by Percy Deift. This work was supported in part by the National Science Foundation (NSF) grant DMS-0140592. It is a pleasure to thank David Damanik and Rowan Killip for telling me about their work and for useful discussions.", "abstract": "In 1971, Golinskii and Ibragimov proved that if the Verblunsky coefficients, {\u03b1_n}_n^\u221e = 0, of a measure d\u03bc on \u2202D obey \u2211_(n=0)^\u221e^n\u2502\u03b1_n\u2502^2 < \u221e, then the singular part, d\u03bcs, of d\u03bc vanishes. We show how to use extensions of their ideas to discuss various cases where \u2211_(n=0)^N^n\u2502\u03b1_n\u2502^2 diverges logarithmically. As an application, we provide an alternative to a part of the proof of a recent theorem of Damanik and Killip.", "date": "2003", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "2003", "number": "36", "publisher": "Oxford University Press", "pagerange": "1973-1986", "id_number": "CaltechAUTHORS:20111027-081142498", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111027-081142498", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0140592" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1155/S107379280313084X", "pub_year": "2003", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/zh7a8-wkf20", "eprint_id": 2395, "eprint_status": "archive", "datestamp": "2023-08-21 23:53:12", "lastmod": "2026-04-16 04:27:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borokhov-V", "name": { "family": "Borokhov", "given": "Vadim" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Wu-Xinkai", "name": { "family": "Wu", "given": "Xinkai" } } ] }, "title": "Monopole operators and mirror symmetry in three dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "field theories in lower dimensions; 1/N expansion; duality in gauge field theories; supersymmetry and duality", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2002. \n\nReceived 6 November 2002, accepted for publication 13 December 2002. Published 27 January 2003. \n\nWe would like to thank Jim Gates, Takuya Okuda, Hiroshi Ooguri, John Preskill, and Mark Wise for discussions. A.K. is also grateful to Matt Strassler for numerous conversations during the years of 1998 and 1999 which contributed to the genesis of this paper. This work was supported in part by a DOE grant DE-FG03-92-ER40701.\n\n

Published - BORjhep02b.pdf

", "abstract": "We study vortex-creating, or monopole, operators in 3d CFTs which are the infrared limit of N = 2 and N = 4 supersymmetric QEDs in three dimensions. Using large-N-f expansion, we construct monopole operators which are primaries of short representations of the superconformal algebra. Mirror symmetry in three dimensions makes a number of predictions about such operators, and our results confirm these predictions. Furthermore, we argue that some of our large-N-f results are exact. This implies, in particular, that certain monopole operators in N = 4 d = 3 SQED with N-f = 1 are free fields. This amounts to a proof of 3d mirror symmetry in a special case.", "date": "2002-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 044", "id_number": "CaltechAUTHORS:BORjhep02b", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BORjhep02b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2002/12/044", "primary_object": { "basename": "BORjhep02b.pdf", "url": "https://authors.library.caltech.edu/records/zh7a8-wkf20/files/BORjhep02b.pdf" }, "pub_year": "2002", "author_list": "Borokhov, Vadim; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/dqvzn-ww591", "eprint_id": 98163, "eprint_status": "archive", "datestamp": "2023-08-21 23:55:36", "lastmod": "2026-04-16 04:01:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "Linearity of artin groups of finite type", "ispublished": "pub", "full_text_status": "public", "keywords": "Induction Hypothesis; Positive Root; Finite Type; Braid Group; Dynkin Diagram", "note": "\u00a9 The Hebrew University Magnes Press 2002. \n\nReceived May 24, 2001. \n\nThis paper was written during a stay of the first author at Caltech. He wants to thank the institute for its hospitality. Shortly after we circulated a preprint of the present paper, we learned that Digne had obtained similar results.\n\n

Submitted - 0010204.pdf

", "abstract": "Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer's faithfulness proof for this linear representation to Artin groups of finite type.", "date": "2002-12", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "131", "number": "1", "publisher": "Springer", "pagerange": "101-123", "id_number": "CaltechAUTHORS:20190823-105106984", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190823-105106984", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/bf02785852", "primary_object": { "basename": "0010204.pdf", "url": "https://authors.library.caltech.edu/records/dqvzn-ww591/files/0010204.pdf" }, "pub_year": "2002", "author_list": "Cohen, Arjeh M. and Wales, David B." }, { "id": "https://authors.library.caltech.edu/records/5xdb4-qdq11", "eprint_id": 79416, "eprint_status": "archive", "datestamp": "2023-08-19 10:22:20", "lastmod": "2026-04-16 01:56:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "Dirk" }, "orcid": "0000-0002-0643-0138" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "An optimal L\u1d56-bound on the Krein spectral shift function", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Hebrew University of Jerusalem 2002. \n\nReceived: 12 June 2001. \n\nWe thank Rowan Killip for a refreshing discussion.", "abstract": "Let \u03be_(A,B) be the Krein spectral shift function for a pair of operatorsA, B, with C =A-B trace class. We establish the bound\n\u222bF(|\u03beA,B(\u03bb)|)d\u03bb\u2a7d\u222bF(|\u03be|C|,0(\u03bb)|)d\u03bb=\u2211_(j=1)^\u221e[F(j)\u2212F(j\u22121)]\u03bcj(C),\nwhere F is any non-negative convex function on [0, \u221e) with F(0) = 0 and \u03bcj (C) are the singular values of C. The choice F(t) = t^p,p \u2265 1, improves a recent bound of Combes, Hislop and Nakamura.", "date": "2002-12", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "87", "number": "1", "publisher": "Hebrew University Magnes Press", "pagerange": "199-208", "id_number": "CaltechAUTHORS:20170726-114229059", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170726-114229059", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02868474", "pub_year": "2002", "author_list": "Hundertmark, Dirk and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/4pmfh-xkc22", "eprint_id": 12588, "eprint_status": "archive", "datestamp": "2023-08-21 23:52:50", "lastmod": "2026-04-16 03:52:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Worldsheet descriptions of wrapped NS five-branes", "ispublished": "pub", "full_text_status": "public", "keywords": "p-branes; String Duality; Conformal Field Models in String Theory", "note": "\u00a9 2002 SISSA. \n\nReceived 27 September 2002, accepted for publication 19 November 2002. Published 21 January 2003. \n\nWe would like to thank Tohru Eguchi, Jaume Gomis, Aki Hashimoto and David Tong for useful discussions, and Juan Maldacena for explanations about the decoupling limit for wrapped five-branes. K.H. was supported in part by NSF-DMS 0074329 and by NSF-PHY 0070928. A. K. was supported in part by DOE grant DE-FG03-92-ER40701.\n\n

Published - HORjhep02.pdf

", "abstract": "We provide a world-sheet description of Neveu-Schwarz five-branes wrapped on a complex projective space. It is an orbifold of the product of an Script N = 2 minimal model and the IR fixed point of a certain linear sigma model. We show how the naked singularity in the supergravity description is resolved by the world-sheet CFT. Applying mirror symmetry, we show that the low-energy theory of NS5-branes wrapped on Bbb CBbb P1 in Eguchi-Hanson space is described by the Seiberg-Witten prepotential for Script N = 2 super-Yang-Mills, with the gauge group given by the ADE-type of the five-brane. The world-sheet CFT is generically regular, but singularities develop precisely at the Argyres-Douglas points and massless monopole points of the space-time theory. We also study the low-energy theory of NS5-branes wrapped on Bbb CBbb P2 in a Calabi-Yau 3-fold and its relation to (2,2) super-Yang-Mills theory in two dimensions.", "date": "2002-11-19", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 038", "id_number": "CaltechAUTHORS:HORjhep02", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:HORjhep02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0074329" }, { "agency": "NSF", "grant_number": "PHY-0070928" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2002/11/038", "primary_object": { "basename": "HORjhep02.pdf", "url": "https://authors.library.caltech.edu/records/4pmfh-xkc22/files/HORjhep02.pdf" }, "pub_year": "2002", "author_list": "Hori, Kentaro and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/6q22f-nrs08", "eprint_id": 27296, "eprint_status": "archive", "datestamp": "2023-08-19 10:17:46", "lastmod": "2026-04-16 06:49:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Consani-C", "name": { "family": "Consani", "given": "Caterina" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Spectral triples in Arakelov geometry", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2002 Acad\u00e9mie des sciences/\u00c9ditions scientifiques et m\u00e9dicales Elsevier SAS.\nReceived 27 June 2002; revised 26 September 2002; Note pr\u00e9sent\u00e9e par Alain Connes. Available online 20 October 2002.", "abstract": "In this Note, we use Connes' theory of spectral triples to provide a connection between Manin's model of the dual graph of the fiber at infinity of an Arakelov surface and the cohomology of the mapping cone of the local monodromy.", "date": "2002-11-15", "date_type": "published", "publication": "Comptes Rendus Mathematique", "volume": "335", "number": "10", "publisher": "Elsevier", "pagerange": "779-784", "id_number": "CaltechAUTHORS:20111019-090624789", "issn": "1631-073X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111019-090624789", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "72016789" }, { "agency": "Humboldt Foundation Sofja Kovalevskaja Award" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S1631-073X(02)02569-4", "pub_year": "2002", "author_list": "Consani, Caterina and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/fjrf4-taq62", "eprint_id": 27295, "eprint_status": "archive", "datestamp": "2023-08-21 23:50:07", "lastmod": "2026-04-16 05:35:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Booss-Bavnbek-B", "name": { "family": "Booss-Bavnbek", "given": "Bernhelm" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Wang-B-L", "name": { "family": "Wang", "given": "Bai-Ling" } } ] }, "title": "Weak UCP and Perturbed Monopole Equations", "ispublished": "pub", "full_text_status": "restricted", "keywords": "weak unique continuation; Dirac operators; Seiberg-Witten equation", "note": "\u00a9 2002 World Scientific Publishing Company. Received 14 March 2002. We thank Hubert Kalf for his generous help and many extremely useful comments and suggestions. The second author's research is partially supported by Humboldt\nFoundation Sofja Kovalevskaja Award, and the third author's research is supported by Australian Research Council.", "abstract": "We give a simple proof of weak Unique Continuation Property for perturbed Dirac operators, using the Carleman inequality. We apply the result to a class of perturbations of the Seiberg\u2013Witten monopole equations that arise in Floer theory.", "date": "2002-11", "date_type": "published", "publication": "International Journal of Mathematics", "volume": "13", "number": "9", "publisher": "World Scientific Publishing", "pagerange": "987-1008", "id_number": "CaltechAUTHORS:20111019-085917147", "issn": "0129-167X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111019-085917147", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Humboldt Foundation Sofja Kovalevskaja Award" }, { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0129167X02001551", "pub_year": "2002", "author_list": "Booss-Bavnbek, Bernhelm; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/2yyek-jdc59", "eprint_id": 2397, "eprint_status": "archive", "datestamp": "2023-08-21 23:49:49", "lastmod": "2026-04-16 05:54:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Borokhov-V", "name": { "family": "Borokhov", "given": "Vadim" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Wu-Xinkai", "name": { "family": "Wu", "given": "Xinkai" } } ] }, "title": "Topological disorder operators in three-dimensional conformal field theory", "ispublished": "pub", "full_text_status": "public", "keywords": "field theories in lower dimensions; solitons monopoles and instantons; 1/N expansion; duality in gauge field theories", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 2002. \n\nReceived 6 November 2002, accepted for publication 26 November 2002. Published 7 January 2003. \n\nThis work grew out of attempts by one of the authors (A.K.) and M. J. Strassler to improve on the last section of ref. [11]. A.K. would like to thank M. J. Strassler for numerous discussions which helped to realize the importance of fermionic zero modes. We also would like to thank J. Maldacena, T. Okuda, and H. Ooguri for useful conversations, and S. Sachdev for informing us about ref. [28]. This work was supported in part by a DOE grant DE-FG03-92-ER40701.\n\n

Published - BORjhep02a.pdf

", "abstract": "Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N-f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N-f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.", "date": "2002-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 049", "id_number": "CaltechAUTHORS:BORjhep02a", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BORjhep02a", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2002/11/049", "primary_object": { "basename": "BORjhep02a.pdf", "url": "https://authors.library.caltech.edu/records/2yyek-jdc59/files/BORjhep02a.pdf" }, "pub_year": "2002", "author_list": "Borokhov, Vadim; Kapustin, Anton; et al." }, { "id": "https://authors.library.caltech.edu/records/trfyf-k1r59", "eprint_id": 66691, "eprint_status": "archive", "datestamp": "2023-08-19 10:10:05", "lastmod": "2026-04-16 05:16:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Tong-David", "name": { "family": "Tong", "given": "David" } } ] }, "title": "D-brane probes of G_2 holonomy manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 The American Physical Society. \n\nReceived 5 March 2002; published 3 October 2002. \n\nWe are grateful to B. Acharya, M. Aganagic, N. Constable, A. Hanany, J. Sparks, N. Seiberg, M. Strassler, C. Vafa and E. Witten for useful discussions. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. D.T. is supported in part by funds provided by the U.S. Department of Energy (DOE) under cooperative research agreement No. DF-FC02-94ER40818.\n\n

Published - PhysRevD.66.087901.pdf

Submitted - 0202125.pdf

", "abstract": "We describe how mirror symmetry of three-dimensional N=1 supersymmetric gauge theories can be used to determine the theory on the world volume of a D2-brane probe of manifolds with G_2 holonomy.", "date": "2002-10-15", "date_type": "published", "publication": "Physical Review D", "volume": "66", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 087901", "id_number": "CaltechAUTHORS:20160505-113949597", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-113949597", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Department of Energy (DOE)", "grant_number": "DF-FC02-94ER40818" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.66.087901", "primary_object": { "basename": "0202125.pdf", "url": "https://authors.library.caltech.edu/records/trfyf-k1r59/files/0202125.pdf" }, "related_objects": [ { "basename": "PhysRevD.66.087901.pdf", "url": "https://authors.library.caltech.edu/records/trfyf-k1r59/files/PhysRevD.66.087901.pdf" } ], "pub_year": "2002", "author_list": "Gukov, Sergei and Tong, David" }, { "id": "https://authors.library.caltech.edu/records/6szbj-5ff75", "eprint_id": 1631, "eprint_status": "archive", "datestamp": "2023-08-21 23:47:52", "lastmod": "2026-04-16 07:05:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Worldsheet derivation of a large N duality", "ispublished": "pub", "full_text_status": "public", "keywords": "2-dimensional black-hole; topological strings; invariants; model; amplitudes; manifolds; gravity; spaces", "note": "\u00a9 2002 Elsevier Science B.V. \n\nReceived 4 July 2002; accepted 25 July 2002. Available online 13 August 2002. \n\nThis article has been registered under preprint number hep-th/0205297. \n\nWe thank M. Aganagic, R. Dijkgraaf, M. Douglas, R. Gopakumar, Y. Hashimoto, S. Katz, M. Marino, A. Strominger, N. Warner and E. Witten for valuable discussions. H.O. would like to thank the hospitality of the theory group at Harvard University. C.V. would like to thank the hospitality of the YITP at Stony Brook. \n\nThe research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329.\n\n

Submitted - OOGnpb02.pdf

", "abstract": "We give a worldsheet proof of the equivalence between the U(N) Chern\u2013Simons gauge theory on S\u00b3 and the topological closed string theory on the resolved conifold geometry. When the 't Hooft coupling of the gauge theory is small, the dual closed string worldsheet develops a new branch. We show that the fluctuations of the worldsheet into this branch effectively correspond to \"holes\" on the worldsheet, generating an open string sector. This leads to a microscopic description of how the 't Hooft expansion of gauge theory amplitudes is reproduced in the closed string computation. We find that the closed string amplitudes also contain terms which are not captured in the 't Hooft expansion but are present in the exact computation in the gauge theory amplitudes. These arise when the whole Riemann surface is in the new branch. We also discuss the cases with SO and Sp gauge groups.", "date": "2002-10-07", "date_type": "published", "publication": "Nuclear Physics B", "volume": "641", "number": "1-2", "publisher": "Elsevier", "pagerange": "3-34", "id_number": "CaltechAUTHORS:OOGnpb02", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGnpb02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9802709" }, { "agency": "NSF", "grant_number": "DMS-0074329" } ] }, "other_numbering_system": { "items": [ { "id": "68-2386", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(02)00620-X", "primary_object": { "basename": "OOGnpb02.pdf", "url": "https://authors.library.caltech.edu/records/6szbj-5ff75/files/OOGnpb02.pdf" }, "pub_year": "2002", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/n5yd3-kpp95", "eprint_id": 66675, "eprint_status": "archive", "datestamp": "2023-08-19 10:02:26", "lastmod": "2026-04-16 03:35:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Haack-M", "name": { "family": "Haack", "given": "Michael" } } ] }, "title": "IIA string theory on Calabi-Yau fourfolds with background fluxes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science B.V.\n\nReceived 24 April 2002, Accepted 30 May 2002, Available online 17 June 2002.\n\nWe thank M. Berg, R. Kallosh, J. Louis, A. Strominger, and E. Witten for useful discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. M.H. would like to thank the University of Princeton and especially I. Klebanov for hospitality at the beginning of the work. Moreover M.H. thanks the DFG for financial support and his work was supported in part by INFN, by the EC contract HPRN-CT-2000-00122, by the EC contract HPRN-CT-2000-00148, by the INTAS contract 99-0-590 and by the MURST-COFIN contract 2001-025492.\n\n

Submitted - 0203267.pdf

", "abstract": "Looking for string vacua with fixed moduli, we study compactifications of type IIA string theory on Calabi\u2013Yau fourfolds in the presence of generic Ramond\u2013Ramond fields. We explicitly derive the (super)potential induced by Ramond\u2013Ramond fluxes performing a Kaluza\u2013Klein reduction of the ten-dimensional effective action. This can be conveniently achieved in a formulation of the massive type IIA supergravity where all Ramond\u2013Ramond fields appear in a democratic way. The result agrees with the general formula for the superpotential written in terms of calibrations. We further notice that for generic Ramond\u2013Ramond fluxes all geometric moduli are stabilized and one finds non-supersymmetric vacua at positive values of the scalar potential.", "date": "2002-09-09", "date_type": "published", "publication": "Nuclear Physics B", "volume": "639", "number": "1-2", "publisher": "Elsevier", "pagerange": "95-128", "id_number": "CaltechAUTHORS:20160505-083954824", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-083954824", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "Istituto Nazionale di Fisica Nucleare (INFN)" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00122" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00148" }, { "agency": "INTAS", "grant_number": "99-0-590" }, { "agency": "Ministero dell 'Universit\u00e0 e della Ricerca Scientifica e Tecnologica (MURST)", "grant_number": "2001-025492" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(02)00442-X", "primary_object": { "basename": "0203267.pdf", "url": "https://authors.library.caltech.edu/records/n5yd3-kpp95/files/0203267.pdf" }, "pub_year": "2002", "author_list": "Gukov, Sergei and Haack, Michael" }, { "id": "https://authors.library.caltech.edu/records/kag81-nk917", "eprint_id": 1702, "eprint_status": "archive", "datestamp": "2023-08-21 23:40:41", "lastmod": "2026-04-16 06:53:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dennis-E", "name": { "family": "Dennis", "given": "Eric" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Landahl-A", "name": { "family": "Landahl", "given": "Andrew" } }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Topological quantum memory", "ispublished": "pub", "full_text_status": "public", "keywords": "ERROR-CORRECTING CODES; ISING-MODEL; GROUND-STATES; 2 DIMENSIONS; COMPUTATION; GEOMETRY", "note": "Copyright \u00a9 2002 American Institute of Physics. \n\nReceived 25 October 2001; accepted 16 May 2002. \n\nWe happily acknowledge helpful discussions with many colleagues, including Dorit Aharonov, Charlie Bennett, Daniel Gottesman, Randy Kamien, Greg Kuperberg, Paul McFadden, Michael Nielsen, Peter Shor, Andrew Steane, Chenyang Wang, and Nathan Wozny. We are especially grateful to Peter Hoyer for discussions of efficient perfect matching algorithms. This work originated in 1997, while E.D. received support from Caltech's Summer Undergraduate Research Fellowship (SURF) program. This work has been supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, by DARPA through the Quantum Information and Computation (QUIC) project administered by the Army Research Office under Grant No. DAAH04-96-1-0386, by the National Science Foundation under Grant No. EIA-0086038, by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374, and by an IBM Faculty Partnership Award.", "abstract": "We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z(2) lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.", "date": "2002-09-01", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "43", "number": "9", "publisher": "Journal of Mathematical Physics", "pagerange": "4452-4505", "id_number": "CaltechAUTHORS:DENjmp02.842", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:DENjmp02.842", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/1.1499754", "primary_object": { "basename": "DENjmp02.pdf", "url": "https://authors.library.caltech.edu/records/kag81-nk917/files/DENjmp02.pdf" }, "pub_year": "2002", "author_list": "Dennis, Eric; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/9t108-2x680", "eprint_id": 2017, "eprint_status": "archive", "datestamp": "2023-08-21 23:38:59", "lastmod": "2026-04-16 05:16:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Acharya-B-S", "name": { "family": "Acharya", "given": "Bobby S." } }, { "id": "De-La-Ossa-X", "name": { "family": "De La Ossa", "given": "Xenia" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "G-flux, supersymmetry and Spin(7) manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "M-Theory, Superstring vacua", "note": "\u00a9 Institute of Physics 2002 \n\nReceived 25 July 2002, accepted for publication 20 September 2002, Published 4 November 2002\n\nWe would like to thank P. Candelas, D. Joyce, J. Sparks, and E. Witten for useful discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296.\n\nE-print number: hep-th/0201227\n\n

Published - ACHjhep02.pdf

", "abstract": "In this note we study warped compactifications of M-theory on manifolds of Spin(7) holonomy in the presence of background 4-form flux. The explicit expression for the superpotential can be given in terms of the self-dual Cayley calibration on the Spin(7) manifold, in agreement with the general formula proposed in hep-th/9911011.", "date": "2002-09", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "9", "publisher": "Springer", "pagerange": "Art. No. 047", "id_number": "CaltechAUTHORS:ACHjhep02", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ACHjhep02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Clay Mathematics Institute" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2002/09/047", "primary_object": { "basename": "ACHjhep02.pdf", "url": "https://authors.library.caltech.edu/records/9t108-2x680/files/ACHjhep02.pdf" }, "pub_year": "2002", "author_list": "Acharya, Bobby S.; De La Ossa, Xenia; et al." }, { "id": "https://authors.library.caltech.edu/records/j5nr6-29v13", "eprint_id": 77388, "eprint_status": "archive", "datestamp": "2023-08-19 10:00:39", "lastmod": "2026-04-16 01:41:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hundertmark-Dirk", "name": { "family": "Hundertmark", "given": "Dirk" }, "orcid": "0000-0002-0643-0138" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Lieb\u2013Thirring Inequalities for Jacobi Matrices", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2002 Elsevier Science (USA). \n\nReceived 30 November 2001, Accepted 3 April 2002, Available online 3 October 2002. \n\nSupported in part by NSF Grant DMS-9707661.", "abstract": "For a Jacobi matrix J on \u2113^2(Z_+) with Ju(n)=a_(n\u22121u)n\u22121)+b_nu(n)+a -nu(n+1), we prove that\u2211\u2223E\u2223>2(E^2\u22124)^(1/2)\u2a7d\u2211n\u2223b_n\u2223+4\u2211n\u2223a_n\u22121\u2223. We also prove bounds on higher moments and some related results in higher dimension.", "date": "2002-09", "date_type": "published", "publication": "Journal of Approximation Theory", "volume": "118", "number": "1", "publisher": "Elsevier", "pagerange": "106-130", "id_number": "CaltechAUTHORS:20170512-073744584", "issn": "0021-9045", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170512-073744584", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jath.2002.3704", "pub_year": "2002", "author_list": "Hundertmark, Dirk and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/ywhbw-r3j61", "eprint_id": 27579, "eprint_status": "archive", "datestamp": "2023-08-19 09:50:10", "lastmod": "2026-04-16 03:42:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gomis-J", "name": { "family": "Gomis", "given": "Jaume" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Penrose Limit of N = 1 Gauge Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science B.V. \n\nReceived 19 March 2002; revised 3 May 2002; Accepted 7 May 2002. Available online 4 June 2002.\n\nWe would like to thank Andreas Brandhuber, Sergio Ferrara, Juan Maldacena, Sunil Mukhi, Horatiu Nastase, and John Schwarz for useful discussion. This research was supported in part by DOE grant DE-FG03-92-ER40701 and by Caltech Discovery Fund.\n\n

Submitted - GOMnpb02.pdf

", "abstract": "We find a Penrose limit of AdS_5 \u00d7 T^(1,1) which gives the pp-wave geometry identical to the one that appears in the Penrose limit of AdS_5 \u00d7 S^5. This leads us to conjecture\nthat there is a subsector of the corresponding N = 1 gauge theory which has enhanced N = 4 supersymmetry. We identify operators in the N = 1 gauge theory with stringy\nexcitations in the pp-wave geometry and discuss how the gauge theory operators fall into N = 4 supersymmetry multiplets. We find similar enhancement of symmetry in some other models, but there are also examples in which there is no supersymmetry enhancement in the Penrose limit.", "date": "2002-07-22", "date_type": "published", "publication": "Nuclear Physics B", "volume": "635", "number": "1-2", "publisher": "Elsevier", "pagerange": "106-125", "id_number": "CaltechAUTHORS:20111102-095258870", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111102-095258870", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Caltech Discovery Fund" } ] }, "other_numbering_system": { "items": [ { "id": "68-2373", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(02)00396-6", "primary_object": { "basename": "GOMnpb02.pdf", "url": "https://authors.library.caltech.edu/records/ywhbw-r3j61/files/GOMnpb02.pdf" }, "pub_year": "2002", "author_list": "Gomis, Jaume and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/54aq6-3ee02", "eprint_id": 27310, "eprint_status": "archive", "datestamp": "2023-08-19 09:40:40", "lastmod": "2026-04-16 06:06:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lee-Peter", "name": { "family": "Lee", "given": "Peter" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Jongwon", "name": { "family": "Park", "given": "Jongwon" } } ] }, "title": "Boundary States for AdS\u2082 Branes in AdS\u2083", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science B.V.\n\nReceived 4 February 2002; Accepted 26 March 2002. Available online 21 April 2002.\n\nWe would like to thank C. Bachas. J. de Boer and R. Dijkgraaf for useful discussion on the holographic interpretation of the AdS_2 branes. This research was supported in part by DOE grant DE-AC03-76SF00098.\n\n

Submitted - LEEnpb02preprint.pdf

", "abstract": "We construct boundary states for the AdS\u2082 D-branes in AdS\u2083. We show that, in the semi-classical limit, the boundary states correctly reproduce geometric configurations of these branes. We use the boundary states to compute the one loop free energy of open string stretched between the branes. The result agrees precisely with the open string computation in hep-th/0106129.", "date": "2002-06-17", "date_type": "published", "publication": "Nuclear Physics B", "volume": "632", "number": "1-3", "publisher": "Elsevier", "pagerange": "283-302", "id_number": "CaltechAUTHORS:20111019-133017114", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111019-133017114", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "other_numbering_system": { "items": [ { "id": "68-2363", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(02)00239-0", "primary_object": { "basename": "LEEnpb02preprint.pdf", "url": "https://authors.library.caltech.edu/records/54aq6-3ee02/files/LEEnpb02preprint.pdf" }, "pub_year": "2002", "author_list": "Lee, Peter; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/7mvw6-pzk76", "eprint_id": 27126, "eprint_status": "archive", "datestamp": "2023-08-19 09:32:55", "lastmod": "2026-04-16 06:52:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Freedman-M-H", "name": { "family": "Freedman", "given": "Michael H." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Wang-Zhenghan", "name": { "family": "Wang", "given": "Zhenghan" }, "orcid": "0000-0002-5253-6400" } ] }, "title": "Simulation of Topological Field Theories by Quantum Computers", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Springer-Verlag. \n\nReceived: 4 May 2001; Accepted: 16 January 2002. \n\nCommunicated by P. Sarnak. \n\nWe would like to thank Greg Kupperberg and Kevin Walker for many stimulating discussions on the material presented here.\n\n

Submitted - FREcmp02preprint.pdf

", "abstract": "Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned \"topological models\" having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H \u2261 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold: \n1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model \"BQP\".\n2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm.", "date": "2002-06", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "227", "number": "3", "publisher": "Springer", "pagerange": "587-603", "id_number": "CaltechAUTHORS:20111007-112002181", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111007-112002181", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s002200200635", "primary_object": { "basename": "FREcmp02preprint.pdf", "url": "https://authors.library.caltech.edu/records/7mvw6-pzk76/files/FREcmp02preprint.pdf" }, "pub_year": "2002", "author_list": "Freedman, Michael H.; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/z78s7-51c44", "eprint_id": 1307, "eprint_status": "archive", "datestamp": "2023-08-21 23:21:10", "lastmod": "2026-04-16 04:26:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bachas-C", "name": { "family": "Bachas", "given": "Constantin" } }, { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Dijkgraaf-R", "name": { "family": "Dijkgraaf", "given": "Robbert" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Permeable conformal walls and holography", "ispublished": "pub", "full_text_status": "public", "keywords": "Boundary Quantum Field Theory, AdS-CFT and dS-CFT Correspondence, D-branes", "note": "Received 21 February 2002, accepted for publication 12 June 2002, Published 4 July 2002 \n\nWe thank the ITP at Santa Barbara and the organizers of the `M-theory' program for their kind hospitality during the initial stages of this work. We are also grateful to C. Albertsson, C. Callan, O. DeWolfe, D. Freedman, J. Fr\u00c4ohlich, D. Kutasov, U. Lindstr\u00c4om, A. Ludwig, J. Maldacena, E. Martinec, G. Moore, N. Reed, R. Russo, V. Schomerus, J. Schwarz, E. Verlinde and M. Zabzine for useful conversations. Finally we thank the JHEP referee for his careful reading of the paper, and for constructive criticisms. This research is supported in part by the European networks \"Superstring Theory\" HPRN-CT-2000-00122 and \"The Quantum Structure of Spacetime\" HPRN-CT-2000-00131, and by DOE grant DE-AC03-76SF00098.\n\nE-print number: hep-th/0111210\n\n

Published - BACjhep02.pdf

Submitted - 0111210.pdf

", "abstract": "We study conformal field theories in two dimensions separated by domain walls, which preserve at least one Virasoro algebra. We develop tools to study such domain walls, extending and clarifying the concept of `folding' discussed in the condensed-matter literature. We analyze the conditions for unbroken supersymmetry, and discuss the holographic duals in AdS3 when they exist. One of the interesting observables is the Casimir energy between a wall and an anti-wall. When these separate free scalar field theories with different target-space radii, the Casimir energy is given by the dilogarithm function of the reflection probability. The walls with holographic duals in AdS3 separate two sigma models, whose target spaces are moduli spaces of Yang-Mills instantons on T4 or K3. In the supergravity limit, the Casimir energy is computable as classical energy of a brane that connects the walls through AdS3. We compare this result with expectations from the sigma-model point of view.", "date": "2002-06", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "6", "publisher": "Springer", "pagerange": "Art. no. 027", "id_number": "CaltechAUTHORS:BACjhep02", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BACjhep02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Union", "grant_number": "HPRN-CT-2000-00122" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00131" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "other_numbering_system": { "items": [ { "id": "01-045", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2002/06/027", "primary_object": { "basename": "0111210.pdf", "url": "https://authors.library.caltech.edu/records/z78s7-51c44/files/0111210.pdf" }, "related_objects": [ { "basename": "BACjhep02.pdf", "url": "https://authors.library.caltech.edu/records/z78s7-51c44/files/BACjhep02.pdf" } ], "pub_year": "2002", "author_list": "Bachas, Constantin; de Boer, Jan; et al." }, { "id": "https://authors.library.caltech.edu/records/ek9as-2p668", "eprint_id": 27125, "eprint_status": "archive", "datestamp": "2023-08-19 09:31:43", "lastmod": "2026-04-16 06:53:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bravyi-S-B", "name": { "family": "Bravyi", "given": "Sergey B." } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei Yu." }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Fermionic Quantum Computation", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier Science.\nReceived March 6, 2002.\nAvailable online 11 June 2002.\n\n

Submitted - BRAaop02preprint.pdf

", "abstract": "We define a model of quantum computation with local fermionic modes (LFMs)\u2014sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.", "date": "2002-05-25", "date_type": "published", "publication": "Annals of Physics", "volume": "298", "number": "1", "publisher": "Elsevier", "pagerange": "210-226", "id_number": "CaltechAUTHORS:20111007-111528069", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111007-111528069", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/aphy.2002.6254", "primary_object": { "basename": "BRAaop02preprint.pdf", "url": "https://authors.library.caltech.edu/records/ek9as-2p668/files/BRAaop02preprint.pdf" }, "pub_year": "2002", "author_list": "Bravyi, Sergey B. and Kitaev, Alexei Yu." }, { "id": "https://authors.library.caltech.edu/records/7dcp7-49a76", "eprint_id": 3205, "eprint_status": "archive", "datestamp": "2023-08-21 23:19:51", "lastmod": "2026-04-16 04:13:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Maldacena-Juan", "name": { "family": "Maldacena", "given": "Juan" }, "orcid": "0000-0002-9127-1687" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Strings in AdS3 and the SL(2,R) WZW model. III. Correlation functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 The American Physical Society \n\nReceived 24 January 2002; published 15 May 2002 \n\nWe would like to thank D. Kutasov, J. Teschner, N. Seiberg, S. Shenker, and A. Zamolodchikov for discussions. We thank the Institute for Theoretical Physics at the University of California, Santa Barbara, for hospitality. H.O. would also like to thank Harvard University and the Aspen Center for Physics. The research of J.M. was supported in part by DOE Grant No. DE-FGO2-91ER40654, NSF Grants No. PHY-9513835 and No. PHY99-07949, the Sloan Foundation, and the David and Lucile Packard Foundation. The research of H.O. was supported in part by DOE Grant No. DE-FG03-92-ER40701 and by the Caltech Discovery Fund.\n\n

Published - MALprd02.pdf

Submitted - 0111180.pdf

", "abstract": "We consider correlation functions for string theory on AdS3. We analyze their singularities and we provide a physical interpretation for them. We explain which worldsheet correlation functions have a sensible physical interpretation in terms of the boundary theory. We consider the operator product expansion of the four-point function and we find that it factorizes only if a certain condition is obeyed. We explain that this is the correct physical result. We compute correlation functions involving spectral flowed operators and we derive a constraint on the amount of winding violation.", "date": "2002-05-15", "date_type": "published", "publication": "Physical Review D", "volume": "65", "number": "10", "publisher": "American Physical Society", "pagerange": "Art. No. 106006", "id_number": "CaltechAUTHORS:MALprd02", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:MALprd02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FGO2-91ER40654" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "NSF", "grant_number": "PHY99-07949" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Caltech Discovery Fund" } ] }, "other_numbering_system": { "items": [ { "id": "01-042", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.65.106006", "primary_object": { "basename": "0111180.pdf", "url": "https://authors.library.caltech.edu/records/7dcp7-49a76/files/0111180.pdf" }, "related_objects": [ { "basename": "MALprd02.pdf", "url": "https://authors.library.caltech.edu/records/7dcp7-49a76/files/MALprd02.pdf" } ], "pub_year": "2002", "author_list": "Maldacena, Juan and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/3e4p9-p4d79", "eprint_id": 1924, "eprint_status": "archive", "datestamp": "2023-08-21 23:14:00", "lastmod": "2026-04-16 07:05:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cherkis-S-A", "name": { "family": "Cherkis", "given": "Sergey A." }, "orcid": "0000-0002-0785-0126" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Hyper-K\u00e4hler metrics from periodic monopoles", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 The American Physical Society \n\nReceived 14 November 2001; published 25 March 2002 \n\nS. Ch. was supported in part by NSF grant PHY9819686. A. K. was supported in part by DOE grants DE-FG02-90-ER40542 and DE-FG03-92-ER40701.\n\n

Published - CHERprd02.pdf

", "abstract": "Relative moduli spaces of periodic monopoles provide novel examples of asymptotically locally flat hyper-K\u00e4hler manifolds. By considering the interactions between well-separated periodic monopoles, we infer the asymptotic behavior of their metrics. When the monopole moduli space is four dimensional, this construction yields interesting examples of metrics with a self-dual curvature (gravitational instantons). We discuss their topology and complex geometry. An alternative construction of these gravitational instantons using moduli spaces of Hitchin equations is also described.", "date": "2002-04-15", "date_type": "published", "publication": "Physical Review D", "volume": "65", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 084015", "id_number": "CaltechAUTHORS:CHEprd02", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHEprd02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9819686" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.65.084015", "primary_object": { "basename": "CHERprd02.pdf", "url": "https://authors.library.caltech.edu/records/3e4p9-p4d79/files/CHERprd02.pdf" }, "pub_year": "2002", "author_list": "Cherkis, Sergey A. and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/00gbd-tq680", "eprint_id": 81889, "eprint_status": "archive", "datestamp": "2023-08-21 23:12:51", "lastmod": "2026-04-16 05:27:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } }, { "id": "Stufken-J", "name": { "family": "Stufken", "given": "John" } } ] }, "title": "The lattice of N-run orthogonal arrays", "ispublished": "pub", "full_text_status": "public", "keywords": "Asymmetrical orthogonal array; Expansive replacement method; Geometric orthogonal array; Linear orthogonal array; Linear programming bound; Mixed Orthogonal array; Mixed spread; Tight array", "note": "\u00a9 2002 Elsevier Science B.V. \n\nAccepted 13 March 2001, Available online 13 March 2002. \n\nWe thank Michele Colgan for computing the properties of the lattices \u039b'_N shown in Table 3. The research of John Stufken was supported by NSF grant DMS-9803684.\n\n

Submitted - 0205299.pdf

", "abstract": "If the number of runs in a (mixed-level) orthogonal array of strength 2 is specified, what numbers of levels and factors are possible? The collection of possible sets of parameters for orthogonal arrays with N runs has a natural lattice structure, induced by the \"expansive replacement\" construction method. In particular the dual atoms in this lattice are the most important parameter sets, since any other parameter set for an N-run orthogonal array can be constructed from them. To get a sense for the number of dual atoms, and to begin to understand the lattice as a function of N, we investigate the height and the size of the lattice. It is shown that the height is at most \u230ac(N\u22121)\u230b, where c=1.4039\u2026, and that there is an infinite sequence of values of N for which this bound is attained. On the other hand, the number of nodes in the lattice is bounded above by a superpolynomial function of N (and superpolynomial growth does occur for certain sequences of values of N). Using a new construction based on \"mixed spreads\", all parameter sets with 64 runs are determined. Four of these 64-run orthogonal arrays appear to be new.", "date": "2002-04-01", "date_type": "published", "publication": "Journal of Statistical Planning and Inference", "volume": "102", "number": "2", "publisher": "Elsevier", "pagerange": "477-500", "id_number": "CaltechAUTHORS:20170927-153859292", "issn": "0378-3758", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170927-153859292", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9803684" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0378-3758(01)00119-7", "primary_object": { "basename": "0205299.pdf", "url": "https://authors.library.caltech.edu/records/00gbd-tq680/files/0205299.pdf" }, "pub_year": "2002", "author_list": "Rains, E. M.; Sloane, N. J. A.; et al." }, { "id": "https://authors.library.caltech.edu/records/y6bfe-6cy93", "eprint_id": 66688, "eprint_status": "archive", "datestamp": "2023-08-19 09:16:46", "lastmod": "2026-04-16 07:11:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Tong-David", "name": { "family": "Tong", "given": "David" } } ] }, "title": "D-Brane probes of Special Holonomy Manifolds, and Dynamics of N=1 Three-Dimensional Gauge Theories", "ispublished": "pub", "full_text_status": "public", "keywords": "Field Theories in Lower Dimensions, Duality in Gauge Field Theories,\nBrane Dynamics in Gauge Theories", "note": "\u00a9 2002 SISSA/ISAS. \n\nReceived: March 20, 2002; Accepted: April 26, 2002. \n\nWe are grateful to B. Acharya, M. Aganagic, N. Constable, A. Hanany, J. Sparks, N. Seiberg, M. Strassler, C. Vafa and E. Witten for useful discussions. This research was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. D.T. is a Pappalardo fellow and would like to thank the Pappalardo family for their largesse. The work of D.T. also supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative research agreement #DF-FC02-94ER40818.\n\n

Submitted - 0202126.pdf

", "abstract": "Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N = 1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a \"G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds withSU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.", "date": "2002-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2002", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 50", "id_number": "CaltechAUTHORS:20160505-110509143", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-110509143", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Pappalardo Fellowship" }, { "agency": "Department of Energy (DOE)", "grant_number": "DF-FC02-94ER40818" }, { "agency": "Clay Mathematics Institute" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2002/04/050", "primary_object": { "basename": "0202126.pdf", "url": "https://authors.library.caltech.edu/records/y6bfe-6cy93/files/0202126.pdf" }, "pub_year": "2002", "author_list": "Gukov, Sergei and Tong, David" }, { "id": "https://authors.library.caltech.edu/records/772f4-g1n44", "eprint_id": 27446, "eprint_status": "archive", "datestamp": "2023-08-21 23:11:03", "lastmod": "2026-04-16 02:03:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Wang-B-L", "name": { "family": "Wang", "given": "Bai-Ling" } } ] }, "title": "Seiberg\u2013Witten and Casson\u2013Walker Invariants for Rational Homology 3-Spheres", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Seiberg-Witten; Casson-Walker; eta-invariants", "note": "\u00a9 2002 Kluwer Academic Publishers. Received: 11 January 2001. Some of our arguments are inspired by the paper of Ozsv\u00e1th and Szab\u00f3 on the theta divisor and the Casson\u2013Walker invariant. The first author is partially supported by\nthe Humboldt Foundation (Sofja Kovalevskaya Award). The second author is supported by the Australian Research Council.", "abstract": "We consider a modified version of the Seiberg\u2013Witten invariants for rational homology\n3-spheres, obtained by adding to the original invariants a correction term which is a combination\nof \u03b7-invariants. We show that these modified invariants are topological invariants.\nWe prove that an averaged version of these modified invariants equals the Casson\u2013Walker\ninvariant. In particular, this result proves an averaged version of a conjecture of Ozsv\u00e1th\nand Szab\u00f3 on the equivalence between their \u03b8 invariant and the Seiberg\u2013Witten invariant of\nrational homology 3-spheres.", "date": "2002-04", "date_type": "published", "publication": "Geometriae Dedicata", "volume": "91", "number": "1", "publisher": "Springer", "pagerange": "45-58", "id_number": "CaltechAUTHORS:20111026-110403593", "issn": "0046-5755", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111026-110403593", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Humboldt Foundation Sofja Kovalevskaya Award" }, { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/A:1016299716922", "pub_year": "2002", "author_list": "Marcolli, Matilde and Wang, Bai-Ling" }, { "id": "https://authors.library.caltech.edu/records/jn6bs-kmc05", "eprint_id": 66712, "eprint_status": "archive", "datestamp": "2023-08-19 09:13:33", "lastmod": "2026-04-16 01:46:22", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Sparks-J", "name": { "family": "Sparks", "given": "James" } } ] }, "title": "M-theory on Spin(7) manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 Elsevier B.V. \n\nReceived 19 November 2001, Accepted 9 January 2002. \n\nWe wish to thank K. Costello, G. Gibbons, C. Herzog, J. Maldacena, N. Nekrasov, C. N\u00fa\u00f1ez, C. Pope, E. Rabinovici, S. Schafer-Nameki, A. Strominger, C. Vafa, and E. Witten for useful discussions. This research was partially conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296.\n\n

Submitted - 0109025.pdf

", "abstract": "We study M-theory on two classes of manifolds of Spin(7) holonomy that are developing an isolated conical singularity. We construct explicitly a new class of Spin(7) manifolds and analyse in detail the topology of the corresponding classical spacetimes. We discover also an intricate interplay between various anomalies in M-theory, string theory, and gauge theory within these models, and in particular find a connection between half-integral G-fluxes in M-theory and Chern\u2013Simons terms of the N=1, D=3 effective theory.", "date": "2002-03-18", "date_type": "published", "publication": "Nuclear Physics B", "volume": "625", "number": "1-2", "publisher": "Elsevier", "pagerange": "3-69", "id_number": "CaltechAUTHORS:20160506-084420068", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-084420068", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(02)00018-4", "primary_object": { "basename": "0109025.pdf", "url": "https://authors.library.caltech.edu/records/jn6bs-kmc05/files/0109025.pdf" }, "pub_year": "2002", "author_list": "Gukov, Sergei and Sparks, James" }, { "id": "https://authors.library.caltech.edu/records/4rebx-j5r09", "eprint_id": 1238, "eprint_status": "archive", "datestamp": "2023-08-21 23:09:01", "lastmod": "2026-04-16 07:14:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Beckman-D", "name": { "family": "Beckman", "given": "David" } }, { "id": "Gottesman-D", "name": { "family": "Gottesman", "given": "Daniel" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Measurability of Wilson loop operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92002 The American Physical Society \n\nReceived 23 October 2001; published 5 March 2002 \n\nWe thank Steve Giddings, Anton Kapustin, Michael Nielsen, Edward Witten, and especially Mark Srednicki for helpful discussions and comments. This work was supported in part by the Department of Energy under Grant No. DEFG03-92-ER40701, by the National Science Foundation under Grant No. EIA-0086038, by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374, by IBM, and by the Clay Mathematics Institute. Some of this work was done at the Aspen Center for Physics.", "abstract": "We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux tubes both link with the loop C, then a nondemolition measurement of W(C) would cause electric charge to be transferred from one flux tube to the other, a violation of relativistic causality. A destructive measurement of W(C) is possible in a non-Abelian gauge theory with suitable matter content. In an Abelian gauge theory, many cooperating parties distributed along the loop C can perform a nondemolition measurement of the Wilson loop operator if they are equipped with a shared entangled ancilla that has been prepared in advance. We also note that Abelian electric charge (but not non-Abelian charge) can be transported superluminally, without any accompanying transmission of information.", "date": "2002-03-15", "date_type": "published", "publication": "Physical Review D", "volume": "65", "number": "6", "publisher": "Physical Review D", "pagerange": "Art. no. 065022", "id_number": "CaltechAUTHORS:BECprd02", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BECprd02", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevD.65.065022", "primary_object": { "basename": "BECprd02.pdf", "url": "https://authors.library.caltech.edu/records/4rebx-j5r09/files/BECprd02.pdf" }, "pub_year": "2002", "author_list": "Beckman, David; Gottesman, Daniel; et al." }, { "id": "https://authors.library.caltech.edu/records/f2hwp-ywb02", "eprint_id": 82295, "eprint_status": "archive", "datestamp": "2023-08-19 08:48:54", "lastmod": "2026-04-16 03:45:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "J. C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "The EKG Sequence", "ispublished": "pub", "full_text_status": "public", "keywords": "Electrocardiagrarn sequence, EKG sequence", "note": "\u00a9 2002 A K Peters, Ltd. \n\nReceived December 12, 2001; accepted in revised form March 11, 2002. \n\nWe thank Jonathan Ayres for discovering this wonderful sequence. We also thank a referee for helpful comments.\n\n

Submitted - 0204011.pdf

", "abstract": "The EKC or electrocardiogram sequence is defined by a(1) = 1, a(2) = 2 and, for n \u2265 3, a(n) is the smallest natural number not already in the sequence with the property that gcd{a(n \u2212 1),a(n)} > 1. In spite of its erratic local behavior, which when plotted resembles an electrocardiogram, its global behavior appears quite regular. We conjecture that almost all a(n) satisfy the asymptotic formula a(n) = n(1+1/(3logn)) + o(n/log n) as n \u2192 \u221e and that the exceptional values a(n) = p and a(n) = 3p, for p a prime, produce the spikes in the EKG sequence. We prove that {a(n) : n \u2265 1) is a permutation of the natural numbers and that c_1 n \u2264 a(n) \u2264 c_2 n for constants c_1,c_2. There remains a large gap between what is conjectured and what is proved.", "date": "2002", "date_type": "published", "publication": "Experimental Mathematics", "volume": "11", "number": "3", "publisher": "A K Peters", "pagerange": "437-446", "id_number": "CaltechAUTHORS:20171011-152214607", "issn": "1058-6458", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171011-152214607", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1080/10586458.2002.10504486", "primary_object": { "basename": "0204011.pdf", "url": "https://authors.library.caltech.edu/records/f2hwp-ywb02/files/0204011.pdf" }, "pub_year": "2002", "author_list": "Lagarias, J. C.; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/6sy4f-ajc11", "eprint_id": 38574, "eprint_status": "archive", "datestamp": "2023-08-21 22:50:17", "lastmod": "2026-03-09 20:35:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jackson-S", "name": { "family": "Jackson", "given": "S." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } } ] }, "title": "Countable Borel equivalence relations", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Borel equivalence relation; reducibility; hyperfinite; polynomial growth; amenable; treeable; universal equivalence relation", "note": "\u00a9 2002 World Scientific Publishing Company & Singapore University Press.\nReceived 1 January 2001.\nResearch partially supported by NSF Grants DMS-9619880 and DMS-9987437.", "abstract": "This paper develops the foundations of the descriptive set theory of countable Borel\nequivalence relations on Polish spaces with particular emphasis on the study of hyper-finite, amenable, treeable and universal equivalence relations.", "date": "2002", "date_type": "published", "publication": "Journal of Mathematical Logic", "volume": "2", "number": "1", "publisher": "World Scientific Publishing", "pagerange": "1-80", "id_number": "CaltechAUTHORS:20130520-104729185", "issn": "0219-0613", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130520-104729185", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9619880" }, { "agency": "NSF", "grant_number": "DMS-9987437" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "2002", "author_list": "Jackson, S.; Kechris, A. S.; et al." }, { "id": "https://authors.library.caltech.edu/records/mt030-bmm91", "eprint_id": 77448, "eprint_status": "archive", "datestamp": "2023-08-19 08:37:52", "lastmod": "2026-04-16 03:25:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kirsch-W", "name": { "family": "Kirsch", "given": "Werner" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Approach to equilibrium for a forced Burgers equation", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Birkh\u00e4user Verlag Basel. \n\nReceived February 26, 2001; accepted April 9, 2001. \n\nSupported in part by NSF Grant No. DMS-9707661.\n\n

Submitted - 0106023.pdf

", "abstract": "We show that approach to equilibrium in certain forced Burgers equations is implied by a decay estimate on a suitable intrinsic semigroup estimate, and we verify this estimate in a variety of cases including a periodic force.", "date": "2001-12", "date_type": "published", "publication": "Journal of Evolution Equations", "volume": "1", "number": "4", "publisher": "Springer", "pagerange": "411-419", "id_number": "CaltechAUTHORS:20170515-105645659", "issn": "1424-3199", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170515-105645659", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/PL00001380", "primary_object": { "basename": "0106023.pdf", "url": "https://authors.library.caltech.edu/records/mt030-bmm91/files/0106023.pdf" }, "pub_year": "2001", "author_list": "Kirsch, Werner and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/9ymcs-f8816", "eprint_id": 3821, "eprint_status": "archive", "datestamp": "2023-08-21 22:42:55", "lastmod": "2026-04-16 04:03:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hashimoto-Koji", "name": { "family": "Hashimoto", "given": "Koji" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Seiberg-Witten transforms of noncommutative solitons", "ispublished": "pub", "full_text_status": "public", "keywords": "GAUGE-THEORY; YANG-MILLS; INSTANTONS; MONOPOLE; R-4", "note": "\u00a9 2001 The American Physical Society. \n\nReceived 12 June 2001; published 3 October 2001. \n\nWe thank Yuji Okawa for useful discussions and for comments on the earlier version of this paper. H.O. thanks the Institute for Theoretical Physics, Santa Barbara, for the hospitality. K.H. was supported in part by Japan Society for the Promotion of Science under the Postdoctoral Research Program (#02482). H.O. was supported in part by the Department of Energy grant DE-FG03-92ER40701 and the Caltech Discovery Fund. In addition, this research was supported in part by the National Science Foundation under Grant No. PHY99-07949. \n\nAlternate preprint/report numbers -- arXiv:hep-th/0105311; CALT-68-2331; CITUSC/01-019; NSF-ITP-01-42\n\n

Published - HASprd01.pdf

Submitted - HASprd01preprint.pdf

", "abstract": "We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the commutative variables. This gives a precise identification of the moduli of these solutions as locations of branes. On the other hand, an instanton solution in four dimensions allows deformation away from the projection operator construction. We evaluate the Seiberg-Witten transform of the U(2) instanton and show that it has a finite size determined by the noncommutative scale and by the deformation parameter \u03c1. For large \u03c1, the profile of the D0-brane density of the instanton agrees surprisingly well with that of the Belavin-Polyakov-Schwarz-Tyupkin (BPST) instanton on commutative space.", "date": "2001-11-15", "date_type": "published", "publication": "Physical Review D", "volume": "64", "number": "10", "publisher": "American Physical Society", "pagerange": "Art. No. 106005", "id_number": "CaltechAUTHORS:HASprd01", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:HASprd01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Japan Society for the Promotion of Science (JSPS)", "grant_number": "02482" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "Caltech Discovery Fund" }, { "agency": "NSF", "grant_number": "PHY99-07949" } ] }, "other_numbering_system": { "items": [ { "id": "01-019", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.64.106005", "primary_object": { "basename": "HASprd01.pdf", "url": "https://authors.library.caltech.edu/records/9ymcs-f8816/files/HASprd01.pdf" }, "related_objects": [ { "basename": "HASprd01preprint.pdf", "url": "https://authors.library.caltech.edu/records/9ymcs-f8816/files/HASprd01preprint.pdf" } ], "pub_year": "2001", "author_list": "Hashimoto, Koji and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/xc2ea-aag61", "eprint_id": 81816, "eprint_status": "archive", "datestamp": "2023-08-19 08:29:00", "lastmod": "2026-03-09 23:04:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "A semidefinite program for distillable entanglement", "ispublished": "pub", "full_text_status": "public", "keywords": "Entanglement distillation, quantum communication,\nsemidefinite programming", "note": "\u00a9 2001 IEEE. \n\nManuscript received August 23, 2000; revised June 8, 2001.\n\n

Published - 00959270.pdf

Submitted - 0008047.pdf

", "abstract": "We show that the maximum fidelity obtained by a positive partial transpose (p.p.t.) distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, becoming a linear program in the case of isotropic and Werner states. Using these techniques, we determine the p.p.t. distillable entanglement of asymmetric Werner states and \"maximally correlated\" states. We conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1-local distillation.", "date": "2001-11", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "47", "number": "7", "publisher": "IEEE", "pagerange": "2921-2933", "id_number": "CaltechAUTHORS:20170925-141527816", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-141527816", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.959270", "primary_object": { "basename": "0008047.pdf", "url": "https://authors.library.caltech.edu/records/xc2ea-aag61/files/0008047.pdf" }, "related_objects": [ { "basename": "00959270.pdf", "url": "https://authors.library.caltech.edu/records/xc2ea-aag61/files/00959270.pdf" } ], "pub_year": "2001", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/0mrqj-pat38", "eprint_id": 81981, "eprint_status": "archive", "datestamp": "2023-08-19 08:29:08", "lastmod": "2026-04-16 03:51:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Baik-J", "name": { "family": "Baik", "given": "Jinho" } }, { "id": "Deift-P", "name": { "family": "Deift", "given": "Percy" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "A Fredholm Determinant Identity and the Convergence of Moments for Random Young Tableaux", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Springer-Verlag Berlin Heidelberg. \n\nReceived: 19 December 2000; Accepted: 23 July 2001. \n\nThe authors would like to thank Xin Zhou for useful comments. The authors would also like to thank Albrecht B\u00f6ttcher for pointing out a calculational error in an earlier version of the text. The work of the first author was supported in part by NSF Grant # DMS 97-29992. The work of the second author was supported in part by NSF Grant # DMS 00-03268, and also by the Guggenheim Foundation.\n\n

Submitted - 0012117.pdf

", "abstract": "We obtain an identity between Fredholm determinants of two kinds of operators, one acting on functions on the unit circle and the other acting on functions on a subset of the integers. This identity is a generalization of an identity between a Toeplitz determinant and a Fredholm determinant that has appeared in the random permutation context. Using this identity, we prove, in particular, convergence of moments for arbitrary rows of a random Young diagram under Plancherel measure.", "date": "2001-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "223", "number": "3", "publisher": "Springer", "pagerange": "627-672", "id_number": "CaltechAUTHORS:20171003-074824665", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-074824665", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 97-29992" }, { "agency": "NSF", "grant_number": "DMS 00-03268" }, { "agency": "John Simon Guggenheim Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s002200100555", "primary_object": { "basename": "0012117.pdf", "url": "https://authors.library.caltech.edu/records/0mrqj-pat38/files/0012117.pdf" }, "pub_year": "2001", "author_list": "Baik, Jinho; Deift, Percy; et al." }, { "id": "https://authors.library.caltech.edu/records/a7jkf-bgb64", "eprint_id": 66709, "eprint_status": "archive", "datestamp": "2023-08-19 08:26:47", "lastmod": "2026-04-16 02:04:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Berkovits-N", "name": { "family": "Berkovits", "given": "Nathan" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Vallilo-B-C", "name": { "family": "Vallilo", "given": "Brenno Carlini" } } ] }, "title": "Superstrings in 2D backgrounds with R\u2013R flux and new extremal black holes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Elsevier B.V. \n\nReceived 7 August 2001, Accepted 15 August 2001, Available online 5 October 2001. \n\nWe are grateful to C.G. Callan, O. Chand\u0131\u0301a, A.T. Filippov, G.T. Horowitz, J. Maldacena, D. Nedel, R. Plesser, H. Ooguri, V. Rivelles, J.H. Schwarz, N. Seiberg, S. Shenker, A. Strominger, C. Vafa, and E. Witten for useful discussions and comments. The work of N.B. is supported in part by CNPq grant 300256/94-9, Pronex 66.2002/1998-9, and FAPESP grant 99/12763-0. This research was partially conducted during the period N.B. served as a Clay Mathematics Institute Prize Fellow and S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. The work of S.G. is also supported in part by the Caltech Discovery Fund, NSF grant No. PHY99-07949, grant RFBR No. 01-02-17488, and the Russian President's grant No. 00-15-99296. The work of B.C.V. is supported by FAPESP grant No 00/02230-3. N.B. and S.G. are grateful to the California Institute of Technology, where part of this work was done, for hospitality.\n\n

Submitted - 0107140.pdf

", "abstract": "The hybrid formalism is used to quantize the superstring compactified to two-dimensional target-space in a manifestly spacetime supersymmetric manner. A quantizable sigma model action is then constructed for the type II superstring in curved two-dimensional supergravity backgrounds which can include Ramond\u2013Ramond flux. Such curved backgrounds include Calabi\u2013Yau four-fold compactifications with Ramond\u2013Ramond flux, and new extremal black hole solutions in two-dimensional dilaton supergravity theory. These black hole solutions are a natural generalization of the CGHS model and might be possible to describe using a supergroup version of the SL(2,R)/U(1) WZW model. We also study some dynamical aspects of the new black holes, such as formation and evaporation.", "date": "2001-10-29", "date_type": "published", "publication": "Nuclear Physics B", "volume": "614", "number": "1-2", "publisher": "Elsevier", "pagerange": "195-232", "id_number": "CaltechAUTHORS:20160506-075145513", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-075145513", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico (CNPq)", "grant_number": "300256/94-9" }, { "agency": "Pronex", "grant_number": "66.2002/1998-9" }, { "agency": "Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Sao Paulo (FAPESP)", "grant_number": "99/12763-0" }, { "agency": "Clay Mathematics Institute" }, { "agency": "Caltech Discovery Fund" }, { "agency": "NSF", "grant_number": "PHY99-07949" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-02-17488" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" }, { "agency": "Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de Sao Paulo (FAPESP)", "grant_number": "00/02230-3" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(01)00413-8", "primary_object": { "basename": "0107140.pdf", "url": "https://authors.library.caltech.edu/records/a7jkf-bgb64/files/0107140.pdf" }, "pub_year": "2001", "author_list": "Berkovits, Nathan; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/egdzc-88960", "eprint_id": 27624, "eprint_status": "archive", "datestamp": "2023-08-19 08:19:19", "lastmod": "2026-04-16 06:22:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Sofronidis-N-E", "name": { "family": "Sofronidis", "given": "N. E." } } ] }, "title": "A strong generic ergodicity property of unitary and self-adjoint operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Cambridge University Press. Received 11 June 1999 and accepted in revised form 14 August 2000. Published online: 02 October 2001. We would like to acknowledge the support of NSF through grant DMS 9619880. We would also like to thank Tom Wolff for suggesting the argument in the\nproof of Proposition 5.6(i)(a).\n\n

Published - KECetds01.pdf

", "abstract": "Consider the conjugacy action of the unitary group of an infinite-dimensional separable Hilbert space on the unitary operators. A strong generic ergodicity property of this action is established, by showing that any conjugacy invariants assigned in a definable way to unitary operators, and taking as values countable structures up to isomorphism, generically trivialize. Similar results are proved for conjugacy of self-adjoint operators and for measure equivalence. The proofs make use of the theory of turbulence for continuous actions of Polish groups, developed by Hjorth. These methods are also used to give a new solution to a problem of Mauldin in measure theory, by showing that any analytic set of pairwise orthogonal measures on the Cantor space is orthogonal to a product measure.", "date": "2001-10", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "21", "publisher": "Cambridge University Press", "pagerange": "1459-1479", "id_number": "CaltechAUTHORS:20111104-093324189", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111104-093324189", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 9619880" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/S0143385701001705", "primary_object": { "basename": "KECetds01.pdf", "url": "https://authors.library.caltech.edu/records/egdzc-88960/files/KECetds01.pdf" }, "pub_year": "2001", "author_list": "Kechris, A. S. and Sofronidis, N. E." }, { "id": "https://authors.library.caltech.edu/records/9rkq1-7ay51", "eprint_id": 66711, "eprint_status": "archive", "datestamp": "2023-08-19 08:17:56", "lastmod": "2026-04-16 03:39:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Brandhuber-A", "name": { "family": "Brandhuber", "given": "Andreas" } }, { "id": "Gomis-J", "name": { "family": "Gomis", "given": "Jaume" } }, { "id": "Gubser-S-S", "name": { "family": "Gubser", "given": "Steven S." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Gauge theory at large N and new G\u2082 holonomy metrics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Elsevier Science B.V. \n\nReceived 14 June 2001, Accepted 16 July 2001, Available online 24 September 2001. \n\nWe are grateful to Michael Atiyah, Vadim Borokhov, Mirjam Cvetic, Igor Klebanov, Chris Pope, and especially Cumrun Vafa and Edward Witten for useful discussions. The work of A. Brandhuber and S. Gubser is supported in part by the DOE under grant No.DE-FG03-92ER40701. The work of J. Gomis is supported in part by the National Science Foundation under grant No. PHY99-07949 and by the DOE under grant No. DE-FG03-92ER40701. The research of S. Gukov is supported in part by the Caltech Discovery Fund, NSF grant No. PHY99-07949, grant RFBR No. 01-01-00549, and the Russian President's grant No. 00-15-99296.\n\n

Submitted - 0106034.pdf

", "abstract": "We find a one-parameter family of new G\u2082 holonomy metrics and demonstrate that it can be extended to a two-parameter family. These metrics play an important role as the supergravity dual of the large N limit of four-dimensional supersymmetric Yang\u2013Mills. We show that these G\u2082 holonomy metrics describe the M theory lift of the supergravity solution describing a collection of D6-branes wrapping the supersymmetric three-cycle of the deformed conifold geometry for any value of the string coupling constant.", "date": "2001-09-17", "date_type": "published", "publication": "Nuclear Physics B", "volume": "611", "number": "1-3", "publisher": "Elsevier", "pagerange": "179-204", "id_number": "CaltechAUTHORS:20160506-081903900", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-081903900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "NSF", "grant_number": "PHY99-07949" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "01-01-00549" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(01)00340-6", "primary_object": { "basename": "0106034.pdf", "url": "https://authors.library.caltech.edu/records/9rkq1-7ay51/files/0106034.pdf" }, "pub_year": "2001", "author_list": "Brandhuber, Andreas; Gomis, Jaume; et al." }, { "id": "https://authors.library.caltech.edu/records/7t755-p5m81", "eprint_id": 27627, "eprint_status": "archive", "datestamp": "2023-08-19 08:15:41", "lastmod": "2026-04-16 06:38:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lee-Peter", "name": { "family": "Lee", "given": "Peter" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Park-Jongwon", "name": { "family": "Park", "given": "Jongwon" } }, { "id": "Tannenhauser-J", "name": { "family": "Tannenhauser", "given": "Jonathan" } } ] }, "title": "Open Strings on AdS\u2082 Branes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Elsevier Science B.V. \n\nReceived 28 June 2001; Accepted 2 July 2001. Available online 5 April 2002. \n\nIt is a pleasure to thank Jaume Gomis and Harlan Robins for enlightening conversations. P.L. , H.O., and J.P. thank the institute for Theoretical Physics, Santa Barbara, for hospitality. This research was supported in part by Department of Energy grant DE-FG03-92ER40701, National Science Foundation grant PHY99-07949, and the Caltech Discovery Fund.\n\n

Submitted - LEEnpb01preprint.pdf

", "abstract": "We study the spectrum of open strings on AdS\u2082 branes in AdS\u2083 in an NS-NS background, using the SL(2,R) WZW model. When the brane carries no fundamental string charge, the\nopen string spectrum is the holomorphic square root of the spectrum of closed strings in AdS\u2083. It contains short and long strings, and is invariant under spectral flow. When the\nbrane carries fundamental string charge, the open string spectrum again contains short and long strings in all winding sectors. However, branes with fundamental string charge break half the spectral flow symmetry. This has different implications for short and long strings. As the fundamental string charge increases, the brane approaches the boundary of AdS\u2083. In this limit, the induced electric field on the worldvolume reaches its critical value, producing noncommutative open string theory on AdS\u2082.", "date": "2001-09-03", "date_type": "published", "publication": "Nuclear Physics B", "volume": "610", "number": "1-2", "publisher": "Elsevier", "pagerange": "3-48", "id_number": "CaltechAUTHORS:20111104-094701527", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111104-094701527", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "NSF", "grant_number": "PHY99-07949" }, { "agency": "Caltech Discovery Fund" } ] }, "other_numbering_system": { "items": [ { "id": "01-20", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(01)00333-9", "primary_object": { "basename": "LEEnpb01preprint.pdf", "url": "https://authors.library.caltech.edu/records/7t755-p5m81/files/LEEnpb01preprint.pdf" }, "pub_year": "2001", "author_list": "Lee, Peter; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/x8cmp-j5871", "eprint_id": 82998, "eprint_status": "archive", "datestamp": "2023-08-21 22:32:37", "lastmod": "2026-04-16 05:46:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nebe-G", "name": { "family": "Nebe", "given": "Gabriele" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "The Invariants of the Clifford Groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Clifford groups; Barnes-Wall lattices; spherical designs; invariants; self-dual codes", "note": "\u00a9 2001 Kluwer Academic Publishers. \n\nReceived December 9, 1999; Revised September 18, 2000; Accepted September 26, 2000. \n\nMost of this work was carried out during G. Nebe's visit to AT&T Labs in the Summer of 1999.\n\n

Submitted - 0001038.pdf

", "abstract": "The automorphism group of the Barnes-Wall lattice L_m in dimension 2^m(m \u2260 3) is a subgroup of index 2 in a certain \"Clifford group\" C_m of structure 2_+^(1+2m). O^+(2m,2). This group and its complex analogue X_m of structure (2^(1+2m)_+YZ_8). Sp(2m, 2) have arisen in recent years in connection with the construction of orthogonal spreads, Kerdock sets, packings in Grassmannian spaces, quantum codes, Siegel modular forms and spherical designs. In this paper we give a simpler proof of Runge@apos;s 1996 result that the space of invariants for C_m degree 2k is spanned by the complete weight enumerators of the codes C\u2297F_(2m), where Cranges over all binary self-dual codes of length 2k; these are a basis if m \u2265 k - 1. We also give new constructions for L_m and C_m: let M be the Z[\u221a2]-lattice with Gram matrix [2 \u221a2 \u221a2 2}. Then L_m is the rational part of M^(\u2297 m), and C_m = Aut(M^(\u2297m)). Also, if C is a binary self-dual code not generated by vectors of weight 2, then C_m is precisely the automorphism group of the complete weight enumerator of C\u2297F_(2m). There are analogues of all these results for the complex group X_m, with \"doubly-even self-dual code\" instead of \"self-dual code.\"", "date": "2001-09", "date_type": "published", "publication": "Designs, Codes and Cryptography", "volume": "24", "number": "1", "publisher": "Springer", "pagerange": "99-122", "id_number": "CaltechAUTHORS:20171106-144248894", "issn": "0925-1022", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-144248894", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/A:1011233615437", "primary_object": { "basename": "0001038.pdf", "url": "https://authors.library.caltech.edu/records/x8cmp-j5871/files/0001038.pdf" }, "pub_year": "2001", "author_list": "Nebe, Gabriele; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/3mgdb-g1w72", "eprint_id": 38565, "eprint_status": "archive", "datestamp": "2023-08-19 08:12:42", "lastmod": "2026-04-16 02:21:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Clemens-J-D", "name": { "family": "Clemens", "given": "John D." } }, { "id": "Gao-Su", "name": { "family": "Gao", "given": "Su" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Polish Metric Spaces: Their Classification and Isometry Groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Association for Symbolic Logic. \n\nReceived November 15, 2000; revised March 27, 2001. \n\nWe would like to thank G. Hjorth, V. Kanovei, A. Louveau and S. Solecki for many useful comments and for allowing us to include their results in this announcement.\n\n

Published - 2687754.pdf

", "abstract": "In this communication we present some recent results on the classification of Polish metric spaces up to isometry and on the isometry groups of Polish metric spaces. A Polish metric space is a complete separable metric space (X,d). Our first goal is to determine the exact complexity of the classification problem of general Polish metric spaces up to isometry. This work was motivated by a paper of Vershik [1998], where he remarks (in the beginning of Section 2): \"The classification of Polish spaces up to isometry is an enormous task. More precisely, this classification is not 'smooth' in the modern terminology.\" Our Theorem 2.1 below quantifies precisely the enormity of this task. After doing this, we turn to special classes of Polish metric spaces and investigate the classification problems associated with them. Note that these classification problems are in principle no more complicated than the general one above. However, the determination of their exact complexity is not necessarily easier. The investigation of the classification problems naturally leads to some interesting results on the groups of isometries of Polish metric spaces. We shall also present these results below.", "date": "2001-09", "date_type": "published", "publication": "Bulletin of Symbolic Logic", "volume": "7", "number": "3", "publisher": "Association for Symbolic Logic", "pagerange": "361-375", "id_number": "CaltechAUTHORS:20130517-132314741", "issn": "1079-8986", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-132314741", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2687754", "primary_object": { "basename": "2687754.pdf", "url": "https://authors.library.caltech.edu/records/3mgdb-g1w72/files/2687754.pdf" }, "pub_year": "2001", "author_list": "Clemens, John D.; Gao, Su; et al." }, { "id": "https://authors.library.caltech.edu/records/mm3vr-z2d76", "eprint_id": 1170, "eprint_status": "archive", "datestamp": "2023-08-21 22:29:46", "lastmod": "2026-04-16 05:05:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Okawa-Yuji", "name": { "family": "Okawa", "given": "Yuji" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Exact solution to the Seiberg-Witten equation of noncommutative gauge theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 The American Physical Society \n\n(Received 13 April 2001; published 26 July 2001) \n\nWe would like to thank John Schwarz, Mark Wise and Edward Witten for discussions. H.O. thanks the Institute for Theoretical Physics, Santa Barbara for hospitality. The research was supported in part by the DOE grant DE-FG03-92ER40701 and the Caltech Discovery Fund. H.O. was also supported in part by the NSF grant PHY99-07949. \n\nTechnical report numbers: CALT-68-2325; CITUSC/01-010; NSF-ITP-01-25; hep-th/0104036\n\n

Published - OKAprd01.pdf

Submitted - 0104036.pdf

", "abstract": "We derive an exact expression for the Seiberg-Witten map of noncommutative gauge theory. It is found by studying the coupling of the gauge field to the Ramond-Ramond potentials in string theory. Our result also proves the earlier conjecture by Liu.", "date": "2001-08-15", "date_type": "published", "publication": "Physical Review D", "volume": "64", "number": "4", "publisher": "American Physical Society", "pagerange": "Art. no. 046009", "id_number": "CaltechAUTHORS:OKAprd01", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OKAprd01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "Caltech Discovery Fund" }, { "agency": "NSF", "grant_number": "PHY99-07949" } ] }, "other_numbering_system": { "items": [ { "id": "01-010", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.64.046009", "primary_object": { "basename": "0104036.pdf", "url": "https://authors.library.caltech.edu/records/mm3vr-z2d76/files/0104036.pdf" }, "related_objects": [ { "basename": "OKAprd01.pdf", "url": "https://authors.library.caltech.edu/records/mm3vr-z2d76/files/OKAprd01.pdf" } ], "pub_year": "2001", "author_list": "Okawa, Yuji and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/ccmwt-q4s21", "eprint_id": 3608, "eprint_status": "archive", "datestamp": "2023-08-21 22:27:46", "lastmod": "2026-04-16 03:41:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry", "ispublished": "pub", "full_text_status": "public", "keywords": "field theories in lower dimensions; supersymmetry and duality; conformal field models in string theory", "note": "\u00a9 SISSA 2001. \n\nReceived 18 July 2001, accepted for publication 21 August 2001. Published 10 October 2001. \n\nWe would like to thank M. Aganagic, M.R. Douglas, P. Fendley, K. Intriligator, A. Karch, J.Maldacena, J. Polchinski, N. Seiberg, S. Shenker, E. Silverstein, D. Tong, C. Vafa, E. Witten, and A.B. Zamolodchikov for discussions. We thank ITP, Santa Barbara, for the support under the grant NSF-PHY-9907949. K.H. would also like to thank Rutgers Physics Department and the Institute for Advanced Study, for hospitality. K.H. was supported in part by NSF-DMS 9709694. A.K. was supported in part by DOE grant DE-FG02-90ER40542. \n\nE-print number: hep-th/0104202\n\n

Published - HORjhep01.pdf

", "abstract": "We prove the equivalence of the SL(2, R)/U(1) Kazama-Suzuki model, which is a fermionic generalization of the 2d Black Hole, and N = 2 Liouville theory. We show that this duality is an example of mirror symmetry. The essential part of the derivation is to realize the fermionic 2d Black Hole as the low energy limit of a gauged linear sigma-model. Liouville theory is obtained by dualizing the charged scalar fields and taking into account the vortex-instanton effects, as proposed recently in non-dilatonic models. The gauged linear sigma-model we study has many useful generalizations which we briefly discuss. In particular, we show how to construct a variety of dilatonic superstring backgrounds which generalize the fermionic 2d Black Hole and admit a mirror description in terms of Toda-like theories.", "date": "2001-08", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2001", "number": "8", "publisher": "Springer", "pagerange": "Art. No. 045", "id_number": "CaltechAUTHORS:HORjhep01", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:HORjhep01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9907949" }, { "agency": "NSF", "grant_number": "DMS-9709694" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2001/08/045", "primary_object": { "basename": "HORjhep01.pdf", "url": "https://authors.library.caltech.edu/records/ccmwt-q4s21/files/HORjhep01.pdf" }, "pub_year": "2001", "author_list": "Hori, Kentaro and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/6nhph-erx02", "eprint_id": 72972, "eprint_status": "archive", "datestamp": "2023-08-19 08:01:08", "lastmod": "2026-03-09 22:05:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "DeWolfe-O", "name": { "family": "DeWolfe", "given": "Oliver" } }, { "id": "Freedman-D-Z", "name": { "family": "Freedman", "given": "Daniel Z." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Holography and Defect Conformal Field Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2002 American Physical Society. \n\n(Received 21 January 2002; published 10 July 2002) \n\nWe are grateful for conversations with Allan Adams, Costas Bachas, Alex Buchel, Jan de Boer, Robbert Dijkgraaf, Noah Graham, Ami Hanany, Petr Ho\u0159ava, Andreas Karch, Igor Klebanov, Andrei Mikhailov, Joe Polchinski, Kostas Skenderis, Witek Skiba, Jan Troost, and Wati Taylor. We also thank Sergey Frolov and Massimo Porrati for pointing out minor errors in the first version. The work of O.D. was supported by the NSF under grant PHY-99-07949. The work of D.Z.F. was supported by the NSF under grant PHY-00-96515. The work of H.O. was supported in part by DOE Grant DE-AC03-76SF000098. D.Z.F. and H.O. would also like to thank ITP, Santa Barbara for hospitality.\n\n

Published - PhysRevD.66.025009.pdf

Submitted - 0111135.pdf

", "abstract": "We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 \"brane\", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel \"defect superconformal field theory\" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O_3 possessing integer conformal dimensions. Gravity calculations of and are given. Spacetime and N-dependence matches expectations from dCFT, while the behavior as functions of \u03bb = g^2 N at strong and weak coupling is generically different. We comment on a class of correlators for which a non-renormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a U(1) gauge group. Some weak coupling arguments which illuminate the duality are presented.", "date": "2001-07-15", "date_type": "published", "publication": "Physical Review D", "volume": "66", "number": "2", "publisher": "American Physical Society", "pagerange": "Art. No. 025009", "id_number": "CaltechAUTHORS:20161220-101329666", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-101329666", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-99-07949" }, { "agency": "NSF", "grant_number": "PHY-00-96515" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF000098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0111135", "primary_object": { "basename": "0111135.pdf", "url": "https://authors.library.caltech.edu/records/6nhph-erx02/files/0111135.pdf" }, "related_objects": [ { "basename": "PhysRevD.66.025009.pdf", "url": "https://authors.library.caltech.edu/records/6nhph-erx02/files/PhysRevD.66.025009.pdf" } ], "pub_year": "2001", "author_list": "DeWolfe, Oliver; Freedman, Daniel Z.; et al." }, { "id": "https://authors.library.caltech.edu/records/9pn21-d2z44", "eprint_id": 3849, "eprint_status": "archive", "datestamp": "2023-08-21 22:23:54", "lastmod": "2026-04-16 07:19:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gottesman-D", "name": { "family": "Gottesman", "given": "Daniel" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Preskill-J", "name": { "family": "Preskill", "given": "John" }, "orcid": "0000-0002-2421-4762" } ] }, "title": "Encoding a qubit in an oscillator", "ispublished": "pub", "full_text_status": "public", "note": "\u00a92001 The American Physical Society \n\nReceived 9 August 2000; published 11 June 2001 \n\nWe gratefully acknowledge helpful discussions with Isaac Chuang, Sumit Daftuar, David DiVincenzo, Andrew Doherty, Steven van Enk, Jim Harrington, Jeff Kimble, Andrew Landahl, Hideo Mabuchi, Harsh Mathur, Gerard Milburn, Michael Nielsen, and Peter Shor. This work was supported in part by the Department of Energy under Grant No. DE-FG03-92-ER40701, and by the Caltech MURI Center for Quantum Networks under ARO Grant No. DAAD19-00-1-0374. Some of this work was done at the Aspen Center for Physics.", "abstract": "Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.", "date": "2001-07-01", "date_type": "published", "publication": "Physical Review A", "volume": "64", "number": "1", "publisher": "Physical Review A", "pagerange": "Art. No. 012310", "id_number": "CaltechAUTHORS:GOTpra01b", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GOTpra01b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevA.64.012310", "primary_object": { "basename": "GOTpra01b.pdf", "url": "https://authors.library.caltech.edu/records/9pn21-d2z44/files/GOTpra01b.pdf" }, "pub_year": "2001", "author_list": "Gottesman, Daniel; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/mbp2t-9qe80", "eprint_id": 66707, "eprint_status": "archive", "datestamp": "2023-08-19 07:56:26", "lastmod": "2026-04-16 04:45:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Kuznetsov-A", "name": { "family": "Kuznetsov", "given": "Alexander" } }, { "id": "Orlov-D", "name": { "family": "Orlov", "given": "Dmitri" }, "orcid": "0000-0002-2230-457X" } ] }, "title": "Noncommutative Instantons and Twistor Transform", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Springer-Verlag. \n\nReceived: 3 May 2000. Accepted: 3 April 2001. \n\nDedicated to A.N. Tyurin on his 60th birthday. \n\nSupported by DOE grant DE-FG02-90ER4054442. Supported by NSF grant DMS97-29992 and RFFI grants 99-01-01144, 99-01-01204. Supported by NSF grant DMS97-29992 and RFFI grant 99-01-01144.\n\nWe are grateful to A. Beilinson, V. Ginzburg, L. Katzarkov, N. Nekrasov, T. Pantev, and A.Yekutieli for useful discussions and to L. Le Bruyn for bringing to our attention Ref. [21].We also wish to thank the Institute for Advanced Study, Princeton, NJ, for a very stimulating atmosphere. \n\nCommunicated by A. Connes.\n\n

Submitted - 0002193.pdf

", "abstract": "Recently N. Nekrasov and A. Schwarz proposed a modification of the ADHM construction of instantons which produces instantons on a noncommutative deformation of \u211d^4. In this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces. We exhibit one-to-one correspondences between three classes of objects: framed bundles on a noncommutative \u2119^2, certain complexes of sheaves on a noncommutative \u2119^3, and the modified ADHM data. The modified ADHM construction itself is interpreted in terms of a noncommutative version of the twistor transform. We also prove that the moduli space of framed bundles on the noncommutative \u2119^2 has a natural hyperk\u00e4hler metric and is isomorphic as a hyperk\u00e4hler manifold to the moduli space of framed torsion free sheaves on the commutative \u2119^2. The natural complex structures on the two moduli spaces do not coincide but are related by an SO(3) rotation. Finally, we propose a construction of instantons on a more general noncommutative \u211d^4 than the one considered by Nekrasov and Schwarz (a q-deformed \u211d^4).", "date": "2001-07", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "221", "number": "2", "publisher": "Springer", "pagerange": "385-432", "id_number": "CaltechAUTHORS:20160506-072313941", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160506-072313941", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER4054442" }, { "agency": "NSF", "grant_number": "DMS97-29992" }, { "agency": "Russian Foundation for Fundamental Investigations (RFFI)", "grant_number": "99-01-01144" }, { "agency": "Russian Foundation for Fundamental Investigations (RFFI)", "grant_number": "99-01-01204" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/PL00005576", "primary_object": { "basename": "0002193.pdf", "url": "https://authors.library.caltech.edu/records/mbp2t-9qe80/files/0002193.pdf" }, "pub_year": "2001", "author_list": "Kapustin, Anton; Kuznetsov, Alexander; et al." }, { "id": "https://authors.library.caltech.edu/records/a3e9r-6bh46", "eprint_id": 27626, "eprint_status": "archive", "datestamp": "2023-08-19 07:55:21", "lastmod": "2026-04-16 03:44:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Wang-Bai-Ling", "name": { "family": "Wang", "given": "Bai-Ling" } } ] }, "title": "Equivariant Seiberg-Witten Floer homology", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 International Press. \n\nReceived June 13, 1997. \n\nWe are deeply grateful to T. Mrowka for the many invaluable comments and suggestions. We thank A. Carey and M. Rothenberg for the many useful conversations. We are grateful to L. Nicolaescu for useful remarks and suggestions. In the early stages of this work useful were comments of R. Brussee, G. Matic, R. Mazzeo, J.W. Morgan, and R.G. Wang. We thank the referee for the very detailed and useful comments and for many valuable suggestions on how to improve various sections of the manuscript. Parts of this work were carried out during visits of the two authors to the Max Planck Institut f\u00fcr Mathematik in Bonn, and visits of the first author to the University of Adelaide and to the Tata Institute of Fundamental Research. We thank these institutions for the kind hospitality and for support. The first author was partially supported by NSF grant DMS-9802480. The second author was supported by ARC fellowship.\n\n

Published - MARcag01.pdf

Submitted - MARcag01preprint.pdf

", "abstract": "In this paper we construct, for all compact oriented three- manifolds, a U(1)-equivariant version of Seiberg-Witten Floer homology, which is invariant under the choice of metric and perturbation. We give a detailed analysis of the boundary structure of the monopole moduli spaces, compactified to smooth manifolds with corners. The proof of the independence of metric and perturbation is then obtained via an analysis of all the relevant obstruction bundles and sections, and the corresponding gluing theorems. The paper also contains a discussion of the chamber structure for the Seiberg-Witten invariant for rational homology 3-spheres, and proofs of the wall crossing formula, obtained by studying the exact sequences relating the equivariant and the non-equivariant Floer homologies and by a local model at the reducible monopole.", "date": "2001-07", "date_type": "published", "publication": "Communications in Analysis and Geometry", "volume": "9", "number": "3", "publisher": "International Press", "pagerange": "451-639", "id_number": "CaltechAUTHORS:20111104-094350111", "issn": "1019-8385", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111104-094350111", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9802480" }, { "agency": "Australian Research Council (ARC)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/CAG.2001.v9.n3.a1", "primary_object": { "basename": "MARcag01preprint.pdf", "url": "https://authors.library.caltech.edu/records/a3e9r-6bh46/files/MARcag01preprint.pdf" }, "related_objects": [ { "basename": "MARcag01.pdf", "url": "https://authors.library.caltech.edu/records/a3e9r-6bh46/files/MARcag01.pdf" } ], "pub_year": "2001", "author_list": "Marcolli, Matilde and Wang, Bai-Ling" }, { "id": "https://authors.library.caltech.edu/records/scq1w-34x22", "eprint_id": 3204, "eprint_status": "archive", "datestamp": "2023-08-21 22:22:06", "lastmod": "2026-04-16 05:30:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Maldacena-Juan", "name": { "family": "Maldacena", "given": "Juan" }, "orcid": "0000-0002-9127-1687" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Son-John", "name": { "family": "Son", "given": "John" } } ] }, "title": "Strings in AdS3 and the SL(2,R) WZW model. II: Euclidean black hole", "ispublished": "pub", "full_text_status": "public", "keywords": "Lie groups; black holes; string theory; nonlinear field theory", "note": "\u00a9 2001 American Institute of Physics. \n\n(Received 2 January 2001; accepted 13 February 2001) \n\nH.O. would like to thank J. Schwarz and the theory group at Caltech for the kind hospitality while this work was carried out. The research of J.M. was supported in part by Department of Energy (DOE) Grant No. DE-FGO2-91ER40654, National Science Foundation (NSF) Grant No. PHY-9513835, the Sloan Foundation and the David and Lucile Packard Foundations. The research of H.O. was supported in part by NSF Grant No. PHY-95-14797, DOE Grant No. DE-AC03-76SF00098, and the Caltech Discovery Fund.\n\n

Published - MALjmp01b.pdf

Submitted - 0005183.pdf

", "abstract": "We consider the one-loop partition function for Euclidean BTZ black hole back-grounds or equivalently thermal AdS3 backgrounds which are quotients of H3 (Euclidean AdS3). The one-loop partition function is modular invariant and we can read off the spectrum which is consistent to that found in hep-th/0001053. We see long strings and discrete states in agreement with the expectations.", "date": "2001-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "42", "number": "7", "publisher": "American Institute of Physics", "pagerange": "2961-2977", "id_number": "CaltechAUTHORS:MALjmp01b", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:MALjmp01b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FGO2-91ER40654" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Caltech Discovery Fund" } ] }, "other_numbering_system": { "items": [ { "id": "00-021", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.1377039", "primary_object": { "basename": "0005183.pdf", "url": "https://authors.library.caltech.edu/records/scq1w-34x22/files/0005183.pdf" }, "related_objects": [ { "basename": "MALjmp01b.pdf", "url": "https://authors.library.caltech.edu/records/scq1w-34x22/files/MALjmp01b.pdf" } ], "pub_year": "2001", "author_list": "Maldacena, Juan; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/5d5jx-t9f74", "eprint_id": 4513, "eprint_status": "archive", "datestamp": "2023-08-21 22:22:17", "lastmod": "2026-04-16 06:19:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gomis-J", "name": { "family": "Gomis", "given": "Jaume" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Nonrelativistic closed string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "superstrings; fluctuations; membrane theory; dual models; perturbation theory; dispersion relations", "note": "\u00a9 2001 American Institute of Physics. \n\nReceived 2 January 2001; accepted 13 February 2001. \n\nWe would like to thank O. Bergman, J. Maldacena, T. Mehen, J. Schwarz, M. Wise, and E. Witten for useful comments. This research is supported in part by the Department of Energy (DOE) Grant No. DE-FG03-92ER40701 and the Caltech Discovery Fund.\n\n

Published - GOMjmp01.pdf

Submitted - 0009181.pdf

", "abstract": "We construct a Galilean invariant nongravitational closed string theory whose excitations satisfy a nonrelativistic dispersion relation. This theory can be obtained by taking a consistent low energy limit of any of the conventional string theories, including the heterotic string. We give a finite first order worldsheet Hamiltonian for this theory and show that this string theory has a sensible perturbative expansion, interesting high energy behavior of scattering amplitudes and a Hagedorn transition of the thermal ensemble. The strong coupling duals of the Galilean superstring theories are considered and are shown to be described by an eleven-dimensional Galilean invariant theory of light membrane fluctuations. A new class of Galilean invariant nongravitational theories of light-brane excitations are obtained. We exhibit dual formulations of the strong coupling limits of these Galilean invariant theories and show that they exhibit many of the conventional dualities of M theory in a nonrelativistic setting.", "date": "2001-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "42", "number": "7", "publisher": "American Institute of Physics", "pagerange": "3127-3151", "id_number": "CaltechAUTHORS:GOMjmp01", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GOMjmp01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" }, { "agency": "Caltech Discovery Fund" } ] }, "other_numbering_system": { "items": [ { "id": "00-055", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.1372697", "primary_object": { "basename": "0009181.pdf", "url": "https://authors.library.caltech.edu/records/5d5jx-t9f74/files/0009181.pdf" }, "related_objects": [ { "basename": "GOMjmp01.pdf", "url": "https://authors.library.caltech.edu/records/5d5jx-t9f74/files/GOMjmp01.pdf" } ], "pub_year": "2001", "author_list": "Gomis, Jaume and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/2vjph-9y185", "eprint_id": 3253, "eprint_status": "archive", "datestamp": "2023-08-21 22:22:11", "lastmod": "2026-04-16 04:45:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gubser-S-S", "name": { "family": "Gubser", "given": "S. S." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "S." }, "orcid": "0000-0002-9486-1762" }, { "id": "Klebanov-I-R", "name": { "family": "Klebanov", "given": "I. R." } }, { "id": "Rangamani-Mukund", "name": { "family": "Rangamani", "given": "M." }, "orcid": "0000-0002-4336-1346" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "E." }, "orcid": "0000-0002-7752-6073" } ] }, "title": "The Hagedorn transition in noncommutative open string theory", "ispublished": "pub", "full_text_status": "public", "keywords": "string theory; differential geometry; membrane theory; gauge field theory", "note": "\u00a92001 American Institute of Physics. \n\n(Received 2 January 2001; accepted 13 February 2001) \n\nWe are grateful to J. Maldacena, E. Rabinovici, and S. Shenker for useful discussions. The work of S.S.G. was supported in part by Department of Energy (DOE) Grant No. DE-FG02-91ER40671, and by a DOE Outstanding Junior Investigator award. The work of S.G. was supported in part by the Caltech Discovery Fund, Grant No. RFBR No. 98-02-16575 and Russian President's Grant No. No 96-15-96939. The work of I.R.K. was supported in part by the National Science Foundation (NSF) Grant No. PHY-9802484 and by the James S. McDonnell Foundation Grant No. 91-48. M.R. was supported in part by NSF Grant No. PHY-980248 and by the Caltech Discovery Fund. S.S.G. and I.R.K. thank the Aspen Center for Physics for hospitality while this work was in progress.\n\n

Published - GUBjmp01.pdf

", "abstract": "The Hagedorn transition in noncommutative open string theory (NCOS) is relatively simple because gravity decouples. For NCOS theories in no more than five space\u2013time dimensions, the Hagedorn transition is second order, and the high temperature phase involves long, nearly straight fundamental strings separating from the D-brane on which the NCOS theory is defined. Above five spacetime dimensions interaction effects become important below the Hagedorn temperature. Although this complicates studies of the transition, we believe that the high temperature phase again involves long strings liberated from the bound state.", "date": "2001-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "42", "number": "7", "publisher": "American Institute of Physics", "pagerange": "2749-2764", "id_number": "CaltechAUTHORS:GUBjmp01", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUBjmp01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-91ER40671" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9802484" }, { "agency": "James S. McDonnell Foundation", "grant_number": "91-48" }, { "agency": "NSF", "grant_number": "PHY-980248" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.1372176", "primary_object": { "basename": "GUBjmp01.pdf", "url": "https://authors.library.caltech.edu/records/2vjph-9y185/files/GUBjmp01.pdf" }, "pub_year": "2001", "author_list": "Gubser, S. S.; Gukov, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/pvfnq-ah218", "eprint_id": 3203, "eprint_status": "archive", "datestamp": "2023-08-21 22:21:59", "lastmod": "2026-04-16 05:51:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Maldacena-Juan", "name": { "family": "Maldacena", "given": "Juan" }, "orcid": "0000-0002-9127-1687" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Strings in AdS3 and the SL(2,R) WZW model. I: The spectrum", "ispublished": "pub", "full_text_status": "public", "keywords": "string theory; Lie groups; nonlinear field theory; Hilbert spaces", "note": "\u00a9 2001 American Institute of Physics. \n\n(Received 2 January 2001; accepted 13 February 2001) \n\nWe would like to thank A. Zamolodchikov for discussions and for giving us a copy of his unpublished notes. We also thank N. Seiberg, C. Vafa, and E. Witten for discussions. We would like to thank S. Hwang for useful comments on the earlier version of this paper. H.O. would like to thank J. Schwarz and the theory group at Caltech for the kind hospitality while the bulk of this work was carried out. H.O. also thanks the hospitality of the theory group at Harvard University, where this work was initiated, ICTP, Trieste, and ITP, Santa Barbara, where parts of this work were done. The research of J.M. was supported in part by DOE Grant No. DE-FGO2-91ER40654, NSF Grant No. PHY-9513835, the Sloan Foundation, and the David and Lucile Packard Foundations. The research of H.O. was supported in part by NSF Grant No. PHY-95-14797, DOE Grant No. DE-AC03-76SF00098, and the Caltech Discovery Fund.\n\n

Published - MALjmp01a.pdf

Submitted - 0001053.pdf

", "abstract": "In this paper we study the spectrum of bosonic string theory on AdS3. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with nonzero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string.", "date": "2001-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "42", "number": "7", "publisher": "American Institute of Physics", "pagerange": "2929-2960", "id_number": "CaltechAUTHORS:MALjmp01a", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:MALjmp01a", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FGO2-91ER40654" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Caltech Discovery Fund" } ] }, "other_numbering_system": { "items": [ { "id": "99-010", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1063/1.1377273", "primary_object": { "basename": "0001053.pdf", "url": "https://authors.library.caltech.edu/records/pvfnq-ah218/files/0001053.pdf" }, "related_objects": [ { "basename": "MALjmp01a.pdf", "url": "https://authors.library.caltech.edu/records/pvfnq-ah218/files/MALjmp01a.pdf" } ], "pub_year": "2001", "author_list": "Maldacena, Juan and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/axq2m-jk983", "eprint_id": 81971, "eprint_status": "archive", "datestamp": "2023-08-19 07:51:09", "lastmod": "2026-03-09 22:11:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Class Groups and Modular Lattices", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2001 Academic Press. \n\nReceived 12 December 1998, Available online 26 February 2002. \n\nThe author thanks J. Lagarias for helpful conversations.", "abstract": "We show that in the case of 2-dimensional lattices, Quebbemann's notion of modular and strongly modular lattices has a natural extension to the class group of a given discriminant, in terms of a certain set of translations. In particular, a 2-dimensional lattice has \"extra\" modularities essentially when it has order 4 in the class group. This allows us to determine the conditions on D under which there exists a strongly modular 2-dimensional lattice of discriminant D, as well as how many such lattices there are. The technique also applies to the question of when a lattice can be similar to its even sublattice.", "date": "2001-06", "date_type": "published", "publication": "Journal of Number Theory", "volume": "88", "number": "2", "publisher": "Elsevier", "pagerange": "211-224", "id_number": "CaltechAUTHORS:20171002-152216783", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-152216783", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1006/jnth.2000.2633", "pub_year": "2001", "author_list": "Rains, E. M." }, { "id": "https://authors.library.caltech.edu/records/zn712-e6r41", "eprint_id": 38610, "eprint_status": "archive", "datestamp": "2023-08-19 07:48:32", "lastmod": "2026-04-16 06:31:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Buss-S-R", "name": { "family": "Buss", "given": "Samuel R." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Pillay-A", "name": { "family": "Pillay", "given": "Anand" } }, { "id": "Shore-R-A", "name": { "family": "Shore", "given": "Richard A." } } ] }, "title": "The prospects for mathematical logic in the twenty-first century", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Association for Symbolic Logic.\n\nReceived January 30, 2001; revised March 20, 2001.\n\nI am grateful to Yiannis Moschovakis, Richard Shore, John Steel, and Hugh Woodin for their comments on an earlier draft of this section.\n\n

Published - 2687773.pdf

", "abstract": "The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.", "date": "2001-06", "date_type": "published", "publication": "Bulletin of Symbolic Logic", "volume": "7", "number": "2", "publisher": "Association for Symbolic Logic", "pagerange": "169-196", "id_number": "CaltechAUTHORS:20130521-132240239", "issn": "1079-8986", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-132240239", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9803515" }, { "agency": "NSF", "grant_number": "DMS-9987437" }, { "agency": "NSF", "grant_number": "DMS-9696268" }, { "agency": "NSF", "grant_number": "DMS-0070179" }, { "agency": "NSF", "grant_number": "DMS-9802843" } ] }, "other_numbering_system": { "items": [ { "id": "MR1839544", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2687773", "primary_object": { "basename": "2687773.pdf", "url": "https://authors.library.caltech.edu/records/zn712-e6r41/files/2687773.pdf" }, "pub_year": "2001", "author_list": "Buss, Samuel R.; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/36wk3-ahr50", "eprint_id": 66698, "eprint_status": "archive", "datestamp": "2023-08-21 22:14:39", "lastmod": "2026-04-16 05:58:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Behrndt-K", "name": { "family": "Behrndt", "given": "Klaus" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Shmakova-M", "name": { "family": "Shmakova", "given": "Marina" } } ] }, "title": "Domain walls, black holes, and supersymmetric quantum mechanics", "ispublished": "pub", "full_text_status": "public", "keywords": "Domain walls; Black holes; Supergravity; Supersymmetric vacua; AdS/CFT", "note": "\u00a9 2001 Elsevier Science B.V. \n\nReceived 2 February 2001, Accepted 7 February 2001, Available online 25 April 2001. \n\nWe are grateful Alexander Chervov, Ori Ganor, Brian Greene, Renata Kallosh, Eric Sharpe, Gary Shiu, Andrew Strominger, Nicholas Warner, and Edward Witten for helpful discussions and comments. The work of K.B. was partly done at the Theory group of Caltech and is supported by a Heisenberg grant of the DFG and by the European Commission RTN programme HPRN-CT-2000-00131. S.G. is supported in part by the Caltech Discovery Fund, grant RFBR No 98-01-00327 and Russian President's grant No 00-15-99296.\n\n

Submitted - 0101119.pdf

", "abstract": "Supersymmetric solutions, such as BPS domain walls or black holes, in four- and five-dimensional supergravity theories with eight supercharges can be described by effective quantum mechanics with a potential term. We show how properties of the latter theory can help us to learn about the physics of supersymmetric vacua and BPS solutions in these supergravity theories. The general approach is illustrated in a number of specific examples where scalar fields of matter multiplets take values in symmetric coset spaces.", "date": "2001-05-07", "date_type": "published", "publication": "Nuclear Physics B", "volume": "601", "number": "1-2", "publisher": "Elsevier", "pagerange": "49-76", "id_number": "CaltechAUTHORS:20160505-151644609", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-151644609", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "European Union", "grant_number": "HPRN-CT-2000-00131" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-01-00327" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "00-15-99296" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(01)00052-9", "primary_object": { "basename": "0101119.pdf", "url": "https://authors.library.caltech.edu/records/36wk3-ahr50/files/0101119.pdf" }, "pub_year": "2001", "author_list": "Behrndt, Klaus; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/qj591-6k954", "eprint_id": 3211, "eprint_status": "archive", "datestamp": "2023-08-21 22:09:17", "lastmod": "2026-04-16 04:10:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Universality class of little string theories", "ispublished": "pub", "full_text_status": "public", "keywords": "RG-FIXED-POINTS; ORBIFOLD SINGULARITIES; MATRIX DESCRIPTION; 6 DIMENSIONS; BRANES; DYNAMICS; T-5", "note": "\u00a9 2001 The American Physical Society. \n\nReceived 28 April 2000; published 28 March 2001. \n\nI would like to thank Ofer Aharony, Korkut Bardakci, and Nati Seiberg for useful comments. This work was supported by a DOE grant DE-FG02-90ER4054442.\n\n

Published - KAPprd01.pdf

", "abstract": "We propose that little string theories in six dimensions are quasilocal quantum held theories. Such field theories obey a modification of Wightman axioms which allows Wightman functions (i.e. vacuum expectation values of products of fundamental fields) to grow exponentially in momentum space. Wightman functions of quasilocal fields in x-space violate microlocality at short distances. With additional assumptions about the ultraviolet behavior of quasilocal fields, one can define approximately local observables associated with big enough compact regions. The minimum size of such a region can be interpreted as the minimum distance which observables can probe. We argue that for little string theories this distance is of the order of root N/Ms.", "date": "2001-04-15", "date_type": "published", "publication": "Physical Review D", "volume": "63", "number": "8", "publisher": "American Physical Society", "pagerange": "Art. No. 086005", "id_number": "CaltechAUTHORS:KAPprd01", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPprd01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER4054442" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.63.086005", "primary_object": { "basename": "KAPprd01.pdf", "url": "https://authors.library.caltech.edu/records/qj591-6k954/files/KAPprd01.pdf" }, "pub_year": "2001", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/8gvfq-hw581", "eprint_id": 66645, "eprint_status": "archive", "datestamp": "2023-08-19 07:31:18", "lastmod": "2026-04-16 03:42:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cherkis-S-A", "name": { "family": "Cherkis", "given": "Sergey" }, "orcid": "0000-0002-0785-0126" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Nahm Transform for Periodic Monopoles and N=2 Super Yang-Mills Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Springer-Verlag. \n\nReceived: 20 July 2000; Accepted: 29 November 2000. \n\nWe are grateful to Nigel Hitchin for a very helpful conversation concerning the definition of the monopole spectral data, and to Dmitri Orlov and Marcos Jardim for discussions. We also wish to thank the organizers of the workshop \"The Geometry and Physics of Monopoles,\" Edinburgh, August-September 1999, for creating a very stimulating atmosphere during the meeting and for providing us with an opportunity to present a preliminary version of this work. The work of S.Ch. was supported in part by NSF grant PHY9819686. The work of A.K. was supported in part by a DOE grant DE-FG02-90ER4054442.\n\n

Submitted - 0006050.pdf

", "abstract": "We study Bogomolny equations on R^2\u00d7S^1. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk\u00e4hler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of N=2 super Yang\u2013Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.", "date": "2001-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "218", "number": "2", "publisher": "Springer", "pagerange": "333-371", "id_number": "CaltechAUTHORS:20160504-104759294", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-104759294", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9819686" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER4054442" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/PL00005558", "primary_object": { "basename": "0006050.pdf", "url": "https://authors.library.caltech.edu/records/8gvfq-hw581/files/0006050.pdf" }, "pub_year": "2001", "author_list": "Cherkis, Sergey and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/4fxym-f9f97", "eprint_id": 27625, "eprint_status": "archive", "datestamp": "2023-08-19 07:15:27", "lastmod": "2026-04-16 03:43:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Mathai-V", "name": { "family": "Mathai", "given": "Varghese" } } ] }, "title": "Twisted Index Theory on Good Orbifolds, II: Fractional Quantum Numbers", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Springer-Verlag.\n\nReceived: 4 November 1999; Accepted: 22 September 2000.\n\nCommunicated by A. Connes.\nWe thank J. Bellissard for his encouragement and for some useful comments. The second\nauthor thanks A. Carey and K. Hannabuss for some helpful comments concerning the Sect. 4. The first\nauthor is partially supported by NSF grant DMS-9802480. Research by the second author is supported by the\nAustralian Research Council. The second author acknowledges that this work was completed in part for the\nClay Mathematical Institute.\n\n

Submitted - 9911103.pdf

", "abstract": "This paper uses techniques in noncommutative geometry as developed by Alain Connes [Co2], in order to study the twisted higher index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group, continuing our earlier work [MM]. We also compute the range of the higher cyclic traces on K-theory for cocompact Fuchsian groups, which is then applied to determine the range of values of the Connes\u2013Kubo Hall conductance in the discrete model of the quantum Hall effect on the hyperbolic plane, generalizing earlier results in [Bel+E+S], [CHMM]. The new phenomenon that we observe in our case is that the Connes\u2013Kubo Hall conductance has plateaux at integral multiples of a fractional valued topological invariant, namely the orbifold Euler characteristic. Moreover the set of possible fractions has been determined, and is compared with recently available experimental data. It is plausible that this might shed some light on the mathematical mechanism responsible for fractional quantum numbers.", "date": "2001-02", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "217", "number": "1", "publisher": "Springer", "pagerange": "55-87", "id_number": "CaltechAUTHORS:20111104-093842954", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111104-093842954", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9802480" }, { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s002200000351", "primary_object": { "basename": "9911103.pdf", "url": "https://authors.library.caltech.edu/records/4fxym-f9f97/files/9911103.pdf" }, "pub_year": "2001", "author_list": "Marcolli, Matilde and Mathai, Varghese" }, { "id": "https://authors.library.caltech.edu/records/wv3tv-f4h81", "eprint_id": 83005, "eprint_status": "archive", "datestamp": "2023-08-19 07:04:10", "lastmod": "2026-03-09 22:48:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Baik-J", "name": { "family": "Baik", "given": "Jinho" } } ] }, "title": "The asymptotics of monotone subsequences of involutions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Duke University Press.\n\nReceived 23 February 2000. Revision received 5 February 2001.\n\nBaik's work supported in part by a Sloan Doctoral Dissertation Fellowship during the academic year 1998\u20131999\nas a graduate student at Courant Institute of Mathematical Sciences.\n\nWe would like to thank Percy Deift for helpful discussions and encouragement, especially for his help in proving Lemma 2.1. We would also like to acknowledge many useful conversations and communications with Peter Forrester,\nKurt Johansson, Charles Newman, and HaroldWidom. Special thanks are due the referee who gave us crucial advice, improving the exposition of the paper significantly.\n\n

Submitted - 9905084.pdf

", "abstract": "We compute the limiting distributions of the lengths of the longest monotone subsequences of random (signed) involutions with or without conditions on the number of fixed points (and negated points) as the sizes of the involutions tend to infinity. The resulting distributions are, depending on the number of fixed points, (1) the Tracy-Widom distributions for the largest eigenvalues of random GOE, GUE, GSE matrices, (2) the normal distribution, or (3) new classes of distributions which interpolate between pairs of the Tracy-Widom distributions. We also consider the second rows of the corresponding Young diagrams. In each case the convergence of moments is also shown. The proof is based on the algebraic work of J. Baik and E. Rains in [7] which establishes a connection between the statistics of random involutions and a family of orthogonal polynomials, and an asymptotic analysis of the orthogonal polynomials which is obtained by extending the Riemann-Hilbert analysis for the orthogonal polynomials by P. Deift, K. Johansson, and Baik in [3].", "date": "2001", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "109", "number": "2", "publisher": "Duke University Press", "pagerange": "205-281", "id_number": "CaltechAUTHORS:20171106-152554249", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-152554249", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/S0012-7094-01-10921-6", "primary_object": { "basename": "9905084.pdf", "url": "https://authors.library.caltech.edu/records/wv3tv-f4h81/files/9905084.pdf" }, "pub_year": "2001", "author_list": "Rains, Eric M. and Baik, Jinho" }, { "id": "https://authors.library.caltech.edu/records/7a0sp-7at39", "eprint_id": 758, "eprint_status": "archive", "datestamp": "2023-08-21 21:47:41", "lastmod": "2026-03-08 18:14:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Burns-D", "name": { "family": "Burns", "given": "D." } }, { "id": "Flach-M", "name": { "family": "Flach", "given": "M." }, "orcid": "0000-0002-4523-9467" } ] }, "title": "Tamagawa Numbers for Motives with (Non-Commutative) Coefficients", "ispublished": "pub", "full_text_status": "public", "note": "Received: September 6, 2001. Revised: January 28, 2002. \n\nCommunicated by Don Blasius", "abstract": "Let $M$ be a motive which is defined over a number field and admits an action of a finite dimensional semisimple $\\bq$-algebra $A$. We formulate and study a conjecture for the leading coefficient of the Taylor expansion at $0$ of the $A$-equivariant $L$-function of $M$. This conjecture simultaneously generalizes and refines the Tamagawa number conjecture of Bloch, Kato, Fontaine, Perrin-Riou et al. and also the central conjectures of classical Galois module theory as developed by Fr\u00f6hlich, Chinburg, M. Taylor et al. The precise formulation of our conjecture depends upon the choice of an order $\\A$ in $A$ for which there exists a `projective $\\A$-structure' on $M$. The existence of such a structure is guaranteed if $\\A$ is a maximal order, and also occurs in many natural examples where $\\A$ is non-maximal. In each such case the conjecture with respect to a non-maximal order refines the conjecture with respect to a maximal order. We develop a theory of determinant functors for all orders in $A$ by making use of the category of virtual objects introduced by Deligne.", "date": "2001", "date_type": "published", "publication": "Documenta Mathematica", "volume": "6", "publisher": "Documenta Mathematica", "pagerange": "501-570", "id_number": "CaltechAUTHORS:BURdm01", "issn": "1431-0635", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:BURdm01", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "BURdm01.pdf", "url": "https://authors.library.caltech.edu/records/7a0sp-7at39/files/BURdm01.pdf" }, "pub_year": "2001", "author_list": "Burns, D. and Flach, M." }, { "id": "https://authors.library.caltech.edu/records/x74mb-92j80", "eprint_id": 82025, "eprint_status": "archive", "datestamp": "2023-08-19 07:04:01", "lastmod": "2026-03-09 22:11:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Baik-J", "name": { "family": "Baik", "given": "Jinho" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Algebraic aspects of increasing subsequences", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2001 Duke University Press. \n\nReceived 23 February 2000. Revision received 26 September 2000. \n\nBaik's work supported in part by a Sloan Doctoral Foundation Fellowship. \n\nWe would like to acknowledge the following people for helpful discussions: Kurt Johansson for telling us about the processes generalized in Section 7, Richard Stanley for telling us about the references for that section, Peter Shor for spotting flaws in earlier versions of the algorithms of Section 8, and Christian Krattenthaler for helpful comments on Section 5. We would also like to thank Jeff Lagarias, Andrew Odlyzko, and Neil Sloane for helpful comments and enthusiasm.\n\n

Submitted - 9905083.pdf

", "abstract": "We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as new proofs of old formulae; relations of these expressions to orthogonal polynomials on the unit circle; and explicit bases for invariant spaces of the classical groups, together with appropriate generalizations of the straightening algorithm.", "date": "2001", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "109", "number": "1", "publisher": "Duke University Press", "pagerange": "1-65", "id_number": "CaltechAUTHORS:20171004-073359453", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171004-073359453", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/S0012-7094-01-10911-3", "primary_object": { "basename": "9905083.pdf", "url": "https://authors.library.caltech.edu/records/x74mb-92j80/files/9905083.pdf" }, "pub_year": "2001", "author_list": "Baik, Jinho and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/2q44f-edc44", "eprint_id": 38881, "eprint_status": "archive", "datestamp": "2023-08-19 06:57:09", "lastmod": "2026-03-09 20:34:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "Greg" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Recent developments in the theory of Borel reducibility", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2001 Institute of Mathematics, Polish Academy of Sciences.\n\nResearch of the first author partially supported by NSF Grant DMS 96-22977.\nResearch of the second author partially supported by NSF Grant DMS 96-19880.", "abstract": "Let E_0 be the Vitali equivalence relation and E_3 the product of countably\nmany copies of E_0. Two new dichotomy theorems for Borel equivalence relations are\nproved. First, for any Borel equivalence relation E that is (Borel) reducible to E_3, either\nE is reducible to E_0 or else E_3 is reducible to E. Second, if E is a Borel equivalence\nrelation induced by a Borel action of a closed subgroup of the infinite symmetric group\nthat admits an invariant metric, then either E is reducible to a countable Borel equivalence\nrelation or else E_3 is reducible to E.\nWe also survey a number of results and conjectures concerning the global structure\nof reducibility on Borel equivalence relations.", "date": "2001", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "170", "number": "1-2", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "21-52", "id_number": "CaltechAUTHORS:20130610-142913085", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130610-142913085", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 96-22977" }, { "agency": "NSF", "grant_number": "DMS 96-19880" } ] }, "other_numbering_system": { "items": [ { "id": "MR1881047", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "2001", "author_list": "Hjorth, Greg and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/3xsqx-a2a84", "eprint_id": 77351, "eprint_status": "archive", "datestamp": "2023-08-19 06:54:40", "lastmod": "2026-04-17 02:18:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Resonances in One Dimension and Fredholm Determinants", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2000 Academic Press. \n\nReceived 5 June 2000, Accepted 8 August 2000, Available online 26 March 2002. \n\nThis material is based upon work supported by the National Science Foundation under Grant DMS-9707661. The U.S. Government's right to retain a nonexclusive royalty-free license in and to the copyright covering this paper, for governmental purposes, is acknowledged.", "abstract": "We discuss resonances for Schr\u00f6dinger operators in whole- and half-line problems. One of our goals is to connect the Fredholm determinant approach of Froese to the Fourier transform approach of Zworski. Another is to prove a result on the number of antibound states\u2014namely, in a half-line problem there are an odd number of antibound states between any two bound states.", "date": "2000-12-20", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "178", "number": "2", "publisher": "Elsevier", "pagerange": "396-420", "id_number": "CaltechAUTHORS:20170510-140505304", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170510-140505304", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.2000.3669", "pub_year": "2000", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/n5tc0-76369", "eprint_id": 78889, "eprint_status": "archive", "datestamp": "2023-08-19 06:54:21", "lastmod": "2026-04-16 15:22:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "On Primitive Linear Representations of Finite Groups", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2000 Academic Press. \n\nReceived 12 April 2000. \n\nThis work was partially supported by National Science Foundation grant NSF-9901367.", "abstract": "Let F be a field, let G be a finite group, and let \u03c0 be a linear representation of G over F; that is, \u03c0 is a group homomorphism \u03c0: G \u2192 GL(V) of G into the general linear group on a finite-dimensional vector space V over F.\nWe say \u03c0 is AI if \u03c0 is completely reducible and for each normal subgroup H of G, each irreducible FH-submodule of V is absolutely irreducible. For example, if F is algebraically closed then all completely reducible representations over F are AI. In particular, all of our theorems hold over the complex numbers without the hypothesis that the representation is AI.", "date": "2000-12-15", "date_type": "published", "publication": "Journal of Algebra", "volume": "234", "number": "2", "publisher": "Elsevier", "pagerange": "627-640", "id_number": "CaltechAUTHORS:20170710-101117286", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170710-101117286", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9901367" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1006/jabr.2000.8532", "pub_year": "2000", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/866an-x9143", "eprint_id": 38595, "eprint_status": "archive", "datestamp": "2023-08-19 06:49:49", "lastmod": "2026-04-17 02:22:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Camerlo-R", "name": { "family": "Camerlo", "given": "Riccardo" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Countable structures with a fixed group of automorphisms", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 2000 Springer-Verlag. \n\nReceived October 25, 1998. \n\nWe wish to thank R. Dougherty, G. Hjorth, A. Marcone and S. Solecki for their important help and suggestions. In particular A. Marcone helped us in clearing the presentation of the main construction, which is now more perspicuous than in an earlier draft of the paper.", "abstract": "We prove that, given a countable group G, the set of countable structures (for a suitable language L)U_G whose automorphism group is isomorphic to G is a complete coanalytic set and if G \u2244 H then U_G is Borel inseparable from U_H . We give also a model theoretic interpretation of this result. We prove, in contrast, that the set of countable structures for L whose automorphism group is isomorphic to \u2124_p^\u2115 ,p a prime number, is \u03a0^1_1&\u03a3^1_1-complete.", "date": "2000-12", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "117", "number": "1", "publisher": "Hebrew University Magnes Press", "pagerange": "105-124", "id_number": "CaltechAUTHORS:20130521-095650096", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-095650096", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/BF02773566", "pub_year": "2000", "author_list": "Camerlo, Riccardo and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/y09pb-rfp20", "eprint_id": 85374, "eprint_status": "archive", "datestamp": "2023-08-21 21:44:20", "lastmod": "2026-04-17 02:37:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramm-A", "name": { "family": "Ramm", "given": "Alexander" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A new approach to inverse spectral theory, III. Short-range potentials", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Energy Resonance; Negative Eigenvalue; Principal Ideal; Inverse Scattering Problem; Schr\u00f6dinger Operator", "note": "\u00a9 2000 Hebrew University of Jerusalem.\n\nReceived September 22, 1999.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9707661. The Government has certain rights in this material.", "abstract": "No abstract.", "date": "2000-12", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "80", "number": "1", "publisher": "Springer-Verlag", "pagerange": "319-334", "id_number": "CaltechAUTHORS:20180320-094238430", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180320-094238430", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02791540", "pub_year": "2000", "author_list": "Ramm, Alexander and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/c39a4-aa811", "eprint_id": 28263, "eprint_status": "archive", "datestamp": "2023-08-19 06:21:51", "lastmod": "2026-04-16 13:46:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On the Classification Problem for Rank 2 Torsion-Free Abelian Groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 London Mathematical Society.\n\nReceived 15 June 1999; revised 16 November 1999.\nResearch partially supported by NSF Grant DMS 9619880.\n\nI would like to thank S. Adams and G. Hjorth for many\nhelpful conversations and G. Mess for bringing up the idea of using groups of the\nform PSL_n(Z[1/p_1,...,1/p_n]) instead of PSL_n(Z).\n\n

Published - KECjlms00.pdf

", "abstract": "We study here some foundational aspects of the classification problem for torsion-free abelian groups of finite rank. These are, up to isomorphism, the subgroups of the additive groups (Q^n, +), for some n = 1, 2, 3,.... The torsion-free abelian groups of rank \u2264 n are the subgroups of (Q^n, +).", "date": "2000-10", "date_type": "published", "publication": "Journal of the London Mathematical Society", "volume": "62", "number": "2", "publisher": "London Mathematical Society", "pagerange": "437-450", "id_number": "CaltechAUTHORS:20111201-082818221", "issn": "0024-6107", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111201-082818221", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9619880" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0024610700001411", "primary_object": { "basename": "KECjlms00.pdf", "url": "https://authors.library.caltech.edu/records/c39a4-aa811/files/KECjlms00.pdf" }, "pub_year": "2000", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/8a4b0-eg244", "eprint_id": 66696, "eprint_status": "archive", "datestamp": "2023-08-19 06:20:23", "lastmod": "2026-04-16 13:40:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gates-S-J-Jr", "name": { "family": "Gates", "given": "S. James, Jr." } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Two two-dimensional supergravity theories from Calabi\u2013Yau four-folds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Elsevier Science B.V. \n\nReceived 25 May 2000, Accepted 13 June 2000, Available online 21 August 2000. \n\nWe are grateful to Marc Grisaru, Martin Ro\u010dek and John H. Schwarz for useful discussions. The research of S.J.G. is supported by the NSF grant No PHY-98-02551; S.G. is supported in part by the Caltech Discovery Fund, grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939. The work of E.W. is supported in part by NSF Grant PHY-9513835 and the Caltech Discovery Fund.\n\n

Submitted - 0005120.pdf

", "abstract": "We consider two-dimensional supergravity theories with four supercharges constructed from compactification of Type II string theory on a generic Calabi\u2013Yau four-fold. In type IIA and type IIB cases, respectively, new superspace formulations of N = (2, 2) and N = (0,4) dilaton supergravities are found and their coupling to matter multiplets is discussed.", "date": "2000-09-18", "date_type": "published", "publication": "Nuclear Physics B", "volume": "584", "number": "1-2", "publisher": "Elsevier", "pagerange": "109-148", "id_number": "CaltechAUTHORS:20160505-142923299", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-142923299", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-98-02551" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9513835" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(00)00374-6", "primary_object": { "basename": "0005120.pdf", "url": "https://authors.library.caltech.edu/records/8a4b0-eg244/files/0005120.pdf" }, "pub_year": "2000", "author_list": "Gates, S. James, Jr.; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/vyrw2-j5e52", "eprint_id": 28253, "eprint_status": "archive", "datestamp": "2023-08-19 06:14:01", "lastmod": "2026-03-18 00:05:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Geszetsy-F", "name": { "family": "Geszetsy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Inverse spectral theory, Weyl-Titchmarsh m-function, spectral\nmeasure.", "note": "\u00a9 2000 Princeton University. Received June 10, 1999. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9707661. The government has certain rights in this material.", "abstract": "We continue the study of the A-amplitude associated to a half-line Schr\u00f6dinger operator, - d^2/dx^2 + q in L^2((0,b)), b \u2264 \u221e A is related to the Weyl-Titchmarsh m-function via m(-k^2) = -k- \u0283^a_0 A(\u03b1)e^(-2\u03b1k) d\u03b1+O(e^(-(2\u03b1-\u0404)k)) for all \u0404 > 0. We discuss five issues here. First, we extend the theory to general q in L^1((0,\u03b1)) for all a, including q's which are limit circle at infinity. Second, we prove the following relation between the A-amplitude and the spectral measure p: A(\u03b1) = -2 ^\u0283\u221e_(-\u221e)\u03bb^(-1/2) sin (2\u03b1\u221a\u03bb) dp(\u03bb) (since the integral is divergent, this formula has to be properly interpreted). Third, we provide a Laplace transform representation for m without error term in the case b < \u221e. Fourth, we discuss m-functions associated to other boundary conditions than the Dirichlet boundary conditions associated to the principal Weyl-Titchmarsh m-function. Finally, we discuss some examples where one can compute A exactly.", "date": "2000-09", "date_type": "published", "publication": "Annals of Mathematics", "volume": "152", "number": "2", "publisher": "Princeton University", "pagerange": "593-643", "id_number": "CaltechAUTHORS:20111130-133257722", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111130-133257722", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.2307/2661393", "pub_year": "2000", "author_list": "Geszetsy, Fritz and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/01tby-7wf38", "eprint_id": 82254, "eprint_status": "archive", "datestamp": "2023-08-21 21:26:57", "lastmod": "2026-04-17 04:05:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Baik-J", "name": { "family": "Baik", "given": "Jinho" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Limiting Distributions for a Polynuclear Growth Model with External Sources", "ispublished": "pub", "full_text_status": "public", "keywords": "PNG; ASEP; directed polymer; random matrix; limiting\ndistribution", "note": "\u00a9 2000 Plenum Publishing Corporation. \n\nReceived March 27, 2000. \n\nThe authors greatly appreciate many enlightening conversations and communications with Michael Pr\u00e4hofer and Herbert Spohn who brought our interest to this problem.\n\n

Submitted - 0003130.pdf

", "abstract": "The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources which was considered by Pr\u00e4hofer and Spohn. Depending on the strength of the sources, the limiting distribution functions are either the Tracy\u2013Widom functions of random matrix theory or a new explicit function which has the special property that its mean is zero. Moreover, we obtain transition functions between pairs of the above distribution functions in suitably scaled limits. There are also similar results for a discrete totally asymmetric exclusion process.", "date": "2000-08", "date_type": "published", "publication": "Journal of Statistical Physics", "volume": "100", "number": "3-4", "publisher": "Springer", "pagerange": "523-541", "id_number": "CaltechAUTHORS:20171010-105909686", "issn": "0022-4715", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171010-105909686", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/A:1018615306992", "primary_object": { "basename": "0003130.pdf", "url": "https://authors.library.caltech.edu/records/01tby-7wf38/files/0003130.pdf" }, "pub_year": "2000", "author_list": "Baik, Jinho and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/amssh-7bb44", "eprint_id": 66641, "eprint_status": "archive", "datestamp": "2023-08-21 21:24:34", "lastmod": "2026-04-17 03:42:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Behrndt-K", "name": { "family": "Behrndt", "given": "Klaus" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Domain walls and superpotentials from M-theory on Calabi-Yau three-folds", "ispublished": "pub", "full_text_status": "public", "keywords": "M-theory; Superpotential; Domain wall", "note": "\u00a9 2000 Elsevier Science B.V. \n\nWe would like to thank K. & M. Becker, J. Gomis, C. Vafa and E. Witten for useful discussions. The work of K.B. was supported by a Heisenberg Fellowship of the DFG. The work of S.G. was supported in part by the Caltech Discovery Fund, grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\n

Submitted - 0001082.pdf

", "abstract": "Compactification of M-theory in the presence of G-fluxes yields N = 2 five-dimensional gauged supergravity with a potential that lifts all supersymmetric vacua. We derive the effective superpotential directly from the Kaluza\u2013Klein reduction of the eleven-dimensional action on a Calabi\u2013Yau three-fold and compare it with the superpotential obtained by means of calibrations. We discuss an explicit domain wall solution, which represents five-branes wrapped over holomorphic cycles. This solution has a \"running volume\" and we comment on the possibility that quantum corrections provide a lower bound allowing for an AdS\u2085 vacuum of the 5-dimensional supergravity.", "date": "2000-07-31", "date_type": "published", "publication": "Nuclear Physics B", "volume": "580", "number": "1-2", "publisher": "Elsevier", "pagerange": "225-242", "id_number": "CaltechAUTHORS:20160504-100830938", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-100830938", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(00)00149-8", "primary_object": { "basename": "0001082.pdf", "url": "https://authors.library.caltech.edu/records/amssh-7bb44/files/0001082.pdf" }, "pub_year": "2000", "author_list": "Behrndt, Klaus and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/xpmhm-8p534", "eprint_id": 765, "eprint_status": "archive", "datestamp": "2023-08-21 21:21:08", "lastmod": "2026-03-09 23:14:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Modularity of the Rankin-Selberg {$L$}-series, and multiplicity one for {${\\rm SL}(2)$}", "ispublished": "pub", "full_text_status": "public", "note": "In memory of my father Sundaram Ramakrishnan (SRK)\n\n(Received October 26, 1998)\n\nWe would like to express our gratitude to Ilya Piatetski-Shapiro for his continued interest in this project, and for kindly writing down, with J. Cogdell, the form of the converse theorem for GL(4) which we need ([CoPS]). Thanks are also due to T. Ikeda for writing down his calculations of the archimedean factors of the triple product L-functions ([Ik2]), to S. Rallis for useful remarks on these L-functions, to F. Shahidi for explaining his approach to the same via Langlands's theory of Eisenstein series and for commenting on an earlier version, to my colleague T. Wolff for helpful conversations on an analytic lemma we use in Section 3.4, and to many others, including H. Jacquet, R. P. Langlands, J. Rogawski and P. Sarnak, who have shown encouragement and interest. Special thanks must go to J. Cogdell for reading the earlier and the revised versions thoroughly and making crucial remarks. Part of the technical typing of this paper was done by Cherie Galvez, whom we thank. Finally, we would like to express our appreciation to the following: the National Science Foundation for support through the grants DMS-9501151 and DMS-9801328, Universit\u00b4e Paris-sud, Orsay, where we spent a fruitful month during September 1996, the DePrima Mathematics House in Sea Ranch, CA, for inviting us to visit and work there during August 1996 and 1998, MATSCIENCE, India, for hospitality in February 98, and \u2014 last, but not the least \u2014 the MSRI, Berkeley, for (twice) providing the right climate to work in; this project was started (in 1994) and essentially ended there.", "abstract": "Let f, g be primitive cusp forms, holomorphic or otherwise, on the upper half-plane H of levels N,M respectively, with (unitarily normalized) L-functions L(s, f) = [equation] and\nL(s, g) = [equation]. When p does not divide N (resp. M), the inverse roots \u03b1p, \u03b2p (resp. \u03b1\u2032p, \u03b2\u2032p ) are nonzero with sum ap (resp. bp). For every p prime to NM, set Lp(s, f \u00d7 g) = [(1 \u2212 \u03b1p\u03b1\u2032pp\u2212s)(1 \u2212 \u03b1p\u03b2\u2032pp\u2212s)(1 \u2212 \u03b2p\u03b1\u2032pp\u2212s)(1 \u2212 \u03b2p\u03b2\u2032pp\u2212s)]^\u22121. Let L\u2217(s, f \u00d7 g) denote the (incomplete Euler) product of Lp(s, f \u00d7 g) over all p not dividing NM. This is closely related to the convolution L-series [sum over n\u22651] a[sub]n b[sub] n n^\u2212s, whose miraculous properties were first studied by Rankin and Selberg.", "date": "2000-07-01", "date_type": "published", "publication": "Annals of Mathematics", "volume": "152", "number": "1", "publisher": "Annals of Mathematics", "pagerange": "45-111", "id_number": "CaltechAUTHORS:RAMaom00", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:RAMaom00", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "RAMaom00.pdf", "url": "https://authors.library.caltech.edu/records/xpmhm-8p534/files/RAMaom00.pdf" }, "pub_year": "2000", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/y88jt-v0y64", "eprint_id": 67061, "eprint_status": "archive", "datestamp": "2023-08-21 21:20:27", "lastmod": "2026-04-17 03:43:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Periwal-V", "name": { "family": "Periwal", "given": "Vipul" } } ] }, "title": "Dbrane phase transitions and monodromy in K-theory", "ispublished": "pub", "full_text_status": "public", "keywords": "Dbranes; K-theory", "note": "\u00a9 2000 Elsevier Science B.V. \n\nReceived 21 September 1999, Available online 1 June 2000. \n\nWe have benefited from discussions with R. Bezrukavnikov, M. Kontsevich, J. Rosenberg, A. Schwarz, A. Sen, E. Sharpe and E. Witten. The work of S.G. was supported in part by grant RFBR No. 98-02-16575 and Russian President's grant No 96-15-96939. The work of V.P. was supported in part by NSF grant PHY-9802484.\n\n

Submitted - 9908166.pdf

", "abstract": "Majumder and Sen have given an explicit construction of a first order phase transition in a non-supersymmetric system of Dbranes that occurs when the B-field is varied. We show that the description of this transition in terms of K-theory involves a bundle of K groups of non-commutative algebras over the K\u00e4hler cone with nontrivial monodromy. Thus the study of monodromy in K groups associated with quantized algebras can be used to predict the phase structure of systems of (non-supersymmetric) Dbranes.", "date": "2000-07", "date_type": "published", "publication": "Journal of Geometry and Physics", "volume": "34", "number": "3-4", "publisher": "Elsevier", "pagerange": "263-269", "id_number": "CaltechAUTHORS:20160513-082826792", "issn": "0393-0440", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-082826792", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9802484" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0393-0440(99)00067-4", "primary_object": { "basename": "9908166.pdf", "url": "https://authors.library.caltech.edu/records/y88jt-v0y64/files/9908166.pdf" }, "pub_year": "2000", "author_list": "Gukov, Sergei and Periwal, Vipul" }, { "id": "https://authors.library.caltech.edu/records/ys610-fae49", "eprint_id": 1323, "eprint_status": "archive", "datestamp": "2023-08-21 21:18:56", "lastmod": "2026-04-17 03:07:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Rahmfeld-J", "name": { "family": "Rahmfeld", "given": "Joachim" } }, { "id": "Robins-H", "name": { "family": "Robins", "given": "Harlan" } }, { "id": "Tannenhauser-J", "name": { "family": "Tannenhauser", "given": "Jonathan" } } ] }, "title": "Holography in superspace", "ispublished": "pub", "full_text_status": "public", "keywords": "Superstrings and Heterotic Strings, Superstring Vacua, AdS-CFT Correspondence", "note": "Received 17 July 2000, accepted for publication 24 July 2000, Published 18 August 2000 \n\nWe would like to thank Martin Cederwall, Piet Claus, Djordje Minic, John Schwarz, and Dmitri Sorokin for useful discussions. \n\nThis research was supported in part by the Caltech Discovery Fund. \n\nH.O., H.R., and J.T. are also supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098. J.R. was also supported in part by DOE grant DE-FG03-92ER40701.\n\n

Published - OOGjhep00.pdf

Submitted - 0007104.pdf

", "abstract": "The AdS/CFT correspondence identifies the coordinates of the conformal boundary of anti-de Sitter space with the coordinates of the conformal field theory. We generalize this identification to theories formulated in superspace. As an application of our results, we study a class of Wilson loops in Script N = 4 super-Yang-Mills theory. A gauge theory computation shows that the expectation values of these loops are invariant under a local \u03ba-symmetry, except at intersections. We identify this with the \u03ba-invariance of the associated string worldsheets in the corresponding bulk superspace.", "date": "2000-07", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "2000", "number": "7", "publisher": "Springer", "pagerange": "Art. no. 045", "id_number": "CaltechAUTHORS:OOGjhep00", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep00", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Discovery Fund" }, { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92ER40701" } ] }, "other_numbering_system": { "items": [ { "id": "00-026", "name": "CITUSC" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/2000/07/045", "primary_object": { "basename": "OOGjhep00.pdf", "url": "https://authors.library.caltech.edu/records/ys610-fae49/files/OOGjhep00.pdf" }, "related_objects": [ { "basename": "0007104.pdf", "url": "https://authors.library.caltech.edu/records/ys610-fae49/files/0007104.pdf" } ], "pub_year": "2000", "author_list": "Ooguri, Hirosi; Rahmfeld, Joachim; et al." }, { "id": "https://authors.library.caltech.edu/records/3975z-hmz45", "eprint_id": 72925, "eprint_status": "archive", "datestamp": "2023-08-19 05:58:11", "lastmod": "2026-04-17 02:37:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Knot Invariants and Topological Strings", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Elsevier Science B.V. \n\nWe are grateful to N. Berkovits, R. Gopakumar, K. Hori, S. Sinha, C. Taubes and T. Taylor for valuable discussions. H.O. would like to thank the theory group of Harvard University, where this work was initiated and completed. The research of H.O. was supported in part by NSF grant PHY-95-14797, DOE grant DE-AC03-76SF00098, and the Caltech Discovery Fund. The research of C.V. is supported by NSF Grant No. PHY-9218167.\n\n

Submitted - 9912123.pdf

", "abstract": "We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S\u00b3 (for any representation) agrees to all orders in N with the corresponding quantity on the topological string side. For a general knot, we find a reformulation of the knot invariant in terms of new integral invariants, which capture the spectrum (and spin) of M2 branes ending on M5 branes embedded in the resolved conifold geometry. We also find an intriguing link between knot invariants and superpotential terms generated by worldsheet instantons in N=1 supersymmetric theories in 4 dimensions.", "date": "2000-06-26", "date_type": "published", "publication": "Nuclear Physics B", "volume": "577", "number": "3", "publisher": "Elsevier", "pagerange": "419-438", "id_number": "CaltechAUTHORS:20161219-085922769", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161219-085922769", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Caltech Discovery Fund" }, { "agency": "NSF", "grant_number": "PHY-9218167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(00)00118-8", "primary_object": { "basename": "9912123.pdf", "url": "https://authors.library.caltech.edu/records/3975z-hmz45/files/9912123.pdf" }, "pub_year": "2000", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/wd197-d4m26", "eprint_id": 38668, "eprint_status": "archive", "datestamp": "2023-08-19 05:57:54", "lastmod": "2026-04-17 01:59:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Adams-Scot", "name": { "family": "Adams", "given": "Scot" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Linear algebraic groups and countable Borel equivalence relations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 American Mathematical Society.\n\nReceived by the editors March 27, 1999 and, in revised form, April 21, 2000. Article electronically published on June 23, 2000. \n\nThe first author's research was partially supported by NSF Grant DMS 9703480. \n\nThe second author's research was partially supported by NSF Grant DMS 9619880 and a Visiting Miller Research Professorship at U.C. Berkeley.\n\n

Published - S0894-0347-00-00341-6.pdf

", "abstract": "This paper is a contribution to the study of Borel equivalence relations on standard\nBorel spaces (i.e., Polish spaces equipped with their Borel structure). In\nmathematics one often deals with problems of classification of objects up to some\nnotion of equivalence by invariants. Frequently these objects can be viewed as elements\nof a standard Borel space X and the equivalence turns out to be a Borel\nequivalence relation E on X. A complete classification of X up to E consists of\nfinding a set of invariants I and a map c : X \u2192 I such that xEy \u21d4 c(x) = c(y).\nFor this to be of any interest both I and c must be explicit or definable and as simple\nand concrete as possible. The theory of Borel equivalence relations studies the\nset-theoretic nature of possible invariants and develops a mathematical framework\nfor measuring the complexity of such classification problems.", "date": "2000-06-23", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "13", "number": "4", "publisher": "American Mathematical Society", "pagerange": "909-943", "id_number": "CaltechAUTHORS:20130524-130949007", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130524-130949007", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9703480" }, { "agency": "NSF", "grant_number": "DMS-9619880" }, { "agency": "U. C. Berkeley Visiting Miller Research Professorship" } ] }, "other_numbering_system": { "items": [ { "id": "MR1775739", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-00-00341-6", "primary_object": { "basename": "S0894-0347-00-00341-6.pdf", "url": "https://authors.library.caltech.edu/records/wd197-d4m26/files/S0894-0347-00-00341-6.pdf" }, "pub_year": "2000", "author_list": "Adams, Scot and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/p3mtq-6pe41", "eprint_id": 86374, "eprint_status": "archive", "datestamp": "2023-08-19 05:52:30", "lastmod": "2026-04-17 01:18:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Copyright 2000 by the Authors. \n\nReceived by the editors October 9, 1997. \n\nThis material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.", "abstract": "We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential q of a one-dimensional Schr\u00f6dinger operator H = -(d^(2)/(dx^(2)) + q determine the potential completely. Included are theorems for finite intervals and for the whole line. In particular, we pose and solve a new type of inverse spectral problem involving fractions of the eigenvalues of H on a finite interval and knowledge of q over a corresponding fraction of the interval. The methods employed rest on Weyl m-function techniques and densities of zeros of a class of entire functions.", "date": "2000-06", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "352", "number": "6", "publisher": "American Mathematical Society", "pagerange": "2765-2787", "id_number": "CaltechAUTHORS:20180511-153128441", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180511-153128441", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9623121" }, { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9947-99-02544-1", "pub_year": "2000", "author_list": "Gesztesy, Fritz and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/dqts0-1zv72", "eprint_id": 8495, "eprint_status": "archive", "datestamp": "2023-08-21 21:13:48", "lastmod": "2026-04-17 04:14:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Schr\u00f6dinger operators in the twentieth century", "ispublished": "pub", "full_text_status": "public", "keywords": "quantum theory; Schrodinger equation; history", "note": "\u00a9 2000 American Institute of Physics. \n\n(Received 4 February 2000; accepted 24 February 2000) \n\nI would like to thank Michael Aizenman, Brian Davies, Percy Deift, Fritz Gesztesy, Dirk Hundertmark, Walter Hunziker, and Rowan Killip for useful input. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9707661. The Government has certain rights in this material. \n\nDedicated to Tosio Kato (1917\u20131999), father of the modern theory of Schr\u00f6dinger operators.\n\n

Published - SIMjmp00.pdf

", "abstract": "This paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics.", "date": "2000-06", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "41", "number": "6", "publisher": "American Institute of Physics", "pagerange": "3523-3555", "id_number": "CaltechAUTHORS:SIMjmp00", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMjmp00", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/1.533321", "primary_object": { "basename": "SIMjmp00.pdf", "url": "https://authors.library.caltech.edu/records/dqts0-1zv72/files/SIMjmp00.pdf" }, "pub_year": "2000", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/x21ny-kfr37", "eprint_id": 27954, "eprint_status": "archive", "datestamp": "2023-08-19 05:49:22", "lastmod": "2026-03-18 00:08:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cordes-H", "name": { "family": "Cordes", "given": "Heinz" } }, { "id": "Jensen-A", "name": { "family": "Jensen", "given": "Arne" } }, { "id": "Kuroda-S-T", "name": { "family": "Kuroda", "given": "S. T." } }, { "id": "Ponce-G", "name": { "family": "Ponce", "given": "Gustavo" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Taylor-M", "name": { "family": "Taylor", "given": "Michael" } } ] }, "title": "Tosio Kato (1917\u20131999)", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 American Mathematical Society.\n\n

Published - CORnames00.pdf

", "abstract": "Tosio Kato was born August 25, 1917, in Kanuma City, Tochigi-ken, Japan. His early training was in physics. He obtained\na B.S. in 1941 and the degree of Doctor of Science in 1951, both at the University of Tokyo. Between these events he published\npapers on a variety of subjects, including pair creation by gamma rays, motion of an object in a fluid, and results\non spectral theory of operators arising in quantum mechanics. His dissertation was entitled \"On the convergence of the\nperturbation method\".\nKato was appointed assistant professor of physics at the University of Tokyo in 1951 and was promoted to professor of\nphysics in 1958. During this time he visited the University of California at Berkeley in 1954\u201355, New York University in 1955,\nthe National Bureau of Standards in 1955\u201356, and Berkeley and the California Institute of Technology in 1957\u201358. He was\nappointed professor of mathematics at Berkeley in 1962 and taught there until his retirement in 1988. He supervised\ntwenty-one Ph.D. students at Berkeley and three at the University of Tokyo.\nKato published over 160 papers and 6 monographs, including his famous book Perturbation Theory for Linear\nOperators [K66b]. Recognition for his important work included the Norbert Wiener Prize in Applied Mathematics, awarded\nin 1980 by the AMS and the Society for Industrial and Applied Mathematics. He was particularly well known for his work on\nSchr\u00f6dinger equations of nonrelativistic quantum mechanics and his work on the Navier-Stokes and Euler equations of\nclassical fluid mechanics. His activity in the latter area remained at a high level well past retirement and continued until his\ndeath on October 2, 1999.", "date": "2000-06", "date_type": "published", "publication": "Notices of the American Mathematical Society", "volume": "47", "number": "6", "publisher": "American Mathematical Society", "pagerange": "650-657", "id_number": "CaltechAUTHORS:20111123-135717828", "issn": "0002-9920", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111123-135717828", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "CORnames00.pdf", "url": "https://authors.library.caltech.edu/records/x21ny-kfr37/files/CORnames00.pdf" }, "pub_year": "2000", "author_list": "Cordes, Heinz; Jensen, Arne; et al." }, { "id": "https://authors.library.caltech.edu/records/6ec67-rew47", "eprint_id": 66995, "eprint_status": "archive", "datestamp": "2023-08-19 05:46:45", "lastmod": "2026-04-16 14:47:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Solitons, superpotentials and calibrations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Elsevier Science B.V. \n\nI would like to express my gratitude to S. James Gates and especially to Edward Witten for helpful discussions and constant encouragement. The work was supported in part by the Caltech Discovery Fund, grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\n

Submitted - 9911011.pdf

", "abstract": "In this paper we study several issues related to the generation of the superpotential induced by background Ramond\u2013Ramond fluxes in compactification of Type IIA string theory on Calabi\u2013Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi\u2013Yau space, we propose a general formula for the superpotential and justify it comparing the supersymmetry conditions in D=2 and D=10 supergravity theories. We also suggest a geometric interpretation to the supersymmetric index in the two-dimensional effective theory in terms of topological invariants of the Calabi\u2013Yau four-fold, and estimate the asymptotic growth of these invariants from BTZ black hole entropy. Finally, we explicitly construct new supersymmetric vacua for Type IIA string theory compactification on a Calabi\u2013Yau four-fold with Ramond\u2013Ramond fluxes.", "date": "2000-05-15", "date_type": "published", "publication": "Nuclear Physics B", "volume": "574", "number": "1-2", "publisher": "Elsevier", "pagerange": "169-188", "id_number": "CaltechAUTHORS:20160511-131311298", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-131311298", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Caltech Discovery Fund" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(00)00053-5", "primary_object": { "basename": "9911011.pdf", "url": "https://authors.library.caltech.edu/records/6ec67-rew47/files/9911011.pdf" }, "pub_year": "2000", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/tjf9m-ajz39", "eprint_id": 81888, "eprint_status": "archive", "datestamp": "2023-08-21 21:11:06", "lastmod": "2026-04-16 15:28:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bonnecaze-A", "name": { "family": "Bonnecaze", "given": "A." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sol\u00e9-P", "name": { "family": "Sol\u00e9", "given": "P." } } ] }, "title": "3-Colored 5-Designs and Z_4-Codes", "ispublished": "pub", "full_text_status": "public", "keywords": "Type II codes; Z_4-codes; Split weight enumerators; Jacobi polynomials; Invariant theory; Colored designs", "note": "\u00a9 2000 Elsevier Science B.V.", "abstract": "New 5-designs on 24 points were constructed recently by Harada by the consideration of Z_4-codes. We use Jacobi polynomials as a theoretical tool to explain their existence as resulting of properties of the symmetrized weight enumerator (swe) of the code. We introduce the notion of a colored t-design and we show that the words of any given Lee composition, in any of the 13 Lee-optimal self-dual codes of length 24 over Z_4, form a colored 5-design. New colored 3-designs on 16 points are also constructed in that way.", "date": "2000-05-01", "date_type": "published", "publication": "Journal of Statistical Planning and Inference", "volume": "86", "number": "2", "publisher": "Elsevier", "pagerange": "349-368", "id_number": "CaltechAUTHORS:20170927-153153707", "issn": "0378-3758", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170927-153153707", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0378-3758(99)00117-2", "pub_year": "2000", "author_list": "Bonnecaze, A.; Rains, E.; et al." }, { "id": "https://authors.library.caltech.edu/records/eaj7m-9zf33", "eprint_id": 1348, "eprint_status": "archive", "datestamp": "2023-08-21 21:08:27", "lastmod": "2026-04-17 02:48:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Flach-M", "name": { "family": "Flach", "given": "M." }, "orcid": "0000-0002-4523-9467" } ] }, "title": "Euler characteristics in relative K-groups", "ispublished": "pub", "full_text_status": "public", "note": "\"Reprinted with the permission of Cambridge University Press.\" \n\nReceived 15 March 1998; revised 23 April 1999. Published Online 08 September 2000\n\nThe author was supported by NSF-grant DMA-9624824 and a Sloan fellowship.\n\n

Published - FLAblms00.pdf

", "abstract": "Suppose that M is a finite module under the Galois group of a local or global field. Ever since Tate's papers [17, 18], we have had a simple and explicit formula for the Euler\u2013Poincar\u00e9 characteristic of the cohomology of M. In this note we are interested in a refinement of this formula when M also carries an action of some algebra [script A], commuting with the Galois action (see Proposition 5.2 and Theorem 5.1 below). This refinement naturally takes the shape of an identity in a relative K-group attached to [script A] (see Section 2). We shall deduce such an identity whenever we have a formula for the ordinary Euler characteristic, the key step in the proof being the representability of certain functors by perfect complexes (see Section 3). This representability may be of independent interest in other contexts. \n\nOur formula for the equivariant Euler characteristic over [script A] implies the 'isogeny invariance' of the equivariant conjectures on special values of the L-function put forward in [3], and this was our motivation to write this note. Incidentally, isogeny invariance (of the conjectures of Birch and Swinnerton-Dyer) was also a motivation for Tate's original paper [18]. I am very grateful to J-P. Serre for illuminating discussions on the subject of this note, in particular for suggesting that I consider representability. I should also like to thank D. Burns for insisting on a most general version of the results in this paper.", "date": "2000-05", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "volume": "32", "number": "3", "publisher": "London Mathematical Society", "pagerange": "272-284", "id_number": "CaltechAUTHORS:FLAblms00", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:FLAblms00", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMA-9624824" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0024609300006950", "primary_object": { "basename": "FLAblms00.pdf", "url": "https://authors.library.caltech.edu/records/eaj7m-9zf33/files/FLAblms00.pdf" }, "pub_year": "2000", "author_list": "Flach, M." }, { "id": "https://authors.library.caltech.edu/records/ex9w5-bc783", "eprint_id": 66989, "eprint_status": "archive", "datestamp": "2023-08-19 05:35:17", "lastmod": "2026-04-17 03:21:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "K-Theory, Reality, and Orientifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Springer-Verlag. \n\nReceived: 9 March 1999; Accepted: 15 October 1999. \n\nI am very grateful to C. Bachas,W. Browder, M. J. Hopkins, I. R. Klebanov, S. Martin, A. Schwarz and especially to E. Witten for interesting and illuminating discussions/correspondence. It is pleasure to thank Harvard University for financial support and hospitality while the manuscript was being completed. The work was supported in part by grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\n

Submitted - 9901042.pdf

", "abstract": "We use equivariant K-theory to classify charges of new (possibly non-supersymmetric) states localized on various orientifolds in Type II string theory. We also comment on the stringy construction of new D-branes and demonstrate the discrete electric-magnetic duality in Type I brane systems with p+q=7, as proposed by Witten.", "date": "2000-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "210", "number": "3", "publisher": "Springer", "pagerange": "621-639", "id_number": "CaltechAUTHORS:20160511-110549355", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-110549355", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Harvard University" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s002200050793", "primary_object": { "basename": "9901042.pdf", "url": "https://authors.library.caltech.edu/records/ex9w5-bc783/files/9901042.pdf" }, "pub_year": "2000", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/tmpmt-dt788", "eprint_id": 81985, "eprint_status": "archive", "datestamp": "2023-08-21 21:03:12", "lastmod": "2026-03-09 22:11:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Bounds for Self-Dual Codes Over \u2124_4", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Hamming, Lee, bounds; self-dual Full-size image Z4 code", "note": "\u00a9 2000 Academic Press. \n\nReceived 3 February 1998, Revised 25 January 1999.", "abstract": "New bounds are given for the minimal Hamming and Lee weights of self-dual codes over \u2124_4. For a self-dual code of length n, the Hamming weight is bounded above by 4[n/24]+f(n mod 24), for an explicitly given function f; the Lee weight is bounded above by 8[n/24]+g(n mod 24), for a different function g. These bounds appear to agree with the full linear programming bound for a wide range of lengths. The proof of these bounds relies on a reduction to a problem of binary codes, namely that of bounding the minimum dual distance of a doubly even binary code.", "date": "2000-04", "date_type": "published", "publication": "Finite Fields and Their Applications", "volume": "6", "number": "2", "publisher": "Elsevier", "pagerange": "146-163", "id_number": "CaltechAUTHORS:20171003-100542142", "issn": "1071-5797", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-100542142", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1006/ffta.1999.0258", "pub_year": "2000", "author_list": "Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/7tws4-2f969", "eprint_id": 72938, "eprint_status": "archive", "datestamp": "2023-08-19 05:35:30", "lastmod": "2026-04-16 14:55:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Gauge Theory and String Theory; An Introduction to the AdS/CFT Correspondence", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Published by Elsevier B.V. \n\nPlenary talk at LATTICE 99 held in Pisa, Itay from June 29 to July 3, 1999. To appear in the Proceedings of the conference. \n\nI would like to thank the organizers of LATTICE 99 for the very stimulating conference and for their hospitality. This research was supported in part by NSF grant PHY-95-14797, DOE grant DE-AC03-76SF00098, and the Caltech Discovery Fund.\n\n

Submitted - 9911027.pdf

", "abstract": "In this talk, I would like to show you some of the recent developments in superstring theory, in particular the relation between gauge theory and string theory. String theory was originally invented as a theory of hadrons, but it was superseded by the gauge theory. It then found its employment in quantum gravity. Now it seems that string theory and gauge theory are meeting again, and I hope this new direction will provide an interesting arena where lattice gauge theorists and string theorists can interact and exchange ideas, benefiting both.", "date": "2000-04", "date_type": "published", "publication": "Nuclear Physics B - Proceedings Supplements", "volume": "83-84", "publisher": "Elsevier", "pagerange": "77-81", "id_number": "CaltechAUTHORS:20161219-105646214", "issn": "0920-5632", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161219-105646214", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Caltech Discovery Fund" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0920-5632(00)91597-4", "primary_object": { "basename": "9911027.pdf", "url": "https://authors.library.caltech.edu/records/7tws4-2f969/files/9911027.pdf" }, "pub_year": "2000", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/xy630-b9z81", "eprint_id": 79655, "eprint_status": "archive", "datestamp": "2023-08-19 05:35:47", "lastmod": "2026-04-16 13:58:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On Local Borg\u2013Marchenko Uniqueness Results", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 Springer-Verlag. \n\nReceived: 22 October 1999;\nAccepted: 2 November 1999.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9707661. \n\nF. G. thanks T. Tombrello for the hospitality of Caltech where this work was done.\n\n

Submitted - 9910089v1.pdf

", "abstract": "We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl\u2013Titchmarsh m-functions, m_j(z), of two Schr\u00f6dinger operators, H_j = -d^2/dx^2 + q_j, j = 1,2 in L^2((O,R)), O < R \u2264 \u221e, are exponentially close, that is, |m_1(z) - m_2(z)|_|z|\u2192\u221e = O(e^(-2 IM(z^1/2)a), O < \u0251", "date": "2000-04", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "211", "number": "2", "publisher": "Springer", "pagerange": "273-287", "id_number": "CaltechAUTHORS:20170801-072515055", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170801-072515055", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9707661" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s002200050812", "primary_object": { "basename": "9910089v1.pdf", "url": "https://authors.library.caltech.edu/records/xy630-b9z81/files/9910089v1.pdf" }, "pub_year": "2000", "author_list": "Gesztesy, Fritz and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/30aw5-jt237", "eprint_id": 5434, "eprint_status": "archive", "datestamp": "2023-08-21 21:00:34", "lastmod": "2026-04-17 03:06:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Wilson loops in large-N theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 IOP Publishing Limited 2000. \n\nReceived 16 September 1999. Print publication: Issue 5 (7 March 2000) \n\nIt is my pleasure to thank the organizers of Strings '99 for giving me the opportunity to present this work at the conference and for their hospitality. I would like to thank Nadav Drukker and David Gross for their collaboration on this work. This research is supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098. \n\nSPECIAL ISSUE OF INVITED PAPERS FROM THE STRINGS '99 CONFERENCE, POTSDAM, 19 - 24 JULY 1999. Classical and Quantum Gravity Volume 17, Number 5, 7 March 2000. \n\nPreprint: arXiv:hep-th/9909040 7 Sep 1999 \n\nTechnical report nos.: UCB-PTH-99/38; LBNL-44209\n\n

Published - OOGcqg00.pdf

Submitted - OOGcqg00preprint.pdf

", "abstract": "We discuss how various aspects of Wilson loops in large-N gauge theories are studied from the point of view of the AdS-CFT correspondence.", "date": "2000-03-07", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "17", "number": "5", "publisher": "IOP", "pagerange": "1225-1233", "id_number": "CaltechAUTHORS:OOGcqg00", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGcqg00", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/0264-9381/17/5/331", "primary_object": { "basename": "OOGcqg00.pdf", "url": "https://authors.library.caltech.edu/records/30aw5-jt237/files/OOGcqg00.pdf" }, "related_objects": [ { "basename": "OOGcqg00preprint.pdf", "url": "https://authors.library.caltech.edu/records/30aw5-jt237/files/OOGcqg00preprint.pdf" } ], "pub_year": "2000", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/8x7bp-ckk33", "eprint_id": 28265, "eprint_status": "archive", "datestamp": "2023-08-19 05:25:39", "lastmod": "2026-04-17 01:05:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Saxl-J", "name": { "family": "Saxl", "given": "Jan" } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } }, { "id": "Wilson-R-A", "name": { "family": "Wilson", "given": "Robert A." } } ] }, "title": "Embeddings of Sz(32) in E_8(5)", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 London Mathematical Society.\n\nReceived 25 March 1998; revised 15 March 1999.\n\n

Published - SAXblms00.pdf

", "abstract": "We show that the Suzuki group Sz(32) is a subgroup of E_8(5), and so is its automorphism group. Both are unique up to conjugacy in E_8(F) for any field F of characteristic 5, and the automorphism group Sz(32):5 is maximal in E_8(5).", "date": "2000-03", "date_type": "published", "publication": "Bulletin of the London Mathematical Society", "volume": "32", "publisher": "London Mathematical Society", "pagerange": "196-202", "id_number": "CaltechAUTHORS:20111201-090234125", "issn": "0024-6093", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111201-090234125", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1112/S0024609399006633", "primary_object": { "basename": "SAXblms00.pdf", "url": "https://authors.library.caltech.edu/records/8x7bp-ckk33/files/SAXblms00.pdf" }, "pub_year": "2000", "author_list": "Saxl, Jan; Wales, David B.; et al." }, { "id": "https://authors.library.caltech.edu/records/absez-hgb80", "eprint_id": 38586, "eprint_status": "archive", "datestamp": "2023-08-19 05:25:46", "lastmod": "2026-03-09 20:39:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "G." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The complexity of the classification of Riemann surfaces and complex manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 by the Board of Trustees of the University of Illinois. \nReceived May 20, 1998; received in final form December 14, 1998. \nResearch partially supported by the National Science Foundation, the first-named author by grant DMS 96-22977 and the second-named author by grant DMS 96-19880.\n\n

Published - euclid.ijm.1255984956.pdf

", "abstract": "In answer to a question by Becker, Rubel, and Henson, we show that countable subsets of \u2102 can be used as complete invariants for Riemann surfaces considered up to conformal equivalence, and that this equivalence relation is itself Borel in a natural Borel structure on the space of all such surfaces. We further proceed to precisely calculate the classification difficulty of this equivalence relation in terms of the modern theory of Borel equivalence relations. \n\nOn the other hand we show that the analog of Becker, Rubel, and Henson's question has a negative solution in (complex) dimension n \u2265 2.", "date": "2000-03", "date_type": "published", "publication": "Illinois Journal of Mathematics", "volume": "44", "number": "1", "publisher": "University of Illinois", "pagerange": "104-137", "id_number": "CaltechAUTHORS:20130521-075724313", "issn": "0019-2082", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-075724313", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 96-22977" }, { "agency": "NSF", "grant_number": "DMS 96-19880" } ] }, "other_numbering_system": { "items": [ { "id": "0954.03052", "name": "Zentralblatt MATH identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "euclid.ijm.1255984956.pdf", "url": "https://authors.library.caltech.edu/records/absez-hgb80/files/euclid.ijm.1255984956.pdf" }, "pub_year": "2000", "author_list": "Hjorth, G. and Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/6s3cy-sx460", "eprint_id": 72941, "eprint_status": "archive", "datestamp": "2023-08-21 20:49:41", "lastmod": "2026-04-17 02:49:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aharony-Ofer", "name": { "family": "Aharony", "given": "Ofer" } }, { "id": "Gubser-S-S", "name": { "family": "Gubser", "given": "Steven S." } }, { "id": "Maldacena-Juan", "name": { "family": "Maldacena", "given": "Juan" }, "orcid": "0000-0002-9127-1687" }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Yaron", "name": { "family": "Oz", "given": "Yaron" } } ] }, "title": "Large N Field Theories, String Theory and Gravity", "ispublished": "pub", "full_text_status": "public", "keywords": "Gauge theories; Supersymmetry; Supergravity; String theory", "note": "\u00a9 2000 Elsevier. \n\nReceived June 1999; editor: A. Schwimmer. \n\nWe would like to thank T. Banks, M. Berkooz, A. Brandhuber, M. Douglas, D. Freedman, S. Giddings, D. Gross, G. Horowitz, K. Jansen, S. Kachru, D. Kutasov, E. Martinec, G. Moore, A. Rajaraman, N. Seiberg, E. Silverstein, L. Susskind, and E. Witten for many useful discussions. The research of O.A. was supported in part by DOE grant DE-FG02-96ER40559. O.A., J.M. and Y.O. would like to thank the Institute for Advanced Studies at the Hebrew University of Jerusalem for hospitality during part of this work. J.M. wants to thank the hospitality of the Institute for Advanced Study at Princeton, where he was a Raymond and Beverly Sackler Fellow. The research of J.M. was supported in part by DOE grant DE-FGO2-91ER40654, NSF grant PHY-9513835, the Sloan Foundation and the David and Lucile Packard Foundations. The research of S.S.G. was supported by the Harvard Society of Fellows, and also in part by the NSF under grant number PHY-98-02709, and by DOE grant DE-FGO2-91ER40654. S.S.G. also thanks the Institute for Theoretical Physics at Santa Barbara for hospitality. The research of H.O. was supported in part by National Science Foundation under Contract PHY-95-14797 and in part by the Director, Office of Science, Office of High Energy and Nuclear Physics, Division of High Energy Physics, of the U.S. Department of Energy under Contract DE-AC03-76SF00098.\n\n

Submitted - 9905111.pdf

", "abstract": "We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. We focus on the case of the N=4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersymmetry, and in particular the relation to QCD. We also discuss some implications for black hole physics.", "date": "2000-01", "date_type": "published", "publication": "Physics Reports", "volume": "323", "number": "3-4", "publisher": "Elsevier", "pagerange": "183-386", "id_number": "CaltechAUTHORS:20161219-110810298", "issn": "0370-1573", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161219-110810298", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40559" }, { "agency": "Princeton University" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FGO2-91ER40654" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "David and Lucile Packard Foundation" }, { "agency": "Harvard Society of Fellows" }, { "agency": "NSF", "grant_number": "PHY-98-02709" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FGO2-91ER40654" }, { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0370-1573(99)00083-6", "primary_object": { "basename": "9905111.pdf", "url": "https://authors.library.caltech.edu/records/6s3cy-sx460/files/9905111.pdf" }, "pub_year": "2000", "author_list": "Aharony, Ofer; Gubser, Steven S.; et al." }, { "id": "https://authors.library.caltech.edu/records/v0a29-75k22", "eprint_id": 81856, "eprint_status": "archive", "datestamp": "2023-08-19 05:13:05", "lastmod": "2026-03-09 22:47:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Polynomial invariants of quantum codes", "ispublished": "pub", "full_text_status": "public", "keywords": "Invariant, quantum code, shadow, weight enumerator", "note": "\u00a9 2000 IEEE. \n\nManuscript received May 26, 1997; revised February 24, 1999.\n\n

Published - 00817508.pdf

Submitted - 9704042.pdf

", "abstract": "The weight enumerators (Shor and Laflamme 1997) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher degree polynomial invariants. We show that the space of degree k invariants of a code of length n is spanned by a set of basic invariants in one-to-one correspondence with S^n_k. We then present a number of equations and inequalities in these invariants; in particular, we give a higher order generalization of the shadow enumerator of a code, and prove that its coefficients are nonnegative. We also prove that the quartic invariants of a ((4, 4, 2))_2 code are uniquely determined, an important step in a proof that any ((4, 4, 2))_2 code is additive (Rains 1999).", "date": "2000-01", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "46", "number": "1", "publisher": "IEEE", "pagerange": "54-59", "id_number": "CaltechAUTHORS:20170926-153330743", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-153330743", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.817508", "primary_object": { "basename": "00817508.pdf", "url": "https://authors.library.caltech.edu/records/v0a29-75k22/files/00817508.pdf" }, "related_objects": [ { "basename": "9704042.pdf", "url": "https://authors.library.caltech.edu/records/v0a29-75k22/files/9704042.pdf" } ], "pub_year": "2000", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/wdrd0-3sb24", "eprint_id": 28333, "eprint_status": "archive", "datestamp": "2023-08-19 05:03:35", "lastmod": "2026-03-09 02:38:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "D-branes in a topologically nontrivial B-field", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 2000 International Press.\n\nI would like to thank Mikhail Khovanov for useful discussions.\nThis work was supported by a DOE grant DE-FG02-90ER40542.\n\n

Published - KAPatmp99.pdf

Submitted - KAPatmp99preprint.pdf

", "abstract": "We study global worldsheet anomalies for open strings ending on several coincident D-branes in the presence of a B-field. We show that cancellation of anomalies is made possible by a correlation between the t'Hooft magnetic flux on the D-branes and the topological class of the B-field. One application of our results is a proper understanding of the geometric nature of the gauge field living on D-branes: rather than being a connection on a vector bundle, it is a connection on a module over a certain noncommutative algebra. Our argument works for a general closed string background. We also explain why in the presence of a topologically nontrivial B-field whose curvature is pure torsion D-branes represent classes in a twisted K-theory, as conjectured by E. Witten.", "date": "2000", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "4", "number": "1", "publisher": "International Press", "pagerange": "127-154", "id_number": "CaltechAUTHORS:20111207-090734635", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111207-090734635", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.2000.v4.n1.a3", "primary_object": { "basename": "KAPatmp99.pdf", "url": "https://authors.library.caltech.edu/records/wdrd0-3sb24/files/KAPatmp99.pdf" }, "related_objects": [ { "basename": "KAPatmp99preprint.pdf", "url": "https://authors.library.caltech.edu/records/wdrd0-3sb24/files/KAPatmp99preprint.pdf" } ], "pub_year": "2000", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/kcbv1-c4f96", "eprint_id": 72958, "eprint_status": "archive", "datestamp": "2023-08-19 05:00:14", "lastmod": "2026-04-16 13:49:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Drukker-N", "name": { "family": "Drukker", "given": "Nadav" } }, { "id": "Gross-D-J", "name": { "family": "Gross", "given": "David J." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Wilson Loops and Minimal Surfaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 American Physical Society. \n\n(Received 13 May 1999; published 15 November 1999) \n\nWe thank Korkut Bardakci, Sunny Itzhaki, Juan Maldacena, Joe Polchinski, Bruno Zumino. N.D. thanks Theory Group of UC Berkeley and LBNL for their hospitality. H.O. thanks the Institute for Theoretical Physics at Santa Barbara, Department of Mathematics and Physics at University of Amsterdam, and Theory Group at CERN, for their hospitality and for providing excellent working environments. The work of H.O. was supported in part by the NSF grant PHY-95-14797 and the DOE grant DE-AC03-76SF00098. This work was supported in part by the NSF under grant No. PHY-94-07194.\n\n

Published - PhysRevD.60.125006.pdf

Submitted - 9904191.pdf

", "abstract": "The AdS/CFT correspondence suggests that the Wilson loop of the large N gauge theory with N=4 supersymmetry in 4 dimensions is described by a minimal surface in AdS_5 x S^5. We examine various aspects of this proposal, comparing gauge theory expectations with computations of minimal surfaces. There is a distinguished class of loops, which we call BPS loops, whose expectation values are free from ultra-violet divergence. We formulate the loop equation for such loops. To the extent that we have checked, the minimal surface in AdS_5 x S^5 gives a solution of the equation. We also discuss the zig-zag symmetry of the loop operator. In the N=4 gauge theory, we expect the zig-zag symmetry to hold when the loop does not couple the scalar fields in the supermultiplet. We will show how this is realized for the minimal surface.", "date": "1999-12-15", "date_type": "published", "publication": "Physical Review D", "volume": "60", "number": "12", "publisher": "American Physical Society", "pagerange": "Art. No. 125006", "id_number": "CaltechAUTHORS:20161220-074236256", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-074236256", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-94-07194" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.60.125006", "primary_object": { "basename": "9904191.pdf", "url": "https://authors.library.caltech.edu/records/kcbv1-c4f96/files/9904191.pdf" }, "related_objects": [ { "basename": "PhysRevD.60.125006.pdf", "url": "https://authors.library.caltech.edu/records/kcbv1-c4f96/files/PhysRevD.60.125006.pdf" } ], "pub_year": "1999", "author_list": "Drukker, Nadav; Gross, David J.; et al." }, { "id": "https://authors.library.caltech.edu/records/j3h88-bxd60", "eprint_id": 81832, "eprint_status": "archive", "datestamp": "2023-08-19 04:56:52", "lastmod": "2026-04-16 13:33:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conway-J-H", "name": { "family": "Conway", "given": "J. H." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "On the Existence of Similar Sublattices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 Canadian Mathematical Society. \n\nReceived by the editors November 11, 1998; revised October 12, 1999. \n\nWe thank H.-G. Quebbemann for suggesting that the similar sublattice problem is best handled via the Hilbert symbol, and for pointing out an error in the first version of this paper. We also thank V. A. Vaishampayan and S. D. Servetto for many conversations concerning vector quantization, and M. Baake and J.Martinet for comments on the manuscript. R. Schulze-Pillot drew our attention to the Chapman references.\n\n

Published - sloanecox.pdf

Submitted - 0207177.pdf

", "abstract": "Partial answers are given to two questions. When does a lattice \u039b contain a sublattice \u039b\u2032 of index that is geometrically similar to \u039b? When is the sublattice \"clean\", in the sense that the boundaries of the Voronoi cells for \u039b' do not intersect \u039b?", "date": "1999-12", "date_type": "published", "publication": "Canadian Journal of Mathematics", "volume": "51", "number": "6", "publisher": "Canadian Mathematical Society", "pagerange": "1300-1306", "id_number": "CaltechAUTHORS:20170926-102111766", "issn": "0008-414X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-102111766", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4153/CJM-1999-059-5", "primary_object": { "basename": "sloanecox.pdf", "url": "https://authors.library.caltech.edu/records/j3h88-bxd60/files/sloanecox.pdf" }, "related_objects": [ { "basename": "0207177.pdf", "url": "https://authors.library.caltech.edu/records/j3h88-bxd60/files/0207177.pdf" } ], "pub_year": "1999", "author_list": "Conway, J. H.; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/52qf3-0zk69", "eprint_id": 12117, "eprint_status": "archive", "datestamp": "2023-08-22 14:10:15", "lastmod": "2026-04-16 15:17:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gremm-M", "name": { "family": "Gremm", "given": "Martin" }, "orcid": "0000-0002-5324-3482" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Heterotic little string theories and holography", "ispublished": "pub", "full_text_status": "public", "keywords": "Superstrings and Heterotic Strings, p-branes, Conformal Field Models in String Theory", "note": "\u00a9 1999 SISSA. \n\nReceived 10 November 1999, accepted for publication 12 November 1999. Published 30 November 1999. \n\nWe would like to thank Micha Berkooz, Emanuel Diaconescu, Nati Seiberg, and Angel Uranga for helpful discussions. The work of M.G was supported in part by DOE grants #DF-FC02-94ER40818 and #DE-FC-02-91ER40671, while that of A.K. by DOE grant #DE-FG02-90ER40542. \n\nE-print number: hep-th/9907210\n\n

Published - GREjhep99b.pdf

", "abstract": "It has been conjectured that little string theories in six dimensions are holographic to critical string theory in a linear dilaton background. We test this conjecture for theories arising on the worldvolume of heterotic fivebranes. We compute the spectrum of chiral primaries in these theories and compare with results following from type-I-heterotic duality and the AdS/CFT correspondence. We also construct holographic duals for heterotic fivebranes near orbifold singularities. Finally we find several new little string theories which have Spin(32)/Bbb Z2 or E8 \u00d7 E8 global symmetry but do not have a simple interpretation either in heterotic or M-theory.", "date": "1999-11-30", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1999", "number": "11", "publisher": "Springer", "pagerange": "Art. No. 018", "id_number": "CaltechAUTHORS:GREjhep99b", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GREjhep99b", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DF-FC02-94ER40818" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FC02-91ER40671" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1999/11/018", "primary_object": { "basename": "GREjhep99b.pdf", "url": "https://authors.library.caltech.edu/records/52qf3-0zk69/files/GREjhep99b.pdf" }, "pub_year": "1999", "author_list": "Gremm, Martin and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/v0gar-w9v18", "eprint_id": 81842, "eprint_status": "archive", "datestamp": "2023-08-19 04:50:52", "lastmod": "2026-03-09 23:05:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Monotonicity of the quantum linear programming bound", "ispublished": "pub", "full_text_status": "public", "keywords": "Quantum codes linear programming", "note": "\u00a9 1999 IEEE. \n\nManuscript received March 29, 1998; revised January 18, 1999.\n\n

Published - 00796387.pdf

Submitted - 9802070.pdf

", "abstract": "The most powerful technique known at present for bounding the size of quantum codes of prescribed minimum distance is the quantum linear programming bound. Unlike the classical linear programming bound, it is not immediately obvious that if the quantum linear programming constraints are satisfiable for dimension K, then the constraints can be satisfied for all lower dimensions. We show that the quantum linear programming bound is monotonic in this sense, and give an explicitly monotonic reformulation.", "date": "1999-11", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "45", "number": "7", "publisher": "IEEE", "pagerange": "2489-2492", "id_number": "CaltechAUTHORS:20170926-133944519", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-133944519", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.796387", "primary_object": { "basename": "00796387.pdf", "url": "https://authors.library.caltech.edu/records/v0gar-w9v18/files/00796387.pdf" }, "related_objects": [ { "basename": "9802070.pdf", "url": "https://authors.library.caltech.edu/records/v0gar-w9v18/files/9802070.pdf" } ], "pub_year": "1999", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/mdxs4-n7769", "eprint_id": 769, "eprint_status": "archive", "datestamp": "2023-08-22 14:06:11", "lastmod": "2026-03-18 00:04:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A new approach to inverse spectral theory, I. Fundamental formalism", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 Annals of Mathematics. \n\nReceived December 30, 1997. \n\nI thank P. Deift, I. Gel\u2032fand, R. Killip, and especially F. Gesztesy, for useful comments, and M. Ben-Artzi for the hospitality of Hebrew University where part of this work was done.\n\n

Published - 121061.pdf

Submitted - SIMaom99.pdf

", "abstract": "We present a new approach (distinct from Gel\u2032fand-Levitan) to the theorem of Borg-Marchenko that the m-function (equivalently, spectral measure) for a finite interval or half-line Schr\u00f6dinger operator determines the potential.\nOur approach is an analog of the continued fraction approach for the moment problem. We prove there is a representation for the m-function m(\u2212\u03ba^2) = -K-\u0283^b_0 A(\u0251)e^(-2\u0251k)d\u0251 + O(e^-(2b-\u0454)^k). A on [0, \u0251] is a function of q on [0, \u0251] and vice-versa. A key role is played by a differential equation that A obeys after allowing x-dependence: \u2202A/\u2202x = \u2202A/\u2202\u0251 + \u0283^\u0251_0 a(\u03b2X)A(\u0251 - \u03b2,x) d\u03b2.\nAmong our new results are necessary and sufficient conditions on the m-functions for potentials q1 and q2 for q1 to equal q2 on [0, \u0251].", "date": "1999-11", "date_type": "published", "publication": "Annals of Mathematics", "volume": "150", "number": "3", "publisher": "Annals of Mathematics", "pagerange": "1029-1057", "id_number": "CaltechAUTHORS:SIMaom99", "issn": "1012-2443", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMaom99", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.2307/121061", "primary_object": { "basename": "121061.pdf", "url": "https://authors.library.caltech.edu/records/mdxs4-n7769/files/121061.pdf" }, "related_objects": [ { "basename": "SIMaom99.pdf", "url": "https://authors.library.caltech.edu/records/mdxs4-n7769/files/SIMaom99.pdf" } ], "pub_year": "1999", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/sz3hm-kp246", "eprint_id": 81850, "eprint_status": "archive", "datestamp": "2023-08-19 04:50:58", "lastmod": "2026-03-09 23:04:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Quantum shadow enumerators", "ispublished": "pub", "full_text_status": "public", "keywords": "Linear programming, quantum error-correcting codes, shadow, upper bounds", "note": "\u00a9 1999 IEEE. \n\nManuscript received November 20, 1996; revised January 12, 1999. \n\nThe author wish to thank P. Shor and N. Sloane for many helpful discussions.\n\n

Published - 00796376.pdf

Submitted - 9611001.pdf

", "abstract": "In a previous paper, Shor and Laflamme (see Phys. Rev. Lett., vol.78, p.1600-02, 1997) define two \"weight enumerators\" for quantum error-correcting codes, connected by a MacWilliams (1977) transform, and use them to give a linear-programming bound for quantum codes. We extend their work by introducing another enumerator, based on the classical theory of shadow codes, that tightens their bounds significantly. In particular, nearly all of the codes known to be optimal among additive quantum codes (codes derived from orthogonal geometry) can be shown to be optimal among all quantum codes. We also use the shadow machinery to extend a bound on additive codes to general codes, obtaining as a consequence that any code of length, can correct at most [(n+1)/6] errors.", "date": "1999-11", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "45", "number": "7", "publisher": "IEEE", "pagerange": "2361-2366", "id_number": "CaltechAUTHORS:20170926-145724451", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-145724451", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.796376", "primary_object": { "basename": "00796376.pdf", "url": "https://authors.library.caltech.edu/records/sz3hm-kp246/files/00796376.pdf" }, "related_objects": [ { "basename": "9611001.pdf", "url": "https://authors.library.caltech.edu/records/sz3hm-kp246/files/9611001.pdf" } ], "pub_year": "1999", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/bscs2-sjw02", "eprint_id": 79074, "eprint_status": "archive", "datestamp": "2023-08-19 04:50:46", "lastmod": "2026-04-16 15:19:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Mathai-V", "name": { "family": "Mathai", "given": "Varghese" } } ] }, "title": "Twisted index theory on good orbifolds, I: noncommutative Bloch theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 World Scientific Publishing Co Pte Ltd. \n\nReceived: 20 April 1999. \n\nThe first author is partially supported by NSF grant DMS-9802480. Research by the second author is supported by the Australian Research Council.\n\n

Submitted - 9911102.pdf

", "abstract": "We study the twisted index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant under a projective action of the orbifold fundamental group. We apply these results to obtain qualitative results on real and complex hyperbolic spaces in two and four dimensions, related to generalizations of the Bethe\u2013Sommerfeld conjecture and the Ten Martini Problem, on the spectrum of self adjoint elliptic operators which are invariant under a projective action of a discrete cocompact group.", "date": "1999-11", "date_type": "published", "publication": "Communications in Contemporary Mathematics", "volume": "1", "number": "4", "publisher": "World Scientific Publishing", "pagerange": "553-587", "id_number": "CaltechAUTHORS:20170713-095029363", "issn": "0219-1997", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170713-095029363", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9802480" }, { "agency": "Australian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0219199799000213", "primary_object": { "basename": "9911102.pdf", "url": "https://authors.library.caltech.edu/records/bscs2-sjw02/files/9911102.pdf" }, "pub_year": "1999", "author_list": "Marcolli, Matilde and Mathai, Varghese" }, { "id": "https://authors.library.caltech.edu/records/2kmtb-b0r70", "eprint_id": 12116, "eprint_status": "archive", "datestamp": "2023-08-22 14:01:38", "lastmod": "2026-04-16 15:16:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gremm-M", "name": { "family": "Gremm", "given": "Martin" }, "orcid": "0000-0002-5324-3482" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "N = 1 theories, T-duality, and AdS/CFT correspondence", "ispublished": "pub", "full_text_status": "public", "keywords": "1/N Expansion; D-branes; Brane Dynamics in Gauge Theories; Supersymmetry and Duality", "note": "\u00a9 1999 SISSA. \n\nReceived 14 June 1999, accepted for publication 2 July 1999. Published 9 September 1999. \n\nIt is a pleasure to thank O. Aharony, E. Gimon, J. Maldacena, G. Moore, E. Katz, and E. Witten for helpful discussions. M.G. would like to thank the Institute for Advanced Study for hospitality while this work was in progress. The work of M.G was supported in part by DOE grants #DF-FC02-94ER40818 and #DE-FC-02-91ER40671, while that of A.K. by DOE grant #DE-FG02-90ER40542.\n\n

Published - GREjhep99a.pdf

", "abstract": "We construct an Script N = 1 superconformal field theory using branes of type IIA string theory. The IIA construction is related via T-duality to a IIB configuration with 3-branes in a background generated by two intersecting O7-planes and 7-branes. The IIB background can be viewed as a local piece of an F-theory compactification previously studied by Sen in connection with the Gimon-Polchinski orientifold. We discuss the deformations of the IIA and IIB constructions and describe a new supersymmetric configuration with curving D6-branes. Starting from the IIB description we find the supergravity dual of the large N field theory and discuss the matching of operators and KK states. The matching of non-chiral primaries exhibits some interesting new features. We also discuss a relevant deformation of the field theory under which it flows to a line of strongly coupled Script N = 1 fixed points in the infrared. For these fixed points we find a partial supergravity description.", "date": "1999-09-09", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1999", "number": "07", "publisher": "Springer", "pagerange": "Art. No.005", "id_number": "CaltechAUTHORS:GREjhep99a", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GREjhep99a", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DF-FC02-94ER40818" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FC02-91ER40671" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1999/07/005", "primary_object": { "basename": "GREjhep99a.pdf", "url": "https://authors.library.caltech.edu/records/2kmtb-b0r70/files/GREjhep99a.pdf" }, "pub_year": "1999", "author_list": "Gremm, Martin and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/js205-g9q18", "eprint_id": 81849, "eprint_status": "archive", "datestamp": "2023-08-19 04:41:08", "lastmod": "2026-03-09 23:04:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Nonbinary quantum codes", "ispublished": "pub", "full_text_status": "public", "keywords": "Finite fields, quantum codes, symplectic", "note": "\u00a9 1999 IEEE. \n\nManuscript received March 25, 1997; revised February 1, 1999.\n\n

Published - 00782103.pdf

Submitted - 9703048.pdf

", "abstract": "We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than two states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional global symmetries. From this standpoint, the analogs of Calderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special cases of the same construction. This allows us to construct families of quantum codes from certain codes over number fields; in particular, we get analogs of quadratic residue codes, including a single-error-correcting code encoding one letter in five, for any alphabet size. We also consider the problem of fault-tolerant computation through such codes, generalizing ideas of Gottesman (see Phys. Rev. A, vol.57, no.1, p127-37, 1998).", "date": "1999-09", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "45", "number": "6", "publisher": "IEEE", "pagerange": "1827-1832", "id_number": "CaltechAUTHORS:20170926-145137075", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-145137075", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.782103", "primary_object": { "basename": "00782103.pdf", "url": "https://authors.library.caltech.edu/records/js205-g9q18/files/00782103.pdf" }, "related_objects": [ { "basename": "9703048.pdf", "url": "https://authors.library.caltech.edu/records/js205-g9q18/files/9703048.pdf" } ], "pub_year": "1999", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/eq3p5-kqv83", "eprint_id": 104417, "eprint_status": "archive", "datestamp": "2023-08-22 13:51:59", "lastmod": "2026-04-17 00:58:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Brouwer-A-E", "name": { "family": "Brouwer", "given": "A. E." } }, { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "R. M." } }, { "id": "Xiang-Qing", "name": { "family": "Xiang", "given": "Qing" } } ] }, "title": "Cyclotomy and Strongly Regular Graphs", "ispublished": "pub", "full_text_status": "restricted", "keywords": "cyclotomy; Gauss sum; strongly regular graph", "note": "\u00a9 1999 Kluwer Academic Publishers. \n\nReceived July 10, 1997. \n\nPartially supported by NSA grant MDA 904-97-0104.", "abstract": "We consider strongly regular graphs defined on a finite field by taking the union of some cyclotomic classes as difference set. Several new examples are found.", "date": "1999-07", "date_type": "published", "publication": "Journal of Algebraic Combinatorics", "volume": "10", "number": "1", "publisher": "Springer", "pagerange": "25-28", "id_number": "CaltechAUTHORS:20200716-154839094", "issn": "0925-9899", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200716-154839094", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "National Security Agency", "grant_number": "MDA 904-97-0104" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/a:1018620002339", "pub_year": "1999", "author_list": "Brouwer, A. E.; Wilson, R. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/yw7zg-jrn74", "eprint_id": 38629, "eprint_status": "archive", "datestamp": "2023-08-19 04:23:33", "lastmod": "2026-04-17 03:21:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "New Directions in Descriptive Set Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 Association for Symbolic Logic. Received October 11, 1998; revised April 14, 1999. This article is based on the G\u00f6del Lecture given at the meeting of the Association for\nSymbolic Logic at Toronto in April 1998. Research and preparation for this paper were supported in part by NSF Grant DMS 96-19880.\n\n

Published - 421088.pdf

", "abstract": "I will start with a quick definition of descriptive set theory: It is the study of the structure of definable sets and functions in separable completely metrizable spaces. Such spaces are usually called Polish spaces. Typical\nexamples are R^n, C^n, (separable) Hilbert space and more generally all separable Banach spaces, the Cantor space 2^N, the Baire space N^N, the infinite symmetric group S_\u221e, the unitary group (of the Hilbert space), the group of\nmeasure preserving transformations of the unit interval, etc.", "date": "1999-06", "date_type": "published", "publication": "Bulletin of Symbolic Logic", "volume": "5", "number": "2", "publisher": "Association for Symbolic Logic", "pagerange": "161-174", "id_number": "CaltechAUTHORS:20130522-095020744", "issn": "1079-8986", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-095020744", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 96-19880" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/421088", "primary_object": { "basename": "421088.pdf", "url": "https://authors.library.caltech.edu/records/yw7zg-jrn74/files/421088.pdf" }, "pub_year": "1999", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/0m820-5k443", "eprint_id": 67062, "eprint_status": "archive", "datestamp": "2023-08-19 04:24:32", "lastmod": "2026-04-17 03:33:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cherkis-S-A", "name": { "family": "Cherkis", "given": "Sergey A." }, "orcid": "0000-0002-0785-0126" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Singular Monopoles and Gravitational Instantons", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 Springer-Verlag. \n\nReceived: 29 May 1998. Accepted: 12 January 1999. \n\nCommunicated by G. Felder. \n\nResearch supported in part by DOE grant DE-FG03-92-ER40701. \n\nResearch supported in part by DOE grant DE-FG02-90-ER40542.\n\n

Submitted - 9803160.pdf

", "abstract": "We model A_k and D_k asymptotically locally flat gravitational instantons on the moduli spaces of solutions of U(2) Bogomolny equations with prescribed singularities. We study these moduli spaces using Ward correspondence and find their twistor description. This enables us to write down the K\u00e4hler potential for A_k and D_k gravitational instantons in a relatively explicit form.", "date": "1999-06", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "203", "number": "3", "publisher": "Springer", "pagerange": "713-728", "id_number": "CaltechAUTHORS:20160513-085204975", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-085204975", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s002200050632", "primary_object": { "basename": "9803160.pdf", "url": "https://authors.library.caltech.edu/records/0m820-5k443/files/9803160.pdf" }, "pub_year": "1999", "author_list": "Cherkis, Sergey A. and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/6e45j-5hw06", "eprint_id": 83014, "eprint_status": "archive", "datestamp": "2023-08-19 04:22:54", "lastmod": "2026-04-16 13:59:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Optimal self-dual codes over \u2124_4", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Classification optimal self-dual Z4, code", "note": "\u00a9 1999 Elsevier Science B.V. \n\nReceived 17 November 1997, Revised 14 August 1998, Accepted 8 September 1998, Available online 7 September 1999.", "abstract": "The optimal minimal Euclidean norm of self-dual codes over \u2124_4 is known through length 24; the purpose of the present note is to determine the optimal minimal Hamming and Lee weights in this range. In the process, we classify all Lee-optimal codes of length 18, 21, 23, and 24. In particular, we find a total of 13 inequivalent codes with the same symmetrized weight enumerator as the Hensel-lifted Golay code.", "date": "1999-05-28", "date_type": "published", "publication": "Discrete Mathematics", "volume": "203", "number": "1-3", "publisher": "Elsevier", "pagerange": "215-228", "id_number": "CaltechAUTHORS:20171107-074528830", "issn": "0012-365X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171107-074528830", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0012-365X(98)00358-6", "pub_year": "1999", "author_list": "Rains, Eric" }, { "id": "https://authors.library.caltech.edu/records/4s90x-zck31", "eprint_id": 2983, "eprint_status": "archive", "datestamp": "2023-08-22 13:43:34", "lastmod": "2026-04-17 03:02:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cs\u00e1ki-C", "name": { "family": "Cs\u00e1ki", "given": "Csaba" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } }, { "id": "Terning-J", "name": { "family": "Terning", "given": "John" } } ] }, "title": "Glueball mass spectrum from supergravity", "ispublished": "pub", "full_text_status": "public", "keywords": "p-branes; D-branes", "note": "\u00a9 1999 IOP Publishing. \n\nReceived 4 November 1998, accepted for publication 14 January 1999. Published 6 April 1999. \n\nWe would like to thank M. Chanowitz, D. Gross, A. Hashimoto, C. Morningstar, S. Sharpe and Y. Takei for discussions and communications. We also thank Harlan Robins and Jonathan Tannenhauser, who participated in an early stage of this project, for discussions. H.O. and Y.O. thank the Institute for Theoretical Physics at Santa Barbara for its hospitality. This work was supported in part by the NSF grant PHY-95-14797 and in part the DOE grant DE-AC03-76SF00098. In addition, H.O. and Y.O. are supported by the NSF grant PHY-94-07194 through the ITP. C.C. is a research fellow of the Miller Institute for Basic Research in Science.\n\n

Published - CSAjhep99.pdf

Submitted - 9806021.pdf

", "abstract": "We calculate the spectrum of glueball masses in non-supersymmetric Yang-Mills theory in three and four dimensions, based on a conjectured duality between supergravity and large N gauge theories. The glueball masses are obtained by solving supergravity wave equations in a black hole geometry. We find that the mass ratios are in good numerical agreement with the available lattice data. We also compute the leading (g^2_(YM)N)^(\u22121) corrections to the glueball masses, by taking into account stringy corrections to the supergravity action and to the black hole metric. We find that the corrections to the masses are negative and of order (g^2_(YM)N)^(\u22123/2). Thus for a fixed ultraviolet cutoff the masses decrease as we decrease the 't Hooft coupling, in accordance with our expectation about the continuum limit of the gauge theories.", "date": "1999-04-21", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1999", "number": "1", "publisher": "Springer", "pagerange": "Art. No. 017", "id_number": "CaltechAUTHORS:CSAjhep99", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CSAjhep99", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-94-07194" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1999/01/017", "primary_object": { "basename": "9806021.pdf", "url": "https://authors.library.caltech.edu/records/4s90x-zck31/files/9806021.pdf" }, "related_objects": [ { "basename": "CSAjhep99.pdf", "url": "https://authors.library.caltech.edu/records/4s90x-zck31/files/CSAjhep99.pdf" } ], "pub_year": "1999", "author_list": "Cs\u00e1ki, Csaba; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/j9tn4-95w04", "eprint_id": 67063, "eprint_status": "archive", "datestamp": "2023-08-22 13:43:28", "lastmod": "2026-04-17 02:10:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "New N = 2 superconformal field theories from M/F-theory orbifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Gauge theory; M-theory; F-theory", "note": "\u00a9 1999 Elsevier B.V. \n\nReceived 13 November 1998, Accepted 7 January 1999, Available online 1 July 1999. \n\nThe authors wish to thank O. Aharony, M. Berkooz, and E. Witten for helpful discussions. The work of S.G. was supported in part by NSF grant PHY-9802484, RFBR grant No 98-02-16575, and Russian President's grant No 96-15-96939. The work of A.K. was supported in part by DOE grant DE-FG02-90-ER40542.\n\n

Submitted - 9808175.pdf

", "abstract": "We consider M-theory on (T^2 \u00d7 R^2)/Zn with M5-branes wrapped on R^2 One can probe this background with M5-branes wrapped on T2. The theories on the probes provide many new examples of N = 2 field theories without Lagrangian description. All these theories have Coulomb branches, and we find the corresponding Seiberg-Witten curves. The exact solution is encoded in a Hitchin system on an orbifolded torus with punctures. The theories we consider also arise from D3 probes in F-theory on K3 \u00d7 K3 orbifolds. Interestingly, the relevant F-theory background has frozen Z_n singularities which are analogous to frozen Z_2 singularities in Type I string theory. We use the F-theory description to find supergravity duals of the probe SCFT's in the large-N limit and compute the spectrum of relevant and marginal operators. We also explain how the decoupling of U(1) factors is manifested in the supergravity description.", "date": "1999-04-19", "date_type": "published", "publication": "Nuclear Physics B", "volume": "545", "number": "1-3", "publisher": "Elsevier", "pagerange": "283-308", "id_number": "CaltechAUTHORS:20160513-090539528", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-090539528", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9802484" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(99)00008-5", "primary_object": { "basename": "9808175.pdf", "url": "https://authors.library.caltech.edu/records/j9tn4-95w04/files/9808175.pdf" }, "pub_year": "1999", "author_list": "Gukov, Sergei and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/0k5td-q9778", "eprint_id": 2060, "eprint_status": "archive", "datestamp": "2023-08-22 13:40:21", "lastmod": "2026-04-16 15:23:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Strassler-M-J", "name": { "family": "Strassler", "given": "Matthew J." } } ] }, "title": "On mirror symmetry in three dimensional Abelian gauge theories", "ispublished": "pub", "full_text_status": "public", "keywords": "field theories in lower dimensions; duality in gauge field theories; Chern-Simons theories; supersymmetry and duality", "note": "Copyright \u00a9 Institute of Physics and IOP Publishing Limited 1999. \n\nReceived 1 April 1999, accepted for publication 23 April 1999. Published 6 August 1999. \n\nWe thank M. Berkooz, S.J. Gates, K. Intriligator, N. Seiberg, F. Wilczek and E. Witten for discussions. The work of A.K. was supported by Department of Energy grant DE-FG02-90ER40542; that of M.J.S. was supported in part by National Science Foundation grant NSF PHY-9513835 and by the W.M. Keck Foundation.\n\n

Published - KAPjhep99.pdf

", "abstract": "We present an identity relating the partition function of N = 4 supersymmetric QED to that of its dual under mirror symmetry. The identity is a generalized Fourier transform. Many known properties of abelian theories can be derived from this formula, including the mirror transforms for more general gauge and matter content. We show that N = 3 Chern-Simons QED and N = 4 QED with BF-type couplings are conformal field theories with exactly marginal couplings. Mirror symmetry acts on these theories as strong-weak coupling duality. After identifying the mirror of the gauge coupling (sometimes called the \"magnetic coupling\") we construct a theory which is exactly mirror - at all scales - to N = 4 SQED. We also study vortex-creation operators in the large N-f limit.", "date": "1999-04", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1999", "number": "4", "publisher": "Springer", "pagerange": "Art. No. 021", "id_number": "CaltechAUTHORS:KAPjhep99", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep99", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "W. M. Keck Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1999/04/021", "primary_object": { "basename": "KAPjhep99.pdf", "url": "https://authors.library.caltech.edu/records/0k5td-q9778/files/KAPjhep99.pdf" }, "pub_year": "1999", "author_list": "Kapustin, Anton and Strassler, Matthew J." }, { "id": "https://authors.library.caltech.edu/records/asenj-pac85", "eprint_id": 81983, "eprint_status": "archive", "datestamp": "2023-08-22 13:36:54", "lastmod": "2026-04-17 02:55:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Calderbank-A-R", "name": { "family": "Calderbank", "given": "A. R." } }, { "id": "Hardin-R-H", "name": { "family": "Hardin", "given": "R. H." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Shor-P-W", "name": { "family": "Shor", "given": "P. W." } }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces", "ispublished": "pub", "full_text_status": "public", "keywords": "Grassmannian packings; quantum computing; orthogonal geometry; Clifford group", "note": "\u00a9 1999 Kluwer Academic Publishers. \n\nReceived February 14, 1997.\n\n

Submitted - 0208002.pdf

", "abstract": "By using totally isotropic subspaces in an orthogonal space \u03a9+ (2i, 2), several infinite families of packings of 2^k-dimensional subspaces of real 2i-dimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with Barnes-Wall lattices, Kerdock sets and quantum-error-correcting codes.", "date": "1999-03", "date_type": "published", "publication": "Journal of Algebraic Combinatorics", "volume": "9", "number": "2", "publisher": "Springer", "pagerange": "129-140", "id_number": "CaltechAUTHORS:20171003-094225780", "issn": "0925-9899", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-094225780", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/A:1018673825179", "primary_object": { "basename": "0208002.pdf", "url": "https://authors.library.caltech.edu/records/asenj-pac85/files/0208002.pdf" }, "pub_year": "1999", "author_list": "Calderbank, A. R.; Hardin, R. H.; et al." }, { "id": "https://authors.library.caltech.edu/records/yqbe0-22922", "eprint_id": 81828, "eprint_status": "archive", "datestamp": "2023-08-19 03:59:22", "lastmod": "2026-04-17 01:22:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bennett-C-H", "name": { "family": "Bennett", "given": "Charles H." } }, { "id": "DiVincenzo-D-P", "name": { "family": "DiVincenzo", "given": "David P." } }, { "id": "Fuchs-C-A", "name": { "family": "Fuchs", "given": "Christopher A." } }, { "id": "Mor-T", "name": { "family": "Mor", "given": "Tal" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric" }, "orcid": "0000-0002-9915-0919" }, { "id": "Shor-P-W", "name": { "family": "Shor", "given": "Peter W." } }, { "id": "Smolin-J-A", "name": { "family": "Smolin", "given": "John A." } }, { "id": "Wootters-W-K", "name": { "family": "Wootters", "given": "William K." } } ] }, "title": "Quantum nonlocality without entanglement", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 The American Physical Society. \n\nReceived 17 June 1998. \n\nPart of this work was completed during the Elsag-Bailey\u2014ISI Foundation research meeting on quantum computation. C.A.F. has been supported by the Lee A. DuBridge Foundation and by DARPA through the Quantum Information and Computing (QUIC) Institute, administered by the U.S. Army Research Office. We thank Micha\u0142 Horodecki, Peter H\u00f8yer, N. David Mermin, Sandu Popescu, Barbara Terhal, and Reinhard Werner for very helpful discussions.\n\n

Published - PhysRevA.59.1070.pdf

Submitted - 9804053.pdf

", "abstract": "We exhibit an orthogonal set of product states of two three-state particles that nevertheless cannot be reliably distinguished by a pair of separated observers ignorant of which of the states has been presented to them, even if the observers are allowed any sequence of local operations and classical communication between the separate observers. It is proved that there is a finite gap between the mutual information obtainable by a joint measurement on these states and a measurement in which only local actions are permitted. This result implies the existence of separable superoperators that cannot be implemented locally. A set of states are found involving three two-state particles that also appear to be nonmeasurable locally. These and other multipartite states are classified according to the entropy and entanglement costs of preparing and measuring them by local operations.", "date": "1999-02", "date_type": "published", "publication": "Physical Review A", "volume": "59", "number": "2", "publisher": "American Physical Society", "pagerange": "1070-1091", "id_number": "CaltechAUTHORS:20170926-092107073", "issn": "1050-2947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-092107073", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Lee A. DuBridge Foundation" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Army Research Office (ARO)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevA.59.1070", "primary_object": { "basename": "9804053.pdf", "url": "https://authors.library.caltech.edu/records/yqbe0-22922/files/9804053.pdf" }, "related_objects": [ { "basename": "PhysRevA.59.1070.pdf", "url": "https://authors.library.caltech.edu/records/yqbe0-22922/files/PhysRevA.59.1070.pdf" } ], "pub_year": "1999", "author_list": "Bennett, Charles H.; DiVincenzo, David P.; et al." }, { "id": "https://authors.library.caltech.edu/records/t9yha-tww91", "eprint_id": 81189, "eprint_status": "archive", "datestamp": "2023-08-19 03:57:59", "lastmod": "2026-04-16 14:31:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kiselev-A", "name": { "family": "Kiselev", "given": "Alexander" } }, { "id": "Remling-C", "name": { "family": "Remling", "given": "Christian" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Effective Perturbation Methods for One-Dimensional Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1999 Academic Press. \n\nReceived 22 September 1997, Revised 29 May 1998. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material. \n\nResearch of A.K. done at MSRI was supported in part by NSF grant DMS-9022140. C.R. is grateful for the hospitality of Caltech, where most of this work was done. He also thanks the Deutsche Forschungsgemeinschaft for financial support.", "abstract": "[No abstract]", "date": "1999-01-20", "date_type": "published", "publication": "Journal of Differential Equations", "volume": "151", "number": "2", "publisher": "Elsevier", "pagerange": "290-312", "id_number": "CaltechAUTHORS:20170906-131540684", "issn": "0022-0396", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170906-131540684", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" }, { "agency": "NSF", "grant_number": "DMS-9022140" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jdeq.1998.3514", "pub_year": "1999", "author_list": "Kiselev, Alexander; Remling, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/mbe97-y1b24", "eprint_id": 38554, "eprint_status": "archive", "datestamp": "2023-08-19 03:57:15", "lastmod": "2026-04-17 01:18:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Solecki-S", "name": { "family": "Solecki", "given": "S." } }, { "id": "Todorcevic-S", "name": { "family": "Todorcevic", "given": "S." } } ] }, "title": "Borel Chromatic Numbers", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1999 by Academic Press. Received November 16, 1996; accepted April 30, 1998. The author acknowledges the support of the Mathematics Department at Caltech during his visits in January 1992 and 1995, the NSERC of Canada, and the Science Foundation of Serbia. Research partially supported by NSF Grant DMS-9317509. We thank A. Ditzen for allowing us to include the joint result 1.1 and A. Louveau for 8.2.", "abstract": "We study in this paper graph coloring problems in the context of descriptive set theory. We consider graphs G=(X, R), where the vertex set X is a standard Borel space (i.e., a complete separable metrizable space equipped with its \u03c3-algebra of Borel sets), and the edge relation R \u2286 X^2 is\n\"definable\", i.e., Borel, analytic, co-analytic, etc.\n\nA Borel n-coloring of such a graph, where 1\u2a7d n \u2a7d N_0 , is a Borel map c: X \u2192 Y with card(Y)=n, such\nthat xRy\u21d2c(x) \u2260 {c( y). If such a Borel coloring exists we define the Borel\nchromatic number of G, in symbols X_B(G), to be the smallest such n.\nOtherwise we say that G has uncountable Borel chromatic number, in symbols X_B(G) > N_0.", "date": "1999-01-15", "date_type": "published", "publication": "Advances in Mathematics", "volume": "141", "number": "1", "publisher": "Elsevier", "pagerange": "1-44", "id_number": "CaltechAUTHORS:20130517-100529842", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-100529842", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" }, { "agency": "Caltech Mathematics Department" }, { "agency": "NSERC (Canada)" }, { "agency": "Science Foundation of Serbia" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1006/aima.1998.1771", "pub_year": "1999", "author_list": "Kechris, A. S.; Solecki, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/nw2rj-89e55", "eprint_id": 81858, "eprint_status": "archive", "datestamp": "2023-09-28 19:42:44", "lastmod": "2026-03-09 22:47:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." }, "orcid": "0000-0001-7386-5222" } ] }, "title": "On Cayley's Enumeration of Alkanes (or 4-Valent Trees)", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 The Authors. \n\nReceived Aug. 13, 1998; published in Journal of Integer Sequences Jan. 10, 1999.\n\n

Published - OnCayleysEnumerationAlkanes4-ValentTrees.pdf

", "abstract": "Cayley's 1875 enumerations of centered and bicentered alkanes (unlabeled trees of valency at most 4) are corrected and extended -- possibly for the first time in 124 years.", "date": "1999-01-10", "date_type": "published", "publication": "Journal of Integer Sequences", "volume": "2", "publisher": "Journal of Integer Sequences", "pagerange": "Art. No. 99.1.1", "id_number": "CaltechAUTHORS:20170926-154926203", "issn": "1530-7638", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-154926203", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0207176", "primary_object": { "basename": "OnCayleysEnumerationAlkanes4-ValentTrees.pdf", "url": "https://authors.library.caltech.edu/records/nw2rj-89e55/files/OnCayleysEnumerationAlkanes4-ValentTrees.pdf" }, "pub_year": "1999", "author_list": "Rains, E. M. and Sloane, N. J. A." }, { "id": "https://authors.library.caltech.edu/records/n6djb-zzw29", "eprint_id": 85379, "eprint_status": "archive", "datestamp": "2023-08-22 13:29:20", "lastmod": "2026-04-17 03:44:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Continuous Spectrum; Transfer Matrice", "note": "\u00a9 1999 Springer-Verlag Berlin Heidelberg.\n\nPublished online: 14 October 1998.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.\n\n

Submitted - 9907023.pdf

", "abstract": "No Abstract.", "date": "1999-01", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "135", "number": "2", "publisher": "Springer", "pagerange": "329-367", "id_number": "CaltechAUTHORS:20180320-104319293", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180320-104319293", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s002220050288", "primary_object": { "basename": "9907023.pdf", "url": "https://authors.library.caltech.edu/records/n6djb-zzw29/files/9907023.pdf" }, "pub_year": "1999", "author_list": "Last, Yoram and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/aw7y0-cay81", "eprint_id": 81848, "eprint_status": "archive", "datestamp": "2023-08-19 03:52:08", "lastmod": "2026-03-09 23:07:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Quantum codes of minimum distance two", "ispublished": "pub", "full_text_status": "public", "keywords": "Automorphisms, classification, quantum codes, uniqueness", "note": "\u00a9 1999 IEEE. \n\nManuscript received May 26, 1997; revised March 4, 1998. \n\nThe author would like to thank A. R. Calderbank, P. Shor, and N. Sloane for many helpful conversations, as well as the anonymous referees for helpful comments.\n\n

Published - 00746807.pdf

Submitted - 9704043.pdf

", "abstract": "It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With this in mind, we present a number of results on codes of minimum distance 2. We first compute the linear programming bound on the dimension of such a code, then show that this bound can only be attained when the code either is of even length, or is of length 3 or 5. We next consider questions of uniqueness, showing that the optimal code of length 2 or 1 is unique (implying that the well-known one-qubit-in-five single-error correcting code is unique), and presenting nonadditive optimal codes of all greater even lengths. Finally, we compute the full automorphism group of the more important distance 2 codes, allowing us to determine the full automorphism group of any GF(4)-linear code.", "date": "1999-01", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "45", "number": "1", "publisher": "IEEE", "pagerange": "266-271", "id_number": "CaltechAUTHORS:20170926-144218757", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-144218757", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.746807", "primary_object": { "basename": "00746807.pdf", "url": "https://authors.library.caltech.edu/records/aw7y0-cay81/files/00746807.pdf" }, "related_objects": [ { "basename": "9704043.pdf", "url": "https://authors.library.caltech.edu/records/aw7y0-cay81/files/9704043.pdf" } ], "pub_year": "1999", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/tzt67-td904", "eprint_id": 66991, "eprint_status": "archive", "datestamp": "2023-08-22 13:20:16", "lastmod": "2026-04-16 14:22:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Diaconescu-D-E", "name": { "family": "Diaconescu", "given": "Duiliu-Emanuel" } }, { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Three-dimensional N = 2 gauge theories and degenerations of Calabi-Yau four-folds", "ispublished": "pub", "full_text_status": "public", "keywords": "Four-folds; Gauge theories; Degenerations", "note": "\u00a9 1998 Elsevier B.V. \n\nWe are very grateful to Cumrun Vafa and Edward Witten for collaboration and valuable suggestions and to Liviu Nicolaescu for mathematical assistance. We would also like to thank Ofer Aharony, Tom Banks, Jan de Boer, Michael Douglas, Rami Entin, Ori Ganor, Jaume Gomis, Brian Greene, Barak Kol, Wolfgang Lerche, Nathan Seiberg and Piljin Yi for very helpful discussions and correspondence. S.G also would like to thank Laboratoire de Physique Th\u00e9orique et Hautes Energies where a part of this work was done, and especially L. Baulieu for kind hospitality and the support of the CNRS grant. The research of S. G. was supported in part by Merit Fellowship in Natural Sciences and Mathematics, grant RFBR-96-15-96939 and CNRS Foundation.\n\n

Submitted - 9804059.pdf

", "abstract": "Three-dimensional N = 2 gauge theories with arbitrary gauge group and fundamental flavors are engineered from degenerations of Calabi-Yau four-folds. We show how Coulomb and Higgs branches emerge in the geometric picture. The analysis of instanton generated superpotentials unravels interesting aspects of the five-brane effective action in M-theory.", "date": "1998-12-07", "date_type": "published", "publication": "Nuclear Physics B", "volume": "535", "number": "1-2", "publisher": "Elsevier", "pagerange": "171-196", "id_number": "CaltechAUTHORS:20160511-111658565", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-111658565", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Merit Fellowship in Natural Sciences and Mathematics" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "Centre National de la Recherche Scientifique (CNRS)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(98)00597-5", "primary_object": { "basename": "9804059.pdf", "url": "https://authors.library.caltech.edu/records/tzt67-td904/files/9804059.pdf" }, "pub_year": "1998", "author_list": "Diaconescu, Duiliu-Emanuel and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/75879-j9y58", "eprint_id": 15979, "eprint_status": "archive", "datestamp": "2023-08-22 13:18:35", "lastmod": "2026-04-17 02:04:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Robins-H", "name": { "family": "Robins", "given": "Harlan" } }, { "id": "Tannenhauser-J", "name": { "family": "Tannenhauser", "given": "Jonathan" } } ] }, "title": "String theory on AdS_3", "ispublished": "pub", "full_text_status": "public", "keywords": "p-branes; Black Holes in String Theory", "note": "\u00a9 1998 SISSA. \n\nReceived 22 December 1998, accepted for publication 27 December 1998. Published 23 February 1999. \n\nWe would like to thank K. Bardak\u00e7i for discussions and J. Teschner for useful correspondence. JdB would like to thank S. Shatashivili for collaboration at an earlier stage of this work. This work was supported in part by the NSF grant PHY-95-14797 and the DOE grant DE-AC03-76SF00098. \n\nE-print number: hep-th/9812046\n\n

Published - BOEjhep98.pdf

Submitted - 9812046.pdf

", "abstract": "It was shown by Brown and Henneaux that the classical theory of gravity on AdS_3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory on AdS_3. In this paper, we explore various aspects of string theory on AdS_3 and study the relation between these two works. We show how semi-classical properties of the string theory reproduce many features of the AdS/CFT duality. Furthermore, we examine how the Virasoro symmetry of Brown and Henneaux is realized in string theory, and show how it leads to the Virasoro Ward identities of the boundary CFT. The Virasoro generators of GKS emerge naturally in this analysis. Our work clarifies several aspects of the GKS construction: why the Brown-Henneaux Virasoro algebra can be realized on the first-quantized Hilbert space, to what extent the free-field approximation is valid, and why the Virasoro generators act on the string worldsheet localized near the boundary of AdS_3. On the other hand, we find that the way the central charge of the Virasoro algebra is generated is different from the mechanism proposed by GKS.", "date": "1998-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1998", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 026", "id_number": "CaltechAUTHORS:20090918-132530709", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20090918-132530709", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1998/12/026", "primary_object": { "basename": "9812046.pdf", "url": "https://authors.library.caltech.edu/records/75879-j9y58/files/9812046.pdf" }, "related_objects": [ { "basename": "BOEjhep98.pdf", "url": "https://authors.library.caltech.edu/records/75879-j9y58/files/BOEjhep98.pdf" } ], "pub_year": "1998", "author_list": "de Boer, Jan; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/rxaw9-91z03", "eprint_id": 81992, "eprint_status": "archive", "datestamp": "2023-08-19 03:36:04", "lastmod": "2026-04-16 14:55:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "The Shadow Theory of Modular and Unimodular Lattices", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Academic Press. \n\nReceived January 26, 1998; revised April 22, 1998. \n\nThe computer language Magma [6], [7], [8] has been helpful in studying particular lattices, testing for modularity, etc.\n\n

Submitted - 0207294.pdf

", "abstract": "It is shown that an n-dimensional unimodular lattice has minimal norm at most 2[n/24]+2, unless n=23 when the bound must be increased by 1. This result was previously known only for even unimodular lattices. Quebbemann had extended the bound for even unimodular lattices to strongly N-modular even lattices for N in {1, 2, 3, 5, 6, 7, 11, 14, 15, 23}, (*) and analogous bounds are established here for odd lattices satisfying certain technical conditions (which are trivial for N=1 and 2). For N>1 in (*), lattices meeting the new bound are constructed that are analogous to the \"shorter\" and \"odd\" Leech lattices. These include an odd associate of the 16-dimensional Barnes\u2013Wall lattice and shorter and odd associates of the Coxeter\u2013Todd lattice. A uniform construction is given for the (even) analogues of the Leech lattice, inspired by the fact that (*) is also the set of square-free orders of elements of the Mathieu group M_(23).", "date": "1998-12", "date_type": "published", "publication": "Journal of Number Theory", "volume": "73", "number": "2", "publisher": "Elsevier", "pagerange": "359-389", "id_number": "CaltechAUTHORS:20171003-105923947", "issn": "0022-314X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171003-105923947", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1006/jnth.1998.2306", "primary_object": { "basename": "0207294.pdf", "url": "https://authors.library.caltech.edu/records/rxaw9-91z03/files/0207294.pdf" }, "pub_year": "1998", "author_list": "Rains, E. M. and Sloane, N. J. A." }, { "id": "https://authors.library.caltech.edu/records/jpk1h-cwr62", "eprint_id": 2016, "eprint_status": "archive", "datestamp": "2023-08-22 13:18:15", "lastmod": "2026-04-16 14:41:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Rangamani-Mukund", "name": { "family": "Rangamani", "given": "Mukund" }, "orcid": "0000-0002-4336-1346" }, { "id": "Witten-E", "name": { "family": "Witten", "given": "Edward" }, "orcid": "0000-0002-7752-6073" } ] }, "title": "Dibaryons, branes, and strings in AdS orbifold models", "ispublished": "pub", "full_text_status": "public", "keywords": "Duality in Gauge Field Theories, Superstring Vacua, Brane Dynamics in Gauge Theories", "note": "\u00a9 Institute of Physics 1998 \n\nReceived 25 November 1998, accepted for publication 26 December 1998, Published 9 March 1999 \n\nIt is pleasure to thank to M. Krogh, S.N. Minwalla, and A. Mikhailov, for helpful discussions and N. Nekrasov for collaboration in an early stage of the project. The work of S.G. was supported in part by grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939. The work of E.W. is supported in part by NSF Grant PHY-9513835 and that of M.R. by NSF Grant PHY-9802484.\n\n

Published - GUKjhep98.pdf

", "abstract": "A generalization of the Maldacena conjecture asserts that Type IIB string theory on AdS5 \u00d7 S5/Bbb Z3 is equivalent to a certain supersymmetric SU(N)3 gauge theory with bifundamental matter. To test this assertion, we analyze the wrapped branes on S5/Bbb Z3 and their interpretation in terms of gauge theory. The wrapped branes are interpreted in some cases as baryons or dibaryons of the gauge theory and in other cases as strings around which there is a global monodromy. In order to successfully match the brane analysis with field theory, we must uncover some aspects of S-duality which are novel even in the case of four-dimensional free field theory.", "date": "1998-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1998", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 025", "id_number": "CaltechAUTHORS:GUKjhep98", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:GUKjhep98", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" }, { "agency": "NSF", "grant_number": "PHY-9513835" }, { "agency": "NSF", "grant_number": "PHY-9802484" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1998/12/025", "primary_object": { "basename": "GUKjhep98.pdf", "url": "https://authors.library.caltech.edu/records/jpk1h-cwr62/files/GUKjhep98.pdf" }, "pub_year": "1998", "author_list": "Gukov, Sergei; Rangamani, Mukund; et al." }, { "id": "https://authors.library.caltech.edu/records/3sxkq-xyh91", "eprint_id": 2102, "eprint_status": "archive", "datestamp": "2023-08-22 13:18:20", "lastmod": "2026-04-17 03:29:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "D-n quivers from branes", "ispublished": "pub", "full_text_status": "public", "keywords": "field theories in lower dimensions; D-branes; supersymmetry and duality; extended supersymmetry", "note": "Copyright \u00a9 Institute of Physics and IOP Publishing Limited 1998. \n\nReceived 31 August 1998, accepted for publication 15 December 1998. Published 9 February 1999. \n\nI am grateful to N. Seiberg and A. Sen for illuminating discussions and for reading a draft of this paper. I also wish to thank O. Aharony for useful comments on the manuscript.\n\n

Published - KAPjhep98.pdf

", "abstract": "D-branes can end on orbifold planes if the action of the orbifold group includes (-1) (FL). We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their worldvolume. We apply our results to gauge theories with eight supercharges in three and four dimensions. We explain how mirror symmetry for N = 4 d = 3 gauge theories with gauge group Sp(k) and matter in the antisymmetric tensor and fundamental representations follows from S-duality of IIB string theory. We argue that some of these theories have hidden Fayet-Iliopoulos deformations, not visible classically. We also study a class of finite N = 2 d = 4 theories (so-called D-n quiver theories) and find their exact solution. The integrable model corresponding to the exact solution is a Hitchin system on an orbifold Riemann surface. We also give a simple derivation of the S-duality group of these theories based on their relationship to SO(2n) instantons on R-2 x T-2.", "date": "1998-12", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1998", "number": "12", "publisher": "Springer", "pagerange": "Art. No. 015", "id_number": "CaltechAUTHORS:KAPjhep98", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjhep98", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1998/12/015", "primary_object": { "basename": "KAPjhep98.pdf", "url": "https://authors.library.caltech.edu/records/3sxkq-xyh91/files/KAPjhep98.pdf" }, "pub_year": "1998", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/7bkq1-p8q25", "eprint_id": 28539, "eprint_status": "archive", "datestamp": "2023-08-22 13:17:43", "lastmod": "2026-04-16 15:09:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Solution of N = 2 gauge theories via compactification to three dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Gauge theories; Integrable models", "note": "\u00a9 1998 Elsevier B.V. \n\nReceived 14 May 1998; Accepted 3 July 1998. Available online 10 February 1999. \n\nResearch supported in part by DOE grant DE-FG02-90-ER40542. I would like to thank S. Cherkis, A. Hanany, S. Sethi, A. Uranga, and E. Witten for useful discussions. I am also grateful to E. Witten for reading a preliminary draft of this paper.\n\n

Submitted - 9804069v1.pdf

", "abstract": "A number of N = 2 gauge theories can be realized by brane configurations in Type IIA string theory. One way of solving them involves lifting the brane configuration to M-theory. In this paper we present an alternative way of analyzing a subclass of these theories (elliptic models). We observe that upon compactification on a circle one can use a version of mirror symmetry to map the original brane configuration into one containing only D-branes. Simultaneously the Coulomb branch of the four-dimensional theory is mapped to the Higgs branch of a five-dimensional theory with three-dimensional impurities. The latter does not receive quantum corrections and can be analyzed exactly. The solution is naturally formulated in terms of an integrable system, which is a version of a Hitchin system on a punctured torus.", "date": "1998-11-23", "date_type": "published", "publication": "Nuclear Physics B", "volume": "534", "number": "1-2", "publisher": "Elsevier", "pagerange": "531-545", "id_number": "CaltechAUTHORS:20111220-132413324", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111220-132413324", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" } ] }, "other_numbering_system": { "items": [ { "id": "98/34", "name": "IASSNS-HEP" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(98)00520-3", "primary_object": { "basename": "9804069v1.pdf", "url": "https://authors.library.caltech.edu/records/7bkq1-p8q25/files/9804069v1.pdf" }, "pub_year": "1998", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/1sdxq-a0229", "eprint_id": 73067, "eprint_status": "archive", "datestamp": "2023-08-19 03:32:38", "lastmod": "2026-04-16 15:14:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gross-D-J", "name": { "family": "Gross", "given": "David J." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Aspects of large N gauge theory dynamics as seen by string theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 The American Physical Society. \n\nReceived 29 May 1998; published 8 October 1998. \n\nWe would like to thank Tom Banks, Gary Horowitz, Emil Martinec, Yaron Oz, John Schwarz and many other participants of ITP Program, Duality in String Theory, for useful discussions. The work of D.G. was supported in part by NSF grants NSF-PHY-94-07194 and NSF-PHY-97-22022. The work of H.O. was supported in part by NSF grant NSF-PHY-95-14797 and by DOE grant DE-AC03-76SF00098, and also by NSF grant NSF-PHY-94-07194.\n\n

Published - PhysRevD.58.106002.pdf

Submitted - 9805129.pdf

", "abstract": "In this paper we explore some of the features of large N supersymmetric and nonsupersymmetric gauge theories using Maldacena's duality conjectures. We show that the resulting strong coupling behavior of the gauge theories is consistent with our qualitative expectations of these theories. Some of these consistency checks are highly nontrivial and give additional evidence for the validity of the proposed dualities.", "date": "1998-11-15", "date_type": "published", "publication": "Physical Review D", "volume": "58", "number": "10", "publisher": "American Physical Society", "pagerange": "Art. No. 106002", "id_number": "CaltechAUTHORS:20161221-104619580", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-104619580", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-94-07194" }, { "agency": "NSF", "grant_number": "PHY-97-22022" }, { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevD.58.106002", "primary_object": { "basename": "9805129.pdf", "url": "https://authors.library.caltech.edu/records/1sdxq-a0229/files/9805129.pdf" }, "related_objects": [ { "basename": "PhysRevD.58.106002.pdf", "url": "https://authors.library.caltech.edu/records/1sdxq-a0229/files/PhysRevD.58.106002.pdf" } ], "pub_year": "1998", "author_list": "Gross, David J. and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/cwnxf-n9d39", "eprint_id": 83016, "eprint_status": "archive", "datestamp": "2023-08-19 03:30:07", "lastmod": "2026-04-16 13:37:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Normal limit theorems for symmetric random matrices", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1998 Springer-Verlag Berlin Heidelberg. \n\nReceived: 3 February 1998\u2009; \u200aRevised version: 11 June 1998. \n\nThe author would like to thank P. Diaconis for suggesting the problems of Theorem 3.2. The author would also like to thank the anonymous referee for pointing out a flaw in the convergence conditions in an earlier draft, as well as J. Lagarias for related helpful discussions, including the proof of Lemma 0.1.", "abstract": "Using the machinery of zonal polynomials, we examine the limiting behavior of random symmetric matrices invariant under conjugation by orthogonal matrices as the dimension tends to infinity. In particular, we give sufficient conditions for the distribution of a fixed submatrix to tend to a normal distribution. We also consider the problem of when the sequence of partial sums of the diagonal elements tends to a Brownian motion. Using these results, we show that if O_n is a uniform random n\u00d7n orthogonal matrix, then for any fixed k>0, the sequence of partial sums of the diagonal of O^k_n tends to a Brownian motion as n\u2192\u221e.", "date": "1998-11", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "112", "number": "3", "publisher": "Springer", "pagerange": "411-423", "id_number": "CaltechAUTHORS:20171107-075613066", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171107-075613066", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s004400050195", "pub_year": "1998", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/5pm0f-99670", "eprint_id": 1324, "eprint_status": "archive", "datestamp": "2023-08-22 13:13:54", "lastmod": "2026-04-17 00:56:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Skenderis-K", "name": { "family": "Skenderis", "given": "Kostas" } } ] }, "title": "On the field theory limit of D-instantons", "ispublished": "pub", "full_text_status": "public", "keywords": "p-branes, D-branes", "note": "Received 28 October 1998, accepted for publication 17 November 1998, Published 7 December 1998 \n\nWe would like to thank Michael Green for discussions. We also thank Tom Banks and Juan Maldacena for comments on the earlier version of this paper. We thank the theory division of CERN where this work was initiated for the hospitality. K.S. would also like to thank the Aspen Center for Physics and the Erwin Schr\u00f6dinger Institute in Vienna where part of this work was completed for their hospitality. The work of H.O. was supported in part by the NSF grant PHY-95-14797 and the DOE grant DEAC03-76SF00098. The research of K.S. is supported by the Netherlands Organization for Scientific Research (NWO). \n\nE-print number: hep-th/9810128 \nReport-no: UCB-PTH-98/49, LBNL-42387, SPIN-1998/1\n\n

Published - OOGjhep98.pdf

Submitted - 9810128.pdf

", "abstract": "We study the dilaton/axion configuration near D-instantons in type IIB superstring theory. In the field theory limit, the metric near the instantons becomes flat in the string frame as well as in the Einstein frame. In the large N limit, the string coupling constant becomes zero except near the origin. The supersymmetry of this configuration is analyzed. An implication of this result to the IIB Matrix Model is discussed.", "date": "1998-11", "date_type": "published", "publication": "Journal of High Energy Physics", "volume": "1998", "number": "11", "publisher": "Springer", "pagerange": "Art. no. 013", "id_number": "CaltechAUTHORS:OOGjhep98", "issn": "1126-6708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:OOGjhep98", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DEAC03-76SF00098" }, { "agency": "Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/1126-6708/1998/11/013", "primary_object": { "basename": "OOGjhep98.pdf", "url": "https://authors.library.caltech.edu/records/5pm0f-99670/files/OOGjhep98.pdf" }, "related_objects": [ { "basename": "9810128.pdf", "url": "https://authors.library.caltech.edu/records/5pm0f-99670/files/9810128.pdf" } ], "pub_year": "1998", "author_list": "Ooguri, Hirosi and Skenderis, Kostas" }, { "id": "https://authors.library.caltech.edu/records/yt2b9-haa17", "eprint_id": 72990, "eprint_status": "archive", "datestamp": "2023-08-19 03:29:33", "lastmod": "2026-04-16 14:02:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "M theory fivebrane and SQCD", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Elsevier. \n\nIt is my pleasure to thank the organizers of Strings '97 for their hospitality and for giving me the opportunity to present this work at the beautifully organized conference. I would like to thank Kentaro Hori and Yaron Oz for the collaboration on this work. I would also like to thank Cumrun Vafa for collaborations on related works and for useful discussions. \n\nThis research is supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098.\n\n

Submitted - 9709211.pdf

", "abstract": "A low energy effective theory of parallel D(irichlet) branes is a gauge theory with sixteen supercharges, but one can consider a web of brane to realize situations with reduced number of supersymmetry [1]. In this talk, I will discuss four-dimensional theories with N = 1 and 2 supersymmetry (i.e. four and eight supercharges). In the case of theories with N = 2 supersymmetry, the exact description of the Coulomb branch is given by reinterpreting the web of branes as a configuration of a single fivebrane in the IIA theory [2,3]. Recently we studied the case with N = 1 supersymmetry, and found that description in term of the fivebrane in M Theory captures strong coupling dynamics of the N = 1 gauge theory in four dimensions [4]. In particular, we found that the configuration of the fivebrane geometrically encodes information on the Affleck-Dine-Seiberg superpotential and the structure of the quantum moduli space of vacua. Simultaneously to our work, the case without matter field was studied in [5]. A related work also appeared in [6].", "date": "1998-11", "date_type": "published", "publication": "Nuclear Physics B - Proceedings Supplements", "volume": "68", "number": "1-3", "publisher": "Elsevier", "pagerange": "84-91", "id_number": "CaltechAUTHORS:20161220-130418424", "issn": "0920-5632", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-130418424", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0920-5632(98)00142-X", "primary_object": { "basename": "9709211.pdf", "url": "https://authors.library.caltech.edu/records/yt2b9-haa17/files/9709211.pdf" }, "pub_year": "1998", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/y1zq4-srm92", "eprint_id": 67072, "eprint_status": "archive", "datestamp": "2023-08-19 03:26:56", "lastmod": "2026-04-17 03:14:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Comments on N = S AdS orbifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Elsevier Science B.V. \n\nReceived 7 July 1998, Available online 21 November 1998. \n\nEditor: P.V. Landshoff. \n\nI am grateful to M. Berkooz, O.J. Ganor, J. Gomis, A. Mikhailov, Y. Oz, M. J. Strassler and A.M. Uranga for helpful conversations. Especially I would like to thank E. Witten for suggesting the problem and stimulating discussions. The work was supported in part by Merit Fellowship in Natural Sciences and Mathematics and grant RFBR No 98-02-16575 and Russian President's grant No 96-15-96939.\n\n

Submitted - 9806180.pdf

", "abstract": "We discuss twisted states of AdS orbifolds which couple to N = 2 chiral primary operators not invariant under exchange of the gauge factors. Kaluza-Klein reduction on the fixed circle gives the correct conformal dimensions of operators in the superconformal theory and involves some aspects of monopole dynamics in the non-trivial background. As a byproduct we found evidence for decoupling of U(1) factors in the four-dimensional gauge theory.", "date": "1998-10-29", "date_type": "published", "publication": "Physics Letters B", "volume": "439", "number": "1-2", "publisher": "Elsevier", "pagerange": "23-28", "id_number": "CaltechAUTHORS:20160513-103122668", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-103122668", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "98-02-16575" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "96-15-96939" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0370-2693(98)01005-3", "primary_object": { "basename": "9806180.pdf", "url": "https://authors.library.caltech.edu/records/y1zq4-srm92/files/9806180.pdf" }, "pub_year": "1998", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/65qzr-x4f12", "eprint_id": 66994, "eprint_status": "archive", "datestamp": "2023-08-22 13:03:29", "lastmod": "2026-04-16 13:52:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cherkis-S-A", "name": { "family": "Cherkis", "given": "Sergey A." }, "orcid": "0000-0002-0785-0126" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Singular monopoles and supersymmetric gauge theories in three dimensions", "ispublished": "pub", "full_text_status": "public", "keywords": "Gauge theories; Supersymmetry; BPS monopoles", "note": "\u00a9 1998 Elsevier B.V. \n\nResearch supported in part by DOE grant DE-FG03-92-ER40701. \nResearch supported in part by DOE grant DE-FG02-90-ER40542. \n\nWe would like to thank Amihay Hanany, Nigel Hitchin, John H. Schwarz, and Edward Witten for helpful conversations.\n\n

Submitted - 9711145.pdf

", "abstract": "According to the proposal of Hanany and Witten, Coulomb branches of N = 4 SU(n) gauge theories in three dimensions are isometric to moduli spaces of BPS monopoles. We generalize this proposal to gauge theories with matter, which allows us to describe the metrics on their spaces of vacua by means of the hyper-K\u00e4hler quotient construction. To check the identification of moduli spaces a comparison is made with field theory predictions. For SU(2) theory with k fundamental hypermultiplets the Coulomb branch is expected to be the D_k ALF gravitational instanton, so our results lead to a construction of such spaces. In the special case of SU(2) theory with four or fewer fundamental hypermultiplets we calculate the complex structures on the moduli spaces and compare them with field-theoretical results. We also discuss some puzzles with brane realizations of three-dimensional N = 4 theories.", "date": "1998-08-10", "date_type": "published", "publication": "Nuclear Physics B", "volume": "525", "number": "1-2", "publisher": "Elsevier", "pagerange": "215-234", "id_number": "CaltechAUTHORS:20160511-130819176", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-130819176", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90-ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(98)00341-1", "primary_object": { "basename": "9711145.pdf", "url": "https://authors.library.caltech.edu/records/65qzr-x4f12/files/9711145.pdf" }, "pub_year": "1998", "author_list": "Cherkis, Sergey A. and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/4m2xh-g1723", "eprint_id": 72987, "eprint_status": "archive", "datestamp": "2023-08-19 03:14:00", "lastmod": "2026-04-17 02:09:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Membrane scattering in curved space with M-momentum transfer", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Elsevier. \n\nReceived 10 February 1998, Accepted 24 March 1998. \n\nHO would like to thank Joe Polchinski for discussions that initiated this work. We would also like to thank Tom Banks, Korkut Bardakci, Mike Douglas, Jeff Harvey, Shamit Kachru, Hitoshi Murayama, Steve Shenker and Stefan Vandoren for discussions. \n\nJdB and HO would also like to thank the organizers of the CERN workshop, \"Nonperturbative Aspects of Strings, Branes and Fields,\" December 8 - 12 for their hospitality. KH and HO thank Institute for Theoretical Physics at Santa Barbara. This work is supported in part by NSF grant PHY-951497 and by DOE grant DEAC03-76SF00098. \n\nKH and HO are also supported in part by NSF grant PHY94-07194 through the Institute for Theoretical Physics. JdB is a fellow of the Miller Institute for Basic Research in Science.\n\n

Submitted - 9802005.pdf

", "abstract": "We study membrane scattering in a curved space with non-zero M-momentum p11 transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N = 4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p11, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that this result is not in contradiction with the large-N Matrix Theory conjecture, by pointing out that cutoff scales of the supergravity and the gauge theory are complementary to each other.", "date": "1998-08-10", "date_type": "published", "publication": "Nuclear Physics B", "volume": "525", "number": "1-2", "publisher": "Elsevier", "pagerange": "257-283", "id_number": "CaltechAUTHORS:20161220-123933919", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-123933919", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY94-07194" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(98)00253-3", "primary_object": { "basename": "9802005.pdf", "url": "https://authors.library.caltech.edu/records/4m2xh-g1723/files/9802005.pdf" }, "pub_year": "1998", "author_list": "de Boer, Jan; Hori, Kentaro; et al." }, { "id": "https://authors.library.caltech.edu/records/tt1bz-bf716", "eprint_id": 80930, "eprint_status": "archive", "datestamp": "2023-08-19 03:07:59", "lastmod": "2026-04-17 04:13:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Classical Moment Problem as a Self-Adjoint Finite Difference Operator", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Academic Press. \n\nReceived 13 November 1997, Accepted 3 January 1998. \n\nThis material is based upon work supported by the National Science Foundation under Grant DMS-9401491.\n\n

Submitted - 9906008.pdf

", "abstract": "This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna functions appear as elements of a transfer matrix and convergence of Pad\u00e9 approximants appears as the strong resolvent convergence of finite matrix approximations to a Jacobi matrix. As a bonus of this, we obtain new results on the convergence of certain Pad\u00e9 approximants for series of Hamburger.", "date": "1998-07-15", "date_type": "published", "publication": "Advances in Mathematics", "volume": "137", "number": "1", "publisher": "Elsevier", "pagerange": "82-203", "id_number": "CaltechAUTHORS:20170829-154200373", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170829-154200373", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/aima.1998.1728", "primary_object": { "basename": "9906008.pdf", "url": "https://authors.library.caltech.edu/records/tt1bz-bf716/files/9906008.pdf" }, "pub_year": "1998", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/rmbqa-3wp33", "eprint_id": 81821, "eprint_status": "archive", "datestamp": "2023-08-22 12:59:12", "lastmod": "2026-04-17 03:40:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Calderbank-A-R", "name": { "family": "Calderbank", "given": "A. Robert" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Shor-P-W", "name": { "family": "Shor", "given": "P. W." } }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "Neil J. A." } } ] }, "title": "Quantum error correction via codes over GF(4)", "ispublished": "pub", "full_text_status": "public", "keywords": "Codes, additive; codes, quantum; codes, quaternary; codes, self-orthogonal, geometry, orthogonal; geometry,\nsymplectic; group, Clifford", "note": "\u00a9 1998 IEEE. \n\nManuscript received July 15, 1996; revised December 4, 1997. \n\nThe work of E. M. Rains was performed while he was with the Institute for Defense Analyses, Princeton, NJ USA. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Ulm, Germany, 1997.\n\nThe authors wish to thank Aaron Gulliver for finding the quasicyclic codes mentioned in Section V, and our colleague Ronald H. Hardin for his contributions to our search for interesting nonadditive codes. We also thank Patrick Sol\u00e9 for drawing our attention to the work of B. Runge and G. H\u00f6hn.\n\n

Published - 00681315.pdf

Submitted - 9608006.pdf

", "abstract": "The problem of finding quantum error correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.", "date": "1998-07", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "44", "number": "4", "publisher": "IEEE", "pagerange": "1369-1387", "id_number": "CaltechAUTHORS:20170925-160358492", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-160358492", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.681315", "primary_object": { "basename": "9608006.pdf", "url": "https://authors.library.caltech.edu/records/rmbqa-3wp33/files/9608006.pdf" }, "related_objects": [ { "basename": "00681315.pdf", "url": "https://authors.library.caltech.edu/records/rmbqa-3wp33/files/00681315.pdf" } ], "pub_year": "1998", "author_list": "Calderbank, A. Robert; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/wne94-5p815", "eprint_id": 81818, "eprint_status": "archive", "datestamp": "2023-08-19 03:05:01", "lastmod": "2026-03-09 23:07:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Quantum weight enumerators", "ispublished": "pub", "full_text_status": "public", "keywords": "Weight enumerators q-ary quantum codes", "note": "\u00a9 1998 IEEE. \n\nManuscript received December 20, 1996; revised December 31, 1997. \n\nThe author wishes to thank P. Shor and N. Sloane for many helpful discussions; he would also like to thank C. Bennett for a helpful discussion on erasures.\n\n

Published - 00681316.pdf

Submitted - 9612015.pdf

", "abstract": "In a recent paper, Shor and Laflamme (see Phys. Rev. Lett., vol.78, p.1600-2, 1997) defined two \"weight enumerators\" for quantum error-correcting codes, connected by a MacWilliams transform, and used them to give a linear programming bound for quantum codes. We introduce two new enumerators which, while much less powerful at producing bounds, are useful tools nonetheless. The new enumerators are connected by a much simpler duality transform, clarifying the duality between Shor and Laflamme's enumerators. We also use the new enumerators to give a simpler condition for a quantum code to have specified minimum distance, and to extend the enumerator theory to codes with block size greater than 2.", "date": "1998-07", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "44", "number": "4", "publisher": "IEEE", "pagerange": "1388-1394", "id_number": "CaltechAUTHORS:20170925-154039545", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-154039545", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.681316", "primary_object": { "basename": "9612015.pdf", "url": "https://authors.library.caltech.edu/records/wne94-5p815/files/9612015.pdf" }, "related_objects": [ { "basename": "00681316.pdf", "url": "https://authors.library.caltech.edu/records/wne94-5p815/files/00681316.pdf" } ], "pub_year": "1998", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/n0297-zpa63", "eprint_id": 72988, "eprint_status": "archive", "datestamp": "2023-08-22 12:57:32", "lastmod": "2026-04-16 14:08:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } } ] }, "title": "Branes and dynamical supersymmetry breaking", "ispublished": "pub", "full_text_status": "public", "keywords": "M theory fivebrane; Supersymmetric gauge theories; Dynamical supersymmetry breaking", "note": "\u00a9 1998 Elsevier. \n\nReceived 10 February 1998, Accepted 25 March 1998. \n\nWe thank Hitoshi Murayama for many useful discussions. We furthermore would like to acknowledge discussions with Amit Giveon, David Kutasov, Joe Lykken, Al Shapere and Scott Thomas. We thank Savas Dimopoulos and Michael Peskin for remarks and questions that lead to an improvement of the paper. \n\nThis work is supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098. JdB is a fellow of the Miller Institute for Basic Research in Science.\n\n

Submitted - 9801060.pdf

", "abstract": "We study dynamical supersymmetry breaking in four dimensions using the fivebrane of M theory, in particular for the Izawa-Yanagida-Intriligator-Thomas (IYIT) model, which we realize as the worldvolume theory of a certain M theory fivebrane configuration. From the brane point of view, supersymmetry is broken when a holomorphic configuration with the proper boundary conditions does not exist. We discuss the difference between explicit and spontaneous supersymmetry breaking and between runaway behavior and having a stable vacuum. As a preparation for the study of the IYIT model, we examine a realization of the orientifold four-plane in M theory. We derive known as well as new results on the moduli spaces of N = 2 and N = 1 theories with symplectic gauge groups. These results are based on a hypothesis that a certain intersection of the fivebrane and the Z_2 fixed plane breaks supersymmetry. In the IYIT model, we show that the brane exhibits runaway behavior when the flavor group is gauged. On the other hand, if the flavor group is not gauged, we find that the brane does not run away. We suggest that a stable supersymmetry-breaking vacuum is realized in the region beyond the reach of the supergravity approximation.", "date": "1998-06-29", "date_type": "published", "publication": "Nuclear Physics B", "volume": "522", "number": "1-2", "publisher": "Elsevier", "pagerange": "20-68", "id_number": "CaltechAUTHORS:20161220-124550810", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-124550810", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(98)00252-1", "primary_object": { "basename": "9801060.pdf", "url": "https://authors.library.caltech.edu/records/n0297-zpa63/files/9801060.pdf" }, "pub_year": "1998", "author_list": "de Boer, Jan; Hori, Kentaro; et al." }, { "id": "https://authors.library.caltech.edu/records/jzzgb-w4761", "eprint_id": 38560, "eprint_status": "archive", "datestamp": "2023-08-22 12:52:26", "lastmod": "2026-04-17 02:03:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Rigidity properties of Borel ideals on the integers", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Borel ideals; Polish groups; Borel actions; Borel equivalence relations", "note": "\u00a9 1998 Elsevier Science B.V. Received 30 September 1996. Research partially supported by NSF grant DMS-9317509.", "abstract": "We classify the Borel ideals I on the set of natural numbers N for which p(N)/I can be Borel embedded into the orbit space of a Borel action of the infinite symmetric group. As a consequence we show that certain Borel ideals I, including the Fr\u00e9chet ideal, are completely characterized by the \"Borel cardinality\" of the set p(N)/I.", "date": "1998-05-22", "date_type": "published", "publication": "Topology and Its Applications", "volume": "85", "number": "1-3", "publisher": "Elsevier", "pagerange": "195-205", "id_number": "CaltechAUTHORS:20130517-113148990", "issn": "0166-8641", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-113148990", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0166-8641(97)00150-8", "pub_year": "1998", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/sj4y2-jyy25", "eprint_id": 73073, "eprint_status": "archive", "datestamp": "2023-08-19 02:52:45", "lastmod": "2026-04-17 03:56:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Horowitz-G-T", "name": { "family": "Horowitz", "given": "Gary T." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Spectrum of Large N Gauge Theory from Supergravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 The American Physical Society. \n\nReceived 26 February 1998. \n\nWe thank Juan Maldacena for discussions. The research of G. H. is supported in part by NSF Grant No. PHY95-07065. The research of H. O. is supported in part by NSF Grant No. PHY95-14797, DOE Grant No. DE-AC03-76SF00098, and NSF Grant No. PHY94-07194 through the Institute for Theoretical Physics.\n\n

Published - PhysRevLett.80.4116.pdf

Submitted - 9802116.pdf

", "abstract": "Recently, Maldacena proposed that the large N limit of the N=4 supersymmetric gauge theory in four dimensions with U(N) gauge group is dual to the type IIB superstring theory on AdS_5 \u00d7S^5. We use this proposal to study the spectrum of the large N gauge theory on R\u00d7S^3 in a low energy regime. We find that the spectrum is discrete and evenly spaced, and the number of states at each energy level is smaller than the one predicted by the naive extrapolation of the Bekenstein-Hawking formula to the low energy regime. We also show that the gauge theory describes a region of spacetime behind the horizon as well as the region in front.", "date": "1998-05-11", "date_type": "published", "publication": "Physical Review Letters", "volume": "80", "number": "19", "publisher": "American Physical Society", "pagerange": "4116-4118", "id_number": "CaltechAUTHORS:20161221-111157185", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-111157185", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY95-07065" }, { "agency": "NSF", "grant_number": "PHY95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY94-07194" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.80.4116", "primary_object": { "basename": "9802116.pdf", "url": "https://authors.library.caltech.edu/records/sj4y2-jyy25/files/9802116.pdf" }, "related_objects": [ { "basename": "PhysRevLett.80.4116.pdf", "url": "https://authors.library.caltech.edu/records/sj4y2-jyy25/files/PhysRevLett.80.4116.pdf" } ], "pub_year": "1998", "author_list": "Horowitz, Gary T. and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/f3zbx-kky59", "eprint_id": 72989, "eprint_status": "archive", "datestamp": "2023-08-22 12:49:32", "lastmod": "2026-04-17 02:25:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } } ] }, "title": "K\u00e4hler potential and higher derivative terms from M-theory fivebrane", "ispublished": "pub", "full_text_status": "public", "keywords": "M-theory fivebrane; Supersymmetric gauge theories; K\u00e4hler potential; Higher derivative terms", "note": "\u00a9 1998 Elsevier. \n\nReceived 12 January 1998, Accepted 9 February 1998. \n\nWe would like to thank G. Horowitz, J. Maldacena, H. Murayama and C. Vafa for useful discussions. This research is supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098. JdB is a fellow of the Miller Institute for Basic Research in Science.\n\n

Submitted - 9711143.pdf

", "abstract": "The construction of four-dimensional supersymmetric gauge theories via the fivebrane of M-theory wrapped around a Riemann surface has been successfully applied to the computation of holomorphic quantities of field theory. In this paper we compute non-holomorphic quantities in the eleven-dimensional supergravity limit of M-theory. While the K\u00e4hler potential on the Coulomb of N = 2 theories is correctly reproduced, higher derivative terms in the N = 2 effective action differ from what is expected for the four-dimensional gauge theory. For the K\u00e4hler potential of N = 1 theories at an abelian Coulomb phase, the result again differs from what is expected for the four-dimensional gauge theory. Using a gravitational back-reaction method for the fivebrane we compute the metric on the Higgs branch of N = 2 gauge theories. Here we find an agreement with the results expected for the gauge theories. A similar computation of the metric on N = 1 Higgs branches yields information on the complex structure associated with the flavor rotation in one case and the classical metric in another. We discuss what four-dimensional field theory quantities can be computed via the fivebrane in the supergravity limit of M-theory.", "date": "1998-05-04", "date_type": "published", "publication": "Nuclear Physics B", "volume": "518", "number": "1-2", "publisher": "Elsevier", "pagerange": "173-211", "id_number": "CaltechAUTHORS:20161220-125221606", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-125221606", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(98)00152-7", "primary_object": { "basename": "9711143.pdf", "url": "https://authors.library.caltech.edu/records/f3zbx-kky59/files/9711143.pdf" }, "pub_year": "1998", "author_list": "de Boer, Jan; Hori, Kentaro; et al." }, { "id": "https://authors.library.caltech.edu/records/m110t-zzn22", "eprint_id": 85373, "eprint_status": "archive", "datestamp": "2023-08-22 12:48:36", "lastmod": "2026-04-17 03:45:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kiselev-A", "name": { "family": "Kiselev", "given": "Alexander" } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Modified Pr\u00fcfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Spectral Analysis; Compact Support; Continuous Spectrum; Hausdorff Dimension; Transfer Matrice", "note": "\u00a9 1998 Springer-Verlag.\n\nReceived: 8 April 1997. Accepted: 19 June 1997.\n\nResearch supported in part by NSF Grant No. DMS-9022140.\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.", "abstract": "Using control of the growth of the transfer matrices, we discuss the spectral analysis of continuum and discrete half-line Schr\u00f6dinger operators with slowly decaying potentials. Among our results we show if, where W has compact support and, then H has purely a.c. (resp. purely s.c.) spectrum on (O,\u221e) if). For \u03bbn^({-1/2}) \u0251_n potentials, where a n are independent, identically distributed random variables with E(\u0251_n ) = O, E(\u0251^2_n)=1, and \u03bb < 2, we find singular continuous spectrum with explicitly computable fractional Hausdorff dimension.", "date": "1998-05", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "194", "number": "1", "publisher": "Springer", "pagerange": "1-45", "id_number": "CaltechAUTHORS:20180320-092711915", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180320-092711915", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9022140" }, { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/s002200050346", "pub_year": "1998", "author_list": "Kiselev, Alexander; Last, Yoram; et al." }, { "id": "https://authors.library.caltech.edu/records/y5dwq-gpb67", "eprint_id": 86375, "eprint_status": "archive", "datestamp": "2023-08-19 02:50:10", "lastmod": "2026-04-16 14:27:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Spectral averaging and the Krein spectral shift", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Copyright 1998 Barry Simon. \n\n(Communicated by Palle E. T. Jorgensen) \n\nReceived by the editors October 14, 1996. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The government has certain rights in this material. \n\nThe author would like to thank M. Ben-Artzi for the hospitality of the Hebrew University, where some of this work was done.", "abstract": "We provide a new proof of a theorem of Birman and Solomyak that if A(s) = A_0 + sB with B \u2265 0 trace class and d\u00b5_s} (\u2022) = Tr(B^{1/2} E_{A(s)}(\u2022) B^(1/2)), then \u222b^1_0[d\u00b5_s(\u03bb)] ds = \u03be(\u03bb)d\u03bb, where \u03be is the Krein spectral shift from A(0) to A(1). Our main point is that this is a simple consequence of the formula d/(ds) Tr(f(A(s)) = Tr(Bf'(A(s))).", "date": "1998-05", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "126", "number": "5", "publisher": "American Mathematical Society", "pagerange": "1409-1413", "id_number": "CaltechAUTHORS:20180511-153846768", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180511-153846768", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-98-04261-0", "pub_year": "1998", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/xk9b0-w6t48", "eprint_id": 81186, "eprint_status": "archive", "datestamp": "2023-08-19 02:46:18", "lastmod": "2026-04-17 01:06:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Last-Y", "name": { "family": "Last", "given": "Yoram" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Modified Pr\u00fcfer and EFGP Transforms and Deterministic Models with Dense Point Spectrum", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1998 Academic Press. \n\nReceived 13 June 1997, Accepted 20 August 1997. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The U.S. Government has certain rights in this material.", "abstract": "We provide a new proof of the theorem of Simon and Zhu that in the region |E|<\u03bb for a.e. energies, \u2212(d^2/dx^2)+\u03bb cos(x^\u03b1), 0<\u03b1<1 has Lyapunov behavior with a quasi-classical formula for the Lyapunov exponent. We also prove Lyapunov behavior for a.e.E\u2208[\u22122, 2] for the discrete model with V(j^2)=e^j,V(n)=0 if n\u2209 {1, 4, 9,\u2026}. The arguments depend on a direct analysis of the equations for the norm of a solution.", "date": "1998-04-20", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "154", "number": "2", "publisher": "Elsevier", "pagerange": "513-530", "id_number": "CaltechAUTHORS:20170906-104652888", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170906-104652888", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1997.3192", "pub_year": "1998", "author_list": "Last, Yoram and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/03qw4-k4b36", "eprint_id": 73090, "eprint_status": "archive", "datestamp": "2023-08-19 02:45:38", "lastmod": "2026-04-16 14:04:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Douglas-M-R", "name": { "family": "Douglas", "given": "Michael R." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Why matrix theory is hard", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Elsevier Science B.V. \n\nReceived 29 October 1997. \n\nWe would like to thank Tom Banks, Kiyoshi Higashijima, Ashoke Sen, Koichi Yamawaki and, in particular, Steve Shenker for discussion. H.O. is supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098.\n\n

Submitted - 9710178.pdf

", "abstract": "Recently Sen and Seiberg gave a prescription for constructing the matrix theory in any superstring background. We use their prescription to test the finite N matrix theory conjecture on an ALE space. Based on our earlier work with Shenker, we find a sharper discrepancy between matrix theory computation and supergravity prediction. We discuss subtleties in the light-front quantization which may lead to a resolution to the discrepancy.", "date": "1998-04-16", "date_type": "published", "publication": "Physics Letters B", "volume": "425", "number": "1-2", "publisher": "Elsevier", "pagerange": "71-76", "id_number": "CaltechAUTHORS:20161221-124148504", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-124148504", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0370-2693(98)00114-2", "primary_object": { "basename": "9710178.pdf", "url": "https://authors.library.caltech.edu/records/03qw4-k4b36/files/9710178.pdf" }, "pub_year": "1998", "author_list": "Douglas, Michael R. and Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/pryh3-whk19", "eprint_id": 38569, "eprint_status": "archive", "datestamp": "2023-08-22 12:41:29", "lastmod": "2026-04-17 03:21:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "Greg" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "title": "Borel equivalence relations induced by actions of the symmetric group", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Borel equivalence relations; Countable models; Infinite symmetric group", "note": "\u00a9 1998 Published by Elsevier Science B.V. Received 16 December 1996; accepted 11 October 1997. Research partially supported by NSF Grant DMS-9317509.", "abstract": "We consider Borel equivalence relations E induced by actions of the infinite symmetric group, or equivalently the isomorphism relation on classes of countable models of bounded Scott rank. We relate the descriptive complexity of the equivalence relation to the nature of its complete invariants. A typical theorem is that E is potentially \u03a0^0_3 iff the invariants are countable sets of reals, it is potentially \u03a0^0_4 iff the invariants are countable sets of countable sets of reals, and so on. The proofs use various techniques, including Vaught transforms, changing topologies, and the Scott analysis of countable models.", "date": "1998-03-11", "date_type": "published", "publication": "Annals of Pure and Applied Logic", "volume": "92", "number": "1", "publisher": "Elsevier", "pagerange": "63-112", "id_number": "CaltechAUTHORS:20130517-142221264", "issn": "0168-0072", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-142221264", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "other_numbering_system": { "items": [ { "id": "MR1624736", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0168-0072(97)00049-3", "pub_year": "1998", "author_list": "Hjorth, Greg; Kechris, Alexander S.; et al." }, { "id": "https://authors.library.caltech.edu/records/x8j7r-er752", "eprint_id": 83341, "eprint_status": "archive", "datestamp": "2023-08-19 02:34:30", "lastmod": "2026-03-09 23:04:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "Jeffrey C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Rationals to and Only to Rationals: 10555", "ispublished": "pub", "full_text_status": "public", "keywords": "Polynomials, Coefficients, Algebra", "note": "\u00a9 1998 Mathematical Association of America.\n\n

Published - 2589100.pdf

", "abstract": "(a) Suppose f(t) \u2208 R[t] is a polynomial that maps rationals to rationals and irrationals to irrationals. Show that f(t) = at + b with a and b rational.\n(b) Does the same conclusion hold under the weaker assumption that f:R \u2192 R is an algebraic function (i.e., if there is a polynomial P(x,y) \u2208 R[x,y] such that P(t,f(t)) is identically zero)?", "date": "1998-03", "date_type": "published", "publication": "American Mathematical Monthly", "volume": "105", "number": "3", "publisher": "Mathematical Association of America", "pagerange": "277-278", "id_number": "CaltechAUTHORS:20171120-110513579", "issn": "0002-9890", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171120-110513579", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2589100.pdf", "url": "https://authors.library.caltech.edu/records/x8j7r-er752/files/2589100.pdf" }, "pub_year": "1998", "author_list": "Lagarias, Jeffrey C. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/9p8ta-f5859", "eprint_id": 81867, "eprint_status": "archive", "datestamp": "2023-08-19 02:20:44", "lastmod": "2026-03-09 23:03:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Shadow bounds for self-dual codes", "ispublished": "pub", "full_text_status": "public", "keywords": "Bound, self-dual code, shadow, singly-even", "note": "\u00a9 1998 IEEE. \n\nManuscript received January 21, 1997; revised June 20, 1997. \n\nThe author wishes to thank N. Sloane for many productive conversations; in particular, for introducing the author to shadow theory.\n\n

Published - 00651000.pdf

", "abstract": "Conway and Sloane (1990) have previously given an upper bound on the minimum distance of a singly-even self-dual binary code, using the concept of the shadow of a self-dual code. We improve their bound, finding that the minimum distance of a self-dual binary code of length n is at most 4[n/24]+4, except when n mod 24=22, when the bound is 4[n/24]+6. We also show that a code of length a multiple of 24 meeting the bound cannot be singly-even. The same technique gives similar results for additive codes over GF(4) (relevant to quantum coding theory).", "date": "1998-01", "date_type": "published", "publication": "IEEE Transactions on Information Theory", "volume": "44", "number": "1", "publisher": "IEEE", "pagerange": "134-139", "id_number": "CaltechAUTHORS:20170927-074638028", "issn": "0018-9448", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170927-074638028", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/18.651000", "primary_object": { "basename": "00651000.pdf", "url": "https://authors.library.caltech.edu/records/9p8ta-f5859/files/00651000.pdf" }, "pub_year": "1998", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/qpnk6-xkp56", "eprint_id": 28540, "eprint_status": "archive", "datestamp": "2023-08-19 02:09:54", "lastmod": "2026-03-09 02:37:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Sethi-S", "name": { "family": "Sethi", "given": "Savdeep" }, "orcid": "0000-0002-7520-680X" } ] }, "title": "The Higgs Branch of Impurity Theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 International Press. \n\nIt is our pleasure to thank S. Cherkis, O. Ganor, G. Moore, N. Nekrasov, J. Park, A. Uranga, C. Vafa and E. Witten for helpful discussions. The work of A.K. is supported by DOE DE-FG02-90ER40542; that of S.S. by NSF grant DMS-9627351.\n\n

Published - KAPatmp98.pdf

Submitted - KAPatmp98_preprint.pdf

", "abstract": "We consider supersymmetric gauge theories with impurities in various dimensions. These systems arise in the study of intersecting branes. Unlike conventional gauge theories, the Higgs branch of an impurity theory can have compact directions. For models with eight supercharges, the Higgs branch is a hyperK\u00e4hler manifold given by the moduli space of solutions of certain differential equations. These equations are the dimensional reductions of self-duality equations with boundary conditions determined by the impurities. They can also be interpreted as Nahm transforms of self-duality equations on toroidally compactified spaces. We discuss the application of our results to the light-cone formulation of Yang-Mills theories and to the solution of certain N=2 d=4 gauge theories.", "date": "1998", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "2", "number": "3", "publisher": "International Press", "pagerange": "571-591", "id_number": "CaltechAUTHORS:20111220-133738420", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111220-133738420", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" }, { "agency": "NSF", "grant_number": "DMS-9627351" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.1998.v2.n3.a6", "primary_object": { "basename": "KAPatmp98.pdf", "url": "https://authors.library.caltech.edu/records/qpnk6-xkp56/files/KAPatmp98.pdf" }, "related_objects": [ { "basename": "KAPatmp98_preprint.pdf", "url": "https://authors.library.caltech.edu/records/qpnk6-xkp56/files/KAPatmp98_preprint.pdf" } ], "pub_year": "1998", "author_list": "Kapustin, Anton and Sethi, Savdeep" }, { "id": "https://authors.library.caltech.edu/records/tjnvz-v5872", "eprint_id": 38691, "eprint_status": "archive", "datestamp": "2023-08-22 12:26:26", "lastmod": "2026-03-09 20:34:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gordon-A-Y", "name": { "family": "Gordon", "given": "Alexander Y." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Measurable enumeration of eigenelements", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Measurable space; eigenvalue; eigenvector; measurable enumeration", "note": "\u00a9 1999 OPA (Overseas Publishers Association) N. V. Published by license under the Gordon and Breach Science Publishers imprint.\n\nReceived: 5 1998; Published online: 20 Jan 2011.\n\nResearch partially supported by NSF Grant DMS 96-19880.\n\nWe are indebted to S. Jitomirskaya, Y. Last, C. Remling, and\nB. Simon for useful discussions. The first named author is grateful for the hospitality of the Division of Physics, Mathematics and Astronomy of Caltech and the Department of\nMathematics of the University of California at Irvine, where parts of this work were done.", "abstract": "We prove that for eigenelements of a measurable family of linear self-adjoint operators in a separable Hilbert space there exists a measurable enumeration. We also prove a similar result for measurable families of bounded linear operators having at most countably many eigenvalues (under certain restrictions on the parameter space). The proof of the latter result is based on descriptive set theory, while in the case of self-adjoint (and some more general) operators the proof is constructive.", "date": "1998", "date_type": "published", "publication": "Applicable Analysis: An International Journal", "volume": "71", "number": "1-4", "publisher": "Taylor and Francis", "pagerange": "41-61", "id_number": "CaltechAUTHORS:20130528-105907286", "issn": "0003-6811", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-105907286", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 96-19880" } ] }, "other_numbering_system": { "items": [ { "id": "MR1690090", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "1998", "author_list": "Gordon, Alexander Y. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/xrxyg-v6r72", "eprint_id": 81819, "eprint_status": "archive", "datestamp": "2023-08-19 02:15:35", "lastmod": "2026-03-09 22:48:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Increasing Subsequences and the Classical Groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Electronic Journal of Combinatorics. \n\nSubmitted: November 24, 1997; Accepted: January 30, 1998. \n\nThe greatest thanks are due to P. Diaconis (the author's thesis advisor), for his many suggestions of problems (one of which appears in the present work). \n\nThanks are also due to the following people and institutions, in no particular order: A. Odlyzko, for many helpful comments; AT&T Bell Laboratories (Murray Hill) and the Center for Communications Research (Princeton) for generous summer support; the Harvard University Mathematics Department and the National Science\nFoundation, for generous support for the rest of the year. Also, thanks are due, for helpful comments, to N. Bergeron, M. Grassl, M. Rojas, R. Stanley, and D. Stroock. Last, but not least, the author owes thanks to W. Woyczynski, both for introducing him to probability theory and for introducing him to Prof. Diaconis; the thesis of which this work is a part would be very different, had either introduction not been made.\n\n

Published - 1350-1429-1-PB.pdf

", "abstract": "We show that the moments of the trace of a random unitary matrix have combinatorial interpretations in terms of longest increasing subsequences of permutations. To be precise, we show that the 2n-th moment of the trace of a random k-dimensional unitary matrix is equal to the number of permutations of length n with no increasing subsequence of length greater than k. We then generalize this to other expectations over the unitary group, as well as expectations over the orthogonal and symplectic groups. In each case, the expectations count objects with restricted \"increasing subsequence\" length.", "date": "1998", "date_type": "published", "publication": "Electronic Journal of Combinatorics", "volume": "5", "publisher": "Electronic Journal of Combinatorics", "pagerange": "Art. No. R12", "id_number": "CaltechAUTHORS:20170925-154914546", "issn": "1077-8926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-154914546", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AT&T Bell Laboratories" }, { "agency": "Princeton University" }, { "agency": "Harvard University" }, { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "1350-1429-1-PB.pdf", "url": "https://authors.library.caltech.edu/records/xrxyg-v6r72/files/1350-1429-1-PB.pdf" }, "pub_year": "1998", "author_list": "Rains, E. M." }, { "id": "https://authors.library.caltech.edu/records/esrpm-55s70", "eprint_id": 56964, "eprint_status": "archive", "datestamp": "2023-08-19 02:13:30", "lastmod": "2026-03-09 21:31:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "Additive extensions of a Barsotti-Tate group", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Universit\u00e0 di Padova. \n\nManuscritto pervenuto in redazione il 12 Iuglio 1996.\n\n

Published - RSMUP_1998__99__161_0.pdf

", "abstract": "In this paper we classify up to isomorphism the additive extensions of a Barsotti-Tate group, in positive characteristic p over a perfect field k and in characteristic 0 over W(k) the ring of Witt vectors with coefficients in k. The extensions arise as group functors associated to suitable submodules of the Dieudonn\u00e9 module. In particular we give an explicit description of the universal additive extension in both cases.", "date": "1998", "date_type": "published", "publication": "Rendiconti del Seminario Matematico della Universit\u00e0 di Padova", "volume": "99", "publisher": "Universit\u00e0 di Padova", "pagerange": "161-185", "id_number": "CaltechAUTHORS:20150424-133320556", "issn": "0041-8994", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150424-133320556", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "RSMUP_1998__99__161_0.pdf", "url": "https://authors.library.caltech.edu/records/esrpm-55s70/files/RSMUP_1998__99__161_0.pdf" }, "pub_year": "1998", "author_list": "Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/5gjgg-sgp16", "eprint_id": 28541, "eprint_status": "archive", "datestamp": "2023-08-19 02:10:01", "lastmod": "2026-03-09 02:47:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cherkis-S-A", "name": { "family": "Cherkis", "given": "Sergey A." }, "orcid": "0000-0002-0785-0126" }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "D_k Gravitational Instantons and Nahm Equations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1999 International Press. \n\nResearch supported in part by DOE grant DE-FG03-92-ER40701. Research supported in part by DOE grant DE-FG02-90ER40542. We would like to thank John H. Schwarz for reading the manuscript. S. Ch. is grateful to LAS for hospitality.\n\n

Published - CHERatmp98.pdf

Submitted - CHERatmp98_preprint.pdf

", "abstract": "We construct D_k asymptotically locally flat gravitational instantons as moduli spaces of solutions of Nahm equations. This allows us to find their twistor spaces and K\u00e4hler potentials.", "date": "1998", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "2", "number": "6", "publisher": "International Press", "pagerange": "1287-1306", "id_number": "CaltechAUTHORS:20111220-134324280", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20111220-134324280", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-90ER40542" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.1998.v2.n6.a3", "primary_object": { "basename": "CHERatmp98.pdf", "url": "https://authors.library.caltech.edu/records/5gjgg-sgp16/files/CHERatmp98.pdf" }, "related_objects": [ { "basename": "CHERatmp98_preprint.pdf", "url": "https://authors.library.caltech.edu/records/5gjgg-sgp16/files/CHERatmp98_preprint.pdf" } ], "pub_year": "1998", "author_list": "Cherkis, Sergey A. and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/3xxyr-f9k46", "eprint_id": 81820, "eprint_status": "archive", "datestamp": "2023-08-19 02:15:40", "lastmod": "2026-03-09 22:11:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Edel-Y", "name": { "family": "Edel", "given": "Yves" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "On Kissing Numbers in Dimensions 32 to 128", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1998 Electronic Journal of Combinatorics. \n\nSubmitted: April 9, 1998; Accepted: April 13, 1998.\n\n

Published - 1360-1439-1-PB.pdf

", "abstract": "An elementary construction using binary codes gives new record kissing numbers in dimensions from 32 to 128.", "date": "1998", "date_type": "published", "publication": "Electronic Journal of Combinatorics", "volume": "5", "publisher": "Electronic Journal of Combinatorics", "pagerange": "Art. No. R22", "id_number": "CaltechAUTHORS:20170925-155652163", "issn": "1077-8926", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-155652163", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "1360-1439-1-PB.pdf", "url": "https://authors.library.caltech.edu/records/3xxyr-f9k46/files/1360-1439-1-PB.pdf" }, "pub_year": "1998", "author_list": "Edel, Yves; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/zvw7k-jcq35", "eprint_id": 84241, "eprint_status": "archive", "datestamp": "2023-08-19 02:05:23", "lastmod": "2026-04-17 13:51:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "m-Functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Hebrew University of Jerusalem 1997. \n\nThis material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.", "abstract": "We study inverse spectral analysis for finite and semi-infinite Jacobi matrices H. Our results include a new proof of the central result of the inverse theory (that the spectral measure determines H). We prove an extension of the theorem of Hochstadt (who proved the result in case n = N) that n eigenvalues of an N \u00d7 N Jacobi matrix H can replace the first n matrix elements in determining H uniquely. We completely solve the inverse problem for (\u03b4_n , (H-z)^(-1) \u03b4_n ) in the case N < \u221e.", "date": "1997-12", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "73", "number": "1", "publisher": "Hebrew University of Jersusalem", "pagerange": "267-297", "id_number": "CaltechAUTHORS:20180110-165033558", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180110-165033558", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9623121" }, { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02788147", "pub_year": "1997", "author_list": "Gesztesy, Fritz and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/rga9k-bv415", "eprint_id": 88005, "eprint_status": "archive", "datestamp": "2023-08-19 02:05:33", "lastmod": "2026-04-17 16:06:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "del-Rio-R", "name": { "family": "del Rio", "given": "Rafael" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Point spectrum and mixed spectral types for rank one perturbations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 R. Del Rio and B. Simon. \n\nReceived by the editors July 3, 1996. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material. \n\nThe first author was partially supported by CONACYT, Project 400316-5-0567PE.\n\nR.d.R. would like to thank Professor Alejandro Bravo for very useful discussions.\n\n

Published - S0002-9939-97-03997-X.pdf

", "abstract": "We consider examples A_ \u03bb = A + \u03bb(\u03d5, \u2022)\u03d5 of rank one perturbations with \u03d5 a cyclic vector for A. We prove that for any bounded measurable set B \u2282 I, an interval, there exist A, \u03d5 so that {E \u2208 I | some A_ \u03bb has E as an eigenvalue} agrees with B up to sets of Lebesgue measure zero. We also show that there exist examples where A_ \u03bb has a.c. spectrum [0,1] for all \u03bb, and for sets of \u03bb's of positive Lebesgue measure, A_ \u03bb also has singular continuous spectrum in [0,1].", "date": "1997-12", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "125", "number": "12", "publisher": "American Mathematical Society", "pagerange": "3593-3599", "id_number": "CaltechAUTHORS:20180719-132519253", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180719-132519253", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" }, { "agency": "Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)", "grant_number": "400316-5-0567PE" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-97-03997-X", "primary_object": { "basename": "S0002-9939-97-03997-X.pdf", "url": "https://authors.library.caltech.edu/records/rga9k-bv415/files/S0002-9939-97-03997-X.pdf" }, "pub_year": "1997", "author_list": "del Rio, Rafael and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/a4j4c-qk598", "eprint_id": 72991, "eprint_status": "archive", "datestamp": "2023-08-19 01:56:58", "lastmod": "2026-04-17 16:45:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Non-Abelian conifold transitions and N = 4 dualities in three dimensions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Elsevier. \n\nReceived 5 June 1997, Accepted 5 August 1997. \n\nWe would like to thank S. Katz, P. Mayr, Y. Oz and A. Zaffaroni for valuable discussions. K.H. would like to thank Institute for Advanced Study and Rutgers Physics Department, H.O. would like to thank Rutgers and Harvard Physics Departments and C.V. would like to thank Institute for Advanced Study, for hospitality. \n\nThe researches of K.H. and H.O. are supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098, and the research of C.V. is in part supported by NSF grant PHY-92-18167.\n\n

Submitted - 9705220.pdf

", "abstract": "We show how the Higgs mechanism for non-Abelian N = 2 gauge theories in four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau 3-folds. We use this result and T-duality of a further compactification on a circle to derive N = 4, d = 3 dual field theories. This reduces the dualities for N = 4 gauge systems in three dimensions to perturbative symmetries of string theory. Moreover, we find that the dual of a gauge system always exists but may or may not correspond to a Lagrangian system. In particular, we verify a conjecture of Intriligator and Seiberg that an ordinary gauge system is dual to compactification of exceptional tensionless string theory down to three dimensions.", "date": "1997-10-27", "date_type": "published", "publication": "Nuclear Physics B", "volume": "504", "number": "1-2", "publisher": "Elsevier", "pagerange": "147-174", "id_number": "CaltechAUTHORS:20161220-131259376", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-131259376", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-92-18167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(97)00529-4", "primary_object": { "basename": "9705220.pdf", "url": "https://authors.library.caltech.edu/records/a4j4c-qk598/files/9705220.pdf" }, "pub_year": "1997", "author_list": "Hori, Kentaro; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/5adgx-v3p72", "eprint_id": 72993, "eprint_status": "archive", "datestamp": "2023-08-19 01:48:14", "lastmod": "2026-04-17 14:24:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Geometry of N = 1 dualities in four dimensions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Elsevier. \n\nReceived 5 March 1997, Accepted 28 April 1997. \n\nWe thank O. Aharony, M. Douglas, K. Hori, P. Mayr, Y. Oz, N. Seiberg, M. Strassler and S.-T. Yau for valuable discussions. In addition we wish to thank Physics Department of Rutgers University for the hospitality. \n\nThe work of H.O. is supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098. The work of C.V. is supported in part by NSF grant PHY-92-18167.\n\n

Submitted - 9702180.pdf

", "abstract": "We discuss how N = 1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS branes.", "date": "1997-09-01", "date_type": "published", "publication": "Nuclear Physics B", "volume": "500", "number": "1-3", "publisher": "Elsevier", "pagerange": "62-74", "id_number": "CaltechAUTHORS:20161220-132709721", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-132709721", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-92-18167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(97)00304-0", "primary_object": { "basename": "9702180.pdf", "url": "https://authors.library.caltech.edu/records/5adgx-v3p72/files/9702180.pdf" }, "pub_year": "1997", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/2c6jq-p1053", "eprint_id": 38580, "eprint_status": "archive", "datestamp": "2023-08-19 01:45:44", "lastmod": "2026-04-17 15:58:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "Greg" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "New Dichotomies for Borel Equivalence Relations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Association for Symbolic Logic. Received April 7, 1997; revised June 20, 1997.\nThe first author's research partially supported by NSF grant DMS 96-22977.\nThe second author's research partially supported by NSF grant DMS 96-19880.\n\n

Published - 421148.pdf

", "abstract": "We announce two new dichotomy theorems for Borel equivalence relations, and present the results in context by giving an overview of related recent developments.", "date": "1997-09", "date_type": "published", "publication": "Bulletin of Symbolic Logic", "volume": "3", "number": "3", "publisher": "Association for Symbolic Logic", "pagerange": "329-346", "id_number": "CaltechAUTHORS:20130520-144530065", "issn": "1079-8986", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130520-144530065", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 96-22977" }, { "agency": "NSF", "grant_number": "DMS 96-19880" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/421148", "primary_object": { "basename": "421148.pdf", "url": "https://authors.library.caltech.edu/records/2c6jq-p1053/files/421148.pdf" }, "pub_year": "1997", "author_list": "Hjorth, Greg and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/7v6jw-7fr17", "eprint_id": 83008, "eprint_status": "archive", "datestamp": "2023-08-19 01:34:15", "lastmod": "2026-04-17 14:32:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Combinatorial Properties of Brownian Motion on the Compact Classical Groups", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Compact lie groups Brownian combinatorics", "note": "\u00a9 1997 Plenum Publishing Corporation.\n\nReceived October 12, 1995; revised May 10, 1996.\n\nThe greatest thanks are due to Persi Diaconis (the author's thesis advisor), for his many suggestions of problems (a small sampling of which appear in the present work), for his helpful advice when it came time to revise what had been written, and for his encouragement of the author's\nprocrastination.\n\nThanks are also due to the following people and institutions, in no particular order: Andrew Odlyzko, for many helpful comments on Section 5 of Ref. 6; AT&T Bell Laboratories (Murray Hill) and the Center for\nCommunications Research (Princeton) for generous summer support; the Harvard University Mathematics Department and the National Science Foundation, for generous support for the rest of the year. Also, thanks are due, for helpful comments, to Nantel Bergeron, Maurice Rojas, Richard\nStanley, and Dan Stroock. Last, but not least, the author owes thanks to Wojbor Woyczynski, both for introducing him to probability theory and for introducing him to Prof. Diaconis; the thesis excerpted here would be very different, had either introduction not been made.", "abstract": "We consider the probability distribution on a classical group G which naturally generalizes the normal distribution (the \"heat kernel\"), defined in terms of Brownian motions on G. As Brownian motion can be defined in terms of the Laplacian on G, much of this work involves the computation of the Laplacian. These results are then used to study the behavior of the normal distribution on U(n) as n\u21a6\u221e. In addition, we show how the results on computing the Laplacian on the classical groups can be used to compute expectations with respect to Haar measure on those groups.", "date": "1997-07", "date_type": "published", "publication": "Journal of Theoretical Probability", "volume": "10", "number": "3", "publisher": "Springer", "pagerange": "659-679", "id_number": "CaltechAUTHORS:20171106-161236257", "issn": "0894-9840", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171106-161236257", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AT&T Bell Laboratories" }, { "agency": "Center for Communications Research (Princeton)" }, { "agency": "Harvard University" }, { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1023/A:1022601711176", "pub_year": "1997", "author_list": "Rains, E. M." }, { "id": "https://authors.library.caltech.edu/records/rrxas-75j33", "eprint_id": 72992, "eprint_status": "archive", "datestamp": "2023-08-19 01:29:18", "lastmod": "2026-04-17 16:39:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Douglas-M-R", "name": { "family": "Douglas", "given": "Michael R." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Shenker-S-H", "name": { "family": "Shenker", "given": "Stephen H." } } ] }, "title": "Issues in M(atrix) theory compactification", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Elsevier. \n\nReceived 11 March 1997. \n\nWe would like to thank Tom Banks, Greg Moore, Hiraku Nakajima, Nathan Seiberg, and Lenny Susskind for valuable discussions and correspondence. H.O. thanks the High Energy Theory Group of Rutgers University, where a part of this work was done, for hospitality. H.O. is supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098. The work of M.R.D. and S.H.S. was supported in part by grant No. DE-FG02-96ER40959.\n\n

Submitted - 9702203.pdf

", "abstract": "We discuss issues concerning M(atrix) theory compactifications on curved spaces. We argue from the form of the graviton propagator on curved space that excited string states do not decouple from the annulus D0-brane \u03c5^4 amplitude, unlike the flat space case. This argurment shows that a large class of quantum mechanical systems with a finite number of degrees of freedom cannot reproduce supergravity answers. We discuss the specific example of an ALE space and suggest sources of possible higher derivative terms that might help reproduce supergravity results.", "date": "1997-06-05", "date_type": "published", "publication": "Physics Letters B", "volume": "402", "number": "1-2", "publisher": "Elsevier", "pagerange": "36-42", "id_number": "CaltechAUTHORS:20161220-131914782", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-131914782", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-96ER40959" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0370-2693(97)00424-3", "primary_object": { "basename": "9702203.pdf", "url": "https://authors.library.caltech.edu/records/rrxas-75j33/files/9702203.pdf" }, "pub_year": "1997", "author_list": "Douglas, Michael R.; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/fzwwc-ewv74", "eprint_id": 38614, "eprint_status": "archive", "datestamp": "2023-08-19 01:25:12", "lastmod": "2026-04-17 16:08:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On the concept of \u03c0^1_1-completeness", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 American Mathematical Society.\n\nReceived by the editors October 2, 1995 and, in revised form, January 15, 1996.\nCommunicated by Andreas R. Blass.\nThe author's research was partially supported by NSF Grant DMS-9317509.\n\n

Published - 2162226.pdf

", "abstract": "It is shown that two natural notions of completeness for co-analytic sets in Polish spaces, one in terms of continuous reductions and the other in terms of Borel reductions, coincide. The proof uses methods of effective descriptive set theory.", "date": "1997-06", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "125", "number": "6", "publisher": "American Mathematical Society", "pagerange": "1811-1814", "id_number": "CaltechAUTHORS:20130521-135837396", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-135837396", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "other_numbering_system": { "items": [ { "id": "1372034", "name": "MathSciNet review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9939-97-03770-2", "primary_object": { "basename": "2162226.pdf", "url": "https://authors.library.caltech.edu/records/fzwwc-ewv74/files/2162226.pdf" }, "pub_year": "1997", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/v3g1f-pn462", "eprint_id": 72995, "eprint_status": "archive", "datestamp": "2023-08-19 01:23:41", "lastmod": "2026-04-17 16:28:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } } ] }, "title": "Mirror symmetry in three-dimensional gauge theories, quivers and D-branes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Elsevier. \n\nReceived 15 November 1996, Accepted 5 February 1997. \n\nWe would like to thank K. Bardak\u00e7i, I. Grojnowski, A. Hanany, K. Intriligator, D. Morrison, H. Nakajima, R. Plesser, E. Silverstein, A. Strominger, C. Vafa and Z. Yin for discussions. This work is supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098. JdB is a fellow of the Miller Institute for Basic Research in Science.\n\n

Submitted - 9611063.pdf

", "abstract": "We construct and analyze dual N = 4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the Fayet-Iliopoulos parameters of the dual. The results generalize the relation between ALE spaces and moduli spaces of SU(n) and SO(2n) instantons. We interpret some of these results from the string theory viewpoint, for SU(n) by analyzing T-duality and extremal transitions in type II string compactifications, for SO(2n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter.", "date": "1997-05-26", "date_type": "published", "publication": "Nuclear Physics B", "volume": "493", "number": "1-2", "publisher": "Elsevier", "pagerange": "101-147", "id_number": "CaltechAUTHORS:20161220-134318183", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-134318183", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Miller Institute for Basic Research in Science" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(97)00125-9", "primary_object": { "basename": "9611063.pdf", "url": "https://authors.library.caltech.edu/records/v3g1f-pn462/files/9611063.pdf" }, "pub_year": "1997", "author_list": "de Boer, Jan; Hori, Kentaro; et al." }, { "id": "https://authors.library.caltech.edu/records/xcnsb-mc498", "eprint_id": 72994, "eprint_status": "archive", "datestamp": "2023-08-19 01:23:36", "lastmod": "2026-04-17 16:39:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "de-Boer-J", "name": { "family": "de Boer", "given": "Jan" } }, { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } }, { "id": "Yin-Zheng", "name": { "family": "Yin", "given": "Zheng" } } ] }, "title": "Mirror symmetry in three-dimensional gauge theories, SL(2,Z) and D-brane moduli spaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Elsevier. \n\nReceived 20 December 1996, Accepted 4 February 1997. \n\nWe would like to thank A. Hanany, K. Intriligator, S. Kachru, H. Nakajima, M. Ro\u010dek, C. Schweigert and N. Seiberg for discussions. This work is supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098. JdB is a fellow of the Miller Institute for Basic Research in Science. Z. Yin is supported in part by a Graduate Research Fellowship of the U.S. Department of Education.\n\n

Submitted - 9612131.pdf

", "abstract": "We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N = 4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL (2, Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane world-volume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping 5-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.", "date": "1997-05-26", "date_type": "published", "publication": "Nuclear Physics B", "volume": "493", "number": "1-2", "publisher": "Elsevier", "pagerange": "148-176", "id_number": "CaltechAUTHORS:20161220-133645222", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-133645222", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Miller Institute for Basic Research in Science" }, { "agency": "Department of Education" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(97)00115-6", "primary_object": { "basename": "9612131.pdf", "url": "https://authors.library.caltech.edu/records/xcnsb-mc498/files/9612131.pdf" }, "pub_year": "1997", "author_list": "de Boer, Jan; Hori, Kentaro; et al." }, { "id": "https://authors.library.caltech.edu/records/9e376-pva23", "eprint_id": 67069, "eprint_status": "archive", "datestamp": "2023-08-19 01:15:37", "lastmod": "2026-04-17 17:32:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "The Coulomb branch of N = 1 supersymmetric gauge theory with adjoint and fundamental matter", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Published by Elsevier. \n\nReceived 23 January 1997, Available online 15 May 1998. \n\nWork supported in part by the U.S. Dept. of Energy under Grant no. DE-FG03-92-ER 40701. \n\nIt is a pleasure to thank John Preskill, David Lowe and Eric Westphal for helpful discussions and comments. I am especially grateful to Adam Leibovich for collaboration on some related matters.\n\n

Submitted - 9611049.pdf

", "abstract": "We consider N = 1 SU(Nc) gauge theory with an adjoint matter field \u03a6, Nf flavors of fundamentals Q and antifundamentals Q, and tree-level superpotential\nof the form Q\u03a6^lQ. This superpotential is relevant or marginal for lN_f \u2264 2N_c. The theory has a Coulomb branch which is not lifted by quantum corrections. We find the exact effective gauge coupling on the Coulomb branch\nin terms of a family of hyperelliptic curves, thus providing a generalization of known results about N = 2 SUSY QCD to N = 1 context. The Coulomb branch has singular points at which mutually nonlocal dyons become massless.\nThese singularities presumably correspond to new N = 1 superconformal fixed points. We discuss them in some detail for N_c = 2,N_f = 1.", "date": "1997-04-10", "date_type": "published", "publication": "Physics Letters B", "volume": "398", "number": "1-2", "publisher": "Elsevier", "pagerange": "104-109", "id_number": "CaltechAUTHORS:20160513-095922684", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-095922684", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER 40701" } ] }, "other_numbering_system": { "items": [ { "id": "68-2086", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0370-2693(97)00209-8", "primary_object": { "basename": "9611049.pdf", "url": "https://authors.library.caltech.edu/records/9e376-pva23/files/9611049.pdf" }, "pub_year": "1997", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/znh2s-jxj39", "eprint_id": 66988, "eprint_status": "archive", "datestamp": "2023-08-19 01:12:16", "lastmod": "2026-04-17 14:51:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "S." }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Supersymmetric spin glass", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 American Institute of Physics. \n\nSubmitted 27 February 1997; resubmitted 4 April 1997. \n\nThis work was supported in part by the Russian Fund for Fundamental Research, Grant No. 96-15-96939.\n\n

Published - art_3A10.1134_2F1.567408.pdf

Submitted - 9702063.pdf

", "abstract": "The manifestly supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta function form the moduli space \u2133=RP^2, where two types of phases are found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase, which may be interpreted as a spin glass phase.", "date": "1997-04", "date_type": "published", "publication": "Journal of Experimental and Theoretical Physics Letters", "volume": "65", "number": "8", "publisher": "American Institute of Physics", "pagerange": "694-700", "id_number": "CaltechAUTHORS:20160511-105722161", "issn": "0021-3640", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-105722161", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Fund for Fundamental Research", "grant_number": "96-15-96939" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1134/1.567408", "primary_object": { "basename": "9702063.pdf", "url": "https://authors.library.caltech.edu/records/znh2s-jxj39/files/9702063.pdf" }, "related_objects": [ { "basename": "art_3A10.1134_2F1.567408.pdf", "url": "https://authors.library.caltech.edu/records/znh2s-jxj39/files/art_3A10.1134_2F1.567408.pdf" } ], "pub_year": "1997", "author_list": "Gukov, S." }, { "id": "https://authors.library.caltech.edu/records/013c4-3kf87", "eprint_id": 83015, "eprint_status": "archive", "datestamp": "2023-08-19 01:02:20", "lastmod": "2026-04-17 15:47:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "High powers of random elements of compact Lie groups", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1997 Springer-Verlag Berlin Heidelberg. \n\nReceived: 15 October 1995; In revised form: 7 March 1996. \n\nThe greatest thanks are due to Persi Diaconis (the author's thesis advisor), for his many suggestions of problems (a small sampling of which appear in the present work), for his helpful advice when it came time to revise what had been written, and for his encouragement of the author's procrastination. Thanks are also due to the following people and institutions, in no particular order: Andrew Odlyzko, for many helpful comments on Sect. 5 of [9]; AT&T Bell Laboratories (Murray Hill) and the Center for Communications Research (Princeton) for generous summer support; the Harvard University Mathematics Department and the National Science Foundation, for generous support for the rest of the year. Also, thanks are due, for helpful comments, to Nantel Bergeron, Maurice Rojas, Richard Stanley, and Dan Stroock. Last, but not least, the author owes thanks to Wojbor Woyczynski, both for introducing him to probability theory and for introducing him to Prof. Diaconis; the thesis excerpted here would be very different, had either introduction not been made.", "abstract": "If a random unitary matrix U is raised to a sufficiently high power, its eigenvalues are exactly distributed as independent, uniform phases. We prove this result, and apply it to give exact asymptotics of the variance of the number of eigenvalues of U falling in a given arc, as the dimension of U tends to infinity. The independence result, it turns out, extends to arbitrary representations of arbitrary compact Lie groups. We state and prove this more general theorem, paying special attention to the compact classical groups and to wreath products. This paper is excerpted from the author's doctoral thesis, [9].", "date": "1997-02", "date_type": "published", "publication": "Probability Theory and Related Fields", "volume": "107", "number": "2", "publisher": "Springer", "pagerange": "219-241", "id_number": "CaltechAUTHORS:20171107-075059031", "issn": "0178-8051", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171107-075059031", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "AT&T Bell Laboratories" }, { "agency": "Center for Communications Research (Princeton)" }, { "agency": "Harvard University" }, { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/s004400050084", "pub_year": "1997", "author_list": "Rains, E. M." }, { "id": "https://authors.library.caltech.edu/records/b4r0g-y0772", "eprint_id": 81831, "eprint_status": "archive", "datestamp": "2023-08-19 00:59:15", "lastmod": "2026-04-17 16:46:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Calderbank-A-R", "name": { "family": "Calderbank", "given": "A. R." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Shor-P-W", "name": { "family": "Shor", "given": "P. W." } }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "N. J. A." } } ] }, "title": "Quantum Error Correction and Orthogonal Geometry", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 American Physical Society. \n\nReceived 9 May 1996; revised manuscript received 3 July 1996. \n\nWe would like to thank David DiVincenzo for discussions about the group L as presented in [7].\n\n

Published - PhysRevLett.78.405.pdf

Submitted - 9605005.pdf

", "abstract": "A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4 to 10 qubits correcting 1 error, 1 to 13 qubits correcting 2 errors, and 1 to 29 qubits correcting 5 errors.", "date": "1997-01-20", "date_type": "published", "publication": "Physical Review Letters", "volume": "78", "number": "3", "publisher": "American Physical Society", "pagerange": "405-408", "id_number": "CaltechAUTHORS:20170926-101535529", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-101535529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.78.405", "primary_object": { "basename": "9605005.pdf", "url": "https://authors.library.caltech.edu/records/b4r0g-y0772/files/9605005.pdf" }, "related_objects": [ { "basename": "PhysRevLett.78.405.pdf", "url": "https://authors.library.caltech.edu/records/b4r0g-y0772/files/PhysRevLett.78.405.pdf" } ], "pub_year": "1997", "author_list": "Calderbank, A. R.; Rains, E. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/0sc38-d2v59", "eprint_id": 67071, "eprint_status": "archive", "datestamp": "2023-08-19 00:57:42", "lastmod": "2026-04-17 15:32:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Polyubin-I", "name": { "family": "Polyubin", "given": "Igor" } } ] }, "title": "Related N = 2 SUSY Yang Mills Theories and Instanton Expansion", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Published by Elsevier. \n\nReceived 23 August 1996, Revised 25 October 1996, Available online 14 May 1998. \n\nWe are indebted to A. Morozov for helpful discussions and comments. S. Gukov would like to thank A. Mironov and S. Khoroshkin for teaching him some useful mathematical background. I. Polyubin is grateful to the Institute of Theoretical Physics at Hannover for kind hospitality where part of this work was done. \n\nThe work of S.G. was partially supported by RFBR grant No. 95-01-00755, the work of I.P. by grants RFBR-96-01-01106 and INTAS-93-1038. I. Polyubin also would like to thank Volkswagen Stiftung project \"Integrable models and strings\" for financial support.\n\n

Submitted - 9607169.pdf

", "abstract": "The low energy effective actions of the N = 2 SUSY SU(N_c) QCD are considered at the symmetric point on the moduli space. The classes of such theories have similar spectral curves. This fact allows us to show that all these models have the same structure of the coupling matrix and to show that the N_f = 2N_c spectral curve can not be presented as a double covering of the sphere. We calculate first instanton contributions to the coupling matrix and get nonperturbative \u03b2-functions in the SU(2) gauge theory with non-zero bare masses of the matter hypermultiplets.", "date": "1997-01-09", "date_type": "published", "publication": "Physics Letters B", "volume": "391", "number": "1-2", "publisher": "Elsevier", "pagerange": "115-123", "id_number": "CaltechAUTHORS:20160513-101814510", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160513-101814510", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Russian Foundation for Basic Research", "grant_number": "95-01-00755" }, { "agency": "Russian Foundation for Basic Research", "grant_number": "RFBR-96-01-01106" }, { "agency": "International Association for Cooperation with Scientifics (INTAS)", "grant_number": "INTAS-93-1038" }, { "agency": "Volkswagen Stiftung" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0370-2693(96)01454-2", "primary_object": { "basename": "9607169.pdf", "url": "https://authors.library.caltech.edu/records/0sc38-d2v59/files/9607169.pdf" }, "pub_year": "1997", "author_list": "Gukov, Sergei and Polyubin, Igor" }, { "id": "https://authors.library.caltech.edu/records/vstx9-czm56", "eprint_id": 833, "eprint_status": "archive", "datestamp": "2023-08-22 11:31:34", "lastmod": "2026-03-09 23:13:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Luo-W", "name": { "family": "Luo", "given": "Wenzhi" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Determination of modular elliptic curves by Heegner points", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Copyright 1997, Pacific Journal of Mathematics. \n\nTo the memory of Olga Taussky-Todd. \n\nThis Note is dedicated to the memory of Olga Taussky-Todd. Perhaps it is fitting that it concerns heights and special values, as it was while attending the lectures of B. Gross on this topic in Quebec in June 1985 that the second author first met Olga. We would like to thank B. Gross and W. Duke for comments on an earlier version of the article. Thanks are also due to different people, Henri Darmon in particular, for suggesting that a result such as Theorem A above might hold by a variant of [LR]. Both authors would also like to acknowledge the support of the NSF, which made this work possible.", "abstract": "For every integer N \u2265 1, consider the set K(N) of imaginary quadratic fields such that, for each K in K(N), its discriminant D is an odd, square-free integer congruent to 1 modulo 4, which is prime to N and a square modulo 4N. For each K, let c = ([x]\u2212[\u221e]) be the divisor class of a Heegner point x of discriminant D on the modular curve X = X(0)(N) as in [GZ]. (Concretely, such an x is the image of a point z in the upper half plane H such that both z and Nz are roots of integral, definite, binary quadratic forms of the same discriminant D ([B]).) Then c defines a point rational over the Hilbert class field H of K on the Jacobian J = J(0)(N) of X. Denote by cK the trace of c to K.", "date": "1997-01-01", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "181", "number": "3", "publisher": "Pacific Journal of Mathematics", "pagerange": "251-258", "id_number": "CaltechAUTHORS:LUOpjm97", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:LUOpjm97", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "LUOpjm97.pdf", "url": "https://authors.library.caltech.edu/records/vstx9-czm56/files/LUOpjm97.pdf" }, "pub_year": "1997", "author_list": "Luo, Wenzhi and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/gp5x2-23y78", "eprint_id": 544, "eprint_status": "archive", "datestamp": "2023-08-22 11:31:24", "lastmod": "2026-03-07 16:32:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Finite groups acting on homology manifolds", "ispublished": "pub", "full_text_status": "public", "note": "Pacific journal of mathematics, Vol. 181, No. 3, 1997 - Dedicated to the Memory of Olga Taussky-Todd. \n\nThis work was partially supported by NSF DMS-9101237 and NSF DMS-9622843.", "abstract": "In this paper we study homology manifolds T admitting the action of a finite group preserving the structure of a regular CW-complex on T. The CW-complex is parameterized by a poset and the topological properties of the manifold are translated into a combinatorial setting via the poset. We concentrate on n-manifolds which admit a fairly rigid group of automorphisms transitive on the n-cells of the complex. This allows us to make yet another translation from a combinatorial into a group theoretic setting. We close by using our machinery to construct representations on manifolds of the Monster, the largest sporadic group. Some of these manifolds are of dimension 24, and hence candidates for examples to Hirzebruch's Prize Question in [HBJ], but unfortunately closer inspection shows the A^-genus of these manifolds is 0 rather than 1, so none is a Hirzebruch manifold.", "date": "1997-01-01", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "181", "number": "3", "publisher": "Pacific Journal of Mathematics", "pagerange": "3-36", "id_number": "CaltechAUTHORS:ASCpjm97", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ASCpjm97", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "ASCpjm97.pdf", "url": "https://authors.library.caltech.edu/records/gp5x2-23y78/files/ASCpjm97.pdf" }, "pub_year": "1997", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/82peq-b8w10", "eprint_id": 28870, "eprint_status": "archive", "datestamp": "2023-08-22 11:29:53", "lastmod": "2026-04-17 16:12:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Wales-D-B", "name": { "family": "Wales", "given": "David B." } } ] }, "title": "Finite Subgroups of F_4(C) and E_6(C)", "ispublished": "pub", "full_text_status": "restricted", "keywords": "complex Liegroup; finite group; representation", "note": "\u00a9 1997 London Mathematical Society.\nReceived 1 February 1995\u2014Revised 14 November 1995.", "abstract": "The isomorphism types of Lie primitive finite subgroups of the complex Lie groups E_6(C) and F_4(C)\nare determined. Some additional information is provided, such as the characters of these finite\nsubgroups on some small-dimensional modules for the Lie groups.", "date": "1997-01", "date_type": "published", "publication": "Proceedings of the London Mathematical Society", "volume": "74", "number": "1", "publisher": "London Mathematical Society", "pagerange": "105-150", "id_number": "CaltechAUTHORS:20120119-142609219", "issn": "0024-6115", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120119-142609219", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1112/S0024611597000051", "pub_year": "1997", "author_list": "Cohen, Arjeh M. and Wales, David B." }, { "id": "https://authors.library.caltech.edu/records/56k1v-f9h12", "eprint_id": 38613, "eprint_status": "archive", "datestamp": "2023-08-19 00:52:12", "lastmod": "2026-04-17 16:36:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "title": "The classification of hypersmooth Borel equivalence relations", "ispublished": "pub", "full_text_status": "public", "keywords": "Borel equivalence relations, hypersmooth, dichotomy theorems.", "note": "\u00a9 1997 American Mathematical Society.\nReceived by the editors September 1, 1994 and, in revised form, June 11, 1996.\nThe first author's research was partially supported by NSF Grant DMS-9317509.\n\n

Published - 2152908.pdf

", "abstract": "This paper is a contribution to the study of Borel equivalence relations in standard Borel spaces, i.e., Polish spaces equipped with their Borel structure. A class of such equivalence relations which has received particular attention is the class of hyperfinite Borel equivalence relations. These can be defined as the increasing unions of sequences of Borel equivalence relations all of whose equivalence classes are finite or, as it turns out, equivalently those induced by the orbits of a single Borel auto-morphism. Hyperfinite equivalence relations have been classified in [DJK], under two notions of equivalence, Borel bi-reducibility, and Borel isomorphism.", "date": "1997-01", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "10", "number": "1", "publisher": "American Mathematical Society", "pagerange": "215-242", "id_number": "CaltechAUTHORS:20130521-133826211", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-133826211", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "other_numbering_system": { "items": [ { "id": "1396895", "name": "MathSciNet review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-97-00221-X", "primary_object": { "basename": "2152908.pdf", "url": "https://authors.library.caltech.edu/records/56k1v-f9h12/files/2152908.pdf" }, "pub_year": "1997", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/ct565-t8k59", "eprint_id": 73095, "eprint_status": "archive", "datestamp": "2023-08-19 00:49:29", "lastmod": "2026-04-17 17:29:57", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Douglas-M-R", "name": { "family": "Douglas", "given": "Michael R." } }, { "id": "Kato-Akishi", "name": { "family": "Kato", "given": "Akishi" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "D-brane actions on K\u00e4hler manifolds", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 International Press. \n\nWe thank B. de Wit, D.-E. Diaconescu and M. Kontsevich for useful conversations. M.R.D. thanks Cern for hospitality. A.K. would like to thank the Theory Group of Lawrence Berkeley National Laboratory for hospitality. \n\nH.O. thanks Physics Departments of Rutgers, Harvard Universities, Laboratoire de Physique Th\u00e9orique et Hautes Energies (L.P.T.H.E.) at Universit\u00e9s Pierre et Marie Curie (Paris VI), and Aspen Center for Physics for hospitality. \n\nM.R.D. is supported in part by DOE grant DE-FG05-90ER40559. H.O. is supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098. A.K is supported by the fellowship from the Japanese Ministry of Education, Science and Culture.\n\n

Published - ATMP-1997-0001-0002-a003.pdf

Submitted - 9708012.pdf

", "abstract": "We consider actions for N D-branes at points in a general K\u00e4hler manifold, which satisfy the axioms of D-geometry, and could be used as starting points for defining M(atrix)-theory in curved space. We show that the axioms cannot be satisfied unless the metric is Ricci flat, and argue that such actions do exist when the metric is Ricci flat. This may provide an argument for Ricci flatness in M(atrix)-theory.", "date": "1997", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "1", "number": "2", "publisher": "International Press", "pagerange": "237-258", "id_number": "CaltechAUTHORS:20161221-131602093", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-131602093", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG05-90ER40559" }, { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.1997.v1.n2.a3", "primary_object": { "basename": "ATMP-1997-0001-0002-a003.pdf", "url": "https://authors.library.caltech.edu/records/ct565-t8k59/files/ATMP-1997-0001-0002-a003.pdf" }, "related_objects": [ { "basename": "9708012.pdf", "url": "https://authors.library.caltech.edu/records/ct565-t8k59/files/9708012.pdf" } ], "pub_year": "1997", "author_list": "Douglas, Michael R.; Kato, Akishi; et al." }, { "id": "https://authors.library.caltech.edu/records/31h7g-g6971", "eprint_id": 73094, "eprint_status": "archive", "datestamp": "2023-08-19 00:49:23", "lastmod": "2026-04-17 17:33:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hori-Kentaro", "name": { "family": "Hori", "given": "Kentaro" } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } } ] }, "title": "Strong coupling dynamics of four-dimensional N = 1 gauge theories from M-theory fivebrane", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 International Press. \n\nWe would like to thank D. Kutasov, H. Murayama, R. Plesser, C. Vafa and E. Witten for valuable discussions. K.H. would like to thank Institute for Advanced Study and Rutgers Physics Department, H.O. would like to thank Harvard and Rutgers Physics Departments and Y.O. would like to thank the Weizmann Institute Physics Department, for hospitality. \n\nThis research is supported in part by NSF grant PHY-95-14797 and DOE grant DE-AC03-76SF00098.\n\n

Published - ATMP-1997-0001-0001-a001.pdf

Submitted - 9706082.pdf

", "abstract": "It has been known that the fivebrane of type IIA theory can be used to give an exact low energy description of N=2 supersymmetric gauge theories in four dimensions. We follow the recent M theory description by Witten and show that it can be used to study theories with N=1 supersymmetry. The N=2 supersymmetry can be broken to N=1 by turning on a mass for the adjoint chiral superfield in the N=2 vector multiplet. We construct the configuration of the fivebrane for both finite and infinite values of the adjoint mass. The fivebrane describes strong coupling dynamics of N=1 theory with SU(N_c) gauge group and N_f quarks. For N_c > N_f, we show how the brane configuration encodes the information of the Affleck-Dine-Seiberg superpotential. For N_c = and < N_f, we study the deformation space of the brane configuration and compare it with the moduli space of the N=1 theory. We find agreement with field theory results, including the quantum deformation of the moduli space at N_c = N_f. We also prove the type II s-rule in M theory and find new non-renormalization theorems for N=1 superpotentials.", "date": "1997", "date_type": "published", "publication": "Advances in Theoretical and Mathematical Physics", "volume": "1", "number": "1", "publisher": "International Press", "pagerange": "1-52", "id_number": "CaltechAUTHORS:20161221-131040211", "issn": "1095-0761", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-131040211", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-95-14797" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.4310/ATMP.1997.v1.n1.a1", "primary_object": { "basename": "9706082.pdf", "url": "https://authors.library.caltech.edu/records/31h7g-g6971/files/9706082.pdf" }, "related_objects": [ { "basename": "ATMP-1997-0001-0001-a001.pdf", "url": "https://authors.library.caltech.edu/records/31h7g-g6971/files/ATMP-1997-0001-0001-a001.pdf" } ], "pub_year": "1997", "author_list": "Hori, Kentaro; Ooguri, Hirosi; et al." }, { "id": "https://authors.library.caltech.edu/records/61xw0-df492", "eprint_id": 81522, "eprint_status": "archive", "datestamp": "2023-08-19 00:49:52", "lastmod": "2026-03-18 00:07:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "del-Rio-R", "name": { "family": "del Rio", "given": "Rafael" } }, { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Inverse spectral analysis with partial information on the potential. III. Updating boundary conditions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1997 Hindawi Publishing Corporation. \n\nReceived 16 June 1997. \n\nThis material is based upon work supported by CONACYT Project 400316-5-0567PE and US National Science Foundation grants DMS-9623121 and DMS-9401491.\n\nRafael del Rio, Fritz Gesztesy, Barry Simon; Corrections and addendum to \"Inverse spectral analysis with partial information on the potential, III. Updating boundary conditions\", International Mathematics Research Notices, Volume 1999, Issue 11, 1 January 1999, Pages 623\u2013625, https://doi.org/10.1155/S107379289900032X\n\n

Published - 266.pdf

Erratum - del_Rio_1999p623.pdf

", "abstract": "This paper is a postscript to two earlier papers [5]; [6] in that it provides a new way of looking at the problems considered in those papers; it allows the same methods to prove additional results.", "date": "1997", "date_type": "published", "publication": "International Mathematics Research Notices", "volume": "1997", "number": "15", "publisher": "Oxford University Press", "pagerange": "751-758", "id_number": "CaltechAUTHORS:20170918-101826478", "issn": "1073-7928", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170918-101826478", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)", "grant_number": "400316-5-0567PE" }, { "agency": "NSF", "grant_number": "DMS-9623121" }, { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1155/S1073792897000494", "primary_object": { "basename": "266.pdf", "url": "https://authors.library.caltech.edu/records/61xw0-df492/files/266.pdf" }, "related_objects": [ { "basename": "del_Rio_1999p623.pdf", "url": "https://authors.library.caltech.edu/records/61xw0-df492/files/del_Rio_1999p623.pdf" } ], "pub_year": "1997", "author_list": "del Rio, Rafael; Gesztesy, Fritz; et al." }, { "id": "https://authors.library.caltech.edu/records/mnx01-0pa63", "eprint_id": 38567, "eprint_status": "archive", "datestamp": "2023-08-19 00:41:31", "lastmod": "2026-04-17 15:33:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "Greg" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Borel equivalence relations and classifications of countable models", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1996 Elsevier Science B.V. Received 25 July 1995. Communicated by T. Jech. Research partially supported by NSF Grant DMS-9317509. We would like to thank A. Hales and G. Melles for many useful discussions concerning the subject matter of this paper, which led, in particular, to our formulation of the cocycle property for actions and motivated the proof that it is equivalent (in the case of logic actions) to the existence of canonical models.", "abstract": "Using the theory of Borel equivalence relations we analyze the isomorphism relation on the countable models of a theory and develop a framework for measuring the complexity of possible complete invariants for isomorphism.", "date": "1996-12-15", "date_type": "published", "publication": "Annals of Pure and Applied Logic", "volume": "82", "number": "3", "publisher": "Elsevier", "pagerange": "221-272", "id_number": "CaltechAUTHORS:20130517-141337004", "issn": "0168-0072", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-141337004", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0168-0072(96)00006-1", "pub_year": "1996", "author_list": "Hjorth, Greg and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/579p4-xz888", "eprint_id": 85338, "eprint_status": "archive", "datestamp": "2023-08-22 11:22:54", "lastmod": "2026-04-17 16:40:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Del-Rio-R", "name": { "family": "Del Rio", "given": "R." } }, { "id": "Jitomirskaya-S", "name": { "family": "Jitomirskaya", "given": "S." } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Y." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Spectral Measure; Hausdorff Dimension; Dynamical Localization; Point Spectrum; Anderson Model", "note": "\u00a9 1996 Hebrew University of Jerusalem.\n\nReceived July 1, 1995.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9208029. The Government has certain rights in this material.\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.", "abstract": "Although concrete operators with singular continuous spectrum have proliferated recently [7, 11, 13, 17, 34, 35, 37, 39], we still don't really understand much about singular continuous spectrum. In part, this is because it is normally defined by what it isn't\u2500neither pure point nor absolutely continuous. An important point of view, going back in part to Rogers and Taylor [27, 28], and studied recently within spectral theory by Last [22] (also see references therein), is the idea of using Hausdorff measures and dimensions to classify measures. Our main goal in this paper is to look at the singular spectrum produced by rank one perturbations (and discussed in [7, 11, 33]) from this point of view.", "date": "1996-12", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "69", "number": "1", "publisher": "Springer-Verlag", "pagerange": "153-200", "id_number": "CaltechAUTHORS:20180315-134316740", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-134316740", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9208029" }, { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02787106", "pub_year": "1996", "author_list": "Del Rio, R.; Jitomirskaya, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/0m5qd-82d13", "eprint_id": 85341, "eprint_status": "archive", "datestamp": "2023-08-22 11:23:02", "lastmod": "2026-04-17 15:35:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Teschl-G", "name": { "family": "Teschl", "given": "G." } } ] }, "title": "Spectral deformations of one-dimensional Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Jacobi Operator; Dirichlet Eigenvalue; Dirichlet Data; Double Commutation; Isospectral Deformation", "note": "\u00a9 1996 Hebrew University of Jerusalem.\n\nReceived July 15, 1996.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.", "abstract": "We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schr\u00f6dinger operators H =\u2212 d^2/dx^2 + V in H =\u2212 d^2/dx^2 + VinL^2(\u211d). Our technique is connected to Dirichlet data, that is, the spectrum of the operator H^D on L^2((\u2212\u221e,x_0)) \u2295 L^2((x_0, \u221e)) with a Dirichlet boundary condition at x_0. The transformation moves a single eigenvalue of H^D and perhaps flips which side of x_0 the eigenvalue lives. On the remainder of the spectrum, the transformation is realized by a unitary operator. For cases such as V(x) \u2192 \u221e as |x| \u2192 \u221e, where V is uniquely determined by the spectrum of H and the Dirichlet data, our result implies that the specific Dirichlet data allowed are determined only by the asymptotics as E \u2192 \u221e.", "date": "1996-12", "date_type": "published", "publication": "Journal d'Analyse Math\u00e9matique", "volume": "70", "number": "1", "publisher": "Springer-Verlag", "pagerange": "267-324", "id_number": "CaltechAUTHORS:20180315-135902699", "issn": "0021-7670", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-135902699", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02820446", "pub_year": "1996", "author_list": "Gesztesy, F.; Simon, B.; et al." }, { "id": "https://authors.library.caltech.edu/records/8zhse-rn236", "eprint_id": 72996, "eprint_status": "archive", "datestamp": "2023-08-22 11:21:21", "lastmod": "2026-04-17 14:07:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Becker-K", "name": { "family": "Becker", "given": "Katrin" } }, { "id": "Becker-M", "name": { "family": "Becker", "given": "Melanie" } }, { "id": "Morrison-D-R", "name": { "family": "Morrison", "given": "David R." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } }, { "id": "Yin-Zheng", "name": { "family": "Yin", "given": "Zheng" } } ] }, "title": "Supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds", "ispublished": "pub", "full_text_status": "public", "keywords": "Calabi-Yau four-folds; Cayley cycles; Exceptional holonomy manifolds; Supersymmetric cycles; Mirror symmetry; 3-brane; Special Lagrangian submanifolds", "note": "\u00a9 1996 Elsevier. \n\nReceived 20 August 1996, Accepted 6 September 1996. \n\nWe would like to thank R. Bryant, G. Moore, R. Plesser, J. Polchinski, A. Schwimmer, A. Strominger, C. Vafa, and Y. Vlassopoulos for useful discussions. D.R.M. and H.O. are grateful for the hospitality of the Aspen Center for Physics during the final stages of this project. The work of K.B. was supported by NSF grant PHY89-04035. The work of M.B. was supported by DOE grant DOE-91ER40618. The work of D.R.M. was supported in part by the National Science Foundation under grant DMS-9401447. The work of H.O. was supported in part by NSF grant PHY-951497 and DOE grant DE-AC03-76SF00098. Y.O. is partially supported by the Israel Science Foundation through the Center for the Physics of Basic Interactions. Z.Y. is supported by a Graduate Research Fellowship of the U.S. Department of Education.\n\n

Submitted - 9608116.pdf

", "abstract": "We derive in the SCFT and low energy effective action frameworks the necessary and sufficient conditions for supersymmetric cycles in exceptional holonomy manifolds and Calabi-Yau four-folds. We show that the Cayley cycles in Spin(7) holonomy eight-manifolds and the associative and coassociative cycles in G2 holonomy seven-manifolds preserve half of the space-time supersymmetry. We find that while the holomorphic and special Lagrangian cycles in Calabi-Yau four-folds preserve half of the space-time supersymmetry, the Cayley submanifolds are novel as they preserve only one quarter of it. We present some simple examples. Finally, we discuss the implications of these supersymmetric cycles on mirror symmetry in higher dimensions.", "date": "1996-11-25", "date_type": "published", "publication": "Nuclear Physics B", "volume": "480", "number": "1-2", "publisher": "Elsevier", "pagerange": "225-238", "id_number": "CaltechAUTHORS:20161220-134740171", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-134740171", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY89-04035" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-91ER40618" }, { "agency": "NSF", "grant_number": "DMS-9401447" }, { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Israel Science Foundation" }, { "agency": "Department of Education" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/S0550-3213(96)00491-9", "primary_object": { "basename": "9608116.pdf", "url": "https://authors.library.caltech.edu/records/8zhse-rn236/files/9608116.pdf" }, "pub_year": "1996", "author_list": "Becker, Katrin; Becker, Melanie; et al." }, { "id": "https://authors.library.caltech.edu/records/hvsty-8jp78", "eprint_id": 81345, "eprint_status": "archive", "datestamp": "2023-08-19 00:32:59", "lastmod": "2026-04-17 17:31:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Holden-H", "name": { "family": "Holden", "given": "H." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Zhao-Z", "name": { "family": "Zhao", "given": "Z." } } ] }, "title": "A Trace Formula for Multidimensional Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1996 Academic Press, Inc.\n\nReceived 7 April 1995. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. \n\nWe thank Peter Lax for telling us of his work prior to publication. F. G. is indebted to M. Aschbacher and G. Neugebauer for the hospitality at Caltech where some of this work was done. F. G. and H. H. were also supported in part by the Norwegian Research Council for Science and the Humanities (NAVF).", "abstract": "We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schr\u00f6dinger operators. For example, letVbe a continuous function on [0, 1]^\u03bd\u2282R^\u03bd. For A\u2282{1,\u2026,\u03bd}, let \u2212\u0394_A be the Laplace operator on [0, 1]^\u03bd with mixed Dirichlet\u2013Neumann boundary conditions[formula]Let |A|= number of points inA. Then we'll prove that[formula]with \u29a0V\u2994 the average of Vat the 2^\u03bd corners of [0, 1]^\u03bd.", "date": "1996-11-01", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "141", "number": "2", "publisher": "Elsevier", "pagerange": "449-465", "id_number": "CaltechAUTHORS:20170912-095106346", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170912-095106346", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" }, { "agency": "Norwegian Research Council for Science and the Humanities" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1996.0137", "pub_year": "1996", "author_list": "Gesztesy, F.; Holden, H.; et al." }, { "id": "https://authors.library.caltech.edu/records/xh5xt-6vk58", "eprint_id": 85319, "eprint_status": "archive", "datestamp": "2023-08-19 00:31:50", "lastmod": "2026-04-17 14:03:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Robinson-R-M", "name": { "family": "Robinson", "given": "Raphael M." } }, { "id": "Goffinet-D", "name": { "family": "Goffinet", "given": "Daniel" } }, { "id": "Poonen-B", "name": { "family": "Poonen", "given": "Bjorn" } }, { "id": "Propp-J", "name": { "family": "Propp", "given": "Jim" } }, { "id": "Stong-R", "name": { "family": "Stong", "given": "Richard" } }, { "id": "Lagarias-J-C", "name": { "family": "Lagarias", "given": "Jeffrey C." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Lewittes-J", "name": { "family": "Lewittes", "given": "Joseph" } }, { "id": "Lehman-H-H", "name": { "family": "Lehman", "given": "Herbert H." } } ] }, "title": "Problems: 10550-10556", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1996 Mathematical Association of America.", "abstract": "No abstract", "date": "1996-11", "date_type": "published", "publication": "American Mathematical Monthly", "volume": "103", "number": "9", "publisher": "Mathematical Association of America", "pagerange": "808-809", "id_number": "CaltechAUTHORS:20180315-070628395", "issn": "0002-9890", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-070628395", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2974454", "pub_year": "1996", "author_list": "Robinson, Raphael M.; Goffinet, Daniel; et al." }, { "id": "https://authors.library.caltech.edu/records/v2nx9-sb625", "eprint_id": 86383, "eprint_status": "archive", "datestamp": "2023-08-19 00:32:06", "lastmod": "2026-04-17 16:46:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Copyright 1996 Barry Simon. \n\nCommunicated by: Palle E. T. Jorgensen. \n\nReceived by the editors April 3, 1995 and, in revised form, April 24, 1995. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.", "abstract": "We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis.", "date": "1996-11", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "124", "number": "11", "publisher": "American Mathematical Society", "pagerange": "3361-3369", "id_number": "CaltechAUTHORS:20180511-162701951", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180511-162701951", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-96-03599-X", "pub_year": "1996", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/4fq9s-qy158", "eprint_id": 73075, "eprint_status": "archive", "datestamp": "2023-08-19 00:26:21", "lastmod": "2026-04-17 14:28:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Summing up Dirichlet Instantons", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1996 The American Physical Society. \n\nReceived 15 August 1996. \n\nWe would like to thank T. Eguchi, B. Greene, K. Intriligator, D. Morrison, J. Polchinski, and A. Strominger for valuable discussions. We gratefully acknowledge the hospitality of the Aspen Center for Physics, where this work was done. H. O. is supported in part by NSF Grant PHY-951497 and DOE Grant DE-AC03-76SF00098. C. V. is supported in part by NSF Grant PHY-92-18167.\n\n

Published - PhysRevLett.77.3296.pdf

Submitted - 9608079.pdf

", "abstract": "We investigate quantum corrections to the moduli space for hypermultiplets for the type IIA string near a conifold singularity. We find a unique quantum deformation based on symmetry arguments which is consistent with a recent conjecture. The correction can be interpreted as an infinite sum coming from multiple wrappings of the Euclidean Dirichlet branes around the vanishing cycle.", "date": "1996-10-14", "date_type": "published", "publication": "Physical Review Letters", "volume": "77", "number": "16", "publisher": "American Physical Society", "pagerange": "3296-3298", "id_number": "CaltechAUTHORS:20161221-111837116", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-111837116", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-92-18167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1103/PhysRevLett.77.3296", "primary_object": { "basename": "9608079.pdf", "url": "https://authors.library.caltech.edu/records/4fq9s-qy158/files/9608079.pdf" }, "related_objects": [ { "basename": "PhysRevLett.77.3296.pdf", "url": "https://authors.library.caltech.edu/records/4fq9s-qy158/files/PhysRevLett.77.3296.pdf" } ], "pub_year": "1996", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/zn0hk-gc189", "eprint_id": 72997, "eprint_status": "archive", "datestamp": "2023-08-19 00:26:15", "lastmod": "2026-04-17 16:43:59", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Oz-Y", "name": { "family": "Oz", "given": "Yaron" } }, { "id": "Yin-Zheng", "name": { "family": "Yin", "given": "Zheng" } } ] }, "title": "D-branes on Calabi-Yau spaces and their mirrors", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1996 Elsevier. \n\nReceived 19 June 1996, Accepted 16 July 1996. \n\nWe would like to thank K. Becker, T. Eguchi, D. Gepner, B. Greene, S. Katz, M. Li, J. Maldacena, D. Morrison, R. Plesser, J. Polchinski, A. Schwimmer, A. Strominger and C. Vafa for useful discussions. Y.O. would like to thank LBNL for hospitality during the final stages of this work. This work was supported in part by the National Science Foundation under grants PHS-9501018 and PHY-951497 and in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. Y.O. is partially supported by the Israel Science Foundation through the Center for the Physics of Basic Interactions. Z.Y. is supported by Graduate Research Fellowship of the U.S. Department of Education.\n\n

Submitted - 9606112.pdf

", "abstract": "We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms D-branes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calabi-Yau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as T-duality are also discussed.", "date": "1996-10-14", "date_type": "published", "publication": "Nuclear Physics B", "volume": "477", "number": "2", "publisher": "Elsevier", "pagerange": "407-430", "id_number": "CaltechAUTHORS:20161220-135624344", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-135624344", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9501018" }, { "agency": "NSF", "grant_number": "PHY-951497" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "Israel Science Foundation" }, { "agency": "Department of Education" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0550-3213(96)00379-3", "primary_object": { "basename": "9606112.pdf", "url": "https://authors.library.caltech.edu/records/zn0hk-gc189/files/9606112.pdf" }, "pub_year": "1996", "author_list": "Ooguri, Hirosi; Oz, Yaron; et al." }, { "id": "https://authors.library.caltech.edu/records/6vswr-vqc95", "eprint_id": 79071, "eprint_status": "archive", "datestamp": "2023-08-19 00:23:27", "lastmod": "2026-04-17 16:13:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Seiberg-Witten Floer Homology and Heegaard Splittings", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1996 World Scientific Publishing. \n\nReceived 9 February 1996; Revised 30 May 1996. \n\nI am grateful to Tom Mrowka for the many useful conversations, for his very helpful comments and criticism, and for his patience. I am grateful to Bai-Ling Wang for the invaluable and always stimulating collaboration. I thank Rong Wang for having informed me of his interesting work on the subject, for having pointed out a mistake in a previous version of this work, and for some very helpful suggestions. I am grateful to my advisor Mel Rothenberg for having supervised this work. I thank Stefan Bauer, Rogier Brussee, Ralph Cohen, Rafe Mazzeo, and Dan Pollack for useful and stimulating conversations.\n\n

Submitted - 9601011.pdf

", "abstract": "The dimensional reduction of Seiberg-Witten theory defines a gauge theory of compact connected three-manifolds. Solutions of the equations modulo gauge symmetries on a three-manifold Y can be interpreted as the critical points of a functional defined on an infinite dimensional configuration space of U(1)-connections and spinors. The original Seiberg-Witten equations on the infinite cylinder Y \u00d7 IR are the downward gradient flow of the functional. Thus, it is possible to construct an infinite dimensional\nMorse theory. The associated Morse homology is the analogue in the context of Seiberg-Witten theory of Floer's instanton homology constructed using Yang-Mills gauge theory. The construction and the properties of\nthis Seiberg-Witten Floer homology are essentially different according to whether the three-manifold Y is a homology sphere or has non-trivial rational homology. In this work we construct the Seiberg-Witten Floer homology for three-manifolds with b^1(Y ) > 0. We define an associated Casson-like invariant and we prove that it satisfies the expected intersection formula under a Heegaard splitting of the three-manifold.", "date": "1996-10", "date_type": "published", "publication": "International Journal of Mathematics", "volume": "7", "number": "5", "publisher": "World Scientific Publishing", "pagerange": "671-696", "id_number": "CaltechAUTHORS:20170713-092558409", "issn": "0129-167X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170713-092558409", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0129167X96000359", "primary_object": { "basename": "9601011.pdf", "url": "https://authors.library.caltech.edu/records/6vswr-vqc95/files/9601011.pdf" }, "pub_year": "1996", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/3m6jw-chr61", "eprint_id": 80014, "eprint_status": "archive", "datestamp": "2023-08-19 00:20:22", "lastmod": "2026-04-17 17:36:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Zhu-Yunfeng", "name": { "family": "Zhu", "given": "Yunfeng" } } ] }, "title": "The Lyapunov Exponents for Schr\u00f6dinger Operators with Slowly Oscillating Potentials", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1996 Academic Press. \n\nReceived 14 August 1995, Accepted 2 November 1995. \n\nThis material is based upon work supported by the National Science Foundation under Grant DMS-9401491. The Government has certain rights in this material.", "abstract": "By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schr\u00f6dinger operator \u2013d^2/dx^2+cos x^\u03bd with 0<\u03bd<1 on L^2[0, \u221e). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.", "date": "1996-09-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "140", "number": "2", "publisher": "Elsevier", "pagerange": "541-556", "id_number": "CaltechAUTHORS:20170809-105308934", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170809-105308934", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1996.0117", "pub_year": "1996", "author_list": "Simon, Barry and Zhu, Yunfeng" }, { "id": "https://authors.library.caltech.edu/records/8k8c1-qrq28", "eprint_id": 86381, "eprint_status": "archive", "datestamp": "2023-08-19 00:04:37", "lastmod": "2026-04-17 13:57:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Stolz-G", "name": { "family": "Stolz", "given": "G." } } ] }, "title": "Operators with singular continuous spectrum, V. Sparse potentials", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 Copyright 1996 B. Simon and G. Stolz. \n\nCommunicated by: Palle E. T. Jorgensen. \n\nReceived by the editors January 9, 1995. \n\nhis material is based upon work supported by the National Science Foundation under grant no. DMS-9101715. The government has certain rights to this material.", "abstract": "By presenting simple theorems for the absence of positive eigenvalues for certain one-dimensional Schr\u00f6dinger operators, we are able to construct explicit potentials which yield purely singular continuous spectrum.", "date": "1996-07", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "124", "number": "7", "publisher": "American Mathematical Society", "pagerange": "2073-2080", "id_number": "CaltechAUTHORS:20180511-161415818", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180511-161415818", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-96-03465-X", "pub_year": "1996", "author_list": "Simon, B. and Stolz, G." }, { "id": "https://authors.library.caltech.edu/records/amm1y-40c68", "eprint_id": 81519, "eprint_status": "archive", "datestamp": "2023-08-18 23:58:41", "lastmod": "2026-04-17 16:44:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Teschl-G", "name": { "family": "Teschl", "given": "G." } } ] }, "title": "Zeros of the Wronskian and Renormalized Oscillation Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1995 Johns Hopkins University Press. \n\nManuscript received May 3, 1995; revised August 16, 1995. \n\nResearch supported in part by NSF Grant DMS-9401491.\n\n

Published - 252.pdf

", "abstract": "For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E_(1,2) \u2208 R and if u_(1,2) solve the differential equation Hu_j = E_ju_j, j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P(E_1,E_2)(H) of H equals the number of zeros of the Wronskian of u_1 and u_2.", "date": "1996-06", "date_type": "published", "publication": "American Journal of Mathematics", "volume": "118", "number": "3", "publisher": "Johns Hopkins University Press", "pagerange": "571-594", "id_number": "CaltechAUTHORS:20170918-100353730", "issn": "0002-9327", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170918-100353730", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1353/ajm.1996.0024", "primary_object": { "basename": "252.pdf", "url": "https://authors.library.caltech.edu/records/amm1y-40c68/files/252.pdf" }, "pub_year": "1996", "author_list": "Gesztesy, F.; Simon, B.; et al." }, { "id": "https://authors.library.caltech.edu/records/051g8-03726", "eprint_id": 12226, "eprint_status": "archive", "datestamp": "2023-08-22 10:59:52", "lastmod": "2026-04-17 16:54:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "A. N." }, "orcid": "0000-0003-3903-5158" }, { "id": "Skorik-S", "name": { "family": "Skorik", "given": "S." } } ] }, "title": "Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 Institute of Physics and IOP Publishing Limited 1996. \n\nReceived 17 August 1995, in final form 29 January 1996. Print publication: Issue 8 (21 April 1996). \n\nOne of the authors (SS) would like to thank H Saleur for helpful discussions. The work of AK was supported in part by the US Department of Energy under grant No DE-FG03-92-ER40701. The work of SS was supported by the grant NSF-PHY-9357207.\n\n

Published - KAPjpa96.pdf

Submitted - 9506067v2.pdf

", "abstract": "We study boundary bound states using the Bethe ansatz formalism for the open XXZ (\u0394 > 1) chain in a boundary magnetic field h. Boundary bound states are represented by the 'boundary strings' similar to those described in Skorik and Saleur. We find that for certain values of h the ground-state wavefunction contains boundary strings and from this infer the existence of two 'critical' fields in agreement with Jimbo et al. An expression for the vacuum surface energy in the thermodynamic limit is derived and found to be an analytic function of h. We argue that boundary excitations appear only in pairs with `bulk' excitations or with boundary excitations at the other end of the chain. We mainly discuss the case where the magnetic fields at the left and the right boundaries are antiparallel, but we also comment on the case of parallel fields. In the Ising (\u0394 = \u221e) and isotropic (\u0394 = 0) limits our results agree with those previously known.", "date": "1996-04-21", "date_type": "published", "publication": "Journal of Physics A: Mathematical and General", "volume": "29", "number": "8", "publisher": "IOP", "pagerange": "1629-1638", "id_number": "CaltechAUTHORS:KAPjpa96", "issn": "0305-4470", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KAPjpa96", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9357207" } ] }, "other_numbering_system": { "items": [ { "id": "68-1998", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/0305-4470/29/8/011", "primary_object": { "basename": "KAPjpa96.pdf", "url": "https://authors.library.caltech.edu/records/051g8-03726/files/KAPjpa96.pdf" }, "related_objects": [ { "basename": "9506067v2.pdf", "url": "https://authors.library.caltech.edu/records/051g8-03726/files/9506067v2.pdf" } ], "pub_year": "1996", "author_list": "Kapustin, A. N. and Skorik, S." }, { "id": "https://authors.library.caltech.edu/records/se78q-nsy23", "eprint_id": 85380, "eprint_status": "archive", "datestamp": "2023-08-20 07:27:13", "lastmod": "2026-04-17 15:57:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Operators with singular continuous spectrum, VI. Graph Laplacians and Laplace-Beltrami operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Continuous spectra, Laplacians, Mathematics, Infinity, Spectral energy distribution, Eigenvalues, Ladders, Topological theorems, Coordination numbers, Topology", "note": "\u00a9 1996 Barry Simon. \n\nReceived by the editors October 7, 1994. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.\n\n

Published - S0002-9939-96-03245-5.pdf

", "abstract": "Examples are constructed of Laplace-Beltrami operators and graph Laplacians with singular continuous spectrum.", "date": "1996-04", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "124", "number": "4", "publisher": "American Mathematical Society", "pagerange": "1177-1183", "id_number": "CaltechAUTHORS:20180320-112111420", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180320-112111420", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-96-03245-5", "primary_object": { "basename": "S0002-9939-96-03245-5.pdf", "url": "https://authors.library.caltech.edu/records/se78q-nsy23/files/S0002-9939-96-03245-5.pdf" }, "pub_year": "1996", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/fy0mv-05860", "eprint_id": 73013, "eprint_status": "archive", "datestamp": "2023-08-22 10:55:52", "lastmod": "2026-04-17 16:05:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "Two-dimensional black hole and singularities of CY manifolds", "ispublished": "pub", "full_text_status": "public", "keywords": "Theory of fundamental strings; Properties of perturbation theory. Conformal field theory, algebraic structures. Compactification and four-dimensional models. Noncritical string theory. Extended classical solutions; cosmic strings, domain walls, texture", "note": "\u00a9 1996 Elsevier. \n\nReceived 23 November 1995, Accepted 4 January 1996. \n\nWe would like to thank S. Shenker, who participated in an earlier stage of this project, for discussions. We also thank the Aspen Center for Physics, where this project was initiated. The work of HO was supported in part by the National Science Foundation under grant PHY-9501018 and in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. The research of CV was supported in part by NSF grant PHY-92-18167.\n\n

Submitted - 9511164.pdf

", "abstract": "We study the degenerating limits of superconformal theories for compactifications on singular K3 and Calabi-Yau threefolds. We find that in both cases the degeneration involves creating an Euclidean two-dimensional black hole coupled weakly to the rest of the system. Moreover we find that the conformal theory of A_n singularities of K3 are the same as that of the symmetric fivebrane. We also find intriguing connections between ADE (1, n) non-critical strings and singular limits of superconformal theories on the corresponding ALE space.", "date": "1996-03-18", "date_type": "published", "publication": "Nuclear Physics B", "volume": "463", "number": "1", "publisher": "Elsevier", "pagerange": "55-72", "id_number": "CaltechAUTHORS:20161220-153626803", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-153626803", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9501018" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-92-18167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0550-3213(96)00008-9", "primary_object": { "basename": "9511164.pdf", "url": "https://authors.library.caltech.edu/records/fy0mv-05860/files/9511164.pdf" }, "pub_year": "1996", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/by79e-q4e86", "eprint_id": 85332, "eprint_status": "archive", "datestamp": "2023-08-22 10:54:29", "lastmod": "2026-04-17 14:00:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Operators with Singular Continuous Spectrum, VII. Examples with Borderline Time Decay", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics; Time Decay", "note": "\u00a9 1996 Springer-Verlag.\n\nReceived: 10 January 1995, in revised form: 30 May 1995.\n\nCommunicated by A. Jaffe.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.", "abstract": "We construct one-dimensional potentials V(x) so that if H = - d^2/dx^2 + V(x) on L^2(\u211d), then H has purely singular spectrum; but for a dense set D, \u03c6 \u0454 D implies that \u2502\u03c6,\u212f^(-itH)\u03c6)\u2502 \u2266 C_\u03c6\u2502t\u2502^(-1/2)In(\u2502t\u2502) for \u2502t\u2502 > 2. This implies the spectral measures have Hausdorff dimension one and also, following an idea of Malozemov-Molchanov, provides counterexamples to the direct extension of the theorem of\nSimon-Spencer on one-dimensional infinity high barriers.", "date": "1996-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "176", "number": "3", "publisher": "Springer", "pagerange": "713-722", "id_number": "CaltechAUTHORS:20180315-112637401", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-112637401", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02099257", "pub_year": "1996", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/18qvf-n1p20", "eprint_id": 29189, "eprint_status": "archive", "datestamp": "2023-08-20 07:03:54", "lastmod": "2026-03-18 00:07:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Uniqueness theorems in inverse spectral theory for one-dimensional Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operators, inverse spectral theory, Krein's spectral shift function.", "note": "\u00a9 1996 by the authors. Received by the editors February 27, 1995. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The U.S. Government has certain rights in this material.\n\n

Published - GEStams96.pdf

", "abstract": "New unique characterization results for the potential V(x) in connection with Schr\u00f6dinger operators on R and on the half-line [0,\u221e)are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for Schr\u00f6dinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for Schr\u00f6dinger operators with confining potentials on the entire real line.", "date": "1996-01", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "348", "number": "1", "publisher": "American Mathematical Society", "pagerange": "349-373", "id_number": "CaltechAUTHORS:20120208-090710174", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120208-090710174", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9947-96-01525-5", "primary_object": { "basename": "GEStams96.pdf", "url": "https://authors.library.caltech.edu/records/18qvf-n1p20/files/GEStams96.pdf" }, "pub_year": "1996", "author_list": "Gesztesy, F. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/krf6r-wtm04", "eprint_id": 38583, "eprint_status": "archive", "datestamp": "2023-09-14 19:50:08", "lastmod": "2026-04-20 18:00:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hjorth-G", "name": { "family": "Hjorth", "given": "Greg" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Analytic Equivalence Relations and Ulm-Type Classifications", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1995 Association for Symbolic Logic.\n\nReceived September 26, 1994; revised March 2, 1995.\n\nThe research of the second author was partially supported by NSF Grant DMS-9317509.\n\n

Published - 2275888.pdf

", "abstract": "Our main goal in this paper is to establish a Glimm-Effros type dichotomy for arbitrary analytic equivalence relations.", "date": "1995-12", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "60", "number": "4", "publisher": "Association for Symbolic Logic", "pagerange": "1273-1300", "id_number": "CaltechAUTHORS:20130520-160211996", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130520-160211996", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "other_numbering_system": { "items": [ { "id": "MR1367210", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2275888", "primary_object": { "basename": "2275888.pdf", "url": "https://authors.library.caltech.edu/records/krf6r-wtm04/files/2275888.pdf" }, "pub_year": "1995", "author_list": "Hjorth, Greg and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/tnfsy-mwn63", "eprint_id": 84693, "eprint_status": "archive", "datestamp": "2023-09-15 05:52:19", "lastmod": "2026-03-18 00:05:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "L^p Norms of the Borel Transform and the Decomposition of Measures", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1995 American Mathematical Society. \n\nReceived by the editors March 25, 1994 and, in revised form, May 23, 1994. \n\nThis material is based upon work supported by National Science Foundation Grant No. DMS-9101715. \n\nIt is a pleasure to thank S. Jitomirskaya, A. Klein, and T. Wolff for valuable discussions.\n\n

Published - 2161903.pdf

", "abstract": "We relate the decomposition over [a, b] of a measure d\u00b5 (on R) into absolutely continuous, pure point, and singular continuous pieces to the behavior of integrals _\u03b1\u222b^b(ImF(x + i\u03b5))^P dx as \u03b5 \u2193 0. Here F is the Borel a transform of d\u00b5, that is, F(z) = (x - z)^(-1) d\u00b5(x).", "date": "1995-12", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "123", "number": "12", "publisher": "American Mathematical Society", "pagerange": "3749-3755", "id_number": "CaltechAUTHORS:20180206-140113065", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180206-140113065", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.2307/2161903", "primary_object": { "basename": "2161903.pdf", "url": "https://authors.library.caltech.edu/records/tnfsy-mwn63/files/2161903.pdf" }, "pub_year": "1995", "author_list": "Simon, B." }, { "id": "https://authors.library.caltech.edu/records/w2n91-czs18", "eprint_id": 85333, "eprint_status": "archive", "datestamp": "2023-08-22 10:40:15", "lastmod": "2026-04-17 22:34:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hof-A", "name": { "family": "Hof", "given": "A." } }, { "id": "Knill-O", "name": { "family": "Knill", "given": "O." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Singular Continuous Spectrum for Palindromic Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics; Large Class", "note": "\u00a9 1995 Springer-Verlag.\n\nReceived: 28 July 1994; in revised form: 28 November 1994.\n\nCommunicated by A. Jaffe.\n\nWork partially supported by NSERC. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.", "abstract": "We give new examples of discrete Schr\u00f6dinger operators with potentials taking finitely many values that have purely singular continuous spectrum. If the hull X of the potential is strictly ergodic, then the existence of just one potentialx in X for which the operator has no eigenvalues implies that there is a generic set in X for which the operator has purely singular continuous spectrum. A sufficient condition for the existence of such anx is that there is a z \u2208 X that contains arbitrarily long palindromes. Thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset in X. The class includes well-known substitutions like Fibonacci, Thue-Morse, Period Doubling, binary non-Pisot and ternary non-Pisot. We also show that the operator has no absolutely continuous spectrum for all x \u2208 X if X derives from a primitive substitution. For potentials defined by circle maps, x_n = 1_J (\u03b8_0 + n\u03b1), we show that the operator has purely singular continuous spectrum for a generic subset in X for all irrational \u03b1 and every half-open interval J.", "date": "1995-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "174", "number": "1", "publisher": "Springer", "pagerange": "149-159", "id_number": "CaltechAUTHORS:20180315-130513176", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-130513176", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02099468", "pub_year": "1995", "author_list": "Hof, A.; Knill, O.; et al." }, { "id": "https://authors.library.caltech.edu/records/bjnyy-epy71", "eprint_id": 38600, "eprint_status": "archive", "datestamp": "2023-08-20 06:21:59", "lastmod": "2026-04-20 16:29:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Solecki-S", "name": { "family": "Solecki", "given": "S." } } ] }, "title": "Approximation of analytic by Borel sets and definable countable chain conditions", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1995 Springer-Verlag. Received July 20, 1993 and in revised form March 6, 1994. Research partially supported by NSF grant DMS-9317509.", "abstract": "Let I be a \u03c3-ideal on a Polish space such that each set from I is contained in a Borel set from I. We say that I fails to fulfil the \u03a3_1^1 countable chain condition if there is a \u03a3_1^1 equivalence relation with uncountably many equivalence classes none of which is in I. Assuming definable determinacy, we show that if the family of Borel sets from I is definable in the codes of Borel sets, then each \u03a3_1^1 set is equal to a Borel set modulo a set from I iff I fulfils the \u03a3_1^1 countable chain condition. Further we characterize the \u03c3-ideals I generated by closed sets that satisfy the countable chain condition or, equivalently in this case, the approximation property for \u03a3_1^1 sets mentioned above. It turns out that they are exactly of the form MGR(F)={A : \u2200F \u2208 F A \u2229F is meager in F} for a countable family F of closed sets. In particular, we verify partially a conjecture of Kunen by showing that the \u03c3-ideal of meager sets is the unique \u03c3-ideal on R, or any Polish group, generated by closed sets which is invariant under translations and satisfies the countable chain condition.", "date": "1995-10", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "89", "number": "1-3", "publisher": "Hebrew University Magnes Press", "pagerange": "343-356", "id_number": "CaltechAUTHORS:20130521-103730289", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-103730289", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/BF02808208", "pub_year": "1995", "author_list": "Kechris, A. S. and Solecki, S." }, { "id": "https://authors.library.caltech.edu/records/474ea-qa207", "eprint_id": 73015, "eprint_status": "archive", "datestamp": "2023-08-20 06:20:39", "lastmod": "2026-04-20 16:46:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "Cumrun" } } ] }, "title": "All loop N = 2 string amplitudes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1995 Elsevier. \n\nReceived 7 June 1995, Accepted 11 July 1995. \n\nWe would like to thank N. Berkovits, R. Dijkgraaf, A. Lesniewski, G. Moore, W. Taylor, E. Witten and S.-T. Yau for valuable discussions. In addition HO thanks Laurent Baulieu, Marco Picco and the members of LPTHE, Universit\u00e9 Pierre et Marie Curie where part of this work was carried out, for their hospitality. The work of HO was supported in part by the National Science Foundation under grant PHY-9501018 and in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098. The work of CV is supported in part by the NSF grant PHY-92-18167.\n\n

Submitted - 9505183.pdf

", "abstract": "Using the N = 4 topological reformulation of N = 2 strings, we compute all loop partition function for special compactifications of N = 2 strings as a function of target moduli. We also reinterpret N = 4 topological amplitudes in terms of slightly modified N = 2 topological amplitudes. We present some preliminary evidence for the conjecture that N = 2 strings is the large N limit of Holomorphic Yang-Mills in four dimensions.", "date": "1995-09-25", "date_type": "published", "publication": "Nuclear Physics B", "volume": "451", "number": "1-2", "publisher": "Elsevier", "pagerange": "121-161", "id_number": "CaltechAUTHORS:20161220-154316012", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-154316012", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-9501018" }, { "agency": "Department of Energy (DOE)", "grant_number": "DE-AC03-76SF00098" }, { "agency": "NSF", "grant_number": "PHY-92-18167" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0550-3213(95)00365-Y", "primary_object": { "basename": "9505183.pdf", "url": "https://authors.library.caltech.edu/records/474ea-qa207/files/9505183.pdf" }, "pub_year": "1995", "author_list": "Ooguri, Hirosi and Vafa, Cumrun" }, { "id": "https://authors.library.caltech.edu/records/cfe5c-9bf02", "eprint_id": 70362, "eprint_status": "archive", "datestamp": "2023-08-20 06:19:45", "lastmod": "2026-04-20 16:12:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" }, { "id": "Ligeti-Z", "name": { "family": "Ligeti", "given": "Zoltan" }, "orcid": "0000-0002-4830-5773" }, { "id": "Politzer-H-D", "name": { "family": "Politzer", "given": "H. David" }, "orcid": "0000-0002-4983-6621" } ] }, "title": "Leading logarithms of the b quark mass in inclusive B \u2192 Xs \u03b3 decay", "ispublished": "pub", "full_text_status": "restricted", "note": "@ 1995 Elsevier Science B.V. \n\nReceived 12 July 1995. \n\nWork supported in part by the U.S. Dept. of Energy under Grant no. DE-FG03-92-ER 40701. \n\nWe thank Mark Wise for many useful discussions and Peter Cho and Ira Rothstein for helpful conversations. After this work was completed we received the preprint [ 171, which also discusses the loss contribution to the photon spectrum. Our result in Eq. (2.3) agrees with Eq. (18) of [ 171. Ref. [ 171 mentions that soft photons could be summed to eliminate the singularity near E, = 0, but our main point is that resumming collinear gluons is relevant for any photon energy.", "abstract": "Part of the order \u03b1s correction to the inclusive B \u2192 Xs \u03b3 photon spectrum is enhanced by log(mb2ms2). We discuss its origin and sum the corrections proportional to [\u03b1s log(mb2\u03bc2)]n to all orders. These are the calculable leading logarithms in the parton fragmentation functions of a quark or gluon into a photon. Although the gluon fragmentation into a photon starts only at order \u03b1s2, its contribution is of the same order as the s quark's in the leading log sum. For not too small values of the photon energy, the resummation.yields a moderate suppression. In the standard model, the coefficient of the operator whose matrix element gives rise to such terms is small. A measurement of the photon spectrum around 1 GeV would provide a theoretically clean determination of C8, the Wilson coefficient of the b \u2192 s g operator.", "date": "1995-09-14", "date_type": "published", "publication": "Physics Letters B", "volume": "357", "number": "4", "publisher": "Elsevier", "pagerange": "653-658", "id_number": "CaltechAUTHORS:20160915-085815399", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160915-085815399", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER 40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0370-2693(95)00962-K", "pub_year": "1995", "author_list": "Kapustin, Anton; Ligeti, Zoltan; et al." }, { "id": "https://authors.library.caltech.edu/records/ym90e-a4824", "eprint_id": 85833, "eprint_status": "archive", "datestamp": "2023-08-20 06:06:12", "lastmod": "2026-04-20 16:13:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Del Rio-R", "name": { "family": "Del Rio", "given": "R." } }, { "id": "Jitomirskaya-S", "name": { "family": "Jitomirskaya", "given": "S." } }, { "id": "Last-Y", "name": { "family": "Last", "given": "Y." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "What is Localization?", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1995 American Physical Society. \n\n(Received 22 March 1995) \n\nWe would like to thank J. Avron and A. Klein for useful discussions. The work of S.J. was supported by the National Science Foundation under Grant No. DMS-9208029. The work of B.S. was supported by the National Science Foundation under Grant No. DMS-9401491.\n\n

Published - PhysRevLett.75.117.pdf

", "abstract": "We examine various issues relevant to localization in the Anderson model. We show there is more to localization than exponentially localized states by presenting an example with such states but where \u27e8x(t)^2\u27e9/t^(2 \u2212 \u03b4) is unbounded for any \u03b4 > 0. We show that the recently discovered instability of localization under rank one perturbations is only a weak instability.", "date": "1995-07-03", "date_type": "published", "publication": "Physical Review Letters", "volume": "75", "number": "1", "publisher": "American Physical Society", "pagerange": "117-119", "id_number": "CaltechAUTHORS:20180413-113435667", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-113435667", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9208029" }, { "agency": "NSF", "grant_number": "DMS-9401491" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.75.117", "primary_object": { "basename": "PhysRevLett.75.117.pdf", "url": "https://authors.library.caltech.edu/records/ym90e-a4824/files/PhysRevLett.75.117.pdf" }, "pub_year": "1995", "author_list": "Del Rio, R.; Jitomirskaya, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/dy7vr-c4834", "eprint_id": 81199, "eprint_status": "archive", "datestamp": "2023-08-20 05:58:17", "lastmod": "2026-04-17 18:26:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kiselev-A", "name": { "family": "Kiselev", "given": "A." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Rank One Perturbations with Infinitesimal Coupling", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1995 Academic Press. \n\nReceived May 24, 1994. \n\nThis material is based upon work supported by the National Science Foundation under Grant DMS-9101715. The Government has certain rights in this material.", "abstract": "We consider a positive self-adjoint operator A and formal rank one perturbations B = A + \u03b1(\u03c6, \u00b7)\u03c6, where \u03c6 \u2208 H\u22122(A) but \u03c6 \u2209 H_(\u22121) (A), with H_s(A) the usual scale of spaces. We show that B can be defined for such \u03c6 and what are essentially negative infinitesimal values of \u03b1. In a sense we will make precise, every rank one perturbation is one of three forms: (i) \u03c6 \u2208 H^(\u22121)(A), \u03b1 \u2208 R; (ii) \u03c6 \u2208 H_(\u22121), \u03b1 = \u221e; or (iii) the new type we consider here.", "date": "1995-06", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "130", "number": "2", "publisher": "Elsevier", "pagerange": "345-356", "id_number": "CaltechAUTHORS:20170906-141427255", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170906-141427255", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1995.1074", "pub_year": "1995", "author_list": "Kiselev, A. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/mqac8-nm031", "eprint_id": 66987, "eprint_status": "archive", "datestamp": "2023-08-20 05:43:35", "lastmod": "2026-04-20 16:32:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gepner-D", "name": { "family": "Gepner", "given": "Doron" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "On the classification of fusion rings", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1995 Elsevier Science B.V. \n\nReceived 25 October 1994. \n\nWork supported in part by the U.S. Department of Energy under Grant No. DE-FG03-92-ER40701. \n\nWe would like to thank S. Cherkis for numerous discussions.\n\n

Submitted - 9410089.pdf

", "abstract": "The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion coefficients. We give a catalogue of fusion rings which can arise for these field theories. It is shown that all such fusion rules can be realized by current algebras. Our results support the conjecture that all rational conformal field theories are related to current algebras.", "date": "1995-04-13", "date_type": "published", "publication": "Physics Letters B", "volume": "349", "number": "1-2", "publisher": "Elsevier", "pagerange": "71-75", "id_number": "CaltechAUTHORS:20160511-105134551", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-105134551", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0370-2693(95)00172-H", "primary_object": { "basename": "9410089.pdf", "url": "https://authors.library.caltech.edu/records/mqac8-nm031/files/9410089.pdf" }, "pub_year": "1995", "author_list": "Gepner, Doron and Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/p1njw-36a74", "eprint_id": 85334, "eprint_status": "archive", "datestamp": "2023-08-22 10:21:09", "lastmod": "2026-04-20 16:29:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Holden-H", "name": { "family": "Holden", "given": "H." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Absolute Summability of the Trace Relation for Certain Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Reflection; Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics", "note": "\u00a9 1995 Springer-Verlag. \n\nReceived: 4 February 1994.\n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.\n\nWe would like to thank Z. Zhao for numerous helpful discussions. F.G. is indebted to the Department of Mathematical Sciences of the University of Trondheim, Norway, and the Department of Mathematics at Caltech, Pasadena, CA for the hospitality extended to him in the summer of 1993. Support by the Norwegian Research Council (NFR) and by Caltech is gratefully acknowledged. H.H. is grateful to the Norwegian Research Council (NFR) for support.\n\nCommunicated by T. Spencer.", "abstract": "A recently established general trace formula for one-dimensional Schr\u00f6dinger operators is systematically studied in the context of short-range potentials, potentials which approach different spatial asymptotes sufficiently fast, and appropriate impurity (defect) interactions in one-dimensional solids. We prove the absolute summability of the trace formula and establish its connections with scattering quantities, such as reflection coefficients, in each case.", "date": "1995-03", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "168", "number": "1", "publisher": "Springer", "pagerange": "137-161", "id_number": "CaltechAUTHORS:20180315-131739823", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-131739823", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" }, { "agency": "Norwegian Research Council" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02099586", "pub_year": "1995", "author_list": "Gesztesy, F.; Holden, H.; et al." }, { "id": "https://authors.library.caltech.edu/records/3995g-fqz59", "eprint_id": 81203, "eprint_status": "archive", "datestamp": "2023-08-20 05:31:48", "lastmod": "2026-04-20 17:00:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Rank One Perturbations at Infinite Coupling", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1995 Academic Press. \n\nReceived February 7, 1994. \n\nCommunicated by L. Gross. \n\nThis material is based on work supported by the National Science Foundation under Grant DMS-9101715. The government has certain rights in this material. \n\nF. G. is indebted to the Department of Mathematics at Caltech for its hospitality and support during the summer of 1993 where some of this work was done.", "abstract": "We discuss rank one perturbations A_\u03b1 = A + \u03b1(\u03c6,\u00b7)\u03c6, \u03b1 \u2208R , A \u2265 0 self-adjoint. Let d\u03bc\u03b1(x) be the spectral measure defined by (\u03c6, (A_\u03b1 - z)^(\u22121) \u03c6) = \u222b d\u03bc_\u03b1(x)/(x - z). We prove there is a measure d\u03c1_\u221e which is the weak limit of (1 + \u03b1^2) d\u03bc_\u03b1(x) as \u03b1 \u2192 \u221e. If \u03c6 is cyclic for A, then A_\u221e, the strong resolvent limit of A_\u03b1, is unitarily equivalent to multiplication by x on L^2(R, d\u03c1_\u221e). This generalizes results known for boundary condition dependence of Sturm-Liouville operators on half-lines to the abstract rank one case.", "date": "1995-02-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "128", "number": "1", "publisher": "Elsevier", "pagerange": "245-252", "id_number": "CaltechAUTHORS:20170906-143042594", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170906-143042594", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1995.1030", "pub_year": "1995", "author_list": "Gesztesy, F. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/0cdje-9vw39", "eprint_id": 79967, "eprint_status": "archive", "datestamp": "2023-08-20 05:15:15", "lastmod": "2026-03-18 00:01:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Operators with Singular Continuous Spectrum: I. General Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1995 Annals of Mathematics. \n\nReceived April 19, 1993. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.", "abstract": "The Baire category theorem implies that the family, F, of dense sets G_ \u03b4 in fixed metric space, X, is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A \u2208 F has uncountable intersections with any open ball in X.", "date": "1995-01", "date_type": "published", "publication": "Annals of Mathematics", "volume": "141", "number": "1", "publisher": "Annals of Mathematics", "pagerange": "131-145", "id_number": "CaltechAUTHORS:20170808-151736465", "issn": "0003-486X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170808-151736465", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "pub_year": "1995", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/6ekk1-jd489", "eprint_id": 81517, "eprint_status": "archive", "datestamp": "2023-08-20 05:10:37", "lastmod": "2026-04-20 17:33:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Holden-H", "name": { "family": "Holden", "given": "H." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Zhao-Z", "name": { "family": "Zhao", "given": "Z." } } ] }, "title": "Higher order trace relations for Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1995 World Scientific. \n\nReceived: 14 November 1994. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. \n\nF.G. is indebted to the Department of Mathematical Sciences of the University of Trondheim, NTH, Norway, and the Department of Mathematics at Caltech Pasadena, CA for the hospitality extended to him in the summer of 1993. Support by the Norwegian Research Council for Science and the Humanities (NAVF) (F.G. and H.H.) and by Caltech (F.G.) is gratefully acknowledged.", "abstract": "We extend the trace formula recently proven for general one-dimensional Schr\u00f6dinger operators which obtains the potential V(x) from a function \u03be(x, \u03bb) by deriving trace relations computing moments of \u03be(\u03bb, x) d\u03bb in terms of polynomials in the derivatives of V at x. We describe the relation of those polynomials to KdV invariants. We also discuss trace formulae for analogs of \u03be associated with boundary conditions other than the Dirichlet boundary condition underlying \u03be.", "date": "1995", "date_type": "published", "publication": "Reviews in Mathematical Physics", "volume": "7", "number": "6", "publisher": "World Scientific", "pagerange": "893-922", "id_number": "CaltechAUTHORS:20170918-092925572", "issn": "0129-055X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170918-092925572", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" }, { "agency": "Norwegian Research Council for Science and the Humanities (NAVF)" }, { "agency": "Caltech" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1142/S0129055X95000347", "pub_year": "1995", "author_list": "Gesztesy, F.; Holden, H.; et al." }, { "id": "https://authors.library.caltech.edu/records/7rnzf-vgg36", "eprint_id": 66985, "eprint_status": "archive", "datestamp": "2023-08-20 05:00:36", "lastmod": "2026-04-20 16:43:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "A. N." }, "orcid": "0000-0003-3903-5158" }, { "id": "Skorik-S", "name": { "family": "Skorik", "given": "S." } } ] }, "title": "On the non-relativistic limit of the quantum sine-Gordon model with integrable boundary condition", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1994 Elsevier Science B.V. \n\nReceived 3 October 1994; accepted for publication 14 October 1994. \n\nOne of the authors (S.S.) would like to thank H. Saleur, S.N.M. Ruijsenaars and V. Korepin for helpful discussions. The work of A.K. was supported in part by the US Department of Energy under Grant No. DE-FG03-92-ER40701, while the work of S.S. was supported by grant NSF-PHY-9357207.\n\n

Submitted - 9409097.pdf

", "abstract": "We show that the generalized Calogero-Moser model with a boundary potential of the P\u00f6schl-Teller type describes the non-relativistic limit of the quantum sine-Gordon model on a half-line with a Dirichlet boundary condition.", "date": "1994-12-19", "date_type": "published", "publication": "Physics Letters A", "volume": "196", "number": "1-2", "publisher": "Elsevier", "pagerange": "47-51", "id_number": "CaltechAUTHORS:20160511-104118415", "issn": "0375-9601", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-104118415", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" }, { "agency": "NSF", "grant_number": "PHY-9357207" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0375-9601(94)91042-1", "primary_object": { "basename": "9409097.pdf", "url": "https://authors.library.caltech.edu/records/7rnzf-vgg36/files/9409097.pdf" }, "pub_year": "1994", "author_list": "Kapustin, A. N. and Skorik, S." }, { "id": "https://authors.library.caltech.edu/records/8effq-49c42", "eprint_id": 73092, "eprint_status": "archive", "datestamp": "2023-08-20 04:45:47", "lastmod": "2026-04-17 22:36:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bershadsky-M", "name": { "family": "Bershadsky", "given": "M." } }, { "id": "Cecotti-S", "name": { "family": "Cecotti", "given": "S." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "H." }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "C." } } ] }, "title": "Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 Springer-Verlag. \n\nReceived 23 November 1993.", "abstract": "We develop techniques to compute higher loop string amplitudes for twisted N=2 theories with \u0109=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of the N=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the 'number' of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the corresponding N=2 theory. Relations with c=1 strings are also pointed out.", "date": "1994-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "165", "number": "2", "publisher": "Springer", "pagerange": "311-427", "id_number": "CaltechAUTHORS:20161221-125723575", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-125723575", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/BF02099774", "pub_year": "1994", "author_list": "Bershadsky, M.; Cecotti, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/vjsg7-gmx86", "eprint_id": 83373, "eprint_status": "archive", "datestamp": "2023-08-20 04:46:37", "lastmod": "2026-04-20 17:06:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Del Rio-R", "name": { "family": "Del Rio", "given": "R." } }, { "id": "Makarov-N-G", "name": { "family": "Makarov", "given": "N." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Operators with singular continuous spectrum: II. Rank one operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 Springer-Verlag. \n\nReceived: 12 July 1993; in revised form October 25, 1993. \n\nResearch partially supported by DGAPA-UNAM and CONACYT. \n\nThis material is based upon work suported by the National Science Foundation under Grant No. DMS-9207071. The Government has certain rights in this material. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.", "abstract": "For an operator, A, with cyclic vector \u03d5, we study A+\u03bbP, where P is the rank one projection onto multiples of \u03d5. If [\u03b1,\u03b2] \u2282 spec (A) and A has no a.c. spectrum, we prove that A+\u03bbP has purely singular continuous spectrum on (\u03b1,\u03b2) for a dense G_\u03b4 of \u03bb's.", "date": "1994-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "165", "number": "1", "publisher": "Springer", "pagerange": "59-67", "id_number": "CaltechAUTHORS:20171120-161021287", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171120-161021287", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Universidad Nacional Aut\u00f3noma de M\u00e9xico (UNAM)" }, { "agency": "Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)" }, { "agency": "NSF", "grant_number": "DMS-9207071" }, { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02099737", "pub_year": "1994", "author_list": "Del Rio, R.; Makarov, N.; et al." }, { "id": "https://authors.library.caltech.edu/records/azshz-6yr94", "eprint_id": 83024, "eprint_status": "archive", "datestamp": "2023-08-20 04:46:31", "lastmod": "2026-04-17 22:31:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jitomirskaya-S", "name": { "family": "Jitomirskaya", "given": "S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Operators with singular continuous spectrum: III. Almost periodic Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 Springer-Verlag. \n\nReceived: 19 October 1993. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.", "abstract": "We prove that one-dimensional Schr\u00f6dinger operators with even almost periodic potential have no point spectrum for a dense G_\u03b4 in the hull. This implies purely singular continuous spectrum for the almost Mathieu equation for coupling larger than 2 and a dense G_\u03b4 in \u03b8 even if the frequency is an irrational with good Diophantine properties.", "date": "1994-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "165", "number": "1", "publisher": "Springer", "pagerange": "201-205", "id_number": "CaltechAUTHORS:20171107-095819082", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171107-095819082", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02099743", "pub_year": "1994", "author_list": "Jitomirskaya, S. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/yxqjj-rtf43", "eprint_id": 85832, "eprint_status": "archive", "datestamp": "2023-08-20 04:46:45", "lastmod": "2026-04-20 16:49:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Del Rio-R", "name": { "family": "Del Rio", "given": "R." } }, { "id": "Jitomirskaya-S", "name": { "family": "Jitomirskaya", "given": "S." } }, { "id": "Makarov-N-G", "name": { "family": "Makarov", "given": "N." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Singular continuous spectrum is generic", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1994 American Mathematical Society. \n\nReceived by the editors May 3, 1993. \n\nThe first author's research was partially supported by DGAPA-UNAM and CONACYT. \n\nThis material is based upon work of the third author supported by National Science Foundation grant DMS-9207071. The government has certain rights in this material. \n\nThis material is based upon work of the first and fourth authors supported by National Science Foundation grant DMS-9101715. The government has certain rights in this material.\n\n

Accepted Version - 9410217.pdf

", "abstract": "In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense G_\u03b4.", "date": "1994-10", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "31", "number": "2", "publisher": "American Mathematical Society", "pagerange": "208-212", "id_number": "CaltechAUTHORS:20180413-112754476", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-112754476", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Universidad Nacional Aut\u00f3noma de M\u00e9xico (UNAM)" }, { "agency": "Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)" }, { "agency": "NSF", "grant_number": "DMS-9207071" }, { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0273-0979-1994-00518-X", "primary_object": { "basename": "9410217.pdf", "url": "https://authors.library.caltech.edu/records/yxqjj-rtf43/files/9410217.pdf" }, "pub_year": "1994", "author_list": "Del Rio, R.; Jitomirskaya, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/p3p13-xp104", "eprint_id": 38558, "eprint_status": "archive", "datestamp": "2023-08-22 10:00:59", "lastmod": "2026-04-17 22:33:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Topology and descriptive set theory", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Polish spaces; Borel sets; Analytic sets; Polish groups; Borel actions; Borel equivalence relations", "note": "\u00a9 1994 Elsevier Science B.V. Received 28 March 1994. Research partially supported by NSF Grant DMS-9317509.", "abstract": "This paper consists essentially of the text of a series of four lectures given by the author in the Summer Conference on General Topology and Applications, Amsterdam, August 1994. \nInstead of attempting to give a general survey of the interrelationships between the two subjects mentioned in the title, which would be an enormous and hopeless task, we chose to illustrate them in a specific context, that of the study of Borel actions of Polish groups and Borel equivalence relations. This is a rapidly growing area of research of much current interest, which has interesting connections not only with topology and set theory (which are emphasized here), but also to ergodic theory, group representations, operator algebras and logic (particularly model theory and recursion theory).\nThere are four parts, corresponding roughly to each one of the lectures. The first contains a brief review of some fundamental facts from descriptive set theory. In the second we discuss Polish groups, and in the third the basic theory of their Borel actions. The last part concentrates on Borel equivalence relations.\nThe exposition is essentially self-contained, but proofs, when included at all, are often given in the barest outline.", "date": "1994-08-15", "date_type": "published", "publication": "Topology and Its Applications", "volume": "58", "number": "3", "publisher": "Elsevier", "pagerange": "195-222", "id_number": "CaltechAUTHORS:20130517-110331634", "issn": "0166-8641", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-110331634", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0166-8641(94)00146-4", "pub_year": "1994", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/5f51c-avv92", "eprint_id": 66984, "eprint_status": "archive", "datestamp": "2023-08-20 04:29:34", "lastmod": "2026-04-20 17:41:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "A. N." }, "orcid": "0000-0003-3903-5158" }, { "id": "Pronin-P-I", "name": { "family": "Pronin", "given": "P. I." } } ] }, "title": "Non-Renormalization Theorem for the Gauge Coupling in 2+1 Dimensions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1994 World Scientific Publishing Co Pte Ltd. \n\nReceived: 3 March 1994. \n\nWork supported in part by the U.S. Dept. of Energy under Grant No. DE-FG03-92-ER40701.\n\n

Submitted - 9401053.pdf

", "abstract": "We prove that the \u03b2-function of the gauge coupling in 2+1 dimensions gauge theory coupled to any renormalizable system of spinor and scalar fields is zero. This result holds both when the gauge field action is the Chern-Simons action and when it is the topologically massive action.", "date": "1994-07-10", "date_type": "published", "publication": "Modern Physics Letters A", "volume": "9", "number": "21", "publisher": "World Scientific", "pagerange": "1925-1932", "id_number": "CaltechAUTHORS:20160511-101438481", "issn": "0217-7323", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160511-101438481", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG03-92-ER40701" } ] }, "other_numbering_system": { "items": [ { "id": "68-1913", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0217732394001787", "primary_object": { "basename": "9401053.pdf", "url": "https://authors.library.caltech.edu/records/5f51c-avv92/files/9401053.pdf" }, "pub_year": "1994", "author_list": "Kapustin, A. N. and Pronin, P. I." }, { "id": "https://authors.library.caltech.edu/records/nev59-rf164", "eprint_id": 76091, "eprint_status": "archive", "datestamp": "2023-08-20 04:19:31", "lastmod": "2026-03-09 23:14:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Barthel-L", "name": { "family": "Barthel", "given": "Laure" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "A nonvanishing result for twists of L-functions of GL(n)", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 Duke University Press. \n\nReceived 6 October 1993. Revision received 30 November 1993. \n\nWe thank the following people: D. Rohrlich for his encouragement and for reading the paper carefully, which led to his discovering an error in the first version, H. Jacquet for very useful comments and conversations on L-functions, F. Shahidi and V. K. Murty for helpful remarks, S. Friedberg for suggestions for improvement, and P. Sarnak for raising the problem of seeing how much better one could do by assuming the Ramanujan conjecture. As it is evident from the statement of the Theorem above, it helps some, but not too much, to assume this conjecture for \u03c0, which says that the Hecke eigenvalues a(n, \u03c0)^2 are bounded. (Remember the unitary normalization.) The Rankin method shows that the average value of la(n, \u03c0)^2 is O(1), and this is nearly as good. Finally, the first author would like to take this opportunity to acknowledge the hospitality of the California Institute of Technology mathematics department during her stay there, when the bulk of this work was completed. The second author would like to thank the Hebrew University for an invitation to visit for two weeks during which time this paper was essentially finalized.", "abstract": "[no abstract]", "date": "1994-06", "date_type": "published", "publication": "Duke Mathematical Journal", "volume": "74", "number": "3", "publisher": "Duke University Press", "pagerange": "681-700", "id_number": "CaltechAUTHORS:20170408-155534575", "issn": "0012-7094", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170408-155534575", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1215/S0012-7094-94-07425-5", "pub_year": "1994", "author_list": "Barthel, Laure and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/e4wzx-gyh85", "eprint_id": 81208, "eprint_status": "archive", "datestamp": "2023-08-20 03:57:46", "lastmod": "2026-04-20 16:08:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J." } }, { "id": "Seiler-R", "name": { "family": "Seiler", "given": "R." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Index of a Pair of Projections", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 Academic Press. \n\nReceived March 1, 1993. \n\nCommunicated by L. Gross. \n\nResearch partially supported by US NSF Grant DMS-9101715. \n\nWe thank M. Ben-Artzi for the hospitality of Hebrew University where some of this work was done and I. Kaplansky for a useful question. The research is partially supported by GIF.", "abstract": "We discuss pairs of self-adjoint projections with P \u2212 Q \u2208 J_(2n + 1), the trace ideal, and prove that for m \u2265 n, tr(P \u2212 Q)^(2m + 1) = tr(P \u2212 Q)^(2n + 1) = dim(Ker Q \u2229 Ran P) \u2212 dim(Ker P \u2229 Ran Q) is an integer. We also prove that there exists a unitary V interchanging P and Q if and only if this integer is 0.", "date": "1994-02-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "120", "number": "1", "publisher": "Elsevier", "pagerange": "220-237", "id_number": "CaltechAUTHORS:20170906-144540972", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170906-144540972", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" }, { "agency": "German-Israeli Foundation for Research and Development" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1994.1031", "pub_year": "1994", "author_list": "Avron, J.; Seiler, R.; et al." }, { "id": "https://authors.library.caltech.edu/records/r3tcq-5nk56", "eprint_id": 38593, "eprint_status": "archive", "datestamp": "2023-08-20 03:41:47", "lastmod": "2026-03-09 20:41:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dougherty-R", "name": { "family": "Dougherty", "given": "R." } }, { "id": "Jackson-S", "name": { "family": "Jackson", "given": "S." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The structure of hyperfinite Borel equivalence relations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1994 American Mathematical Society.\nReceived by the editors September 24, 1991. \nResearch of the authors was partially supported by NSF grants DMS-9158092 (R.D.), DMS-9007808 (S.J.) and DMS-9020153 (A.S.K.).\n\n

Published - 2154620.pdf

", "abstract": "We study the structure of the equivalence relations induced by the orbits of a single Borel automorphism on a standard Borel space. We show that any two such equivalence relations which are not smooth, i.e., do not admit Borel selectors, are Borel embeddable into each other. (This utilizes among other things work of Effros and Weiss.) Using this and also results of Dye, Varadarajan, and recent work of Nadkarni, we show that the cardinality of the set of ergodic invariant measures is a complete invariant for Borel isomorphism of aperiodic nonsmooth such equivalence relations. In particular, since the only possible such cardinalities are the finite ones, countable infinity, and the cardinality of the continuum, there are exactly countably infinitely many isomorphism types. Canonical examples of each type are also discussed.", "date": "1994-01", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "341", "number": "1", "publisher": "American Mathematical Society", "pagerange": "193-225", "id_number": "CaltechAUTHORS:20130521-092754518", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-092754518", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9158092" }, { "agency": "NSF", "grant_number": "DMS-9007808" }, { "agency": "NSF", "grant_number": "DMS-9020153" } ] }, "other_numbering_system": { "items": [ { "id": "1149121", "name": "MathSciNet review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2154620", "primary_object": { "basename": "2154620.pdf", "url": "https://authors.library.caltech.edu/records/r3tcq-5nk56/files/2154620.pdf" }, "pub_year": "1994", "author_list": "Dougherty, R.; Jackson, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/2whnz-a9y96", "eprint_id": 38670, "eprint_status": "archive", "datestamp": "2023-08-20 03:41:51", "lastmod": "2026-03-09 20:35:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Countable Sections for Locally Compact Group Actions. II", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1993 American Mathematical Society. Received by the editors April 14, 1992. Communicated by Andreas R. Blass. Research partially supported by NSF grant DMS-9020153.\n\n

Published - 2160191.pdf

", "abstract": "In this paper we study the structure of the orbit equivalence relation induced by a Borel action of a second countable locally compact group on a standard Borel space.", "date": "1994-01", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "120", "number": "1", "publisher": "American Mathematical Society", "pagerange": "241-247", "id_number": "CaltechAUTHORS:20130524-135334590", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130524-135334590", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9020153" } ] }, "other_numbering_system": { "items": [ { "id": "MR1169035", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2160191.pdf", "url": "https://authors.library.caltech.edu/records/2whnz-a9y96/files/2160191.pdf" }, "pub_year": "1994", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/xngff-fx024", "eprint_id": 83026, "eprint_status": "archive", "datestamp": "2023-08-20 03:43:42", "lastmod": "2026-03-18 00:07:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "Joseph E." } }, { "id": "Seiler-R", "name": { "family": "Seiler", "given": "Ruedi" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Charge deficiency, charge transport and comparison of dimensions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1994 Springer-Verlag. \n\nReceived: January 19, 1993. \n\nPart of this work was written while the authors enjoyed the hospitality of the Landau Center at the Hebrew University. The work is supported by BSF, DFG, GIF, NSF, the fund for the Promotion of Research at the Technion and the Technion VPR-Steigman research fund. One of the authors (RS) should like to acknowledge the hospitality of the Mittag-Leffler Institute. \n\nWe are grateful to S. Agmon, E. Akkermans, J. Bellissard, S, Borac, J. Fr\u00f6hlich, I. Kaplansky, M. Klein, A. Pnueli and U. Sivan for useful discussions and comments.\n\n

Submitted - 9803014.pdf

", "abstract": "We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.", "date": "1994-01", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "159", "number": "2", "publisher": "Springer", "pagerange": "399-422", "id_number": "CaltechAUTHORS:20171107-101426795", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171107-101426795", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "German-Israeli Foundation for Research and Development" }, { "agency": "NSF" }, { "agency": "Technion" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02102644", "primary_object": { "basename": "9803014.pdf", "url": "https://authors.library.caltech.edu/records/xngff-fx024/files/9803014.pdf" }, "pub_year": "1994", "author_list": "Avron, Joseph E.; Seiler, Ruedi; et al." }, { "id": "https://authors.library.caltech.edu/records/fzdqp-zs169", "eprint_id": 88009, "eprint_status": "archive", "datestamp": "2023-08-20 03:38:20", "lastmod": "2026-03-18 00:08:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "del-Rio-R", "name": { "family": "del Rio", "given": "R." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Stolz-G", "name": { "family": "Stolz", "given": "G." } } ] }, "title": "Stability of Spectral Types for Sturm-Liouville Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 International Press of Boston. \n\nReceived March 7, 1994. \n\nThe work of R. del Rio is partially supported by DGAPA-UNAM and CONACYT. \n\nThe work of R. del Rio and B. Simon is partially supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. \n\nR. del Rio would like to thank J. Weidmann for having initiated him in the study of stability of spectral types. R.del Rio and G.Stolz would also like to thank C. Peck and M. Aschbacher for the hospitality at Caltech.", "abstract": "For Sturm-Liouville operators on the half line, we show that the property of having singular, singular continuous, or pure point spectrum for a set of boundary conditions of positive measure depends only on the behavior of the potential at infinity. We also prove that existence of recurrent spectrum implies that of singular spectrum and that \"almost sure\" existence of L_2-solutions implies pure point spectrum for almost every boundary condition. The same results hold for Jacobi matrices on the discrete half line.", "date": "1994", "date_type": "published", "publication": "Mathematical Research Letters", "volume": "1", "number": "4", "publisher": "International Press", "pagerange": "437-450", "id_number": "CaltechAUTHORS:20180719-140605491", "issn": "1073-2780", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180719-140605491", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Direcci\u00f3n General de Asuntos del Personal Acad\u00e9mico (DGAPA)" }, { "agency": "Consejo Nacional de Ciencia y Tecnolog\u00eda (CONACYT)" }, { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.4310/MRL.1994.v1.n4.a4", "pub_year": "1994", "author_list": "del Rio, R.; Simon, B.; et al." }, { "id": "https://authors.library.caltech.edu/records/8fg1w-dt521", "eprint_id": 81515, "eprint_status": "archive", "datestamp": "2023-08-20 03:37:59", "lastmod": "2026-03-18 00:01:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Cyclic vectors in the Anderson model", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1994 World Scientific. \n\nTo Elliott Lieb on his 60th birthday. \n\nReceived: 7 April 1993. \n\nThis material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.", "abstract": "We prove that for Anderson models in the localized regime, the vectors \u03b4_n are cyclic with probability one and, in particular, the spectrum is simple.", "date": "1994", "date_type": "published", "publication": "Reviews in Mathematical Physics", "volume": "6", "number": "5a", "publisher": "World Scientific", "pagerange": "1183-1185", "id_number": "CaltechAUTHORS:20170918-091225249", "issn": "0129-055X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170918-091225249", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1142/S0129055X94000420", "pub_year": "1994", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/mmdmm-1je69", "eprint_id": 85831, "eprint_status": "archive", "datestamp": "2023-08-20 03:12:10", "lastmod": "2026-03-18 00:01:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Holden-H", "name": { "family": "Holden", "given": "H." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Zhao-Z", "name": { "family": "Zhao", "given": "Z." } } ] }, "title": "Trace formulae and inverse spectral theory for Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1993 American Mathematical Society. \n\nReceived by the editors February 2, 1993. \n\nThe first author gratefully acknowledges support by the Norwegian Research Council for Science and the Humanities (NAVF) and by Caltech. The second author is grateful to the Norwegian Research Council for Science and the Humanities (NAVF) for support. The research of the third author was partially supported by USNSF Grant DMS-9101716.\n\n

Published - S0273-0979-1993-00431-2.pdf

Accepted Version - 9310229

", "abstract": "We extend the well-known trace formula for Hill's equation to general one-dimensional Schr\u00f6dinger operators. The new function \u03be, which we introduce, is used to study absolutely continuous spectrum and inverse problems.", "date": "1993-10", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "29", "number": "2", "publisher": "American Mathematical Society", "pagerange": "250-256", "id_number": "CaltechAUTHORS:20180413-112125582", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-112125582", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Norwegian Research Council for Science and the Humanities" }, { "agency": "Caltech" }, { "agency": "NSF", "grant_number": "DMS-9101716" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0273-0979-1993-00431-2", "primary_object": { "basename": "9310229", "url": "https://authors.library.caltech.edu/records/mmdmm-1je69/files/9310229" }, "related_objects": [ { "basename": "S0273-0979-1993-00431-2.pdf", "url": "https://authors.library.caltech.edu/records/mmdmm-1je69/files/S0273-0979-1993-00431-2.pdf" } ], "pub_year": "1993", "author_list": "Gesztesy, F.; Holden, H.; et al." }, { "id": "https://authors.library.caltech.edu/records/v10sz-mbe07", "eprint_id": 85830, "eprint_status": "archive", "datestamp": "2023-08-20 03:12:04", "lastmod": "2026-03-18 00:01:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Holden-H", "name": { "family": "Holden", "given": "H." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Zhao-Z", "name": { "family": "Zhao", "given": "Z." } } ] }, "title": "On the Toda and Kac-van Moerbeke systems", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1993 American Mathematical Society. \n\nDedicated to Michael J. Moravcsik (1928-1989) \n\nReceived by the editors July 22, 1991. \n\nThe second and third authors were partially supported by USNSF Grant DMS-8801918.", "abstract": "Given a solution of the Toda lattice we explicitly construct a solution of the Kac-van Moerbeke system related to each other by a Miura-type transformation. As an illustration of our method we derive the N-soliton solutions of the Kac-van Moerbeke lattice.", "date": "1993-10", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "339", "number": "2", "publisher": "American Mathematical Society", "pagerange": "849-868", "id_number": "CaltechAUTHORS:20180413-111511219", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-111511219", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801918" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9947-1993-1153014-1", "pub_year": "1993", "author_list": "Gesztesy, F.; Holden, H.; et al." }, { "id": "https://authors.library.caltech.edu/records/ebt1v-qxf41", "eprint_id": 85330, "eprint_status": "archive", "datestamp": "2023-08-22 09:34:56", "lastmod": "2026-04-20 18:34:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gordon-Y-A", "name": { "family": "Gordon", "given": "Y. A." } }, { "id": "Jak\u0161i\u0107-V", "name": { "family": "Jak\u0161i\u0107", "given": "V." } }, { "id": "Mol\u010danov-S", "name": { "family": "Mol\u010danov", "given": "S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Spectral Properties of Random Schr\u00f6dinger Operators with Unbounded Potentials", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics; Spectral Property", "note": "\u00a9 1993 Springer-Verlag.\n\nReceived May 25, 1992.\n\nResearch partially supported by a Sloan Doctoral Dissertation Fellowship and NSERC under grant OGP-0007901. \nResearch partially supported by NSF grant DMS-9101716.\n\nCommunicated by T. Spencer.", "abstract": "We investigate spectral properties of random Schr\u00f6dinger operators H_\u03c9 = - \u0394 + \u03be_n(\u03c9)(1 + \u2502n\u2502^\u0251) acting on l^2(Z^d), where \u03be_n, are independent random variables uniformly distributed on [0, 1].", "date": "1993-10", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "157", "number": "1", "publisher": "Springer", "pagerange": "23-50", "id_number": "CaltechAUTHORS:20180315-110824542", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-110824542", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "OGP-0007901" }, { "agency": "NSF", "grant_number": "DMS-9101716" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02098017", "pub_year": "1993", "author_list": "Gordon, Y. A.; Jak\u0161i\u0107, V.; et al." }, { "id": "https://authors.library.caltech.edu/records/sy49s-dgx92", "eprint_id": 73016, "eprint_status": "archive", "datestamp": "2023-08-20 03:08:58", "lastmod": "2026-04-20 18:35:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bershadsky-M", "name": { "family": "Bershadsky", "given": "M." } }, { "id": "Cecotti-S", "name": { "family": "Cecotti", "given": "S." } }, { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "H." }, "orcid": "0000-0001-6021-3778" }, { "id": "Vafa-C", "name": { "family": "Vafa", "given": "C." } } ] }, "title": "Holomorphic anomalies in topological field theories", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1993 Elsevier. \n\nReceived 5 March 1993, Accepted 26 April 1993. \n\nWe would like to thank I. Antoniadis, L. Dixon and S.T. Yau for valuable discussions. We would also like to thank S. Hosono for sharing his Mathematica program for the examples we used in this paper. We are also grateful to S. Katz for explaining the origin of the genus zero contribution (see appendix B) that we had discovered experimentally. \n\nThe research of M. B., H. O. and C. V. was supported in part by Packard fellowship and NSF grants PHY-87-14654 and PHY-89-57162. The research of S. C. was supported in part by INFN. The research of H. O. was also supported in part by Grant-in-Aid for Scientific Research on Priority Areas 231 'Infinite Analysis' from the Ministry of Education, Science and Culture of Japan.\n\n

Submitted - 9302103.pdf

", "abstract": "We study the stringy genus-one partition function of N = 2 SCFTs. It is shown how to compute this using an anomaly in decoupling of BRST trivial states from the partition function. A particular limit of this partition function yields the partition function of topological theory coupled to topological gravity. As an application we compute the number of holomorphic elliptic curves over certain Calabi-Yau manifolds including the quintic threefold. This may be viewed as the first application of mirror symmetry at the string quantum level.", "date": "1993-09-20", "date_type": "published", "publication": "Nuclear Physics B", "volume": "405", "number": "2-3", "publisher": "Elsevier", "pagerange": "279-304", "id_number": "CaltechAUTHORS:20161220-154852744", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-154852744", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "David and Lucile Packard Foundation" }, { "agency": "NSF", "grant_number": "PHY-87-14654" }, { "agency": "NSF", "grant_number": "PHY-89-57162" }, { "agency": "Istituto Nazionale di Fisica Nucleare (INFN)" }, { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0550-3213(93)90548-4", "primary_object": { "basename": "9302103.pdf", "url": "https://authors.library.caltech.edu/records/sy49s-dgx92/files/9302103.pdf" }, "pub_year": "1993", "author_list": "Bershadsky, M.; Cecotti, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/hgkgt-0dm64", "eprint_id": 38599, "eprint_status": "archive", "datestamp": "2023-08-20 03:03:59", "lastmod": "2026-04-20 18:30:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Amenable Versus Hyperfinite Borel Equivalence Relations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1993 Association for Symbolic Logic.\nReceived April 1, 1992; revised August 20, 1992.\n\n

Published - 2275102.pdf

", "abstract": "Let X be a standard Borel space (i.e., a Polish space with the associated Borel structure), and let E be a countable Borel equivalence relation on X, i.e., a Borel equivalence relation E for which every equivalence class [X]_E is countable. By a result of Feldman-Moore [FM], E is induced by the orbits of a Borel action of a countable group G on X.", "date": "1993-09", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "58", "number": "3", "publisher": "Association for Symbolic Logic", "pagerange": "894-907", "id_number": "CaltechAUTHORS:20130521-103113640", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-103113640", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR1242044", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2275102", "primary_object": { "basename": "2275102.pdf", "url": "https://authors.library.caltech.edu/records/hgkgt-0dm64/files/2275102.pdf" }, "pub_year": "1993", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/vyqnv-cp613", "eprint_id": 85829, "eprint_status": "archive", "datestamp": "2023-08-20 02:47:23", "lastmod": "2026-03-18 00:02:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Large time behavior of the heat kernel: on a theorem of Chavel and Karp", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1993 American Mathematical Society. \n\n(Communicated by Palle E. T. Jorgensen) \n\nReceived by the editors October 5, 1991. \n\nResearch partially supported by USNSF under grant number DMS-9101715.", "abstract": "We show that a theorem of Chavel and Karp follows from the spectral theorem and elliptic regularity.", "date": "1993-06", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "118", "number": "2", "publisher": "American Mathematical Society", "pagerange": "513-514", "id_number": "CaltechAUTHORS:20180413-110907644", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-110907644", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101715" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-1993-1139473-4", "pub_year": "1993", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/x9yyz-sa445", "eprint_id": 103145, "eprint_status": "archive", "datestamp": "2023-08-22 09:24:54", "lastmod": "2026-04-20 20:26:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Simple connectivity of p-group complexes", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Finite Group; Simple Group; Prime Divisor; Homotopy Type; Outer Automorphism", "note": "\u00a9 1993 Springer Verlag. \n\nReceived 22 June 1992; Revised 07 September 1992; Issue Date June 1993. \n\nTo John Thompson on the occasion of his receipt of the Wolf Prize. \n\nThis work was partially supported by NSF DMS-8721480 and NSA MDA90-88-H-2032.", "abstract": "We investigate the simple connectivity ofp-subgroup complexes of finite groups.", "date": "1993-06", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "82", "number": "1-3", "publisher": "Springer", "pagerange": "1-43", "id_number": "CaltechAUTHORS:20200512-131404038", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-131404038", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8721480" }, { "agency": "National Security Agency", "grant_number": "MDA90-88-H-2032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf02808107", "pub_year": "1993", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/raqc2-nra14", "eprint_id": 38655, "eprint_status": "archive", "datestamp": "2023-08-20 02:32:11", "lastmod": "2026-03-09 20:35:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Becker-H", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Borel actions of Polish groups", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1993 American Mathematical Society.\n\nReceived by the editors April 16, 1992 and, in revised form, October 15, 1992.\n\nThe first author's research was partially supported by NSF Grant DMS-8914426. The second\nauthor's research was partially supported by NSF Grant DMS-9020153.\n\n

Published - S0273-0979-1993-00383-5.pdf

", "abstract": "We show that a Borel action of a Polish group on a standard Borel space is Borel isomorphic to a continuous action of the group on a Polish space, and we apply this result to three aspects of the theory of Borel actions of Polish groups: universal actions, invariant probability measures and the topological Vaught conjecture. We establish the existence of universal actions for any given Polish group, extending a result of Mackey and Varadarajan for the locally compact case. We prove an analogue of Tarski's theorem on paradoxical decompositions, by showing that the existence of an invariant Borel probability measure is equivalent to the nonexistence of paradoxical decompositions with countably many Borel pieces. We show that various natural versions of the topological Vaught conjecture are equivalent to each other and, in the case of the group of permutations of N, with the model-theoretic Vaught conjecture for infinitary logic; this depends on our identification of the universal action for that group.", "date": "1993-04", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "28", "number": "2", "publisher": "American Mathematical Society", "pagerange": "334-341", "id_number": "CaltechAUTHORS:20130523-095229531", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130523-095229531", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8914426" }, { "agency": "NSF", "grant_number": "DMS-9020153" } ] }, "other_numbering_system": { "items": [ { "id": "MR1185149", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0273-0979-1993-00383-5", "primary_object": { "basename": "S0273-0979-1993-00383-5.pdf", "url": "https://authors.library.caltech.edu/records/raqc2-nra14/files/S0273-0979-1993-00383-5.pdf" }, "pub_year": "1993", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/1rs4g-9na43", "eprint_id": 81212, "eprint_status": "archive", "datestamp": "2023-08-20 02:27:22", "lastmod": "2026-04-20 19:47:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Graf-G-M", "name": { "family": "Graf", "given": "Gian Michele" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Asymptotic Series for the Ground State Energy of Schr\u00f6dinger Operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1993 Academic Press. \n\nReceived April 29, 1992. \n\nCommunicated by L. Gross. \n\nResearch supported under NSF Grant DMS-9101716.", "abstract": "We find sufficient conditions for the ground state energy e(\u03bb) of \u2212\u0394 + \u03bbV to have an asymptotic series \u2211 \u0251_n\u03bb^n \u2193 0. Included are a class of almost periodic functions.", "date": "1993-03", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "112", "number": "2", "publisher": "Elsevier", "pagerange": "442-446", "id_number": "CaltechAUTHORS:20170906-150023173", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170906-150023173", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9101716" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1006/jfan.1993.1039", "pub_year": "1993", "author_list": "Graf, Gian Michele and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/9wknz-s4s53", "eprint_id": 83334, "eprint_status": "archive", "datestamp": "2023-08-20 02:16:30", "lastmod": "2026-03-18 00:03:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A Short Proof of Zheludev's Theorem", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Eigenvalues, Spectral theory, Integrands, Mathematical theorems, Mathematics, Continuous spectra, Increasing functions, Greens function, Riemann surfaces, Mathematical physics", "note": "\u00a9 1993 American Mathematical Society. \n\nReceived by the editors October 16, 1990. \n\nThe second author was partially funded by NSF Grant DMS-8801981. \n\nF. Gesztesy would like to acknowledge an illuminating discussion with M. Klaus.", "abstract": "We give a short proof of Zheludev's theorem that states the existence of precisely one eigenvalue in sufficiently distant spectral gaps of a Hill operator subject to certain short-range perturbations. As a by-product we simultaneously\nrecover Rofe-Beketov's result about the finiteness of the number of eigenvalues in essential spectral gaps of the perturbed Hill operator. Our methods are operator theoretic in nature and extend to other one-dimensional systems such as perturbed periodic Dirac operators and weakly perturbed second order finite difference operators. We employ the trick of using a selfadjoint Birman-Schwinger operator (even in cases where the perturbation changes sign),\na method that has already been successfully applied in different contexts and appears to have further potential in the study of point spectra in essential spectral gaps.", "date": "1993-01", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "335", "number": "1", "publisher": "American Mathematical Society", "pagerange": "329-340", "id_number": "CaltechAUTHORS:20171120-095049793", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171120-095049793", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801981" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "pub_year": "1993", "author_list": "Gesztesy, F. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/rnytz-txt10", "eprint_id": 73096, "eprint_status": "archive", "datestamp": "2023-08-20 02:15:38", "lastmod": "2026-04-20 19:52:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1992 The Physical Society of Japan. \n\nReceived October 11, 1992.\n\nI would like to thank J Ambj\u00f8rn, B. Durhuus, T. Eguchi, A. Jevicki and T. Matsumoto for discussions and comments. I would also like to thank M. Atiyah and P. Goddard for their hospitality at the Isaac Newton Institute for Mathematical Sciences, University of Cambridge, where part of this work was done. This research is supported in part by the Grant-in-Aid for Scientific Research on Priority Areas 231 \"Infinite Analysis\" from the Minstry of Education, Science and Culture of Japan.\n\n

Published - Prog._Theor._Phys.-1993-Ooguri-1-22.pdf

Submitted - 9210028v1.pdf

", "abstract": "We study the simplicial quantum gravity in three dimensions. Motivated by Boulatov's model which generates a sum over simplicial complexes weighted with the Turaev-Viro invariant, we introduce boundary operators in the simplicial gravity associated to compact orientable surfaces. An amplitude of the boundary operator is given by a sum over triangulations in the interior of the boundary surface. It turns out that the amplitude solves the Schwinger-Dyson equation even if we restrict the topology in the interior of the surface, as far as the surface is no-degenerate. We propose a set of factorization conditions on the amplitudes which singles out a solution associated to triangulations of S^3.", "date": "1993-01", "date_type": "published", "publication": "Progress of Theoretical Physics", "volume": "89", "number": "1", "publisher": "Progress of Theoretical Physics", "pagerange": "1-22", "id_number": "CaltechAUTHORS:20161221-133310666", "issn": "0033-068X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-133310666", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Ministry of Education, Culture, Sports, Science and Technology (MEXT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1143/ptp/89.1.1", "primary_object": { "basename": "9210028v1.pdf", "url": "https://authors.library.caltech.edu/records/rnytz-txt10/files/9210028v1.pdf" }, "related_objects": [ { "basename": "Prog._Theor._Phys.-1993-Ooguri-1-22.pdf", "url": "https://authors.library.caltech.edu/records/rnytz-txt10/files/Prog._Theor._Phys.-1993-Ooguri-1-22.pdf" } ], "pub_year": "1993", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/1g45c-vf493", "eprint_id": 83339, "eprint_status": "archive", "datestamp": "2023-08-20 01:57:26", "lastmod": "2026-03-18 00:01:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Weyl Transform and L^p Functions on Phase Space", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Mathematical theorems, Mathematical inequalities, Mathematical functions", "note": "\u00a9 1992 American Mathematical Society. \n\nReceived by the editors February 21, 1991 and, in revised form, April 19, 1991. \n\nResearch partially funded under NSF grant number DMS-8801918.", "abstract": "This is primarily a negative paper showing that a bound of the\nform ||W(f)||_(operator norm) \u2264 c|| f ||p fails for the Weyl transform if p > 2. L^p properties of Wigner distribution functions are discussed as well as Cwikel's theorem.", "date": "1992-12", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "116", "number": "4", "publisher": "American Mathematical Society", "pagerange": "1045-1047", "id_number": "CaltechAUTHORS:20171120-104432614", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171120-104432614", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801918" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "pub_year": "1992", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/0xgqd-p8x79", "eprint_id": 103143, "eprint_status": "archive", "datestamp": "2023-08-22 09:01:29", "lastmod": "2026-04-20 20:12:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "M." } }, { "id": "Segev-Y", "name": { "family": "Segev", "given": "Y." } } ] }, "title": "Locally connected simplicial maps", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Fundamental Group; Local System; Simplicial Complex; Order Complex; Connect SIMPLICIAL", "note": "\u00a9 1992 Springer-Verlag. \n\nReceived 05 May 1991; Revised 11 November 1991; Issue Date October 1992. \n\nThis work was partially supported by BSF 88-00164. The first author is partially supported by NSF DMS-8721480 and NSA MDA90-88-H-2032.", "abstract": "In Propositions 1.6 and 7.6 of his paper onp-group complexes of finite groups [5], Quillen establishes fundamental results comparing the homology and the fundamental group of the order complexes of posetsP, Q admitting a mapf :P \u2192Q of posets with good local behavior. We prove the analogue of Quillen's results for mapsf :K\u2192L of simplicial complexesK andL in a more general setup.", "date": "1992-10", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "77", "number": "3", "publisher": "Springer", "pagerange": "285-303", "id_number": "CaltechAUTHORS:20200512-125900851", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-125900851", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "88-00164" }, { "agency": "NSF", "grant_number": "DMS-8721480" }, { "agency": "National Security Agency", "grant_number": "MDA90-88-H-2032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf02773693", "pub_year": "1992", "author_list": "Aschbacher, M. and Segev, Y." }, { "id": "https://authors.library.caltech.edu/records/yxadn-txz42", "eprint_id": 73017, "eprint_status": "archive", "datestamp": "2023-08-20 01:44:37", "lastmod": "2026-04-20 18:15:56", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Topological Lattice Models in Four Dimensions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1992 World Scientific Publishing. \n\nReceived: 3 June 1992. \n\nDedicated to Professors Huzihiro Araki and Noboru Nakanishi on the occasion of their sixtieth birthdays. \n\nI would like to thank T. Eguchi, K. Higashijima, T. Inami, N. Ishibashi, Y. Yamada, S. Yahikozawa and T. Yoneya for discussions. I would also like to thank the members of the theory group in KEK, where part of this work was done, for their hospitality.\n\n

Submitted - 9205090.pdf

", "abstract": "We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G=SU(2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.", "date": "1992-09-28", "date_type": "published", "publication": "Modern Physics Letters A", "volume": "7", "number": "30", "publisher": "World Scientific", "pagerange": "2799-2810", "id_number": "CaltechAUTHORS:20161220-155721883", "issn": "0217-7323", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-155721883", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0217732392004171", "primary_object": { "basename": "9205090.pdf", "url": "https://authors.library.caltech.edu/records/yxadn-txz42/files/9205090.pdf" }, "pub_year": "1992", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/f31tq-qav92", "eprint_id": 73018, "eprint_status": "archive", "datestamp": "2023-08-20 01:42:42", "lastmod": "2026-04-20 19:51:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1992 Elsevier. \n\nReceived 27 December 1991, Accepted 15 April 1992. \n\nThe author would like to thank N. Sakakura for discussions. He is also thankful to T. Maskawa for explaining him some group theoretical facts and to L. Kauffman for encouragements.\n\n

Submitted - 9112072.pdf

", "abstract": "We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the one in the ISO(3) Chern-Simons theory. It is shown that, for a handlebody of any genus, a Hartle-Hawking-type wave function of the lattice gravity transforms into the corresponding state in the Chern-Simons theory under this isomorphism. Using the Heegaard splitting of a three-dimensional manifold, the partition functions of each of these theories is expressed as an inner product of such wave functions. Since the isomorphism preserves the inner products, the partition functions of the two theories are the same for any closed orientable manifold. We also discuss a class of topology-changing amplitudes in the lattice gravity and their relation to the ones in the Chern-Simons theory.", "date": "1992-09-07", "date_type": "published", "publication": "Nuclear Physics B", "volume": "382", "number": "2", "publisher": "Elsevier", "pagerange": "276-304", "id_number": "CaltechAUTHORS:20161220-160213579", "issn": "0550-3213", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-160213579", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0550-3213(92)90188-H", "primary_object": { "basename": "9112072.pdf", "url": "https://authors.library.caltech.edu/records/f31tq-qav92/files/9112072.pdf" }, "pub_year": "1992", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/tywsd-ezx59", "eprint_id": 81129, "eprint_status": "archive", "datestamp": "2023-08-20 01:30:28", "lastmod": "2026-04-20 19:47:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Best constants in some operator smoothness estimates", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1992 Elsevier Inc. \n\nReceived 25 March 1991. \n\nCommunicated by L. Gross. \n\nI thank M. Ben-Artzi for a useful conversation.", "abstract": "We provide a short proof of the inequality (cf. Ben-Artzi and Klainerman [Regularity and decay of evolution equations, preprint] and Kato and Yajima [Rev. Math. Phys. 1 (1989), 481\u2013496]) \u221d\u2212\u221e^\u221e\u2225(1 + x^2)^(\u221212)(1 \u2212 \u0394)^(14)e^(it\u0394)u\u2225^2dt \u2a7d C \u2225u\u2225^2 with explicit (essentially exact) values for C.", "date": "1992-07", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "107", "number": "1", "publisher": "Elsevier", "pagerange": "66-71", "id_number": "CaltechAUTHORS:20170905-100002232", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170905-100002232", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(92)90100-W", "pub_year": "1992", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/1b42s-01575", "eprint_id": 38550, "eprint_status": "archive", "datestamp": "2023-08-20 01:24:36", "lastmod": "2026-04-20 20:30:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Countable sections for locally compact group actions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1992 Cambridge University Press.\nReceived 1 March 1991.\nPublished online: 19 September 2008.\nResearch partially supported by a NSF Grant DMS-9020153.\n\n

Published - Kechris_1992p283.pdf

", "abstract": "It has been shown by J. Feldman, P. Hahn and C. C. Moore that every\nnon-singular action of a second countable locally compact group has a countable\n(in fact so-called lacunary) complete measurable section. This is extended here to\nthe purely Borel theoretic category, consisting of a Borel action of such a group on\nan analytic Borel space (without any measure). Characterizations of when an\narbitrary Borel equivalence relation admits a countable complete Borel section are\nalso established.", "date": "1992-06-01", "date_type": "published", "publication": "Ergodic Theory and Dynamical Systems", "volume": "12", "number": "2", "publisher": "Cambridge University Press", "pagerange": "283-295", "id_number": "CaltechAUTHORS:20130516-154918991", "issn": "0143-3857", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130516-154918991", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9020153" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/S0143385700006751", "primary_object": { "basename": "Kechris_1992p283.pdf", "url": "https://authors.library.caltech.edu/records/1b42s-01575/files/Kechris_1992p283.pdf" }, "pub_year": "1992", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/0kbz6-x3q75", "eprint_id": 38624, "eprint_status": "archive", "datestamp": "2023-08-20 01:22:02", "lastmod": "2026-04-20 20:07:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } } ] }, "title": "Descriptive Set Theory and Harmonic Analysis", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1992 Association for Symbolic Logic.\nReceived May 29, 1991.\nThe research of the first author was partially supported by NSF grant DMS-9020153.\n\n

Published - 2275277.pdf

", "abstract": "During the 1989 European ASL Summer Meeting in Berlin, the\nauthors gave a series of eight lectures (short course) on the topic of the title. This\nsurvey article consists basically of the lecture notes for that course distributed to\nthe participants of that conference. We have purposely tried in this printed version\nto preserve the informal style of the original notes.", "date": "1992-06", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "57", "number": "2", "publisher": "Association for Symbolic Logic", "pagerange": "413-441", "id_number": "CaltechAUTHORS:20130522-082635644", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-082635644", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9020153" } ] }, "other_numbering_system": { "items": [ { "id": "MR1169179", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2275277", "primary_object": { "basename": "2275277.pdf", "url": "https://authors.library.caltech.edu/records/0kbz6-x3q75/files/2275277.pdf" }, "pub_year": "1992", "author_list": "Kechris, A. S. and Louveau, A." }, { "id": "https://authors.library.caltech.edu/records/8d464-y0p04", "eprint_id": 80019, "eprint_status": "archive", "datestamp": "2023-08-20 01:20:28", "lastmod": "2026-04-20 20:31:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Jak\u0161i\u0107-V", "name": { "family": "Jak\u0161i\u0107", "given": "V." } }, { "id": "Mol\u010danov-B", "name": { "family": "Mol\u010danov", "given": "S." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Eigenvalue asymptotics of the Neumann Laplacian of regions and manifolds with cusps", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1992 Elsevier Inc. \n\nReceived 17 June 1991. \n\nCommunicated by L. Gross. \n\nWe are greateful to E. B. Davies for useful discussions and to L. Romans for comments on the manuscript. S. Moleanov thanks B. Simon and D. Wales for their hospitality at Caltech, where this work was done.", "abstract": "We study the eigenvalue asymptotics of a Neumann Laplacian \u2212\u0394_N^\u03a9 in unbounded regions \u03a9 of R^2 with cusps at infinity (a typical example is \u03a9 = {(x, y) \u03f5R^2: x > 1, \u00a6y\u00a6< e^(\u2212x)^2}) and prove that N_E(\u2212\u0394_N^\u03a9) ~ N_E(H_v) +E2Vol(\u03a9), where H_v is the canonical one-dimensional Schr\u00f6dinger operator associated to the problem. We establish a similar formula for manifolds with cusps and derive the eigenvalue asymptotics of a Dirichlet Laplacian \u2212\u0394_D^\u03a9 for a class of cusp-type regions of infinite volume.", "date": "1992-05-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "106", "number": "1", "publisher": "Elsevier", "pagerange": "59-79", "id_number": "CaltechAUTHORS:20170809-113325669", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170809-113325669", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(92)90063-O", "pub_year": "1992", "author_list": "Jak\u0161i\u0107, V.; Mol\u010danov, S.; et al." }, { "id": "https://authors.library.caltech.edu/records/brwkk-5p671", "eprint_id": 85297, "eprint_status": "archive", "datestamp": "2023-08-22 08:45:23", "lastmod": "2026-04-20 19:20:04", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Davies-E-B", "name": { "family": "Davies", "given": "E. B." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Spectral properties of Neumann Laplacian of horns", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Spectral Property; Continuous Spectrum; Compact Resolvent; Asymptotic Dynamic; Unbounded Region", "note": "\u00a9 1992 Birkh\u00e4user Verlag.\n\nSubmitted: March 1991.\n\nThe second author's research is partially funded under NSF grand number DMS-8801918.", "abstract": "We study the Neumann Laplacian of unbounded regions in \u211d^n with cusps at infinity so that the corresponding Dirichlet Laplacian has compact resolvent. Typical of our results is that of the region {(x, y)_\u2208\u211d^2 \u2225xy|<1} the Neumann Laplacian has absolutely continuous spectrum [0, \u221e) of uniform multiplicity four and an infinity of eigenvalues E_0 < E_ 1 \u2264... \u2192 \u221e and that for the region {(x, y)_\u2208\u211d^2\u2225y|\u2264 e^-^(\u2223x\u2223)}, it has absolutely continuous spectrum [1/4, \u221e) of uniform multiplicity 2 and an infinity of eigenvalues E_0 = 0 < E_1 \u2264... \u2192 \u221e. We use the Enss theory with a suitable asymptotic dynamics.", "date": "1992-03", "date_type": "published", "publication": "Geometric and Functional Analysis", "volume": "2", "number": "1", "publisher": "Springer", "pagerange": "105-117", "id_number": "CaltechAUTHORS:20180314-071625612", "issn": "1016-443X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180314-071625612", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801918" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF01895707", "pub_year": "1992", "author_list": "Davies, E. B. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/971dv-53319", "eprint_id": 85828, "eprint_status": "archive", "datestamp": "2023-08-20 01:08:02", "lastmod": "2026-03-18 00:00:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Neumann Laplacian of a jelly roll", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1992 American Mathematical Society. \n\nReceived by the editors October 11, 1990. \n\n(Communicated by Paul S. Muhly) \n\nResearch partially funded under NSF grant number DMS-8801918.", "abstract": "We consider the Laplacian with Neumann boundary conditions of a bounded connected region obtained by removing a suitable infinite spiral from an annulus. We show that the spectrum has an absolutely continuous component.", "date": "1992-03", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "114", "number": "3", "publisher": "American Mathematical Society", "pagerange": "783-785", "id_number": "CaltechAUTHORS:20180413-110242629", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-110242629", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801918" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9939-1992-1076578-X", "pub_year": "1992", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/12cp0-nth62", "eprint_id": 85288, "eprint_status": "archive", "datestamp": "2023-08-20 00:52:29", "lastmod": "2026-03-18 00:01:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Graf-G-M", "name": { "family": "Graf", "given": "G. M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The ground state energy of Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1992 Springer-Verlag. \n\nReceived April 30, 1992; in revised form June 8, 1992. \n\nOne of us (F.G.) would like to thank H. Holden for discussions and G. Neugebauer and D. Wales for the hospitality extended by Caltech during a month's stay in the summer of 1991.", "abstract": "We study e(\u03bb) = inf spec ( - \u0394 + \u03bbV) and examine when e(\u03bb) < 0 for all \u03bb \u256a 0. We prove that - c\u03bb^2 \u2264 e(\u03bb) \u2264 - d\u03bb^2 for suitable V and all small |\u03bb|.", "date": "1992", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "150", "number": "2", "publisher": "Springer", "pagerange": "375-384", "id_number": "CaltechAUTHORS:20180313-152512594", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180313-152512594", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "pub_year": "1992", "author_list": "Gesztesy, F.; Graf, G. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/0xtzx-sj082", "eprint_id": 73019, "eprint_status": "archive", "datestamp": "2023-08-20 00:42:08", "lastmod": "2026-04-21 04:13:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" }, { "id": "Sasakura-Naoki", "name": { "family": "Sasakura", "given": "Naoki" } } ] }, "title": "Discrete and Continuum Approaches to Three-Dimensional Quantum Gravity", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1991 World Scientific Publishing. \n\nReceived: 10 September 1991. \n\nThe authors would like to thank R.Sorkin for discussion on the model of Ponzano and Regge, and A.Shapere for bringing the paper by Turaev and Viro into their attention. They are grateful to T. Kohno and T. Takata for information on the work by Turaev.\n\n

Submitted - 9108006.pdf

", "abstract": "It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern\u2013Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k^2, where q=e^(2\u03c0i/(k+2)).", "date": "1991-12-21", "date_type": "published", "publication": "Modern Physics Letters A", "volume": "6", "number": "39", "publisher": "World Scientific", "pagerange": "3591-3600", "id_number": "CaltechAUTHORS:20161220-160613387", "issn": "0217-7323", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161220-160613387", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1142/S0217732391004140", "primary_object": { "basename": "9108006.pdf", "url": "https://authors.library.caltech.edu/records/0xtzx-sj082/files/9108006.pdf" }, "pub_year": "1991", "author_list": "Ooguri, Hirosi and Sasakura, Naoki" }, { "id": "https://authors.library.caltech.edu/records/9835e-b1834", "eprint_id": 103120, "eprint_status": "archive", "datestamp": "2023-08-22 08:33:21", "lastmod": "2026-04-20 23:04:38", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Kleidman-P-B", "name": { "family": "Kleidman", "given": "Peter B." } }, { "id": "Liebeck-M-W", "name": { "family": "Liebeck", "given": "Martin W." } } ] }, "title": "Exponents of almost simple groups and an application to the restricted Burnside problem", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Simple Group; Outer Automorphism; Finite Simple Group; Split Extension; Outer Automorphism Group", "note": "\u00a9 1991 Springer-Verlag. \n\nReceived 04 August 1989; Accepted 22 November 1990; Issue Date December 1991. \n\nPartially supported by NSF DMS-8721480 and NSA MDA 90-88-H-2032.", "abstract": "This paper is motivated by: The Restricted Burnside Problem R(n). For each r, are there only finitely many r-generator finite groups of exponent n?", "date": "1991-12", "date_type": "published", "publication": "Mathematische Zeitschrift", "volume": "208", "number": "1", "publisher": "Springer Verlag", "pagerange": "401-409", "id_number": "CaltechAUTHORS:20200512-074240672", "issn": "0025-5874", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-074240672", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8721480" }, { "agency": "National Security Agency", "grant_number": "MDA 90-88-H-2032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf02571536", "pub_year": "1991", "author_list": "Aschbacher, Michael; Kleidman, Peter B.; et al." }, { "id": "https://authors.library.caltech.edu/records/jfx14-rqt98", "eprint_id": 80884, "eprint_status": "archive", "datestamp": "2023-08-20 00:37:58", "lastmod": "2026-04-20 21:16:25", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Hempel-R", "name": { "family": "Hempel", "given": "Rainer" } }, { "id": "Seco-L-A", "name": { "family": "Seco", "given": "Luis A." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The essential spectrum of Neumann Laplacians on some bounded singular domains", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Elsevier Inc. \n\nReceived 2 August 1990. \n\nResearch supported by Deutsche Forschungsgemeinschaft and by USNSF under Grant DMS-8807816.", "abstract": "In the present paper we consider Neumann Laplacians on singular domains of the type \"rooms and passages\" or \"combs\" and we show that, in typical situations, the essential spectrum can be determined from the geometric data. Moreover, given an arbitrary closed subset S of the non-negative reals, we construct domains \u03a9 = \u03a9(S) such that the essential spectrum of the Neumann Laplacian on \u03a9 is just this set S.", "date": "1991-12", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "102", "number": "2", "publisher": "Elsevier", "pagerange": "448-483", "id_number": "CaltechAUTHORS:20170829-073525996", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170829-073525996", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "NSF", "grant_number": "DMS-8807816" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(91)90130-W", "pub_year": "1991", "author_list": "Hempel, Rainer; Seco, Luis A.; et al." }, { "id": "https://authors.library.caltech.edu/records/pbths-spv27", "eprint_id": 103122, "eprint_status": "archive", "datestamp": "2023-08-20 00:39:09", "lastmod": "2026-04-21 00:26:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Segev-Y", "name": { "family": "Segev", "given": "Yoav" } } ] }, "title": "The uniqueness of groups of type J\u2084", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Springer-Verlag. \n\nOblatum VIII-1990 & 31-I-1991. \n\nThis work was partially supported by BSF 88-00164. The first author is partially supported by NSF DMS-8721480 and NSA MDA 90-88-H-2032.", "abstract": "We give the first computer free proof of the uniqueness of groups of type J\u2084. In addition we supply simplified proofs of some properties of such groups, such as the structure of certain subgroups.\nA group of type J\u2084 is a finite group G possessing an involution z such that H=C_G(z) satisfies F*(H)=Q is extraspecial of order 2\u00b9\u00b3, H/Q is isomorphic to Z\u2083 extended by Aut (M\u2082\u2082), and z^G \u22c2 Q \u2260 {z}. We prove: Main Theorem. Up to isomorphism there exists at most one group of type J\u2084.", "date": "1991-12", "date_type": "published", "publication": "Inventiones Mathematicae", "volume": "105", "number": "1", "publisher": "Springer", "pagerange": "589-607", "id_number": "CaltechAUTHORS:20200512-075747975", "issn": "0020-9910", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-075747975", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "88-00164" }, { "agency": "NSF", "grant_number": "DMS-8721480" }, { "agency": "National Security Agency", "grant_number": "MDA 90-88-H-2032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf01232280", "pub_year": "1991", "author_list": "Aschbacher, Michael and Segev, Yoav" }, { "id": "https://authors.library.caltech.edu/records/gjj3c-nbj78", "eprint_id": 80943, "eprint_status": "archive", "datestamp": "2023-08-20 00:34:26", "lastmod": "2026-04-20 22:57:13", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Davies-E-B", "name": { "family": "Davies", "given": "E. B." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "L^p norms of non-critical Schr\u00f6dinger semigroups", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Academic Press. \n\nReceived 3 October 1990. \n\nResearch partially funded under NSF Grant DMS-8801981.", "abstract": "We consider Schr\u00f6dinger semigroups e^(\u2212tH), H = \u2212\u0394 + V on R^n with V ~ \u2212c\u2758x\u2758^(\u22122), as \u2758x\u2758 \u2192 \u221e, 0 < c < [(12)(n\u22122)]^2, with H \u2a7e 0. We determine the exact power law divergence of \u2225e^(\u2212tH)\u2225_(p,p) and of some \u2225e^(\u2212tH)\u2225_(q,p) as maps from L^p to L^q. The results are expressed most naturally in terms of the power \u03b1 for which there exists a positive resonance \u03b7 such that H\u03b7 = 0, \u03b7(x) ~ \u2758x\u2758^(\u2212\u03b1).", "date": "1991-11-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "102", "number": "1", "publisher": "Elsevier", "pagerange": "95-115", "id_number": "CaltechAUTHORS:20170830-081216215", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170830-081216215", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801981" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(91)90137-T", "pub_year": "1991", "author_list": "Davies, E. B. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/bewz5-6x728", "eprint_id": 38555, "eprint_status": "archive", "datestamp": "2023-08-20 00:17:26", "lastmod": "2026-04-21 03:57:16", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dougherty-R", "name": { "family": "Dougherty", "given": "Randall" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Complexity of Antidifferentiation", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Academic Press Inc. Research partially supported by an NSF postdoctoral fellowship. Research partially supported by NSF Grant DMS-8416349.", "abstract": "We consider real-valued functions defined on the interval [0, 1]. We denote by \u0394 the set of derivatives; i.e., \u0192 \u0404 \u0394 iff there is a differentiable function F such that F' = \u0192. Any such F is a primitive of \u0192 and is uniquely determined up to a constant. To normalize, we denote by F(x)=\u0192^x_0\u0192 the\nprimitive determined by F(0)=0. This is the original Newtonian concept of integration as antidifferentiation.", "date": "1991-08", "date_type": "published", "publication": "Advances in Mathematics", "volume": "88", "number": "2", "publisher": "Elsevier", "pagerange": "145-169", "id_number": "CaltechAUTHORS:20130517-102333066", "issn": "0001-8708", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-102333066", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF postdoctoral fellowship" }, { "agency": "NSF", "grant_number": "DMS-8416349" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0001-8708(91)90006-S", "pub_year": "1991", "author_list": "Dougherty, Randall and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/7xm22-r2z73", "eprint_id": 85381, "eprint_status": "archive", "datestamp": "2023-08-20 00:13:42", "lastmod": "2026-04-20 22:14:07", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Brown-R-W", "name": { "family": "Brown", "given": "Robert W." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Taylor-C-C", "name": { "family": "Taylor", "given": "Cyrus C." } } ] }, "title": "Harmonic analysis of the relativistic string in spinorial coordinates", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 IOP Publishing Ltd. \n\nReceived 20 September 1990, in final form 25 February 1991. \n\nThis paper was produced under a grant from the National Science Foundation.", "abstract": "The authors present the finite-harmonic solution of the constraint equations of the spinor representation of the relativistic string. Choosing a gauge, they make a harmonic decomposition in the form of a product representation. This finite-harmonic approach is then compared with that of Hughston and Shaw (1988). They describe a recursive method for relating series and product parameters, and comment briefly on the question of a generalization for the infinite harmonic case and on the quantization of such systems.", "date": "1991-07", "date_type": "published", "publication": "Classical and Quantum Gravity", "volume": "8", "number": "7", "publisher": "IOP", "pagerange": "1245-1253", "id_number": "CaltechAUTHORS:20180320-123640344", "issn": "0264-9381", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180320-123640344", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1088/0264-9381/8/7/003", "pub_year": "1991", "author_list": "Brown, Robert W.; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/q6sdf-63e75", "eprint_id": 38594, "eprint_status": "archive", "datestamp": "2023-08-20 00:06:13", "lastmod": "2026-04-21 01:30:21", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Hereditary properties of the class of closed sets of uniqueness for trigonometric series", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Springer-Verlag. Received October 3, 1989 and in revised form October 9, 1990. Research partially supported by NSF Grant DMS-8718847.", "abstract": "It is shown that the\u03c3-ideal U_0 of closed sets of extended uniqueness in T is hereditarily non-Borel, i.e. every \"non-trivial\" \u03c3-ideal of closed sets I \u2286 U_0 is non-Borel. This implies both the result of Solovay, Kaufman that both U_0 and U(the \u03c3-ideal of closed sets of uniqueness) are not Borel as well as the theorem of Debs-Saint Raymond that every Borel subset of T of extended uniqueness is of the first category. A further extension to ideals contained in U_0 is given.", "date": "1991-06", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "73", "number": "2", "publisher": "Hebrew University Magnes Press", "pagerange": "189-198", "id_number": "CaltechAUTHORS:20130521-093201219", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-093201219", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8718847" } ] }, "other_numbering_system": { "items": [ { "id": "MR1135211", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/BF02772948", "pub_year": "1991", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/rpe3d-v3t39", "eprint_id": 80052, "eprint_status": "archive", "datestamp": "2023-08-20 00:04:13", "lastmod": "2026-04-21 00:39:39", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Holden-H", "name": { "family": "Holden", "given": "H." } }, { "id": "Saab-E", "name": { "family": "Saab", "given": "E." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Explicit construction of solutions of the modified Kadomtsev-Petviashvili equation", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Academic Press, Inc. \n\nReceived 13 November 1989. \n\nCommunicated by L. Gross. \n\nOn leave from: Division of Mathematical Sciences, Norwegian Institute of Technology, University of Trondheim, N-7034 Trondheim. Norway. Partially supported by the Norwegian Research Council for Science and the Humanities (NAVF). Partially supported by USNSF Grant DMS-8801918. \n\nF.G. would like to thank D. Boll\u00e9 for the great hospitality extended to him at the Institute for Theoretical Physics of the University of Leuven, Belgium during summer 1989 where parts of this work were completed. He also gratefully acknowledges support by the Onderzoeksfonds of the University of Leuven during that period. H. H. is grateful to Professor D. Wales for his kind invitation to Caltech.", "abstract": "Given a solution of the Kadomtsev-Petviashvili equation we explicitly construct a solution of the modified Kadomtsev-Petviashvili equation related to one another by a generalized Miura transformation. The construction is modeled after a previous treatment of the modified Korteweg-de Vries case. As an illustration of our method we derive the soliton solutions of the modified Kadomtsev-Petviashvili equation.", "date": "1991-05-15", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "98", "number": "1", "publisher": "Elsevier", "pagerange": "211-228", "id_number": "CaltechAUTHORS:20170810-072646814", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170810-072646814", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "University of Trondheim", "grant_number": "N-7034" }, { "agency": "Norwegian Research Council for Science and the Humanities" }, { "agency": "NSF", "grant_number": "DMS-8801918" }, { "agency": "University of Leuven" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(91)90096-N", "pub_year": "1991", "author_list": "Gesztesy, F.; Holden, H.; et al." }, { "id": "https://authors.library.caltech.edu/records/3b1ft-4qg60", "eprint_id": 38557, "eprint_status": "archive", "datestamp": "2023-08-19 23:56:55", "lastmod": "2026-04-21 05:36:10", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Woodin-W-H", "name": { "family": "Woodin", "given": "W. H." } } ] }, "title": "A strong boundedness theorem for dilators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Elsevier Science Publishers B. V. Communicated by D. van Dalen. Received 15 June 1989. Research partially supported by NSF Grant.", "abstract": "We prove a strong boundedness theorem for dilators: if A \u2286 DIL is \u03a3^1_1, then there is a recursive dilator D_0 such that \u2200D \u2208 A (D can be embedded into D_0).", "date": "1991-04-15", "date_type": "published", "publication": "Annals of Pure and Applied Logic", "volume": "52", "number": "1-2", "publisher": "Elsevier Masson", "pagerange": "93-97", "id_number": "CaltechAUTHORS:20130517-105346791", "issn": "0168-0072", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-105346791", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "MR1104056", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0168-0072(91)90041-J", "pub_year": "1991", "author_list": "Kechris, A. S. and Woodin, W. H." }, { "id": "https://authors.library.caltech.edu/records/sfhk2-sa892", "eprint_id": 38556, "eprint_status": "archive", "datestamp": "2023-08-19 23:56:48", "lastmod": "2026-04-21 06:49:09", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Boundedness theorems for dilators and ptykes", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1991 Elsevier Science Publishers B. V. Communicated by D. van Dalen. Received 15 June 1989. Research partially supported by NSF Grant.", "abstract": "The main theorem of this paper is: If \u0192 is a partial function from \u2135_1 to \u2135_1 which is \u2211^1_1-bounded, then there is a weakly finite primitive recursive dilator D such that for all infinite \u03b1 \u03f5 dom(\u0192), \u0192(\u03b1) \u2a7d D(\u03b1). The proof involves only elementary combinatorial constructions of trees. A generalization to ptykes is also given.", "date": "1991-04-15", "date_type": "published", "publication": "Annals of Pure and Applied Logic", "volume": "52", "number": "1-2", "publisher": "Elsevier Masson", "pagerange": "79-92", "id_number": "CaltechAUTHORS:20130517-103738099", "issn": "0168-0072", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130517-103738099", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0168-0072(91)90040-S", "pub_year": "1991", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/045xq-6ed37", "eprint_id": 76004, "eprint_status": "archive", "datestamp": "2023-08-19 23:53:45", "lastmod": "2026-04-21 01:24:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Schweiger-W", "name": { "family": "Schweiger", "given": "W." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Commutation methods applied to the mKdV-equation", "ispublished": "pub", "full_text_status": "restricted", "keywords": "mKdV-equation, commutation methods, soliton-like solutions, periodic solutions, singular solutions", "note": "\u00a9 1991 American Mathematical Society. \n\nDedicated to Raphael Heegh-Krohn (1938-1988). Received by the editors January 15, 1990. \n\nThe first author is a Max Kade Foundation Fellow and, with the third author, was partially supported by USNSF under Grant DMS-8801918. \n\nThe second author was supported by BMFT, Federal Republic of Germany. \n\nWe are indebted to David Gurarie for several most stimulating discussions. F. Gesztesy is indebted to D. Wales for the hospitality extended to him at Caltech. He also gratefully acknowledges financial support from the Max Kade Foundation and from USNSF under Grant DMS-8801918.", "abstract": "An explicit construction of solutions of the modified Korteweg-de Vries equation given a solution of the (ordinary) Korteweg-de Vries equation is provided. Our theory is based on commutation methods (i.e., N = 1 supersymmetry) underlying Miura's transformation that links solutions of the two evolution equations.", "date": "1991-04", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "324", "number": "2", "publisher": "American Mathematical Society", "pagerange": "465-525", "id_number": "CaltechAUTHORS:20170408-144611234", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170408-144611234", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Max Kade Foundation" }, { "agency": "NSF", "grant_number": "DMS-8801918" }, { "agency": "Bundesministerium f\u00fcr Forschung und Technologie (BMFT)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/S0002-9947-1991-1029000-7", "pub_year": "1991", "author_list": "Gesztesy, F.; Schweiger, W.; et al." }, { "id": "https://authors.library.caltech.edu/records/rc9pp-sqd71", "eprint_id": 38619, "eprint_status": "archive", "datestamp": "2023-08-19 23:46:04", "lastmod": "2026-03-09 20:34:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } }, { "id": "Tardivel-V", "name": { "family": "Tardivel", "given": "V." } } ] }, "title": "The Class Of Synthesizable Pseudomeasures", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1991 Board of Trustees of the University of Illinois.\nReceived November 22, 1988.\nResearch partially supported by the National Science Foundation.\n\n

Published - euclid.ijm.1255987982.pdf

", "abstract": "In this paper we study descriptive set theoretic questions related to\nconcepts of harmonic synthesis on the unit circle T, and their relationship\nwith the structure of uniqueness sets.", "date": "1991-03", "date_type": "published", "publication": "Illinois Journal of Mathematics", "volume": "35", "number": "1", "publisher": "Illinois Journal of Mathematics", "pagerange": "107-146", "id_number": "CaltechAUTHORS:20130521-150609710", "issn": "0019-2082", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-150609710", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "0706.43008", "name": "Zentralblatt MATH identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "euclid.ijm.1255987982.pdf", "url": "https://authors.library.caltech.edu/records/rc9pp-sqd71/files/euclid.ijm.1255987982.pdf" }, "pub_year": "1991", "author_list": "Kechris, A. S.; Louveau, A.; et al." }, { "id": "https://authors.library.caltech.edu/records/q6c4c-5ar39", "eprint_id": 38618, "eprint_status": "archive", "datestamp": "2023-08-19 23:46:00", "lastmod": "2026-04-21 06:10:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Amenable Equivalence Relations and Turing Degrees", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1991 Association for Symbolic Logic.\nReceived July 19, 1989; revised February 1, 1990.\nThis research was partially supported by NSF grant DMS-8718847.\n\n

Published - 2274913.pdf

", "abstract": "In [12] Slaman and Steel posed the following problem:\nAssume ZF + DC + AD. Suppose we have a function assigning to each Turing\ndegree d a linear order <_d of d. Then must the rationals embed order preservingly in\n<_d for a cone of d's?", "date": "1991-03", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "56", "number": "1", "publisher": "Association for Symbolic Logic", "pagerange": "182-194", "id_number": "CaltechAUTHORS:20130521-150404346", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-150404346", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8718847" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2274913", "primary_object": { "basename": "2274913.pdf", "url": "https://authors.library.caltech.edu/records/q6c4c-5ar39/files/2274913.pdf" }, "pub_year": "1991", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/tzbk6-99d36", "eprint_id": 80053, "eprint_status": "archive", "datestamp": "2023-08-19 23:21:13", "lastmod": "2026-04-21 03:38:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "On conjectures of Guralnick and Thompson", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1990 Academic Press, Inc. \n\nReceived 9 June 1988. \n\nPartially supported by NSF Grant DMS-8721480 and NSA Grant MDA 90-88-H-2032.", "abstract": "Given a permutation s on a finite set \u03a9 of order n, define c(s) to be the number of cycles of sand Ind(s) = n - c(s).\nDefine a genus g system to be a triple ( G, \u03a9, S), where \u03a9 is a finite set, G is a transitive subgroup of Sym(\u03a9), and S = (g_j: 1 \u2a7dj\u2a7dr is a family of elements of G^# such that G = \u27e8S\u27e9, g_1...g_r = 1, and 2(\u2758\u03a9\u2758 + g-1)= \u2211_(j=1) Ind(g_j).", "date": "1990-12", "date_type": "published", "publication": "Journal of Algebra", "volume": "135", "number": "2", "publisher": "Elsevier", "pagerange": "277-343", "id_number": "CaltechAUTHORS:20170810-072647371", "issn": "0021-8693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170810-072647371", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8721480" }, { "agency": "NSF", "grant_number": "MDA 90-88-H-2032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0021-8693(90)90292-V", "pub_year": "1990", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/bg0z5-1z980", "eprint_id": 85336, "eprint_status": "archive", "datestamp": "2023-08-22 07:48:20", "lastmod": "2026-04-21 04:10:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Absence of Ballistic Motion", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics; Large Classis", "note": "\u00a9 1990 Springer-Verlag.\n\nReceived February 20, 1990.\n\nResearch partially supported by NSF grant number DMS-8801918\n\nCommunicated by T. Spencer.", "abstract": "For large classes of Schr\u00f6dinger operators and Jacobi matrices we prove that if h has only one point spectrum then for \u03c6_0 of compact support\nlim/_(t\u2192\u221e)^(t\u22122)\u2225xe^(\u2212ith)\u03d5_0\u2225^2 = 0.", "date": "1990-11", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "134", "number": "1", "publisher": "Springer", "pagerange": "209-212", "id_number": "CaltechAUTHORS:20180315-132837134", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180315-132837134", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801918" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02102095", "pub_year": "1990", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/4w1m5-jrg60", "eprint_id": 85284, "eprint_status": "archive", "datestamp": "2023-08-19 23:12:16", "lastmod": "2026-04-21 00:51:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "Joseph E." } }, { "id": "Seiler-R", "name": { "family": "Seiler", "given": "Ruedi" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Quantum Hall effect and the relative index for projections", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1990 American Physical Society. \n\nReceived 10 July 1990. \n\nThis work is supported in part by the U.S.-Israel Binational Science Foundation under Grant No. 80-00365, by the Fund for the Promotion of Research at the Technion, and by U.S. NSF under Grant No. DMS-8807816. J.E.A. thanks Jean Bellissard and D. J. Thouless for useful conversations and B.S. thanks the Technion for its hospitality. R.S. acknowledges the support of the Akademie der Wissenschaften zu Berlin and the Deutsche Forschungsgemeinschaft.\n\n

Published - PhysRevLett.65.2185.pdf

", "abstract": "We define the relative index, Index(P,Q), for a pair of infinite-dimensional projections on a Hilbert space to be the integer that is the natural generalization of dim(P)-dim(Q) in finite-dimensional vector spaces. We show that the Hall conductance for independent electrons in the plane is the relative index where P and Q project on the states below the Fermi energy for Hamiltonians that differ by a quantum flux and the Fermi energy is appropriately placed. This approach is closely related to, and sheds light on, Bellissard's interpretation of the Hall conductance as an index.", "date": "1990-10-22", "date_type": "published", "publication": "Physical Review Letters", "volume": "65", "number": "17", "publisher": "American Physical Society", "pagerange": "2185-2188", "id_number": "CaltechAUTHORS:20180313-142926573", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180313-142926573", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "80-00365" }, { "agency": "Technion" }, { "agency": "NSF", "grant_number": "DMS-8807816" }, { "agency": "Akademie der Wissenschaften zu Berlin" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.65.2185", "primary_object": { "basename": "PhysRevLett.65.2185.pdf", "url": "https://authors.library.caltech.edu/records/4w1m5-jrg60/files/PhysRevLett.65.2185.pdf" }, "pub_year": "1990", "author_list": "Avron, Joseph E.; Seiler, Ruedi; et al." }, { "id": "https://authors.library.caltech.edu/records/cvb33-qt212", "eprint_id": 38609, "eprint_status": "archive", "datestamp": "2023-08-19 23:08:13", "lastmod": "2026-03-09 21:10:19", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrington-L-A", "name": { "family": "Harrington", "given": "L. A." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } } ] }, "title": "A Glimm-Effros dichotomy for Borel equivalence relations", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1990 American Mathematical Society.\n\nReceived by the editors March 2, 1990.\n\nThe first and second authors were partially supported by NSF grants.\n\n

Published - S0894-0347-1990-1057041-5.pdf

", "abstract": "A basic dichotomy concerning the structure of the orbit space of a transformation group has been discovered by Glimm [G12] in the locally compact group action case and extended by Effros [E 1, E2] in the Polish group action\ncase when additionally the induced equivalence relation is F\u03c3. It is the purpose of this paper to extend the Glimm-Effros dichotomy to the very general context of an arbitrary Borel equivalence relation (not even necessarily induced by a group action). Despite the totally classical descriptive set-theoretic nature of our result, our proof requires the employment of methods of effective descriptive\nset theory and thus ultimately makes crucial use of computability (or recursion) theory on the integers.", "date": "1990-10", "date_type": "published", "publication": "Journal of the American Mathematical Society", "volume": "3", "number": "4", "publisher": "American Mathematical Society", "pagerange": "903-928", "id_number": "CaltechAUTHORS:20130521-131913642", "issn": "0894-0347", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-131913642", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "MR1057041", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0894-0347-1990-1057041-5", "primary_object": { "basename": "S0894-0347-1990-1057041-5.pdf", "url": "https://authors.library.caltech.edu/records/cvb33-qt212/files/S0894-0347-1990-1057041-5.pdf" }, "pub_year": "1990", "author_list": "Harrington, L. A.; Kechris, A. S.; et al." }, { "id": "https://authors.library.caltech.edu/records/pgbqn-knm13", "eprint_id": 103116, "eprint_status": "archive", "datestamp": "2023-08-22 07:44:04", "lastmod": "2026-04-21 00:55:06", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "The existence of J\u2083 and its embeddings in E\u2086", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Chevalley Group; Existence Proof; Sporadic Group; Previous Existence; Simple Chevalley Group", "note": "\u00a9 1990 Kluwer Academic Publishers. \n\nReceived 25 August 1989; Issue Date September 1990. \n\nTo Jacques Tits on his sixtieth birthday. \n\nPartially supported by NSF DMS-8721480 and NSA MDA90-88-H-2032.", "abstract": "We determine the embeddings of the third sporadic group J\u2083 of Janko in simple Chevalley groups of type E\u2086 over finite and algebraically closed fields. As a corollary we obtain a short elegant existence proof of J\u2083. This is of interest as J\u2083 is one of the few sporadic groups not contained in the Monster, so its existence cannot be verified within that group. Previous existence proofs were highly computational; cf. [4] and [6].", "date": "1990-09", "date_type": "published", "publication": "Geometriae Dedicata", "volume": "35", "number": "1-3", "publisher": "Springer", "pagerange": "143-154", "id_number": "CaltechAUTHORS:20200512-071755284", "issn": "0046-5755", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-071755284", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8721480" }, { "agency": "National Security Agency", "grant_number": "MDA 90-88-H-2032" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf00147344", "pub_year": "1990", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/dpjep-vcf30", "eprint_id": 103119, "eprint_status": "archive", "datestamp": "2023-08-19 23:04:37", "lastmod": "2026-04-21 05:23:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Kleidman-P-B", "name": { "family": "Kleidman", "given": "Peter B." } } ] }, "title": "On a conjecture of Quillen and a lemma of Robinson", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1990 Birkh\u00e4user Verlag, Basel. \n\nReceived 20 February 1989; Issue Date September 1990.", "abstract": "In this note we are concerned with finite groups G and primes p satisfying the Robinson Properties.", "date": "1990-09", "date_type": "published", "publication": "Archiv der Mathematik", "volume": "55", "number": "3", "publisher": "Springer", "pagerange": "209-217", "id_number": "CaltechAUTHORS:20200512-073808676", "issn": "0003-889X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-073808676", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf01191159", "pub_year": "1990", "author_list": "Aschbacher, Michael and Kleidman, Peter B." }, { "id": "https://authors.library.caltech.edu/records/h9jgg-ybn02", "eprint_id": 83025, "eprint_status": "archive", "datestamp": "2023-08-19 22:59:39", "lastmod": "2026-04-21 02:54:02", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J." } }, { "id": "van-Mouche-P-H-M", "name": { "family": "v. Mouche", "given": "P. H. M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On the measure of the spectrum for the almost Mathieu operator", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1990 Springer-Verlag. \n\nReceived: 04 December 1989. \n\nResearch partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325.", "abstract": "We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, \u03b1, the measure of the spectrum, S(\u03b1, \u03bb, \u03d1)=|4\u20132|\u03bb\u2016. For |\u03bb|\u22602 we show that if \u03b1_n is rational and \u03b1_n\u2192\u03b1 irrational, then S+(\u03b1_n,\u03bb,\u03b8)\u2192|4\u22122|\u03bb||.", "date": "1990-08", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "132", "number": "1", "publisher": "Springer", "pagerange": "103-118", "id_number": "CaltechAUTHORS:20171107-100226114", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171107-100226114", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8801918" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "88-00325" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/BF02278001", "pub_year": "1990", "author_list": "Avron, J.; v. Mouche, P. H. M.; et al." }, { "id": "https://authors.library.caltech.edu/records/14zzn-q9175", "eprint_id": 86523, "eprint_status": "archive", "datestamp": "2023-08-19 22:49:27", "lastmod": "2026-04-20 23:30:18", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carmona-E", "name": { "family": "Carmona", "given": "Ren\u00e9" } }, { "id": "Masters-W-C", "name": { "family": "Masters", "given": "Wen Chen" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Relativistic Schr\u00f6dinger operators: Asymptotic behavior of the eigenfunctions", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1990 Published by Elsevier. \n\nReceived December 19, 1988; received March 10, 1989. \n\nCommunicated by L. Gross. \n\nPartially supported by NSF Grant DMS-8701320. \n\nPartially supported by NSF Grant DMS 84-16049. \n\nWe thank E. Lieb for his comments on a first version of the paper. Moreover. the first named author (R.C.) thanks D. Bakry and S. Port for enlightening discussions on some of the facts of the theory of L\u00e9vy processes.", "abstract": "Nonrelativistic Schr\u00f6dinger operators are perturbations of the negative Laplacian and the connection with stochastic processes (and Brownian motion in particular) is well known and usually goes under the name of Feynman and Kac. We present a similar connection between a class of relativistic Schr\u00f6dinger operators and a class of processes with stationary independent increments. In particular, we investigate the decay of the eigenfunctions of these operators and we show that not only exponential decay but also polynomial decay can occur.", "date": "1990-06", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "91", "number": "1", "publisher": "Elsevier", "pagerange": "117-142", "id_number": "CaltechAUTHORS:20180521-151747020", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-151747020", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8701320" }, { "agency": "NSF", "grant_number": "DMS 84-16049" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(90)90049-Q", "pub_year": "1990", "author_list": "Carmona, Ren\u00e9; Masters, Wen Chen; et al." }, { "id": "https://authors.library.caltech.edu/records/8933n-59g11", "eprint_id": 69952, "eprint_status": "archive", "datestamp": "2023-08-19 22:33:50", "lastmod": "2026-04-20 23:11:55", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Constructing solutions of the mKdV-equation", "ispublished": "pub", "full_text_status": "public", "note": "Received 23 August 1988, Available online 7 September 2004.\n\nPartially supported by USNSF under Grant DMS-8416049. Max Kade Foundation Fellow. On leave of absence from the Institute for Theoretical Physics, University of Graz, A-8010 Graz, Austria. Present address: Department of Mathematics, University of Missouri, Columbia, MO 65211.\n\n

Published - 1-s2.0-0022123690900034-main.pdf

", "abstract": "Using commutation methods (i.e., N = 1 supersymmetry) underlying Miura's transformation, an explicit construction of solutions of the modified Korteweg-de Vries equation, given a solution of the (ordinary) Korteweg-de Vries equation, is provided.", "date": "1990-03-01", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "89", "number": "1", "publisher": "Elsevier", "pagerange": "53-60", "id_number": "CaltechAUTHORS:20160825-154251595", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160825-154251595", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8416049" }, { "agency": "Max Kade Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(90)90003-4", "primary_object": { "basename": "1-s2.0-0022123690900034-main.pdf", "url": "https://authors.library.caltech.edu/records/8933n-59g11/files/1-s2.0-0022123690900034-main.pdf" }, "pub_year": "1990", "author_list": "Gesztesy, F. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/xtm8s-6zw43", "eprint_id": 38639, "eprint_status": "archive", "datestamp": "2023-08-19 22:31:02", "lastmod": "2026-03-09 20:41:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } } ] }, "title": "A Classification of Baire Class 1 Functions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1990 American Mathematical Society. Received by the editors December 15, 1987 and, in revised form, June 3, 1988. Research of the first author was partially supported by NSF Grant DMS-8718847.\n\n

Published - 2001236.pdf

", "abstract": "We study in this paper various ordinal ranks of (bounded) Baire class 1 functions and we show their essential equivalence. This leads to a natural classification of the class of bounded Baire class 1 functions B_1 in a transfinite hierarchy B^\u03be_1 \u03be < \u03c9_1) of \"small\" Baire classes, for which (for example) an analysis similar to the Hausdorff-Kuratowski analysis of \u0394^0_2 sets via transfinite differences of closed sets can be carried out. The notions of pseudouniform convergence of a sequence of functions and optimal convergence of a sequence of continuous functions to a Baire class 1 function \u0192 are introduced and used in this study.", "date": "1990-03", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "318", "number": "1", "publisher": "American Mathematical Society", "pagerange": "209-236", "id_number": "CaltechAUTHORS:20130522-151355415", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-151355415", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8718847" } ] }, "other_numbering_system": { "items": [ { "id": "MR0946424", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2001236.pdf", "url": "https://authors.library.caltech.edu/records/xtm8s-6zw43/files/2001236.pdf" }, "pub_year": "1990", "author_list": "Kechris, A. S. and Louveau, A." }, { "id": "https://authors.library.caltech.edu/records/ryk0a-81x05", "eprint_id": 38901, "eprint_status": "archive", "datestamp": "2023-08-19 22:08:06", "lastmod": "2026-03-09 20:41:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "title": "Covering theorems for uniqueness and extended uniqueness sets", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1990 Polish Academy of Sciences. Re\u00e7u par la Redaction le 20.12.1988. Research partially supported by NSF Grant.", "abstract": "A covering theorem for a class of sets C asserts that every set in C can be covered by a countable union of sets in some (somehow simpler) class C. In the theory of sets of uniqueness on the unit circle T the first result of this\nkind is Piatetski-Shapiro's theorem in [PS], which states that every closed set of uniqueness can be covered by countably many closed sets in the class U'_1, consisting of those closed sets E \u2286 T for which there exists a sequence of\nfunctions in A(T), vanishing on E, which converges to the function 1 in the weak^*-topology.", "date": "1990", "date_type": "published", "publication": "Colloquium Mathematicum", "volume": "59", "number": "1", "publisher": "Polish Academy of Sciences, Institute of Mathematics", "pagerange": "63-79", "id_number": "CaltechAUTHORS:20130612-084032401", "issn": "0010-1354", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-084032401", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "MR1078293", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "1990", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/x6qt8-jqp29", "eprint_id": 38676, "eprint_status": "archive", "datestamp": "2023-08-19 21:51:51", "lastmod": "2026-03-09 20:41:27", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Marker-D", "name": { "family": "Marker", "given": "David" } }, { "id": "Sami-R-L", "name": { "family": "Sami", "given": "Ramez L." } } ] }, "title": "\u03a0^1_1 Borel Sets", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1989, Association for Symbolic Logic. Received January 28, 1988; revised May 9, 1988. The first two authors were partially supported by the National Science Foundation.\n\n

Published - 2274751.pdf

", "abstract": "The results in this paper were motivated by the following\nquestion of Sacks. Suppose T is a recursive theory with countably many countable models. What can you say about the least ordinal \u0251 such that all models of T have Scott rank below \u0251? If Martin's conjecture is true for T then \u0251 \u2264 \u03c9\u00b72.", "date": "1989-09", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "54", "number": "3", "publisher": "Association for Symbolic Logic", "pagerange": "915-920", "id_number": "CaltechAUTHORS:20130528-084327264", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-084327264", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "0686.03025", "name": "Zentralblatt MATH Identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2274751.pdf", "url": "https://authors.library.caltech.edu/records/x6qt8-jqp29/files/2274751.pdf" }, "pub_year": "1989", "author_list": "Kechris, Alexander S.; Marker, David; et al." }, { "id": "https://authors.library.caltech.edu/records/wwr0g-prk26", "eprint_id": 38667, "eprint_status": "archive", "datestamp": "2023-08-19 21:31:26", "lastmod": "2026-03-09 20:35:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dougherty-R", "name": { "family": "Dougherty", "given": "R." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Hausdorff Measures and Sets of Uniqueness for Trigonometric Series", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1989 American Mathematical Society. Received by the editors April 21, 1988 and, in revised form, June 1, 1988. The second author was partially supported by NSF Grant DMS-8718847.\n\n

Published - 2047049.pdf

", "abstract": "We characterize the closed sets E in the unit circle T which have the property that, for some nondecreasing h: (0, \u221e) \u2192(0, \u221e) with h(0+) = 0, all the Hausdorff h-measure 0 closed sets F \u2286 E are sets of uniqueness (for trigonometric series). In conjunction with K\u00f6rner's result on the existence of Helson sets of multiplicity, this implies the existence of closed sets of multiplicity (M-sets) within which Hausdorff h-measure 0 implies uniqueness, for some h. This is contrasted with the case of closed sets of strict multiplicity (M_0-sets), where results of Ivashev-Musatov and Kaufman establish the opposite.", "date": "1989-04", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "105", "number": "4", "publisher": "American Mathematical Society", "pagerange": "894-897", "id_number": "CaltechAUTHORS:20130524-113257744", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130524-113257744", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8718847" } ] }, "other_numbering_system": { "items": [ { "id": "MR0946633", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2047049", "primary_object": { "basename": "2047049.pdf", "url": "https://authors.library.caltech.edu/records/wwr0g-prk26/files/2047049.pdf" }, "pub_year": "1989", "author_list": "Dougherty, R. and Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/659n3-xge56", "eprint_id": 98236, "eprint_status": "archive", "datestamp": "2023-08-22 06:06:57", "lastmod": "2026-04-21 08:18:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Sigal-I-M", "name": { "family": "Sigal", "given": "Israel M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Thirring-W", "name": { "family": "Thirring", "given": "Walter" } } ] }, "title": "Approximate neutrality of large-Z ions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Neural Network; Statistical Physic; Complex System; Quantum Mechanic; Nonlinear Dynamics", "note": "\u00a9 Springer-Verlag 1988. \n\nResearch partially supported by the NSERC under Grant NA7901 and by the USNSF under Grants DMS-8416049 and PHY 85-15288-A01.\n\nCommunicated by A. Jaffe.", "abstract": "Let N(Z) denote the number of electrons which a nucleus of chargeZ can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove that N(Z)/Z\u21921 as Z\u2192\u221e.", "date": "1988-12", "date_type": "published", "publication": "Communications in Mathematical Physics", "volume": "116", "number": "4", "publisher": "Springer", "pagerange": "635-644", "id_number": "CaltechAUTHORS:20190826-124739793", "issn": "0010-3616", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190826-124739793", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)", "grant_number": "NA7901" }, { "agency": "NSF", "grant_number": "DMS-8416049" }, { "agency": "NSF", "grant_number": "PHY 85-15288-A01" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/bf01224904", "pub_year": "1988", "author_list": "Lieb, Elliott H.; Sigal, Israel M.; et al." }, { "id": "https://authors.library.caltech.edu/records/wj2dt-qcf58", "eprint_id": 38636, "eprint_status": "archive", "datestamp": "2023-08-19 21:02:59", "lastmod": "2026-03-09 20:34:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Lyons-R", "name": { "family": "Lyons", "given": "Russell" } } ] }, "title": "Ordinal Rankings on Measures Annihilating Thin Sets", "ispublished": "pub", "full_text_status": "public", "keywords": "Rajchman measures, thin sets, sets of uniqueness, rank", "note": "\u00a9 1988 American Mathematical Society. Received by the editors September 10, 1987. Research of the first author partially supported by NSF grant DMS8718847. The second author was partially supported by an NSF Postdoctoral Fellowship.\n\n

Published - 2000989.pdf

", "abstract": "We assign a countable ordinal number to each probability measure which annihilates all H-sets. The descriptive-set theoretic structure of this assignment allows us to show that this class of measures is coanalytic non-Borel. In addition, it allows us to quantify the failure of Rajchman's conjecture. Similar results are obtained for measures annihilating Dirichlet sets.", "date": "1988-12", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "310", "number": "2", "publisher": "American Mathematical Society", "pagerange": "747-758", "id_number": "CaltechAUTHORS:20130522-131009335", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-131009335", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS8718847" }, { "agency": "NSF Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "MR0951888", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2000989", "primary_object": { "basename": "2000989.pdf", "url": "https://authors.library.caltech.edu/records/wj2dt-qcf58/files/2000989.pdf" }, "pub_year": "1988", "author_list": "Kechris, Alexander S. and Lyons, Russell" }, { "id": "https://authors.library.caltech.edu/records/4r7sk-33e81", "eprint_id": 85866, "eprint_status": "archive", "datestamp": "2023-08-19 20:55:25", "lastmod": "2026-04-21 02:06:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J. E." } }, { "id": "Sadun-L", "name": { "family": "Sadun", "given": "L." } }, { "id": "Segert-J", "name": { "family": "Segert", "given": "J." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Topological Invariants in Fermi Systems with Time-Reversal Invariance", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1988 American Physical Society. \n\n(Received 6 July 1988) \n\nWe thank Peter Weichman for useful discussions. The research of one of us (J.E.A.) was partially supported by National Science Foundation Grants No. DMS-8416049 and No. BSF-84-00376. The research of another one of us (B.S.) was partially supported by National Science Foundation Grant No. DMS-8416049.\n\n

Published - PhysRevLett.61.1329.pdf

", "abstract": "We discuss topological invariants for Fermi systems that have time-reversal invariance. The TKN^2 integers (first Chern numbers) are replaced by second Chern numbers, and Berry's phase becomes a unit quaternion, or equivalently an element of SU(2). The canonical example playing much the same role as spin \u00bd in a magnetic field is spin \u00bd in a quadrupole electric field. In particular, the associated bundles are nontrivial and have \u00b1 1 second Chern number. The connection that governs the adiabatic evolution coincides with the symmetric SU(2) Yang-Mills instanton.", "date": "1988-09-19", "date_type": "published", "publication": "Physical Review Letters", "volume": "61", "number": "12", "publisher": "American Physical Society", "pagerange": "1329-1332", "id_number": "CaltechAUTHORS:20180413-164425306", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-164425306", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8416049" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "BSF-84-00376" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.61.1329", "primary_object": { "basename": "PhysRevLett.61.1329.pdf", "url": "https://authors.library.caltech.edu/records/4r7sk-33e81/files/PhysRevLett.61.1329.pdf" }, "pub_year": "1988", "author_list": "Avron, J. E.; Sadun, L.; et al." }, { "id": "https://authors.library.caltech.edu/records/05kez-pp410", "eprint_id": 85865, "eprint_status": "archive", "datestamp": "2023-08-19 20:55:05", "lastmod": "2026-04-21 08:00:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Englisch-H", "name": { "family": "Englisch", "given": "H." } }, { "id": "Kirsch-W", "name": { "family": "Kirsch", "given": "W." } }, { "id": "Schroder-M", "name": { "family": "Schroder", "given": "M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Density of Surface States in Discrete Models", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1988 American Physical Society. \n\n(Received 14 April 1988) \n\nThis research was partially supported by U.S. National Science Foundation under Grant No. DMS-8416049.\n\n

Published - PhysRevLett.61.1261.pdf

", "abstract": "We consider a simple quantum model with a surface and prove the existence of a surface density of states. We show that the energy spectrum of the model is the union of the support of the bulk densities of states of the media forming the surface and the support of the surface density of states.", "date": "1988-09-12", "date_type": "published", "publication": "Physical Review Letters", "volume": "61", "number": "11", "publisher": "American Physical Society", "pagerange": "1261-1262", "id_number": "CaltechAUTHORS:20180413-164117904", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180413-164117904", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8416049" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.61.1261", "primary_object": { "basename": "PhysRevLett.61.1261.pdf", "url": "https://authors.library.caltech.edu/records/05kez-pp410/files/PhysRevLett.61.1261.pdf" }, "pub_year": "1988", "author_list": "Englisch, H.; Kirsch, W.; et al." }, { "id": "https://authors.library.caltech.edu/records/b1b1j-x5y91", "eprint_id": 10730, "eprint_status": "archive", "datestamp": "2023-08-22 05:43:33", "lastmod": "2026-04-21 02:37:17", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Chung-F-R-K", "name": { "family": "Chung", "given": "F. R. K." } }, { "id": "Graham-R-L", "name": { "family": "Graham", "given": "R. L." } }, { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "R. M." } } ] }, "title": "Quasi-Random Graphs", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1988 by the National Academy of Sciences. \n\nContributed by R. L. Graham, October 23, 1987. \n\nThe publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked \"advertisement\" in accordance with 18 U.S.C. \u00a71734 solely to indicate this fact.\n\n

Published - CHUpnas88.pdf

", "abstract": "We introduce a large equivalence class of graph properties, all of which are shared by so-called random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this class.", "date": "1988-02-15", "date_type": "published", "publication": "Proceedings of the National Academy of Sciences of the United States of America", "volume": "85", "number": "4", "publisher": "National Academy of Sciences", "pagerange": "969-970", "id_number": "CaltechAUTHORS:CHUpnas88", "issn": "0027-8424", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:CHUpnas88", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1073/pnas.85.4.969", "pmcid": "PMC279681", "primary_object": { "basename": "CHUpnas88.pdf", "url": "https://authors.library.caltech.edu/records/b1b1j-x5y91/files/CHUpnas88.pdf" }, "pub_year": "1988", "author_list": "Chung, F. R. K.; Graham, R. L.; et al." }, { "id": "https://authors.library.caltech.edu/records/sfx6b-9r313", "eprint_id": 105683, "eprint_status": "archive", "datestamp": "2023-08-19 20:19:25", "lastmod": "2026-04-20 23:30:58", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Some multilinear forms with large isometry groups", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1988 by D. Reidel Publishing Company. \n\nPartially supported by the National Science Foundation.", "abstract": "Many groups are best described as the group of automorphisms of some natural object. I'm interested in obtaining such descriptions of the finite simple groups, and more generally descriptions of the groups of Lie type over arbitrary fields. The representation of the alternating group of degree n as the group of automorphisms of a set of order n\nis an excellent example of such a description. The representation of the classical groups as the isometry groups of bilinear or sequilinear forms is another.", "date": "1988-01", "date_type": "published", "publication": "Geometriae Dedicata", "volume": "25", "number": "1-3", "publisher": "Springer", "pagerange": "417-465", "id_number": "CaltechAUTHORS:20200930-113055206", "issn": "0046-5755", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200930-113055206", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf00191936", "pub_year": "1988", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/hpg12-cvn82", "eprint_id": 38635, "eprint_status": "archive", "datestamp": "2023-08-19 19:40:53", "lastmod": "2026-03-09 20:36:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ajtai-M", "name": { "family": "Ajtai", "given": "M." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Set of Continuous Functions with the Everywhere Convergent Fourier Series", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1987 American Mathematical Society. Received by the editors June 11, 1985 and, in revised form, June 20, 1986. Research partially supported by NSF Grant DMS-8416349.\n\n

Published - 2000906.pdf

", "abstract": "This paper deals with the descriptive set theoretic properties of the class EC of continuous functions with everywhere convergent Fourier series. It is shown that this set is a complete coanalytic set in C(T). A natural coanalytic rank function on EC is studied that assigns to each \u0192 \u0404 EC a countable ordinal number, which measures the \"complexity\" of the convergence of the Fourier series of \u0192. It is shown that there exist functions in EC (in fact even differentiable ones) which have arbitrarily large countable rank, so that this provides a proper hierarchy on EC with \u03c9_1 distinct levels.", "date": "1987-07", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "302", "number": "1", "publisher": "American Mathematical Society", "pagerange": "207-221", "id_number": "CaltechAUTHORS:20130522-115611198", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-115611198", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8416349" } ] }, "other_numbering_system": { "items": [ { "id": "MR0887506", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2000906", "primary_object": { "basename": "2000906.pdf", "url": "https://authors.library.caltech.edu/records/hpg12-cvn82/files/2000906.pdf" }, "pub_year": "1987", "author_list": "Ajtai, M. and Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/vt2fk-tvw55", "eprint_id": 32024, "eprint_status": "archive", "datestamp": "2023-08-19 19:40:38", "lastmod": "2026-04-21 06:11:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Boll\u00e9-D", "name": { "family": "Boll\u00e9", "given": "D." } }, { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "F." } }, { "id": "Grosse-H", "name": { "family": "Grosse", "given": "H." } }, { "id": "Schweiger-W", "name": { "family": "Schweiger", "given": "W." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Witten index, axial anomaly, and Krein's spectral shift function in supersymmetric quantum mechanics", "ispublished": "pub", "full_text_status": "public", "keywords": "QUANTUM MECHANICS, SUPERSYMMETRY, SCATTERING, INVARIANCE PRINCIPLES, SPECTRAL FUNCTIONS, SPECTRAL SHIFT, MAGNETIC FIELDS, MAGNETIC FLUX, QUANTUM FIELD THEORY, QUANTUM NUMBERS, QUANTUM OPERATORS, HAMILTONIANS, TOPOLOGY, FUNCTIONAL ANALYSIS", "note": "\u00a9 1987 American Institute of Physics. Received 13 November 1986; accepted 11 February 1987. We gratefully acknowledge stimulating discussions with Professor R. Blankenbecler. F. G. is indebted to Professor K. Chadan for the warm hospitality extended to him at LPTHE-Orsay, and to E. Stone and D. Wales for hospitality at Caltech. D. B. is an Onderzoeksleider of the National Fonds voor Wetenschappelijk Onderzoek, Belgium. The work of F. G. and H. G. is partially supported by Fonds zur F\u00f6rderung der Wissenschaftlichen Forschung in \u00d6sterreich, Project No. P5588. The research of B. S. is partially supported by the USNSF under Grant No. DMS-84-16049.\n\n

Published - BOLjmp87.pdf

", "abstract": "A new method is presented to study supersymmetric quantum mechanics. Using relative scattering techniques, basic relations are derived between Krein's spectral shift function, the Witten index, and the anomaly. The topological invariance of the spectral shift function is discussed. The power of this method is illustrated by treating various models and calculating explicitly the spectral shift function, the Witten index, and the anomaly. In particular, a complete treatment of the two\u2010dimensional magnetic field problem is given, without assuming that the magnetic flux is quantized.", "date": "1987-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "28", "number": "7", "publisher": "American Institute of Physics", "pagerange": "1512-1525", "id_number": "CaltechAUTHORS:20120622-081911618", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120622-081911618", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Fonds Zur F\u00f6rderung der Wissenschaftlichen Forschung", "grant_number": "P5588" }, { "agency": "NSF", "grant_number": "DMS-84-16049" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/1.527508", "primary_object": { "basename": "BOLjmp87.pdf", "url": "https://authors.library.caltech.edu/records/vt2fk-tvw55/files/BOLjmp87.pdf" }, "pub_year": "1987", "author_list": "Boll\u00e9, D.; Gesztesy, F.; et al." }, { "id": "https://authors.library.caltech.edu/records/ymnan-6h009", "eprint_id": 38631, "eprint_status": "archive", "datestamp": "2023-08-19 19:31:45", "lastmod": "2026-03-09 20:41:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } }, { "id": "Woodin-W-H", "name": { "family": "Woodin", "given": "W. H." } } ] }, "title": "The Structure of \u03c3-Ideals of Compact Sets", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1987 American Mathematical Society. Received by the editors October 15, 1985. Partially supported by NSF Grant DMS-8416349.\n\n

Published - 2000338.pdf

", "abstract": "Motivated by problems in certain areas of analysis, like measure theory and harmonic analysis, where \u03c3-ideals of compact sets are encountered very often as notions of small or exceptional sets, we undertake in this paper a descriptive set theoretic study of \u03c3-ideals of compact sets in compact metrizable spaces. In the first part we study the complexity of such ideals, showing that the structural condition of being a \u03c3-ideal imposes severe definability\nrestrictions. A typical instance is the dichotomy theorem, which states that \u03c3-ideals which are analytic or coanalytic must be actually either complete coanalytic or else G_\u03b4. In the second part we discuss (generators or as we call\nthem here) bases for \u03c3-ideals and in particular the problem of existence of Borel bases for coanalytic non-Borel \u03c3-ideals. We derive here a criterion for the nonexistence of such bases which has several applications. Finally in the\nthird part we develop the connections of the definability properties of \u03c3-ideals with other structural properties, like the countable chain condition, etc.", "date": "1987-05", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "301", "number": "1", "publisher": "American Mathematical Society", "pagerange": "263-288", "id_number": "CaltechAUTHORS:20130522-103643006", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-103643006", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8416349" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/2000338", "primary_object": { "basename": "2000338.pdf", "url": "https://authors.library.caltech.edu/records/ymnan-6h009/files/2000338.pdf" }, "pub_year": "1987", "author_list": "Kechris, A. S.; Louveau, A.; et al." }, { "id": "https://authors.library.caltech.edu/records/xaers-p8324", "eprint_id": 38698, "eprint_status": "archive", "datestamp": "2023-08-22 05:03:44", "lastmod": "2026-04-21 06:20:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Woodin-W-H", "name": { "family": "Woodin", "given": "W. Hugh" } } ] }, "title": "Ranks of differentiable functions", "ispublished": "pub", "full_text_status": "restricted", "keywords": "03E15; Mathematical Logic and Foundations; Set Theory; Descriptive Set Theory", "note": "\u00a9 1987 University College London.\n\nReceived on the 1st of July, 1985.\nResearch partially supported by a U.S. NSF Grant.", "abstract": "The purpose of this paper is to define and study a natural rank function\nwhich associates to each differentiable function (say on the interval [0, 1]) a\ncountable ordinal number, which measures the complexity of its derivative.\nFunctions with continuous derivatives have the smallest possible rank 1, a\nfunction like x^2 sin (x^(-1)) has rank 2, etc., and we show that functions of any\ngiven countable ordinal rank exist. This exhibits an underlying hierarchical\nstructure of the class of differentiable functions, consisting of \u03c9_1 distinct levels.\nThe definition of rank is invariant under addition of constants, and so it\nnaturally assigns also to every derivative a unique rank, and an associated\nhierarchy for the class of all derivatives.\n\nThe set D of functions in C[0, 1] which are everywhere differentiable is a\ncomplete coanalytic (and thus non-Borel) set (Mazurkiewicz [Maz]; see Section\n2 below) and it will tum out that the rank function we define has the\nright descriptive set theoretic properties summarized in the concept of a\ncoanalytic norm, explained in Section 1.\n\nOur original description of the rank function was in terms of wellfounded\ntrees and is given in Section 4. In Section 3 we give an equivalent description\nin terms of a Cantor-Bendixson type analysis. We would like to acknowledge\nhere the contribution of D. Preiss. It was in a conversation with one of the\nauthors that this equivalent description was formulated.", "date": "1986-12", "date_type": "published", "publication": "Mathematika", "volume": "33", "number": "2", "publisher": "University College London", "pagerange": "252-278", "id_number": "CaltechAUTHORS:20130528-145231519", "issn": "0025-5793", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-145231519", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "MR0882498", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0025579300011244", "pub_year": "1986", "author_list": "Kechris, Alexander S. and Woodin, W. Hugh" }, { "id": "https://authors.library.caltech.edu/records/ht63b-dxb43", "eprint_id": 715, "eprint_status": "archive", "datestamp": "2023-08-22 04:46:36", "lastmod": "2026-03-18 00:00:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Schr\u00f6dinger semigroups on the scale of Sobolev spaces", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1986 Pacific Journal of Mathematics. \n\nReceived December 17, 1984 and in revised form March 26, 1985. \n\nResearch suported by USNSF under grant MCS-81-20833.\n\n

Published - SIMpjm86.pdf

", "abstract": "We consider the action of semigroups e(-tH), with H = -\u0394 + V on L(2)(R(v)), on the scale of Sobolev spaces H(\u03b1). We show that while e(-tH) maps L(2)=H(0) to H(2) under great generality, there exist bounded V so that, for all \u03b2 > 0, e(-tH)[H(\u03b2)] is not contained in any H(\u03b1) with a > 2.", "date": "1986-04", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "122", "number": "2", "publisher": "Pacific Journal of Mathematics", "pagerange": "475-480", "id_number": "CaltechAUTHORS:SIMpjm86", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMpjm86", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "SIMpjm86.pdf", "url": "https://authors.library.caltech.edu/records/ht63b-dxb43/files/SIMpjm86.pdf" }, "pub_year": "1986", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/k35mp-zkr91", "eprint_id": 38630, "eprint_status": "archive", "datestamp": "2023-08-19 17:51:38", "lastmod": "2026-03-09 20:39:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Solovay-R-M", "name": { "family": "Solovay", "given": "Robert M." } } ] }, "title": "On the Relative Consistency Strength of Determinacy Hypothesis", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1985 American Mathematical Society. Received by the editors July 6, 1984. Partially supported by NSF Grant MCS 79-20465 and an A. P. Sloan Foundation Fellowship. Partially supported by NSF Grant MCS 79-06077.\n\n

Published - 1999790.pdf

", "abstract": "For any collection of sets of reals C, let C-DET be the statement that all sets of reals in C are determined. In this paper we study questions of the form: For given C \u2286 C', when is C'-DET equivalent, equiconsistent or strictly stronger in consistency strength than C-DET (modulo ZFC)? We focus especially on classes C contained in the projective sets.", "date": "1985-07", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "290", "number": "1", "publisher": "American Mathematical Society", "pagerange": "179-211", "id_number": "CaltechAUTHORS:20130522-101108599", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-101108599", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 79-20465" }, { "agency": "A. P. Sloan Foundation Fellowship" }, { "agency": "NSF", "grant_number": "MCS 79-06077" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.2307/1999790", "primary_object": { "basename": "1999790.pdf", "url": "https://authors.library.caltech.edu/records/k35mp-zkr91/files/1999790.pdf" }, "pub_year": "1985", "author_list": "Kechris, Alexander S. and Solovay, Robert M." }, { "id": "https://authors.library.caltech.edu/records/zx0q4-q1d11", "eprint_id": 38640, "eprint_status": "archive", "datestamp": "2023-08-19 17:48:15", "lastmod": "2026-03-09 20:41:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Determinacy with Complicated Strategies", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1985 American Mathematical Society. Received by the editors January 3, 1984.\n\n

Published - 2045400.pdf

", "abstract": "For any class of functions F from R into R, AD(F) is the assertion that in every two person game on integers one of the two players has a winning strategy in the class F. It is shown, in ZF + DC + V = L(R), that for any F of cardinality < 2^(N0)(i.e. any F which is a surjective image of R) AD(F) implies AD (the Axiom of Determinacy).", "date": "1985-06", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "94", "number": "2", "publisher": "American Mathematical Society", "pagerange": "333-336", "id_number": "CaltechAUTHORS:20130522-152728059", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-152728059", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9939-1985-0784188-0", "primary_object": { "basename": "2045400.pdf", "url": "https://authors.library.caltech.edu/records/zx0q4-q1d11/files/2045400.pdf" }, "pub_year": "1985", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/nde8t-2pt80", "eprint_id": 85900, "eprint_status": "archive", "datestamp": "2023-08-19 17:44:06", "lastmod": "2026-04-21 00:53:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Taylor-M", "name": { "family": "Taylor", "given": "Michael" } }, { "id": "Wolff-T", "name": { "family": "Wolff", "given": "Tom" } } ] }, "title": "Some Rigorous Results for the Anderson Model", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1985 American Physical Society. \n\n(Received 10 January 1985) \n\nTwo of us (B.S. and M.T.) would like to thank T. Spencer for valuable discussions related to theorem 1, and one of us (B.S.) would like to thank S. Kotani and T. Spencer for useful discussions related to theorems 2 and 3. This research was partially supported by the National Science Foundation under Grants No. MCS-81-20833, No. MCS-82-01766A01, and No. DMS-84-07099.\n\n

Published - PhysRevLett.54.1589.pdf

", "abstract": "We discuss two results for the Anderson model of random quantum Hamiltonians: (1) smoothness of the density of states in the one-dimensional model, even in many cases where the potential distribution is not smooth; and (2) a criterion for localization which, among other consequences, implies that certain estimates of Fr\u00f6hlich and Spencer yield a dense point spectrum for the multidimensional model at large randomness or large energies.", "date": "1985-04-08", "date_type": "published", "publication": "Physical Review Letters", "volume": "54", "number": "14", "publisher": "American Physical Society", "pagerange": "1589-1592", "id_number": "CaltechAUTHORS:20180417-104515007", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104515007", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" }, { "agency": "NSF", "grant_number": "MCS-82-01766A01" }, { "agency": "NSF", "grant_number": "DMS-84-07099" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.54.1589", "primary_object": { "basename": "PhysRevLett.54.1589.pdf", "url": "https://authors.library.caltech.edu/records/nde8t-2pt80/files/PhysRevLett.54.1589.pdf" }, "pub_year": "1985", "author_list": "Simon, Barry; Taylor, Michael; et al." }, { "id": "https://authors.library.caltech.edu/records/36vnr-v6195", "eprint_id": 88112, "eprint_status": "archive", "datestamp": "2023-08-19 17:31:42", "lastmod": "2026-04-20 23:20:30", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Almost periodic Schr\u00f6dinger operators IV. The Maryland model", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1985 Published by Elsevier. \n\nReceived March 5, 1984.\n\nResearch partially supported by USNSF Grant MCS-81-20833. \n\nI would like to thank R. Prange for useful correspondence and his friendly encouragement, and T. Spencer and D. Thouless for useful discussions. Finally, I would like to express my tremendous debt of gratitude to J. Avron in connection with this paper. He suggested the model to me for further analysis and provided me with many useful discussions and comments on the manuscript. I regret that in the end he felt his contributions did not warrant his being a co-author of this paper.", "abstract": "The analysis of discrete Schr\u00f6dinger operators of the form (hu)(n) = u(n + 1) + u(n \u2212 1) + \u03bb tan(\u03c0\u03b1n + \u03b8) u(n) is discussed. Depending on Diophantine properties of \u03b1, the spectrum may be dense point, singular continuous or a mixture of the two.", "date": "1985-01", "date_type": "published", "publication": "Annals of Physics", "volume": "159", "number": "1", "publisher": "Elsevier", "pagerange": "157-183", "id_number": "CaltechAUTHORS:20180720-164402687", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180720-164402687", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0003-4916(85)90196-4", "pub_year": "1985", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/nsb41-q3752", "eprint_id": 86519, "eprint_status": "archive", "datestamp": "2023-08-19 17:18:58", "lastmod": "2026-04-21 08:23:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Semiclassical analysis of low lying elgenvalues. III. Width of the ground state band in strongly coupled solids", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1984 Published by Elsevier. \n\nReceived January 17. 1984. \n\nResearch partially supported by USNSF Grant MCS-81-20833. \n\nIt is a pleasure to thank J. Keller and M. Weinstein for discussions which stimulated this work.", "abstract": "A smooth periodic potential, V, with one minima per unit cell, is considered. Let \u0394(\u03bb) be the width of the ground state band for \u2212\u0394 + \u03bb^2V. It is rigorously proved that lim(\u03bb\u2192\u221e) \u2212 \u03bb^(\u22121) ln \u0394(\u03bb) is given by the minimum action among all instantons connecting two distinct minima of V.", "date": "1984-12", "date_type": "published", "publication": "Annals of Physics", "volume": "158", "number": "2", "publisher": "Elsevier", "pagerange": "415-420", "id_number": "CaltechAUTHORS:20180521-145200393", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-145200393", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0003-4916(84)90125-8", "pub_year": "1984", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/8cbah-jq771", "eprint_id": 85899, "eprint_status": "archive", "datestamp": "2023-08-19 16:58:55", "lastmod": "2026-04-21 05:17:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Deylon-F", "name": { "family": "Delyon", "given": "Francois" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Souillard-B", "name": { "family": "Souillard", "given": "Bernard" } } ] }, "title": "From Power-Localized to Extended States in a Class of One-Dimensional Disordered Systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1984 American Physical Society. \n\n(Received 12 March 1984) \n\nOne of us (B.So.) is glad to thank W. Kohn and the Institute for Theoretical Physics at Santa Barbara, where part of this work has been done. Two of us (F.D. and B. So.) are glad to thank E. Stone and W. Luxemburg for the hospitality of the California Institute of Technology, where part of this work has been done. This research was partially supported by the National Science Foundation under Grant No. MCS-81-20833.\n\n

Published - PhysRevLett.52.2187.pdf

", "abstract": "We study a one-dimensional random Kronig-Penney model in the presence of a constant electric field. We rigorously prove for the first time the existence of a transition between a regime of extended states for large field and a regime of power-localized states for small field. There the large-distance behavior of the states is |x|^(\u2212\u03b1(F)) with \u03b1(F) \u223c C/F for small field F, confirming a numerical computation of Soukoulis et al.", "date": "1984-06-11", "date_type": "published", "publication": "Physical Review Letters", "volume": "52", "number": "24", "publisher": "American Physical Society", "pagerange": "2187-2189", "id_number": "CaltechAUTHORS:20180417-104514705", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514705", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.52.2187", "primary_object": { "basename": "PhysRevLett.52.2187.pdf", "url": "https://authors.library.caltech.edu/records/8cbah-jq771/files/PhysRevLett.52.2187.pdf" }, "pub_year": "1984", "author_list": "Delyon, Francois; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/tragq-jrx10", "eprint_id": 86534, "eprint_status": "archive", "datestamp": "2023-08-19 16:52:27", "lastmod": "2026-04-21 04:41:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrell-E-M", "name": { "family": "Harrell", "given": "Evans M." } }, { "id": "Corngold-N", "name": { "family": "Corngold", "given": "Noel" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The mathematical theory of resonances whose widths are exponentially small, II", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1984 Published by Elsevier. \n\nSubmitted by C. L. Dolph. \n\nResearch partially supported by NSF grant MCS-79-26408. \n\nResearch partially supported by NSF grant MCS-81-20833.", "abstract": "It is shown how the rigorous justification of resonance widths in Paper I [5] can be simplified by exploiting Langer's trick of expanding the independent variable rather than the dependent variable [9].", "date": "1984-04-15", "date_type": "published", "publication": "Journal of Mathematical Analysis and Applictions", "volume": "99", "number": "2", "publisher": "Elsevier", "pagerange": "447-457", "id_number": "CaltechAUTHORS:20180521-163704706", "issn": "0022-247X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-163704706", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-79-26408" }, { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-247X(84)90225-7", "pub_year": "1984", "author_list": "Harrell, Evans M.; Corngold, Noel; et al." }, { "id": "https://authors.library.caltech.edu/records/q1br4-0x928", "eprint_id": 85898, "eprint_status": "archive", "datestamp": "2023-08-19 16:48:44", "lastmod": "2026-04-21 00:52:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Sigal-I-M", "name": { "family": "Sigal", "given": "Israel M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Thirring-W", "name": { "family": "Thirring", "given": "Walter" } } ] }, "title": "Asymptotic Neutrality of Large-Z Ions", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1984 American Physical Society. \n\n(Received 4 January 1984) \n\nParts of this work were done while some of us were visiting others of us: B.S. should like to thank H. Dym and I. Sigal for the hospitality of the Weizmann Institute, and W.T. would like to thank E. Lieb for the hospitality of Princeton University and M. Goldberger and R. Vogt for the hospitality of the California Institute of Technology. This work was supported in part by National Science Foundation Grants No. PHY-81-16101-A01 and No. MCS-81-20833 and by U. S.-Israel Binational Science Foundation Grant No. 3188/83.\n\n

Published - PhysRevLett.52.994.pdf

", "abstract": "Let N(Z) denote the number of electrons that a nucleus of charge Z binds in nonrelativistic quantum theory. It is proved that (N(Z))/Z \u2192 1 as Z \u2192 \u221e. The Pauli principle plays a critical role.", "date": "1984-03-19", "date_type": "published", "publication": "Physical Review Letters", "volume": "52", "number": "12", "publisher": "American Physical Society", "pagerange": "994-996", "id_number": "CaltechAUTHORS:20180417-104514421", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514421", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-81-16101-A01" }, { "agency": "NSF", "grant_number": "MCS-81-20833" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "3188/83" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.52.994", "primary_object": { "basename": "PhysRevLett.52.994.pdf", "url": "https://authors.library.caltech.edu/records/q1br4-0x928/files/PhysRevLett.52.994.pdf" }, "pub_year": "1984", "author_list": "Lieb, Elliott H.; Sigal, Israel M.; et al." }, { "id": "https://authors.library.caltech.edu/records/afzqs-0pg39", "eprint_id": 38675, "eprint_status": "archive", "datestamp": "2023-08-19 16:45:30", "lastmod": "2026-03-09 20:34:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Axiom of Determinacy Implies Dependent Choices in L(R)", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1984, Association for Symbolic Logic. Received April 29, 1982. Research partially supported by NSF Grant No. MCS-8117804. The author is an A. P. Sloan Foundation Fellow.\n\n

Published - 2274099.pdf

", "abstract": "We prove the following Main Theorem: ZF+AD+V=L(R)\u21d2DC. As a corollary we have that Con(ZF+AD)\u21d2Con(ZF+AD+DC). Combined with the result of Woodin that Con(ZF+AD)\u21d2Con(ZF+AD+\u00acAC^\u03c9) it follows that DC (as well as AC^\u03c9) is independent relative to ZF+AD. It is finally shown (jointly with H. Woodin) that ZF+AD+\u00acDC_R, where DC_R is DC restricted to reals, implies the consistency of ZF+AD+DC, in fact implies R^# (i.e. the sharp of L(R)) exists.", "date": "1984-03", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "49", "number": "1", "publisher": "Association for Symbolic Logic", "pagerange": "161-173", "id_number": "CaltechAUTHORS:20130528-083650112", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-083650112", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-8117804" } ] }, "other_numbering_system": { "items": [ { "id": "MR0736611", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2274099.pdf", "url": "https://authors.library.caltech.edu/records/afzqs-0pg39/files/2274099.pdf" }, "pub_year": "1984", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/2pepc-k9f58", "eprint_id": 85897, "eprint_status": "archive", "datestamp": "2023-08-19 16:25:18", "lastmod": "2026-04-21 07:15:29", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1983 American Physical Society. \n\n(Received 18 October 1983) \n\nIt is a pleasure to thank D. Robinson and N. Trudinger for the hospitality of the Australian National University, where this work was done, M. Berry for telling me of his work, and B. Souillard for the remark (via M. Berry) that there must be a connection between Berry's work and that of TKN. This research was partially supported by the National Science Foundation through Grant No. MCS-81-20833.\n\n

Published - PhysRevLett.51.2167.pdf

", "abstract": "It is shown that the \"geometrical phase factor\" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem naturally defines a connection in such a bundle. This not only takes the mystery out of Berry's phase factor and provides calculational simple formulas, but makes a connection between Berry's work and that of Thouless et al. This connection allows the author to use Berry's ideas to interpret the integers of Thouless et al. in terms of eigenvalue degeneracies.", "date": "1983-12-12", "date_type": "published", "publication": "Physical Review Letters", "volume": "51", "number": "24", "publisher": "American Physical Society", "pagerange": "2167-2170", "id_number": "CaltechAUTHORS:20180417-104514087", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104514087", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.51.2167", "primary_object": { "basename": "PhysRevLett.51.2167.pdf", "url": "https://authors.library.caltech.edu/records/2pepc-k9f58/files/PhysRevLett.51.2167.pdf" }, "pub_year": "1983", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/8hr7d-f8j27", "eprint_id": 85896, "eprint_status": "archive", "datestamp": "2023-08-19 16:07:12", "lastmod": "2026-04-21 05:10:26", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J. E." } }, { "id": "Seiler-R", "name": { "family": "Seiler", "given": "R." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Homotopy and Quantization in Condensed Matter Physics", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1983 American Physical Society. \n\n(Received 31 May 1983) \n\nWe would like to thank P. Deift, R. Feynman, B.Fuller, R. Johnson, L. Romans, T. Spencer, B. Souillard, D. Thouless, G. Toulouse, J. Zak, and especially S. Cappell for useful discussions. We thank J. Sokoloff for drawing our attention to Ref. 13. This work was supported part in part through National Science Foundation Grant No. MCS-81-20833.\n\n

Published - PhysRevLett.51.51.pdf

", "abstract": "It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may not be preserved but their sum is preserved.", "date": "1983-07-04", "date_type": "published", "publication": "Physical Review Letters", "volume": "51", "number": "1", "publisher": "American Physical Society", "pagerange": "51-53", "id_number": "CaltechAUTHORS:20180417-104513799", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104513799", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.51.51", "primary_object": { "basename": "PhysRevLett.51.51.pdf", "url": "https://authors.library.caltech.edu/records/8hr7d-f8j27/files/PhysRevLett.51.51.pdf" }, "pub_year": "1983", "author_list": "Avron, J. E.; Seiler, R.; et al." }, { "id": "https://authors.library.caltech.edu/records/0hvz2-f3453", "eprint_id": 2764, "eprint_status": "archive", "datestamp": "2023-08-22 03:30:26", "lastmod": "2026-04-21 02:40:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J." } }, { "id": "Craig-W", "name": { "family": "Craig", "given": "W." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Large coupling behaviour of the Lyapunov exponent for tight binding one-dimensional random systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1983 IOP Publishing Limited \n\nReceived 18 January 1983 \n\nResearch partially supported by USNSF under Grant MCS-81-20833.\n\n

Published - AVRjpa83.pdf

", "abstract": "Studies the Lyapunov exponent gamma lambda (E) of (hu)(n)=u(n+1)+u(n-1)+ lambda V(n)u(n) in the limit as lambda to infinity where V is a suitable random potential. The authors prove that gamma lambda (E) approximately ln lambda as lambda to infinity uniformly as E/ lambda runs through compact sets. They also describe a formal expansion (to order lambda -2) for random and almost periodic potentials.", "date": "1983-05-11", "date_type": "published", "publication": "Journal of Physics A: Mathematical and General", "volume": "16", "number": "7", "publisher": "IOP", "pagerange": "L209-L211", "id_number": "CaltechAUTHORS:AVRjpa83.791", "issn": "0305-4470", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:AVRjpa83.791", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1088/0305-4470/16/7/002", "primary_object": { "basename": "AVRjpa83.pdf", "url": "https://authors.library.caltech.edu/records/0hvz2-f3453/files/AVRjpa83.pdf" }, "pub_year": "1983", "author_list": "Avron, J.; Craig, W.; et al." }, { "id": "https://authors.library.caltech.edu/records/6x4k8-ghn42", "eprint_id": 9597, "eprint_status": "archive", "datestamp": "2023-08-22 03:26:34", "lastmod": "2026-03-09 20:41:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Woodin-W-H", "name": { "family": "Woodin", "given": "W. Hugh" } } ] }, "title": "Equivalence of partition properties and determinacy", "ispublished": "pub", "full_text_status": "public", "keywords": "set theory; descriptive set theory; constructible from the reals universe", "note": "\u00a9 1983 by the National Academy of Sciences. \n\nCommunicated by Stephen C. Kleene, December 15, 1982. \n\nThis research was partially supported by National Science Foundation Grant MCS 81-17804. A.S.K. is an A.P. Sloan Foundation Fellow. \n\nThe publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked \"advertisement\" in accordance with 18 U.S.C. \u00a71734 solely to indicate this fact.\n\n

Published - KECpnas83.pdf

", "abstract": "It is shown that, within L(R), the smallest inner model of set theory containing the reals, the axiom of determinacy is equivalent to the existence of arbitrarily large cardinals below \u0398 with the strong partition property \u0138 \u2192 (\u0138)^\u0138.", "date": "1983-03-15", "date_type": "published", "publication": "Proceedings of the National Academy of Sciences of the United States of America", "volume": "80", "number": "6", "publisher": "National Academy of Sciences", "pagerange": "1783-1786", "id_number": "CaltechAUTHORS:KECpnas83", "issn": "0027-8424", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KECpnas83", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 81-17804" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pmcid": "PMC393690", "primary_object": { "basename": "KECpnas83.pdf", "url": "https://authors.library.caltech.edu/records/6x4k8-ghn42/files/KECpnas83.pdf" }, "pub_year": "1983", "author_list": "Kechris, Alexander S. and Woodin, W. Hugh" }, { "id": "https://authors.library.caltech.edu/records/qmcb6-5en59", "eprint_id": 86510, "eprint_status": "archive", "datestamp": "2023-08-19 15:52:55", "lastmod": "2026-04-21 00:30:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Equality of the density of states in a wide class of tight-binding Lorentzian random models", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1983 American Physical Society. \n\n(Received 5 November 1982) \n\nIt is a pleasure to thank J. Avron and T. Spencer for useful discussions. This research was supported in part by the National Science Foundation (U.S.) under Grant No. MCS-81-20833.\n\n

Published - PhysRevB.27.3859.pdf

", "abstract": "We prove directly the equality of the density of states in a wide class of tight-binding Lorentzian random models, including the Lloyd model, the tan (2\u03c0\u03b1n + \u03b8) model of Grempel, Fishman, and Prange, and a model with potential \u03a3i\u03c8_i tan(2\u03c0\u03b1_in), where \u03a3i\u03c8_i = 1 and the \u03b1_i are rationally independent.", "date": "1983-03-15", "date_type": "published", "publication": "Physical Review B", "volume": "27", "number": "6", "publisher": "American Physical Society", "pagerange": "3859-3860", "id_number": "CaltechAUTHORS:20180521-140632144", "issn": "1098-0121", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-140632144", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevB.27.3859", "primary_object": { "basename": "PhysRevB.27.3859.pdf", "url": "https://authors.library.caltech.edu/records/qmcb6-5en59/files/PhysRevB.27.3859.pdf" }, "pub_year": "1983", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/4ahvp-yy937", "eprint_id": 86533, "eprint_status": "archive", "datestamp": "2023-08-19 15:51:22", "lastmod": "2026-04-20 23:24:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Some quantum operators with discrete spectrum but classically continuous spectrum", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1983 Published by Elsevier. \n\nReceived September 22, 1982. \n\nResearch partially supported by USNSF under Grant MCS-81-20833. \n\nIt is a pleasure to thank J. Goldstone and R. Jackiw for raising their question, C. Fefferman for telling me of his work with D. Phong, and M. Aizenman, C. Fefferman, M. Peskin, and most especially J. Avron. for valuable discussions.", "abstract": "We consider a number of simple quantum Hamiltonians H(\u2212i\u2207,x) with the following property: H(\u2212i\u2207,x) has discrete spectrum even though {(p,q) | H(p,q)", "date": "1983-03", "date_type": "published", "publication": "Annals of Physics", "volume": "146", "number": "1", "publisher": "Elsevier", "pagerange": "209-220", "id_number": "CaltechAUTHORS:20180521-162122666", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-162122666", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-81-20833" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0003-4916(83)90057-X", "pub_year": "1983", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/vx90y-b8346", "eprint_id": 105862, "eprint_status": "archive", "datestamp": "2023-08-19 15:29:19", "lastmod": "2026-04-21 00:59:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Almost periodic Schr\u00f6dinger operators: A Review", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1982 Published by Elsevier Under an Elsevier user license. \n\nBased, in part, on a talk at the VIth International Conference on Mathematical Physics, Berlin, August 11\u201320, 1981. \n\nResearch partially supported by USNSF Grant MCS-78-01885. \n\nIt is a pleasure to thank J. Bellisard, R. Johnson, J. Moser, and P. Sarnak for information on their work before publication, and to thank Gordon and Molchanov for discussions of Gordon's work. But most of all, I must express my gratitude to Yossi Avron; any insights in this paper are the result of a fruitful year of discussion, collaboration, and occasional argument.", "abstract": "We review the recent rigorous literature on the one-dimensional Schr\u00f6dinger equation, H = \u2212d\u00b2/dx\u00b2 + V(x) with V(x) almost periodic and the discrete (= tight binding) analog, i.e., the doubly infinite Jacobi matrix, h_(ij) = \u03b4_(i,j+1) + \u03b4_(i,j\u22121) + V_i\u03b4_(i,j) with V_n almost periodic on the integers. Two themes dominate. The first is that the gaps in the spectrum tend to be dense, so that the spectrum is a Cantor set. We describe intuitions for this from the point of view of where gaps open, and from the point of view of anomalous long time behavior. We give a theorem of Avron and Simon, Chulaevsky, and Moser that for a generic sequence with \u03a3|a_n| < \u221e, the continuum operator with V(x) = \u03a3a_ncos(x/2^n) has a Cantor spectrum. The second theme involves unusual spectral types that tend to occur. We describe recurrent absolutely continuous spectrum, and show it occurs in some examples of the type just discussed. We give an intuition for dense point spectrum to occur, and some theorems on the occurrence of point spectrum. We sketch the proof of Avron and Simon, that for the discrete case with V_n = \u03bb cos(2\u03c0\u03b1n + \u03d1), if \u03bb > 2 and \u03b1 is a Liouville number, then for a.e. \u03d1, h has purely singular continuous spectrum.", "date": "1982-12", "date_type": "published", "publication": "Advances in Applied Mathematics", "volume": "3", "number": "4", "publisher": "Elsevier", "pagerange": "463-490", "id_number": "CaltechAUTHORS:20201007-081705850", "issn": "0196-8858", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201007-081705850", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/s0196-8858(82)80018-3", "pub_year": "1982", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/jwp7t-4zz75", "eprint_id": 32517, "eprint_status": "archive", "datestamp": "2023-08-22 03:11:39", "lastmod": "2026-04-21 04:26:50", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Continuity of the density of states in a magnetic field", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Mathematical physics; Quantum information and quantum mechanics", "note": "\u00a9 1982 The Institute of Physics.\nReceived 22 March 1982.\nIt is a pleasure to thank S Novikov for raising the questions answered here, and D Thouless for a valuable discussion. Research partially supported by USNSF Grant MCS 78-01885.", "abstract": "Fix a periodic potential, V, and let k(E,B) be the integrated density of states up to energy E in a constant magnetic field B. We prove that k(E,B) is continuous in B at all points where it is continuous in E. We prove a similar result when V is zero and B is a multiple of a periodic magnetic field.", "date": "1982-09-01", "date_type": "published", "publication": "Journal of Physics A: Mathematical and General", "volume": "15", "number": "9", "publisher": "IOP", "pagerange": "2981-2983", "id_number": "CaltechAUTHORS:20120717-114851010", "issn": "0305-4470", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120717-114851010", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1088/0305-4470/15/9/043", "pub_year": "1982", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/1ttt9-hw631", "eprint_id": 38689, "eprint_status": "archive", "datestamp": "2023-08-19 14:32:05", "lastmod": "2026-03-09 20:35:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Forcing with \u0394 perfect trees and minimal \u0394-degrees", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1982 Association for Symbolic Logic.\n\nReceived November 9, 1979.\n\nThe preparation of this paper was partially supported by NSF Grant MCS76-17254 A01. The author is an A. P. Sloan Foundation Fellow.\n\n

Published - Kechris_1981p803.pdf

", "abstract": "This paper is a sequel to [3] and it contains, among other things, proofs of the results announced in the last section of that paper. In \u00a71, we use the general method of [3] together with reflection arguments to study the properties of forcing with \u0394 perfect trees, for certain Spector pointclasses \u0393, obtaining as a main result the existence of a continuum of minimal \u0394-degrees for such \u0393's, under determinacy hypotheses. In particular, using PD, we prove the existence of continuum many minimal \u0394^(1)_(2n+1)-degrees, for all n.^(2) Following an idea of Leo Harrington, we extend these results in \u00a72 to show the existence of minimal strict upper bounds for sequences of \u0394-degrees which are not too far apart. As a corollary, it is computed that the length of the natural hierarchy of \u0394^(1)_(2n+1)-degrees is equal to \u03c9 when n \u2265 1. (By results of Sacks and Richter the length of the natural hierarchy of \u0394^(1)_(1)-degrees is known to be equal to the first recursively inaccessible ordinal.)", "date": "1981-12", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "46", "number": "4", "publisher": "Association for Symbolic Logic", "pagerange": "803-816", "id_number": "CaltechAUTHORS:20130528-105719531", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-105719531", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS76-17254 A01" } ] }, "other_numbering_system": { "items": [ { "id": "MR0641493", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "Kechris_1981p803.pdf", "url": "https://authors.library.caltech.edu/records/1ttt9-hw631/files/Kechris_1981p803.pdf" }, "pub_year": "1981", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/nbyj5-zed19", "eprint_id": 86525, "eprint_status": "archive", "datestamp": "2023-08-19 14:16:32", "lastmod": "2026-04-21 00:54:36", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Spectrum and continuum eigenfunctions of Schr\u00f6dinger operators", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1981 Published by Elsevier. \n\nReceived November 19. 1980; revised December 2, 1980. \n\nCommunicated by Peter D. Lax. \n\nresearch partially supported by USNSF under Grant MCS-78-21885. \n\nIt is a pleasure to thank B. Souiliard for raising the question of converses to Theorem 1.1.", "abstract": "We consider Schr\u00f6dinger operators H = \u22121/2 \u0394 + V for a large class of potentials. V. We show that if H\u03d5 = E\u03d5 has a polynomially bounded solution \u03d5 then E is in the spectrum of H. This is accomplished by proving that the spectrum of H as an operator on L^2 is identical to its spectrum as an operator on the weighted L^2 space, L^2_\u03b4.", "date": "1981-07", "date_type": "published", "publication": "Journal of Functional Analysis", "volume": "42", "number": "3", "publisher": "Elsevier", "pagerange": "347-355", "id_number": "CaltechAUTHORS:20180521-152345997", "issn": "0022-1236", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-152345997", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-78-21885" }, { "agency": "Sherman Fairchild Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-1236(81)90094-X", "pub_year": "1981", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/m56ts-pbx63", "eprint_id": 38627, "eprint_status": "archive", "datestamp": "2023-08-19 14:12:11", "lastmod": "2026-04-21 00:58:51", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrington-L-A", "name": { "family": "Harrington", "given": "Leo A." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On the determinacy of games on ordinals", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1981 North Holland Publishing Company. Received 21 March 1980. Work partially supported by NSF Grant MCS 79-07774.\nWork partially supported by NSF Grant MCS 76-17254 A01. The author is an A.P. Sloan Foundation Fellow.", "abstract": "Let \u03bb be an ordinal and A \u2286 \u03bb^\u03c9 x \u03bb^\u03c9. As usual we associate with it the game G(A;\u03bb): I II I and II alternatively \u03be0 \u03b70 play \u03be0, \u03b70, \u03be1,\u03b71,.... from \u03bb; \u03be1 I wins iff (\u03be, \u03ae) \u03b5A.\n\u03b71 \u03be \u03ae.", "date": "1981-06", "date_type": "published", "publication": "Annals of Mathematical Logic", "volume": "20", "number": "2", "publisher": "Elsevier", "pagerange": "109-154", "id_number": "CaltechAUTHORS:20130522-085823503", "issn": "0003-4843", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-085823503", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 79-07774" }, { "agency": "NSF", "grant_number": "MCS 76-17254 A01" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0003-4843(81)90001-2", "pub_year": "1981", "author_list": "Harrington, Leo A. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/jz1wr-23234", "eprint_id": 86521, "eprint_status": "archive", "datestamp": "2023-08-19 14:13:48", "lastmod": "2026-04-21 02:38:23", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "Joseph" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "The Asymptotics of the Gap in the Mathieu Equation", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1981 Published by Elsevier. \n\nReceived November 20, 1980. \n\nResearch partially supported by NSF Grant MCS-78-01885. \n\nSimon would like to thank the Sherman Fairchild Visiting Scholar Program for its support.", "abstract": "We provide a simple proof that the kth gap, \u0394_k, for the Mathieu operator \u2212d^2dx^2 + 2\u03bacos(2x) is \u0394_k = 8(\u03ba4)^k[(k \u2212 1)!]^(\u22122)(1 + o(k^(\u22122))), a result obtained (up to the value of an integral) by Harrell. The key observation is that what is involved is tunneling in momentum space.", "date": "1981-06", "date_type": "published", "publication": "Annals of Physics", "volume": "134", "number": "1", "publisher": "Elsevier", "pagerange": "76-84", "id_number": "CaltechAUTHORS:20180521-145909947", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-145909947", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-78-01885" }, { "agency": "Sherman Fairchild Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0003-4916(81)90005-1", "pub_year": "1981", "author_list": "Avron, Joseph and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/wvrgq-r3r49", "eprint_id": 85894, "eprint_status": "archive", "datestamp": "2023-08-19 14:07:35", "lastmod": "2026-04-21 01:13:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "Joseph E." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Almost Periodic Hill's Equation and the Rings of Saturn", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1981 American Physical Society. \n\n(Received 30 January 1981) \n\nWe thank J. Moser and R. Johnson for telling us of their work before publication, A. Dekel, L. Yaffe, and particularly P. Goldreich for useful discussions and criticism, I. Mikolic-Torreira for writing a computer program for us, and F. Dyson and P. Lax for encouragement. We would also like to thank the S. Fairchild Visiting Scholar Program and the California Institute of Technology Mathematics Department for their hospitality. This research is supported in part by the National Science Foundation under Grant No. MCS-78-01885.\n\n

Published - PhysRevLett.46.1166.pdf

", "abstract": "Incommensurate perturbations of classical orbits lead to an almost periodic Hill's operator whose spectrum, we argue, is a Cantor set, but one with large Lebesgue measure. Applied to the rings of Saturn, this implies that the complex groove structure in the rings approximates a Cantor set. We also emphasize the possible relevance of the sun in producing \"side gaps\" which magnify the apparent gap size.", "date": "1981-04-27", "date_type": "published", "publication": "Physical Review Letters", "volume": "46", "number": "17", "publisher": "American Physical Society", "pagerange": "1166-1168", "id_number": "CaltechAUTHORS:20180417-104513184", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104513184", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Sherman Fairchild Foundation" }, { "agency": "NSF", "grant_number": "MCS-78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.46.1166", "primary_object": { "basename": "PhysRevLett.46.1166.pdf", "url": "https://authors.library.caltech.edu/records/wvrgq-r3r49/files/PhysRevLett.46.1166.pdf" }, "pub_year": "1981", "author_list": "Avron, Joseph E. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/tyv7n-38m73", "eprint_id": 837, "eprint_status": "archive", "datestamp": "2023-08-22 02:32:52", "lastmod": "2026-03-18 00:02:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Pointwise domination of matrices and comparison of \u2110_p norms", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1981 Pacific Journal of Mathematics. \n\nReceived December 19, 1980. \n\nResearch partially supported by NSF Grant MCS-78-01885. Sherman Fairchild Visiting Scholar; on leave from Departments of Mathematics and Physics, Princeton University. \n\nIt is a pleasure to thank V. Peller for most valuable correspondence and S. Friedland for useful discussions.\n\n

Published - SIMpjm81.pdf

", "abstract": "Let p be a real number in [1, \u221e) which is not an even integer. Let N = 2[p/2] + 5. We give examples of N X N matrices A and B, so that |aij| \u2264 bij but Tr([A*A]p/2) > Tr([B*B]p/2).", "date": "1981", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "97", "number": "2", "publisher": "Pacific Journal of Mathematics", "pagerange": "471-475", "id_number": "CaltechAUTHORS:SIMpjm81", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SIMpjm81", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-78-01885" }, { "agency": "Sherman Fairchild Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "primary_object": { "basename": "SIMpjm81.pdf", "url": "https://authors.library.caltech.edu/records/tyv7n-38m73/files/SIMpjm81.pdf" }, "pub_year": "1981", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/95ns3-zwc43", "eprint_id": 86522, "eprint_status": "archive", "datestamp": "2023-08-19 13:39:31", "lastmod": "2026-04-21 05:41:24", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Klaus-M", "name": { "family": "Klaus", "given": "M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Coupling Constant Thresholds in Nonrelativistic Quantum Mechanics. I. Short-Range Two-Body Case", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1980 Published by Elsevier. \n\nReceived April 4, 1980; revised May 16, 1980. \n\nResearch supported by Swiss National Science Foundation. \n\nResearch supported by USNSF Grant MCS-78-01885. \n\nWe should like to thank J. Morgan III and R. Newton for valuable discussions. One of us (B.S.) would like to thank the Technion Physics Department for its hospitality during the completion of this work.", "abstract": "Consider \u2212\u0394 + \u03bbV with V short range at a value \u03bb_0 where some eigenvalue e(\u03bb) \u2192 0 as \u03bb \u2193 \u03bb_0. We analyze two questions: (i) What is the leading order of e(\u03bb), i.e., for what \u03b1 does e(\u03bb) \u223c c(\u03bb \u2212 \u03bb_0)^\u03b1? (ii) Is e(\u03bb) analytic at \u03bb = \u03bb_0 and, if not, what is the natural expansion parameter? The results are highly dimension dependent.", "date": "1980-12", "date_type": "published", "publication": "Annals of Physics", "volume": "130", "number": "2", "publisher": "Elsevier", "pagerange": "251-281", "id_number": "CaltechAUTHORS:20180521-150501792", "issn": "0003-4916", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-150501792", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Swiss National Science Foundation (SNSF)" }, { "agency": "NSF", "grant_number": "MCS-78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0003-4916(80)90338-3", "pub_year": "1980", "author_list": "Klaus, M. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/7m0f4-mvx39", "eprint_id": 86535, "eprint_status": "archive", "datestamp": "2023-08-19 13:32:07", "lastmod": "2026-04-20 21:53:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Schechter-M", "name": { "family": "Schecter", "given": "M." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Unique continuation for Schrodinger operators with unbounded potentials", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1980 Published by Elsevier. \n\nSubmitted by C. L. Dolph. \n\nResearch partially supported by U.S. National Science Foundation under Grants MCS-76-04833 (Schechter) and MCS-78-01885 (Simon). \n\nWe would like to thank Lavine for raising this problem and one of us (B.S.) would like to thank Yeshiva University for its hospitality in 1976-77 when he was a visitor and this research was initiated. We would like to thank W. Amrein, A. M. Berthier and V. Georesgu for pointing out an error in a preliminary version of this paper.", "abstract": "We consider unique continuation theorems for solution of inequalities \u00a6\u0394u(x)\u00a6 \u2a7d W(x) \u00a6u(x)\u00a6 with W allowed to be unbounded. We obtain two kinds of results. One allows W \u03f5 L^p_(loc)(R^n) with p \u2a7e n \u2212 2forn > 5, p >13(2n \u2212 1)forn \u2a7d 5. The other requires fW^2 to be \u2212\u0394-form bounded for all f \u03f5 C_0^\u221e.", "date": "1980-10", "date_type": "published", "publication": "Journal of Mathematical Analysis and Applictions", "volume": "77", "number": "2", "publisher": "Elsevier", "pagerange": "482-492", "id_number": "CaltechAUTHORS:20180521-164135228", "issn": "0022-247X", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-164135228", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-76-04833" }, { "agency": "NSF", "grant_number": "MCS-78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0022-247X(80)90242-5", "pub_year": "1980", "author_list": "Schecter, M. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/vzk95-v5r06", "eprint_id": 85893, "eprint_status": "archive", "datestamp": "2023-08-19 13:19:40", "lastmod": "2026-04-21 01:29:45", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Miller-K", "name": { "family": "Miller", "given": "Keith" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Quantum Magnetic Hamiltonians with Remarkable Spectral Properties", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1980 American Physical Society. \n\n(Received 3 March 1980) \n\nIt is a pleasure to thank J. Hopfield and V. Enss for emphasizing to us that we should look at the classical case. This research was supported in part by the National Science Foundation under Grant No. MCS-78-01885.\n\n

Published - PhysRevLett.44.1706.pdf

", "abstract": "The Hamiltonian, H, of a spinless particle moving in two dimensions in an axially symmetric magnetic field B(\u03c1) is considered. If B(\u03c1) \u223c \u03c1^(\u2212\u03b1) for \u03c1, large with 0 < \u03b1 < 1, then it is shown that H has spectrum [0, \u221e) with only eigenvectors and eigenvalues dense in [0, \u221e). If \u03b1 = 1, then the spectrum is a dense point spectrum in [0, c] for suitable c and absolutely continuous in [c, \u221e).", "date": "1980-06-23", "date_type": "published", "publication": "Physical Review Letters", "volume": "44", "number": "25", "publisher": "American Physical Society", "pagerange": "1706-1707", "id_number": "CaltechAUTHORS:20180417-104512905", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104512905", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship" }, { "agency": "NSF", "grant_number": "MCS-78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.44.1706", "primary_object": { "basename": "PhysRevLett.44.1706.pdf", "url": "https://authors.library.caltech.edu/records/vzk95-v5r06/files/PhysRevLett.44.1706.pdf" }, "pub_year": "1980", "author_list": "Miller, Keith and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/bh4sn-ayp61", "eprint_id": 97884, "eprint_status": "archive", "datestamp": "2023-08-22 02:22:13", "lastmod": "2026-04-21 07:13:37", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Classification of the Finite Simple Groups", "ispublished": "pub", "full_text_status": "public", "keywords": "Finite Group; Simple Group; Prime Order; Component Type; Chevalley Group", "note": "\u00a9 1980 Springer Science+Business Media, Inc.", "abstract": "The classification of the finite simple groups was completed sometime during the summer of 1980. To the extent that I can reconstruct things, the last piece in the puzzle was filled in by Ronald Solomon of Ohio State University. At the other chronological extreme, the theory of finite groups can be traced back to its beginnings in the early nineteenth century in the work of Abel, Cauchy, and Galois. Hence the problem of classifying the finite simple groups has a history of over a century and a half. The proof of the Classification Theorem is made up of thousands of pages in various mathematical journals with at least another thousand pages still left to appear in print. Many mathematicians have contributed to the proof; some have spent their entire mathematical lives working\non the problem.", "date": "1980-06", "date_type": "published", "publication": "Mathematical Intelligencer", "volume": "3", "number": "2", "publisher": "Springer", "pagerange": "59-65", "id_number": "CaltechAUTHORS:20190814-100802612", "issn": "0343-6993", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190814-100802612", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/bf03022850", "pub_year": "1980", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/xrpge-2vd10", "eprint_id": 85892, "eprint_status": "archive", "datestamp": "2023-08-19 13:03:54", "lastmod": "2026-04-21 01:10:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Decay of Correlations in Ferromagnets", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1980 American Physical Society. \n\n(Received 7 December 1979) \n\nThe author acknowledges partial support of the National Science Foundation under Grant No. MCS-78-01885.\n\n

Published - PhysRevLett.44.547.pdf

", "abstract": "Some new correlation inequalities are described which bound large-distance behavior of correlations in ferromagnets from above by correlations at intermediate distances. Among applications are (1) an inequality, \u03b7 < 1, on the decay of correlations at the critical point; (2) an inequality \u03c7 \u2267 coth(1/2 m) relating the zero-field susceptibility and the mass gap in a nearest-neighbor ferromagnet; (3) a finite algorithm for rigorously computing a sequence of upper bounds guaranteed to converge to the true transition temperature in Ising ferromagnets.", "date": "1980-02-25", "date_type": "published", "publication": "Physical Review Letters", "volume": "44", "number": "8", "publisher": "American Physical Society", "pagerange": "547-549", "id_number": "CaltechAUTHORS:20180417-104512511", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-104512511", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.44.547", "primary_object": { "basename": "PhysRevLett.44.547.pdf", "url": "https://authors.library.caltech.edu/records/xrpge-2vd10/files/PhysRevLett.44.547.pdf" }, "pub_year": "1980", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/wttwq-4tj24", "eprint_id": 85904, "eprint_status": "archive", "datestamp": "2023-08-19 13:03:32", "lastmod": "2026-04-21 00:51:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Enss-V", "name": { "family": "Enss", "given": "V." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Bounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1980 American Physical Society. \n\n(Received 19 November 1979) \n\nIt is a pleasure to thank W. Thirring for having emphasized that there should be a direct physical approach to the problem and P. Deift for valuable discussions. One of us (V.E.) would like to thank the Institute for Advanced Study for its hospitality and support under the Albert Einstein visiting professorship endowed by the Federal Republic of Germany and for a travel grant provided by Deutsche Forschungsgemeinschaft. Another of us (B.S.) acknowledges partial support by the National Science Foundation under Grant No. MCS 78-01885.\n\nBounds on Total Cross Sections in Atom-Atom and Atom-Ion Collisions by Geometric Methods.\nV. Enss and B. Simon\nPhys. Rev. Lett. 44, 764\n\n

Published - PhysRevLett.44.319.pdf

Erratum - PhysRevLett.44.764-errata.pdf

", "abstract": "A method is presented for obtaining explicit bounds for the total cross section (including scattering into several final charged fragments) for the scattering of two bound clusters of nuclei and electrons so long as either both clusters are neutral or one is neutral and without an electric dipole moment.", "date": "1980-02-04", "date_type": "published", "publication": "Physical Review Letters", "volume": "44", "number": "5", "publisher": "American Physical Society", "pagerange": "319-322", "id_number": "CaltechAUTHORS:20180417-124706801", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-124706801", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Institute for Advanced Study" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" }, { "agency": "NSF", "grant_number": "MCS 78-01885" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.44.319", "primary_object": { "basename": "PhysRevLett.44.319.pdf", "url": "https://authors.library.caltech.edu/records/wttwq-4tj24/files/PhysRevLett.44.319.pdf" }, "related_objects": [ { "basename": "PhysRevLett.44.764-errata.pdf", "url": "https://authors.library.caltech.edu/records/wttwq-4tj24/files/PhysRevLett.44.764-errata.pdf" } ], "pub_year": "1980", "author_list": "Enss, V. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/m8zek-8j230", "eprint_id": 85924, "eprint_status": "archive", "datestamp": "2023-08-19 12:49:44", "lastmod": "2026-04-23 19:57:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J. E." } }, { "id": "Herbst-I-W", "name": { "family": "Herbst", "given": "I. W." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Strongly bound states of hydrogen in intense magnetic field", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1979 American Physical Society. \n\n(Received 26 March 1979) \n\nThe work of one of us (I.W.H.) was supported by the NSF under Grant No. MCS-78-00101; one of us (B.S.) was partially supported by NSF Grant No. MCS-78-01885. Publication partially supported by NSF Grant No. PHY-78-23952.\n\n

Published - PhysRevA.20.2287.pdf

", "abstract": "The authors derive asymptotic formulas for the energies of the strongly bound states of hydrogen for large magnetic fields. Rigorous lower bounds on the binding and also upper bounds are given based on generous estimates of the errors. Comparison with variational and other previous numerical results shows their tendency to underestimate the binding.", "date": "1979-12", "date_type": "published", "publication": "Physical Review A", "volume": "20", "number": "6", "publisher": "American Physical Society", "pagerange": "2287-2296", "id_number": "CaltechAUTHORS:20180417-154003229", "issn": "0556-2791", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154003229", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-78-00101" }, { "agency": "NSF", "grant_number": "MCS-78-01885" }, { "agency": "NSF", "grant_number": "PHY-78-23952" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevA.20.2287", "primary_object": { "basename": "PhysRevA.20.2287.pdf", "url": "https://authors.library.caltech.edu/records/m8zek-8j230/files/PhysRevA.20.2287.pdf" }, "pub_year": "1979", "author_list": "Avron, J. E.; Herbst, I. W.; et al." }, { "id": "https://authors.library.caltech.edu/records/j2ja7-wr071", "eprint_id": 85923, "eprint_status": "archive", "datestamp": "2023-09-15 05:53:03", "lastmod": "2026-04-21 18:56:15", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Benassi-L", "name": { "family": "Benassi", "given": "L." } }, { "id": "Grecchi-V", "name": { "family": "Grecchi", "given": "V." } }, { "id": "Harrell-E", "name": { "family": "Harrell", "given": "E." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Bender-Wu Formula and the Stark Effect in Hydrogen", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1979 American Physical Society. \n\n(Received 23 October 1978) \n\nIt is a pleasure to thank S. Graffi and I. Herbst for their interest and valuable comments. This research was supported in part by the National Science Foundation, Grant No. MCS 78-01885 and in part by the Istituto Nazionale di Fisica Nucleare, Sezione di Bologna. One of us (E.H. ) acknowledges receipt of a National Science Foundation National Needs Fellowship.\n\n

Published - PhysRevLett.42.704.pdf

", "abstract": "We discuss a close connection between the formula of Banks, Bender, and Wu for the asymptotics of the Rayleigh-Schr\u00f6dinger coefficients of the two-dimensional rotationally symmetric anharmonic oscillator and the behavior of resonances of the hydrogen Stark problem in two regimes: small field (Oppenheimer's formula) and large field (where we obtain the new results arg E \u2192 \u2212\u03c0/3, \u2223E\u2223 \u223c\u03b1[F(lnF)^(2/3) for F, the electric field strength, going to infinity). We also announce a rigorous proof of Bender-Wu-type formulas.", "date": "1979-03-12", "date_type": "published", "publication": "Physical Review Letters", "volume": "42", "number": "11", "publisher": "American Physical Society", "pagerange": "704-707", "id_number": "CaltechAUTHORS:20180417-154002869", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154002869", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 78-01885" }, { "agency": "Istituto Nazionale di Fisica Nucleare (INFN)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.42.704", "primary_object": { "basename": "PhysRevLett.42.704.pdf", "url": "https://authors.library.caltech.edu/records/j2ja7-wr071/files/PhysRevLett.42.704.pdf" }, "pub_year": "1979", "author_list": "Benassi, L.; Grecchi, V.; et al." }, { "id": "https://authors.library.caltech.edu/records/0ypgb-1hd98", "eprint_id": 38880, "eprint_status": "archive", "datestamp": "2023-08-19 12:04:05", "lastmod": "2026-03-09 20:38:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "An overview of descriptive set theory", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1979 Universit\u00e9 Pierre et Marie Curie.", "abstract": "Understanding the structure of sets of reals is one of the\nfundamental problems of set theory.\nOf course, an arbitrary subset of the continuum is immensely complicated,\nand exhibits in general no regularities. For example it could be non(Lebesgue)-measurable\nor fail to have the property of Baire. So from the early days of\nset theory, about a hundred years ago, mathematicians have concentrated on the\nstudy of various classes of definable sets of reals, wide enough to include the\nusual sets appearing in analysis, topology, etc., but also restricted to possibly\nexhibit a regular behaviour.\nThe study of such classes of definable sets is the purpose of descriptive\nset theory. Indeed, to a large extent descriptive set theory is mainly concerned\nwith the structure of the projective sets of reals, which we proceed to define.", "date": "1979-02", "date_type": "published", "publication": "Publications Math\u00e9matiques de l'Universit\u00e9 Pierre et Marie Curie", "volume": "4", "publisher": "Universit\u00e9 Pierre et Marie Curie", "id_number": "CaltechAUTHORS:20130610-140456846", "issn": "1151-1745", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130610-140456846", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR0670761", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "1979", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/9ewfk-rwc14", "eprint_id": 38623, "eprint_status": "archive", "datestamp": "2023-08-19 11:44:53", "lastmod": "2026-04-23 16:10:49", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Countable ordinals and the analytical hierarchy, II", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1978 North Holland Publishing Company. Received 1 June 1977.\nResearch and preparation for this paper were partially supported by NSF Grants MPS 75-07562 and MCS 76-17254 resp.", "abstract": "This paper is a contribution to the study of projective sets under the hypothesis of definable determinacy. For our purposes here this can be understood as the hypothesis every set of rea1s in L[\u03c9^\u03c9] (= the smallest inner model of ZF containing \u03c9^\u03c9) is determined. Since questions about the projective hierarchy are absolute between the real world and\nL[\u03c9^\u03c9] it is innocuous to work entirely within L[\u03c9^\u03c9].", "date": "1978-12", "date_type": "published", "publication": "Annals of Mathematical Logic", "volume": "15", "number": "3", "publisher": "Elsevier", "pagerange": "193-223", "id_number": "CaltechAUTHORS:20130522-081838953", "issn": "0003-4843", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-081838953", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS 75-07562" }, { "agency": "NSF", "grant_number": "MCS 76-17254" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0003-4843(78)90010-4", "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/4c62c-cpc60", "eprint_id": 38673, "eprint_status": "archive", "datestamp": "2023-08-19 11:44:58", "lastmod": "2026-03-09 20:40:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Perfect Set Theorem and Definable Wellorderings of the Continuum", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1979, Association for Symbolic Logic. Received November 15, 1976. Research partially supported by NSF Grant MPS75-07562.\n\n

Published - 2273501.pdf

", "abstract": "Let \u0393 be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for \u0393 if every set in \u0393 with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on \u0393 and M): If M is a perfect set basis for \u0393, the field of every wellordering in \u0393 is contained in M. An immediate corollary is Mansfield's Theorem that the existence of a \u03a3^1_2 wellordering of the reals implies that every real is constructible. Other applications and extensions of the main result are also given.", "date": "1978-12", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "43", "number": "4", "publisher": "Association for Symbolic Logic", "pagerange": "630-634", "id_number": "CaltechAUTHORS:20130528-081912845", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-081912845", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS75-07562" } ] }, "other_numbering_system": { "items": [ { "id": "0401.03023", "name": "Zentralblatt MATH Identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2273501.pdf", "url": "https://authors.library.caltech.edu/records/4c62c-cpc60/files/2273501.pdf" }, "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/rbpcw-3vz95", "eprint_id": 38674, "eprint_status": "archive", "datestamp": "2023-08-19 11:35:46", "lastmod": "2026-03-09 20:38:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Minimal Upper Bounds for Sequences of \u0394^1_(2n)-Degrees", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1978, Association for Symbolic Logic. Received April 15, 1977. Research and preparation for this paper were partially supported by NSF Grants MPS75-07562 and MCS76-17254 respectively.\n\n

Published - 2273527.pdf

", "abstract": "It is proved here, assuming Projective Determinacy, that every ascending sequence of \u0394^1_(2n)-degrees has a minimal strict upper bound but no least strict upper bound. This generalizes a result of Friedman for n = 1.", "date": "1978-09", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "43", "number": "3", "publisher": "Association for Symbolic Logic", "pagerange": "502-507", "id_number": "CaltechAUTHORS:20130528-083000082", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-083000082", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS75-07562" }, { "agency": "NSF", "grant_number": "MCS76-17254" } ] }, "other_numbering_system": { "items": [ { "id": "0405.03019", "name": "Zentralblatt MATH Identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2273527.pdf", "url": "https://authors.library.caltech.edu/records/rbpcw-3vz95/files/2273527.pdf" }, "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/b7sek-evh49", "eprint_id": 85922, "eprint_status": "archive", "datestamp": "2023-08-19 11:31:15", "lastmod": "2026-04-23 20:15:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Herbst-I-W", "name": { "family": "Herbst", "given": "I. W." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Stark Effect Revisited", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1978 American Physical Society.\n\n(Received 8 May 1978) \n\nIt is a pleasure to thank W. Reinhardt and J. Howland for stimulating discussions and S. Graffi and V. Grecchi for correspondence and copies of their preprints. This work was supported in part by the National Science Foundation, Grant No. MPS-75-11864.\n\n

Published - PhysRevLett.41.67.pdf

", "abstract": "We extend the rigorous theory of complex scaling to atoms in constant electric field. This allows one to give a precise mathematical definition of resonance and leads to several results about the perturbation series: Borel summability at nonreal field and a relation between the asymptotics of the perturbation coefficients for large n and the width of the resonance for small field.", "date": "1978-07-10", "date_type": "published", "publication": "Physical Review Letters", "volume": "41", "number": "2", "publisher": "American Physical Society", "pagerange": "67-69", "id_number": "CaltechAUTHORS:20180417-154002598", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154002598", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS-75-11864" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.41.67", "primary_object": { "basename": "PhysRevLett.41.67.pdf", "url": "https://authors.library.caltech.edu/records/b7sek-evh49/files/PhysRevLett.41.67.pdf" }, "pub_year": "1978", "author_list": "Herbst, I. W. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/x826v-knz27", "eprint_id": 39092, "eprint_status": "archive", "datestamp": "2023-08-19 11:10:32", "lastmod": "2026-03-09 20:34:48", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "D. A." } } ] }, "title": "On the theory of \u220f_3^1 sets of reals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1978 American Mathematical Society.\nCommunicated by Solomon Feferman, June 2, 1977. Research partially supported by NSF Grant MCS 76-17254.\n\n

Published - S0002-9904-1978-14447-4.pdf

", "abstract": "Assuming that \u2200x \u0404 \u03c9^\u03c9 (x^# exists), let u_\u0251 be the \u0251th uniform indiscernible (see [3] or [2] ). A canonical coding system for ordinals < u_\u03c9 can be defined by letting W0_\u03c9 = {w \u0404 \u03c9^\u03c9: w = (n, x^#), for some n \u0404 \u03c9, x \u0404 \u03c9^\u03c9} and for w = (n, x^#) \u0454 W0_\u03c9, \u2502w\u2502 = \u01ac^L_n [x](u_l',... , u_k_n),\nwhere T_n is the nth term in a recursive enumeration of all terms in the language of ZF + V = L [x], x a constant, taking always ordinal values. Call a relation P(\u03be x), where ~varies over u^\u03c9 and x over \u03c9^\u03c9, \u220f^1_k if P^*(w, x)\u21d4 w \u0404 W0_\u03c9 \u039b P(\u2502w\u2502, x) is \u220f^1_k. An ordinal \u03be < u_\u03c9 is called \u0394^1_k if it has a \u0394^1_k notation i.e. \u2203 w \u0404 W0_\u03c9 (w \u0404 \u0394^1_k \u039b \u2502w\u2502 = \u03be).", "date": "1978-01", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "84", "number": "1", "publisher": "American Mathematical Society", "pagerange": "149-151", "id_number": "CaltechAUTHORS:20130625-140857081", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130625-140857081", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 76-17254" } ] }, "other_numbering_system": { "items": [ { "id": "MR0465867", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1090/S0002-9904-1978-14447-4", "primary_object": { "basename": "S0002-9904-1978-14447-4.pdf", "url": "https://authors.library.caltech.edu/records/x826v-knz27/files/S0002-9904-1978-14447-4.pdf" }, "pub_year": "1978", "author_list": "Kechris, A. S. and Martin, D. A." }, { "id": "https://authors.library.caltech.edu/records/f7stg-s1b50", "eprint_id": 85921, "eprint_status": "archive", "datestamp": "2023-08-19 10:56:20", "lastmod": "2026-04-23 19:48:52", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Avron-J-E", "name": { "family": "Avron", "given": "J." } }, { "id": "Herbst-I-W", "name": { "family": "Herbst", "given": "I." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Formation of Negative Ions in Magnetic Fields", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1977 American Physical Society. \n\n(Received 9 June 1977) \n\nIt is a pleasure to thank A. K. Ramdas and A. H. Hutson for useful conversations, as well as D. Licciardello for his enthusiasm. This work was supported by National Science Foundation Grants No. MPS 75-22514, No. MPS 74-22844, and No. MPS 75-11864.\n\n

Published - PhysRevLett.39.1068.pdf

", "abstract": "It is argued that the negative helium ion exists in magnetic fields. Similarly, nontrapping isoelectronic impurities in semiconductors trap with magnetic fields. Crude estimates of binding energies are given.", "date": "1977-10-24", "date_type": "published", "publication": "Physical Review Letters", "volume": "39", "number": "17", "publisher": "American Physical Society", "pagerange": "1068-1070", "id_number": "CaltechAUTHORS:20180417-154002275", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154002275", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS 75-22514" }, { "agency": "NSF", "grant_number": "MPS 74-22844" }, { "agency": "NSF", "grant_number": "MPS 75-11864" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.39.1068", "primary_object": { "basename": "PhysRevLett.39.1068.pdf", "url": "https://authors.library.caltech.edu/records/f7stg-s1b50/files/PhysRevLett.39.1068.pdf" }, "pub_year": "1977", "author_list": "Avron, J.; Herbst, I.; et al." }, { "id": "https://authors.library.caltech.edu/records/vymew-27z56", "eprint_id": 38638, "eprint_status": "archive", "datestamp": "2023-08-19 10:36:49", "lastmod": "2026-03-09 20:41:34", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On a notion of smallness for subsets of the Baire space", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1977 American Mathematical Society. Received by the editors December 10, 1975.\n\n

Published - 1998505.pdf

", "abstract": "Let us call a set A \u2286 \u03c9^\u03c9 of functions from \u03c9 into \u03c9 \u03c3-bounded if there is a countable sequence of functions (\u03b1_n: n \u0404 \u03c9)\u2286 \u03c9^\u03c9 such that every member of A is pointwise dominated by an element of that sequence. We study in this paper definability questions concerning this notion of smallness for subsets of \u03c9^\u03c9. We show that most of the usual definability results about the structure of countable subsets of \u03c9^\u03c9 have corresponding versions which hold about \u03c3-bounded subsets of \u03c9^\u03c9. For example, we show that every \u03a3_(2n+1^1 \u03c3-bounded subset of \u03c9^\u03c9 has a \u0394_(2n+1)^1 \"bound\" {\u03b1_m: m \u0404 \u03c9} and also that for any n \u2265 0 there are largest \u03c3-bounded \u03a0_(2n+1)^1 and \u03a3_(2n+2)^1 sets. We need here the axiom of projective determinacy if n \u2265 1. In order to study the notion of \u03c3-boundedness a simple game is devised which plays here a role similar to that of the standard ^*-games (see [My]) in the theory of countable sets. In the last part of the paper a class of games is defined which generalizes the ^*- and ^(**)-(or Banach-Mazur) games (see [My]) as well as the game mentioned above. Each of these games defines naturally a notion of smallness for subsets of \u03c9^\u03c9 whose special cases include countability, being of the first category and \u03c3-boundedness and for which one can generalize all the main results of the present paper.", "date": "1977-05", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "229", "publisher": "American Mathematical Society", "pagerange": "191-207", "id_number": "CaltechAUTHORS:20130522-135105483", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-135105483", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR0450070", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "1998505.pdf", "url": "https://authors.library.caltech.edu/records/vymew-27z56/files/1998505.pdf" }, "pub_year": "1977", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/8hmze-w5k35", "eprint_id": 38692, "eprint_status": "archive", "datestamp": "2023-08-19 10:20:40", "lastmod": "2026-03-09 20:34:35", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrington-L-A", "name": { "family": "Harrington", "given": "Leo" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "\u220f^1_2 singletons and O^#", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1977.\n\nAccept\u00e9 par la R\u00e8daction le 1.4.1975.", "abstract": "A conjecture of Solovay states: Assuming that for every real \u0251, \u0251^# exists, the constructibility degrees of \u220f^1_2 singletons are wellordered and the successor steps in this wellordering are given by the sharps. In this paper we prove among others things that (assuming \u2200\u0251 (\u0251^# exists))\nfor every \u220f^1_2 singleton a either O^# is constructible from \u0251 or \u0251^# is constructible from O^#. From a relativized version of this result it follows that the constructibility degrees of O^#, O^(##), O^(###),... are the first \u03c9 constructibility degrees of sharps of \u220f^1_2 singletons.", "date": "1977", "date_type": "published", "publication": "Fundamenta Mathematicae", "volume": "95", "number": "3", "publisher": "Institute of Mathematics, Polish Academy of Sciences", "pagerange": "167-171", "id_number": "CaltechAUTHORS:20130528-111450945", "issn": "0016-2736", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-111450945", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR0460121", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "pub_year": "1977", "author_list": "Harrington, Leo and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/wa8kx-t2j47", "eprint_id": 38686, "eprint_status": "archive", "datestamp": "2023-08-19 10:20:33", "lastmod": "2026-03-09 20:39:20", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Classifying Projective-like Hierarchies", "ispublished": "pub", "full_text_status": "public", "keywords": "descriptive set theory, reduction and prewellordering properties, projective-like hierarchies", "note": "\u00a9 1977.\n\nReceived November 9, 1977. Dedicated to the memory of Christos D. Papakyriakopoulos. \n\nThe author would like to thank R. Solovay, J. Steel and R.\nVan Wesep for many helpful discussions on this subject.\n\nResearch and preparation for this paper were partially supported by National Science Foundation Grant MPS 76-17254.\n\n

Published - Kechris_1977p254.pdf

", "abstract": "The starting point for the investigations reported in this paper is the following surprising result of Steel [St]:\nAssuming AD + DC let \u0413 be a collection of pointsets containing all open sets and closed under continuous preimages and countable intersections and unions. Then either \u0413 or \u0413 ( = the dual of \u0413) has the reduction property.\nThis result raises naturally the question if a similar phenomenon occurs with the stronger prewellordering property, perhaps under stronger closure assumptions on \u0413.", "date": "1977", "date_type": "published", "publication": "Bulletin of the Greek Mathematical Society", "volume": "18", "number": "2", "publisher": "Bulletin of the Greek Mathematical Society", "pagerange": "254-275", "id_number": "CaltechAUTHORS:20130528-103036161", "issn": "0072-7466", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-103036161", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS 76-17254" } ] }, "other_numbering_system": { "items": [ { "id": "MR0528183", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "Kechris_1977p254.pdf", "url": "https://authors.library.caltech.edu/records/wa8kx-t2j47/files/Kechris_1977p254.pdf" }, "pub_year": "1977", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/836bv-kns72", "eprint_id": 39042, "eprint_status": "archive", "datestamp": "2023-08-19 10:14:53", "lastmod": "2026-03-09 20:35:05", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrington-L-A", "name": { "family": "Harrington", "given": "Leo A." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On Monotone vs. Nonmonotone Induction", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1976 American Mathematical Society.\n\n

Published - S0002-9904-1976-14194-8.pdf

", "abstract": "Introduction. For definitions and notation in what follows, see [4] and [5].", "date": "1976-11", "date_type": "published", "publication": "Bulletin of the American Mathematical Society", "volume": "82", "number": "6", "publisher": "American Mathematical Society", "pagerange": "888-890", "id_number": "CaltechAUTHORS:20130624-085131170", "issn": "0273-0979", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130624-085131170", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "0363.02044", "name": "Zentralblatt MATH identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "S0002-9904-1976-14194-8.pdf", "url": "https://authors.library.caltech.edu/records/836bv-kns72/files/S0002-9904-1976-14194-8.pdf" }, "pub_year": "1976", "author_list": "Harrington, Leo A. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/essr9-jzd21", "eprint_id": 85917, "eprint_status": "archive", "datestamp": "2023-08-19 10:06:46", "lastmod": "2026-04-21 15:57:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Dyson-F-J", "name": { "family": "Dyson", "given": "Freeman J." } }, { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Phase Transitions in the Quantum Heisenberg Model", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1976 American Physical Society. \n\n(Received 10 May 1976) \n\nIt is a pleasure to thank J. Frohlich for valuable correspondence and J. Dames for doing the numerical calculations appearing in Table I. \n\nResearch supported by U. S. National Science Foundation Grant No. GP-40768X. \n\nResearch supported by U. S. National Science Foundation Grant No. MCS 75-21648. \n\nAlfred Sloan Fellow. Research supported by U. S. National Science Foundation Grant No. GP-39048.\n\n

Published - PhysRevLett.37.120.pdf

", "abstract": "We rigorously prove that in three or more dimensions, the nearest-neighbor, simple-cubic, ferromagnetic, quantum Heisenberg model of spin S(= 1/2, 1, \u2026) has a phase transition at nonzero temperature.", "date": "1976-07-19", "date_type": "published", "publication": "Physical Review Letters", "volume": "37", "number": "3", "publisher": "American Physical Society", "pagerange": "120-123", "id_number": "CaltechAUTHORS:20180417-154001196", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154001196", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP-40768X" }, { "agency": "NSF", "grant_number": "MCS 75-21648" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "GP-39048" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.37.120", "primary_object": { "basename": "PhysRevLett.37.120.pdf", "url": "https://authors.library.caltech.edu/records/essr9-jzd21/files/PhysRevLett.37.120.pdf" }, "pub_year": "1976", "author_list": "Dyson, Freeman J.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/kgxzn-tnb32", "eprint_id": 85916, "eprint_status": "archive", "datestamp": "2023-08-19 10:02:11", "lastmod": "2026-04-23 17:25:00", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Universal Diamagnetism of Spinless Bose Systems", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1976 American Physical Society. \n\n(Received 22 March 1976) \n\nAlfred P. Sloan Foundation Fellow. Research partially supported by U. S. National Science Foundation Grant No. GP 39048.\n\n

Published - PhysRevLett.36.1083.pdf

", "abstract": "I prove that the ground-state energy of an arbitrary system of nonrelativistic spinless Bose particles increases when any (arbitrarily strong or inhomogeneous) magnetic field is turned on.", "date": "1976-05-03", "date_type": "published", "publication": "Physical Review Letters", "volume": "36", "number": "18", "publisher": "American Physical Society", "pagerange": "1083-1084", "id_number": "CaltechAUTHORS:20180417-154000938", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154000938", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "GP 39048" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.36.1083", "primary_object": { "basename": "PhysRevLett.36.1083.pdf", "url": "https://authors.library.caltech.edu/records/kgxzn-tnb32/files/PhysRevLett.36.1083.pdf" }, "pub_year": "1976", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/225v3-pqd69", "eprint_id": 38705, "eprint_status": "archive", "datestamp": "2023-08-19 09:39:20", "lastmod": "2026-03-09 20:36:33", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrington-L-A", "name": { "family": "Harrington", "given": "Leo A." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "A Basis Result for \u03a3^0_3 Sets of Reals with an Application to Minimal Covers", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1975, American Mathematical Society. Received by the editors April 3, 1974 and, in revised form, July 19, 1974 and\nSeptember 6, 1974.\n\n

Published - 2040033.pdf

", "abstract": "It is shown that every \u2211^0_3 set of reals which contains reals of arbitrarily high Turing degree in the hyperarithmetic hierarchy contains reals of every Turing degree above the degree of Kleene's O. As an application it is shown that every Turing degree above the Turing degree of Kleene's O is a minimal cover.", "date": "1975-12", "date_type": "published", "publication": "Proceedings of the American Mathematical Society", "volume": "53", "number": "2", "publisher": "American Mathematical Society", "pagerange": "445-448", "id_number": "CaltechAUTHORS:20130529-152738529", "issn": "0002-9939", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130529-152738529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR0398832", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2040033.pdf", "url": "https://authors.library.caltech.edu/records/225v3-pqd69/files/2040033.pdf" }, "pub_year": "1975", "author_list": "Harrington, Leo A. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/ceccy-yc974", "eprint_id": 1459, "eprint_status": "archive", "datestamp": "2023-08-22 00:53:37", "lastmod": "2026-03-17 23:59:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Seiler-E", "name": { "family": "Seiler", "given": "E." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "An inequality among determinants", "ispublished": "pub", "full_text_status": "public", "keywords": "exterior algebra, Fredholm theory", "note": "\u00a9 1975 by the National Academy of Sciences. \n\nCommunicated by A. S. Wightman, June 9, 1975. \n\nIt is a pleasure to thank E. Lieb for a useful discussion. E.S. was partially supported by USNSF under Grant GP-40768X. B.S. is an A. Sloan Fellow, partially supported by USNSF under Grant GP-39048.\n\n

Published - SEIpnas75.pdf

", "abstract": "We prove that for any trace class operators, A,B, det (1+|A+B|) \u2264 det (1+|A|) det (1+|B|) where |C| = (C*C)1/2.", "date": "1975-09", "date_type": "published", "publication": "Proceedings of the National Academy of Sciences of the United States of America", "volume": "72", "number": "9", "publisher": "National Academy of Sciences", "pagerange": "3277-3278", "id_number": "CaltechAUTHORS:SEIpnas75", "issn": "0027-8424", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:SEIpnas75", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP-40768X" }, { "agency": "Alfred P. Sloan Foundation" }, { "agency": "NSF", "grant_number": "GP-39048" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "pmcid": "PMC432972", "primary_object": { "basename": "SEIpnas75.pdf", "url": "https://authors.library.caltech.edu/records/ceccy-yc974/files/SEIpnas75.pdf" }, "pub_year": "1975", "author_list": "Seiler, E. and Simon, B." }, { "id": "https://authors.library.caltech.edu/records/ayz3c-rjf46", "eprint_id": 38699, "eprint_status": "archive", "datestamp": "2023-08-19 09:26:16", "lastmod": "2026-03-09 20:34:01", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "D. A." } } ] }, "title": "A note on universal sets for classes of countable G_\u03b4'S", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1975 University College London. Received June 27 1974. Published online: 26 February 2010.", "abstract": "In a recent article [2] D. G. Larman and C. A. Rogers proved the following two results in Descriptive Set Theory (where R = the space of real numbers): (1) There is no analytic set in the plane R^2, which is universal for the countable closed subsets of R; (2) there is no Borel set in R^2, which is universal for the countable G_\u03b4 subsets of R. Recall that, if b is a class of subsets of a space X, a set U \u2286 X \u00d7 X is called universal for C if (\u0251) for each x \u0454 X, U_x = def {y : (x, y) U} \u0454 C, and (b) for each A \u0454 C there is an x such that A = U_x. (Larman and Rogers have also shown that in both cases coanalytic universal sets exist.)", "date": "1975-06", "date_type": "published", "publication": "Mathematika", "volume": "22", "number": "1", "publisher": "University College London", "pagerange": "43-45", "id_number": "CaltechAUTHORS:20130529-073254315", "issn": "0025-5793", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130529-073254315", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR0420579", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1112/S0025579300004484", "pub_year": "1975", "author_list": "Kechris, A. S. and Martin, D. A." }, { "id": "https://authors.library.caltech.edu/records/wvp16-k7081", "eprint_id": 38671, "eprint_status": "archive", "datestamp": "2023-08-19 09:19:07", "lastmod": "2026-03-09 20:40:54", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Harrington-L-A", "name": { "family": "Harrington", "given": "Leo A." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On Characterizing Spector Classes", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1975, Association for Symbolic Logic. Received September 1, 1973. During the preparation of this paper the second author was partially supported by NSF grant P-29079.\n\n

Published - 2272264.pdf

", "abstract": "We study in this paper characterizations of various interesting classes of relations arising in recursion theory. We first determine which Spector classes on the structure of arithmetic arise from recursion in normal type 2 objects, giving a partial answer to a problem raised by Moschovakis [8], where the notion of Spector class was first\nessentially introduced. Our result here was independently discovered by S. G. Simpson (see [3]). We conclude our study of Spector classes by examining two simple relations between them and a natural hierarchy to which they give rise.", "date": "1975-03", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "40", "number": "1", "publisher": "Association for Symbolic Logic", "pagerange": "19-24", "id_number": "CaltechAUTHORS:20130524-135424900", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130524-135424900", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "P-29079" } ] }, "other_numbering_system": { "items": [ { "id": "0312.02033", "name": "Zentralblatt MATH Identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2272264.pdf", "url": "https://authors.library.caltech.edu/records/wvp16-k7081/files/2272264.pdf" }, "pub_year": "1975", "author_list": "Harrington, Leo A. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/qjq3h-yjz89", "eprint_id": 38637, "eprint_status": "archive", "datestamp": "2023-08-19 09:17:25", "lastmod": "2026-03-09 20:35:28", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Theory of Countable Analytical Sets", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1975 American Mathematical Society. Received by the editors September 13, 1973. Research partially supported by NSF grant GP 27964.\n\n

Published - 1997311.pdf

", "abstract": "The purpose of this paper is the study of the structure of countable sets in the various levels of the analytical hierarchy of sets of reals. It is first shown that, assuming projective determinacy, there is for each odd n a largest countable \u220f_n^1 set of reals, C_n (this is also true for n even, replacing \u220f_n^1 by \u03a3_n^1 and has been established earlier by Solovay for n = 2 and by Moschovakis and the author for all even n > 2). The internal structure of the sets C_n is then investigated in detail, the point of departure being the fact that each C_n is a set of \u0394_n^1-degrees, wellordered under their usual partial ordering. Finally, a number of applications of the preceding theory is presented, covering a variety of topics such as specification of bases, \u03c9-models of analysis, higher-level analogs of the constructible universe, inductive definability, etc.", "date": "1975-02", "date_type": "published", "publication": "Transactions of the American Mathematical Society", "volume": "202", "number": "2", "publisher": "American Mathematical Society", "pagerange": "259-297", "id_number": "CaltechAUTHORS:20130522-132343731", "issn": "0002-9947", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-132343731", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP 27964" } ] }, "other_numbering_system": { "items": [ { "id": "MR0419235", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "1997311.pdf", "url": "https://authors.library.caltech.edu/records/qjq3h-yjz89/files/1997311.pdf" }, "pub_year": "1975", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/hyf93-2sr27", "eprint_id": 841, "eprint_status": "archive", "datestamp": "2023-08-22 00:41:58", "lastmod": "2026-03-09 20:40:47", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Countable ordinals and the analytical hierarchy, I", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1975 Pacific Journal of Mathematics. \n\nReceived August 29, 1974. Research partially supported by NSF grant GP 27964.", "abstract": "The following results are proved, using the axiom of Projective Determinacy: (i) For n \u2265 1, every II(1/2n+1) set of countable ordinals contains a \u0394(1/2n+1) ordinal, (ii) For n \u2265 1, the set of reals \u0394(1/2n) in an ordinal is equal to the largest countable \u03a3(1/2n) set and (iii) Every real is \u0394(1/n) inside some transitive model of set theory if and only if n \u2265 4.", "date": "1975", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "60", "number": "1", "publisher": "Pacific Journal of Mathematics", "pagerange": "223-227", "id_number": "CaltechAUTHORS:KECpjm75", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:KECpjm75", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR0387053", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "KECpjm75.pdf", "url": "https://authors.library.caltech.edu/records/hyf93-2sr27/files/KECpjm75.pdf" }, "pub_year": "1975", "author_list": "Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/8q2ev-n7z83", "eprint_id": 38919, "eprint_status": "archive", "datestamp": "2023-08-19 09:11:33", "lastmod": "2026-03-09 20:34:41", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Countable ordinals and the analytical hierarchy. I.", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1975 Pacific Journal of Mathematics. Received August 29, 1974. Research partially supported by NSF grant GP 27964.\n\n

Published - euclid.pjm.1102868636.pdf

", "abstract": "The following results are proved, using the axiom of Projective Determinacy: (i) For n \u2ab4 1, every \u220f^1_(2n+1) set of countable ordinals contains a \u0394^1_(2n+1) ordinal, (ii) For n \u2ab4 1, the set of reals \u0394^1_(2n) in an ordinal is equal to the largest countable \u03a3^1_(2n) set and (iii) Every real is \u0394^1_n inside some transitive model of set theory if and only if n \u2ab4 4.", "date": "1975", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "60", "number": "1", "publisher": "Pacific Journal of Mathematics", "pagerange": "223-227", "id_number": "CaltechAUTHORS:20130612-115543154", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-115543154", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP 27964" } ] }, "other_numbering_system": { "items": [ { "id": "0287.02042", "name": "Zentralblatt MATH identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "euclid.pjm.1102868636.pdf", "url": "https://authors.library.caltech.edu/records/8q2ev-n7z83/files/euclid.pjm.1102868636.pdf" }, "pub_year": "1975", "author_list": "Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/k61kb-3by18", "eprint_id": 38704, "eprint_status": "archive", "datestamp": "2023-08-19 08:55:17", "lastmod": "2026-03-09 20:38:43", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On Projective Ordinals", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1974 Association for Symbolic Logic. Received August 5, 1972. The results in this paper are included in the author's doctoral dissertation submitted to the University of California, Los Angeles, in June 1972. The author would like to express his sincerest thanks to his thesis advisor, Professor Yiannis N. Moschovakis, both for creating his interest in descriptive set theory and for his guidance and encouragement. The preparation of the paper was partially supported by NSF grant GP-27964.\n\n

Published - 2272639.pdf

", "abstract": "We study in this paper the projective ordinals \u03b4^1_n, where \u03b4^1_n = sup{\u03be: \u03be is the length of \u0251 \u0394^1_n prewellordering of the continuum}. These ordinals were introduced by Moschovakis in [8] to serve as a measure of the \"definable length\" of the continuum. We prove first in \u00a72 that projective determinacy implies \u03b4^1_n < \u03b4^1_n for all even n > 0 (the same result for odd n is due to Moschovakis). Next, in the context of full determinacy, we partly generalize (in \u00a73) the classical fact that \u03b4^1_1 \u2135_l and the result of Martin that \u03b4^1_3 = \u2135_(\u03c9 + 1) by proving that \u03b4^1_(n2+1) = \u03bb^+_(2n+1), where \u03bb_(2n+1) is a cardinal of cofinality \u03c9. Finally we discuss in \u00a74 the connection between the projective ordinals and Solovay's uniform indiscernibles. We prove among other things that \u2200\u03b1 (\u03b1^# exists) implies that every \u03b4^1_n with n \u2265 3 is a fixed point of the increasing enumeration of the uniform indiscernibles.", "date": "1974-06", "date_type": "published", "publication": "Journal of Symbolic Logic", "volume": "39", "number": "2", "publisher": "Association for Symbolic Logic", "pagerange": "269-282", "id_number": "CaltechAUTHORS:20130529-103426984", "issn": "0022-4812", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130529-103426984", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP-27964" } ] }, "other_numbering_system": { "items": [ { "id": "0292.02056", "name": "Zentralblatt MATH Identifier" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "2272639.pdf", "url": "https://authors.library.caltech.edu/records/k61kb-3by18/files/2272639.pdf" }, "pub_year": "1974", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/a79qz-qba20", "eprint_id": 85914, "eprint_status": "archive", "datestamp": "2023-08-19 08:34:56", "lastmod": "2026-04-23 20:19:44", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Lieb-E-H", "name": { "family": "Lieb", "given": "Elliott H." }, "orcid": "0000-0001-5843-3587" }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Thomas-Fermi Theory Revisited", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1973 American Physical Society. \n\n(Received 8 June 1973) \n\nWork partially supported by National Science Foundation Grant No. GP-81674X and by a Guggenheim Memorial Foundation Fellowship. \n\nAlfred P. Sloan Foundation Fellow.\n\n

Published - PhysRevLett.31.681.pdf

", "abstract": "We show that the Thomas-Fermi theory is exact for atoms, molecules, and solids as Z\u2192\u221e.\n.", "date": "1973-09-10", "date_type": "published", "publication": "Physical Review Letters", "volume": "31", "number": "11", "publisher": "American Physical Society", "pagerange": "681-683", "id_number": "CaltechAUTHORS:20180417-154000408", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154000408", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP-81674X" }, { "agency": "John Simon Guggenheim Foundation" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.31.681", "primary_object": { "basename": "PhysRevLett.31.681.pdf", "url": "https://authors.library.caltech.edu/records/a79qz-qba20/files/PhysRevLett.31.681.pdf" }, "pub_year": "1973", "author_list": "Lieb, Elliott H. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/ymvrw-ces91", "eprint_id": 38693, "eprint_status": "archive", "datestamp": "2023-08-19 08:31:23", "lastmod": "2026-04-21 16:08:12", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Measure and category in effective descriptive set theory", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1973 North-Holland Publishing Company. \nSome of the main results in this paper have been announced in [11] (The final statement in this abstract about \u0394^1_(2(n+1) reals is wrong.) Part of Section 4 has been also included in the author's Ph.D. thesis (UCLA, June 1972) written under the supervision of Professor Y.N. Moschovakis whom we wish to thank for his guidance and encouragement. We would like also to thank Professor G.E. Sacks and L. Harrington for many interesting and helpful discussions. The preparation of this manuscript was partially supported by NSF Grant GP 27964.", "abstract": "We are concerned in this paper with some definability aspects of the theory of measure and category on the continuum. Our objects of study are the projective subsets of the reals and their structure from a measure theoretic and topological point of view.", "date": "1973-07", "date_type": "published", "publication": "Annals of Mathematical Logic", "volume": "5", "number": "4", "publisher": "Elsevier", "pagerange": "337-384", "id_number": "CaltechAUTHORS:20130528-122128969", "issn": "0003-4843", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-122128969", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP 27964" } ] }, "other_numbering_system": { "items": [ { "id": "MR0369072", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1016/0003-4843(73)90012-0", "pub_year": "1973", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/jsad4-z3321", "eprint_id": 85913, "eprint_status": "archive", "datestamp": "2023-08-19 08:27:15", "lastmod": "2026-04-23 16:30:11", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Griffiths-R-B", "name": { "family": "Griffiths", "given": "Robert B." } } ] }, "title": "Griffiths-Hurst-Sherman Inequalities and a Lee-Yang Therorem for the(\u03d5^4)_2 Field Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1973 American Physical Society. \n\n(Received 19 March 1973) \n\nWe should like to thank Professor J. Lebowitz and Professor E. Lieb for valuable discussions. In addition, one of us (B.S.) would like to thank Professor N. Kuiper for the hospitality shown him while a visitor at the Institut des Haute Etudes Scientifique, and Professor A. Visconti for the hospitality of the Centre National de la Recherche Scientifique. The other (R.B.G.) is grateful for the hospitality of the Cornell Chemistry Department.\n\n

Published - PhysRevLett.30.931.pdf

", "abstract": "The Griffiths-Hurst-Sherman inequalities and the Lee-Yang zero theorem in the theory of Ising ferromagnets are shown to hold in a two-dimensional self-coupled Bose quantume field theory with interaction: a\u03d5^4 + b\u03d5^2 \u2212 \u03bc\u03d5:. Applications include the continuity of the infinite-volume \"magnetization,\" \n\u27e8\u03d5(0)\u27e9, away from \u03bc = 0. Our results should carry over to three or four dimensions once it is known how to control the ultraviolet divergences in these theories.", "date": "1973-05-07", "date_type": "published", "publication": "Physical Review Letters", "volume": "30", "number": "19", "publisher": "American Physical Society", "pagerange": "931-933", "id_number": "CaltechAUTHORS:20180417-154000112", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154000112", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "John Simon Guggenheim Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.30.931", "primary_object": { "basename": "PhysRevLett.30.931.pdf", "url": "https://authors.library.caltech.edu/records/jsad4-z3321/files/PhysRevLett.30.931.pdf" }, "pub_year": "1973", "author_list": "Simon, Barry and Griffiths, Robert B." }, { "id": "https://authors.library.caltech.edu/records/679ps-2b104", "eprint_id": 542, "eprint_status": "archive", "datestamp": "2023-08-22 00:18:41", "lastmod": "2026-03-07 04:14:53", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "A characterization of the unitary and symplectic groups over finite fields of characteristic at least $5$", "ispublished": "pub", "full_text_status": "public", "note": "Received February 25, 1972 and in revised form February 26, 1973. \n\nEuclid Identifier: euclid.pjm/1102946071 \nZentralblatt Math Identifier : 0299.20009 \nMathmatical Reviews number (MathSciNet): MR0338151", "abstract": "The following characterization is obtained: \n\nTHEOREM. Let G be a finite group generated by a conjugacy class D of subgroups of prime order p ^ 5, such that for any choice of distinct A and B in D, the subgroup generated by A and B is isomorphic to Zp x Zp, L2(pm) or SL2(pm), where m depends on A and B. Assume G has no nontrivial solvable normal subgroup. Then G is isomorphic to Spn(q) or Un(q) for some power q of p.", "date": "1973", "date_type": "published", "publication": "Pacific Journal of Mathematics", "volume": "47", "number": "1", "publisher": "Pacific Journal of Mathematics", "pagerange": "5-26", "id_number": "CaltechAUTHORS:ASCpjm73", "issn": "0030-8730", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:ASCpjm73", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "ASCpjm73.pdf", "url": "https://authors.library.caltech.edu/records/679ps-2b104/files/ASCpjm73.pdf" }, "pub_year": "1973", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/ekx2r-k0d03", "eprint_id": 38706, "eprint_status": "archive", "datestamp": "2023-08-19 08:09:11", "lastmod": "2026-04-21 18:06:32", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "title": "Two theorems about projective sets", "ispublished": "pub", "full_text_status": "restricted", "note": "\u00a9 1972 Springer. Received October 19, 1971. Y. N. Moschovakis is a Sloan Foundation Fellow. During the preparation of this paper, both authors were partially supported by NSF Grant GP-27964.", "abstract": "In this paper we prove two (rather unrelated) theorems about projective sets. The first one asserts that subsets of \u2135_1 which are \u2211^1_2 in the codes are constructible; thus it extends the familiar theorem of Shoenfield that \u2211^1_2 subsets of \u03c9 are constructible. The second is concerned with largest countable \u2211^1_(2n) sets and establishes their existence under the hypothesis of Projective Determinacy and the assumption that there exist only countably many ordinal definable reals.", "date": "1972-12", "date_type": "published", "publication": "Israel Journal of Mathematics", "volume": "12", "number": "4", "publisher": "Springer", "pagerange": "391-399", "id_number": "CaltechAUTHORS:20130529-155104187", "issn": "0021-2172", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130529-155104187", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP-27964" } ] }, "other_numbering_system": { "items": [ { "id": "MR0323544", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/BF02764630", "pub_year": "1972", "author_list": "Kechris, Alexander S. and Moschovakis, Yiannis N." }, { "id": "https://authors.library.caltech.edu/records/a46v3-sg172", "eprint_id": 85912, "eprint_status": "archive", "datestamp": "2023-08-19 07:55:13", "lastmod": "2026-04-23 16:32:14", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Summability Methods, the Strong Asymptotic Condition, and Unitarity in Quantum Field Theory", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1972 American Physical Society. \n\n(Received 28 February 1972) \n\nResearch partially supported by the U. S. Air Force Office of Scientific Research under Contract No. F44620-71-C-0108. \n\nAlfred P. Sloan Foundation Fellow.\n\n

Published - PhysRevLett.28.1145.pdf

", "abstract": "We discuss a summability mechanism which preserves nonlinear perturbative conditions such as unitarity of the Feynman series. This condition, which relates a function \nf(z) and a series \u03a3a_nz^n by the requirement \u2223f(z) \u2212\u03a3n =^N 0a_nz^n\u2223 <~ A\u03c3^(N+1)(N+1)!|z|^(N+1) is applicable to certain divergent series.", "date": "1972-04-24", "date_type": "published", "publication": "Physical Review Letters", "volume": "28", "number": "17", "publisher": "American Physical Society", "pagerange": "1145-1146", "id_number": "CaltechAUTHORS:20180417-153959845", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-153959845", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F44620-71-C-0108" }, { "agency": "Alfred P. Sloan Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.28.1145", "primary_object": { "basename": "PhysRevLett.28.1145.pdf", "url": "https://authors.library.caltech.edu/records/a46v3-sg172/files/PhysRevLett.28.1145.pdf" }, "pub_year": "1972", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/p0tfz-4m980", "eprint_id": 85911, "eprint_status": "archive", "datestamp": "2023-08-19 07:16:47", "lastmod": "2026-04-23 16:32:08", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Borel Summability of the Ground-State Energy in Spatially Cutoff (\u03d5^4)_2", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1970 American Physical Society. \n\n(Received 1 October (1970) \n\nResearch partially sponsored by the U. S. Air Force Office of Scientific Research under Contract No. AF 49(638)1545.\n\n

Published - PhysRevLett.25.1583.pdf

", "abstract": "We show that the ground-state energy for a Hamiltonian H_0 + \u222bg(x) : \u03d5^4(x) : dx (g\u2208L^1 \u2229 L^2; g >~ 0; H_0 = free Hamiltonian for Bose particle of mass m in space-time of two dimensions) may be determined from the Feynman perturbation series by the method of Borel summability. This demonstrates that summability methods can be applicable to divergent series in systems with a continuous infinity of degrees of freedom.", "date": "1970-11-30", "date_type": "published", "publication": "Physical Review Letters", "volume": "25", "number": "22", "publisher": "American Physical Society", "pagerange": "1583-1586", "id_number": "CaltechAUTHORS:20180417-153959480", "issn": "0031-9007", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-153959480", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "AF 49(638)1545" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevLett.25.1583", "primary_object": { "basename": "PhysRevLett.25.1583.pdf", "url": "https://authors.library.caltech.edu/records/p0tfz-4m980/files/PhysRevLett.25.1583.pdf" }, "pub_year": "1970", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/6wrj2-fmx96", "eprint_id": 85925, "eprint_status": "archive", "datestamp": "2023-08-19 07:02:29", "lastmod": "2026-04-23 16:31:46", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Some Comments on the Jin-Martin Lower Bound", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1970 American Physical Society. \n\n(Received 6 October 1969) \n\nResearch partially sponsored by the U. S. Air Force Once of Scientific Research, under Contract No. AF49(638)1545.\n\n

Published - PhysRevD.1.1240.pdf

", "abstract": "We present an extremely simple derivation of the Jin-Martin bound in a slightly weakened form. Explicitly, let f^(AB\u2192AB)(s) be the spin-averaged forward-scattering amplitude for the process AB\u2192AB [normalized by \u03c3_(tot) = 4\u03c0(Im f(s))/k\u221as]. Then we prove that there is a constant C and a sequence \ns_n\u2192\u221e such that either f^(AB\u2192AB)(s_n) > Cs_n^(\u22122) (all \nn) or f^(A\u00afB\u2192A\u00afB)(s_n)) > Cs_n^(\u22122) (all n). We also clarify the connection between allowable asymptotic behavior and the sign of the scattering length found by Jin and Martin.", "date": "1970-02-15", "date_type": "published", "publication": "Physical Review D", "volume": "1", "number": "4", "publisher": "American Physical Society", "pagerange": "1240-1241", "id_number": "CaltechAUTHORS:20180417-154003485", "issn": "2470-0010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180417-154003485", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "AF49(638)1545" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1103/PhysRevD.1.1240", "primary_object": { "basename": "PhysRevD.1.1240.pdf", "url": "https://authors.library.caltech.edu/records/6wrj2-fmx96/files/PhysRevD.1.1240.pdf" }, "pub_year": "1970", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/esnpf-h2238", "eprint_id": 91076, "eprint_status": "archive", "datestamp": "2023-08-19 06:54:34", "lastmod": "2026-04-23 16:34:40", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Loeffel-J-J", "name": { "family": "Loeffel", "given": "J. J." } }, { "id": "Martin-Andr\u00e9-D.", "name": { "family": "Martin", "given": "A." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" }, { "id": "Wightman-A-S", "name": { "family": "Wightman", "given": "A. S." } } ] }, "title": "Pade approximants and the anharmonic oscillator", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1969 Published by Elsevier . \n\nReceived 27 November 1969. \n\nIt is a pleasure to thank A. Dicke, H. Epstein, V. Glaser, D. Masson, E. Stein and K. Symanzik for very valuable comments. Two of us (A. M. and B. S.) are grateful to N. N. Khuri for arranging a meeting which stimulated this work.\n\n

Published - 1-s2.0-0370269369900872-main.pdf

", "abstract": "The diagonal Pad\u00e9 approximants of the perturbation series for the eigenvalues of the anharmonic oscillator (a \u03b2\u03ba^1 perturbation of p^2 + \u03ba^2) converge to the eigenvalues.", "date": "1969-12-22", "date_type": "published", "publication": "Physics Letters B", "volume": "30", "number": "9", "publisher": "Elsevier", "pagerange": "656-658", "id_number": "CaltechAUTHORS:20181120-133838806", "issn": "0370-2693", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181120-133838806", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/0370-2693(69)90087-2", "primary_object": { "basename": "1-s2.0-0370269369900872-main.pdf", "url": "https://authors.library.caltech.edu/records/esnpf-h2238/files/1-s2.0-0370269369900872-main.pdf" }, "pub_year": "1969", "author_list": "Loeffel, J. J.; Martin, A.; et al." }, { "id": "https://authors.library.caltech.edu/records/hyh04-hgp53", "eprint_id": 91062, "eprint_status": "archive", "datestamp": "2023-08-19 06:30:20", "lastmod": "2026-04-23 18:22:42", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On the Growth of the Ground\u2010State Binding Energy with Increase in Potential Strength", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1969 American Institute of Physics. \n\n(Received 7 February 1969) \n\nThe author would like to thank M. Reed for an enlightening conversation on the nonpower growth of convex functions. \n\nThis research partially sponsored under Air Force Office of Scientific Research under Contract AF49(638)-1545.\n\n

Published - 1_2E1664983.pdf

", "abstract": "We study the asymptotic behavior of the ground\u2010state binding energy G(\u03bb) of \u2212\u0394 + \u03bbV as \u03bb \u2192 \u221e. Unlike the number of bound states, G(\u03bb) does not have a universal power growth as \u03bb \u2192 \u221e. It is shown, however, that as \u03bb \u2192 \u221e for Kato potentials\nA\u03bb", "date": "1969-08", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "10", "number": "8", "publisher": "American Institute of Physics", "pagerange": "1415-1421", "id_number": "CaltechAUTHORS:20181119-161054026", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181119-161054026", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "AF49(638)-1545" }, { "agency": "NSF Graduate Research Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/1.1664983", "primary_object": { "basename": "1_2E1664983.pdf", "url": "https://authors.library.caltech.edu/records/hyh04-hgp53/files/1_2E1664983.pdf" }, "pub_year": "1969", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/c6pkz-e4e28", "eprint_id": 91075, "eprint_status": "archive", "datestamp": "2023-08-19 06:29:00", "lastmod": "2026-04-23 16:32:03", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "On the Growth of the Number of Bound States with Increase in Potential Strength", "ispublished": "pub", "full_text_status": "public", "note": "\u00a9 1969 The American Institute of Physics. \n\n(Received 21 November 1968) \n\nThis research partially sponsored under Air Force Research and Development Command contract AF49(638)1545. \n\nIt is a pleasure to thank Professor V. Bargmann and Professor A. S. Wightman for their interest and perceptive comments.\n\n

Published - 1_2E1664948.pdf

", "abstract": "For a wide class of potentials, it is shown that N(\u03bb), the number of bound states (including multiplicity) of \u2212\u0394 + \u03bbV, obeys the conditions A\u03bb^(3/2) < N(\u03bb) < B\u03bb^(3/2) for \u03bb sufficiently large. A and B are positive finite numbers. In the centrally symmetric cases, a related growth condition on l_(max)(\u03bb), the largest l channel with bound states, is also obtained, namely, a\u03bb^(1/2) < l_(max)(\u03bb) < b\u03bb^(1/2). Finally, we discuss analogous results for a larger class of central potentials and for the many\u2010body case.", "date": "1969-07", "date_type": "published", "publication": "Journal of Mathematical Physics", "volume": "10", "number": "7", "publisher": "American Institute of Physics", "pagerange": "1123-1126", "id_number": "CaltechAUTHORS:20181120-133838721", "issn": "0022-2488", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181120-133838721", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "AF 49(638)1545" }, { "agency": "NSF Graduate Research Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1063/1.1664948", "primary_object": { "basename": "1_2E1664948.pdf", "url": "https://authors.library.caltech.edu/records/c6pkz-e4e28/files/1_2E1664948.pdf" }, "pub_year": "1969", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/ez3xa-4pj48", "eprint_id": 91093, "eprint_status": "archive", "datestamp": "2023-08-21 23:47:19", "lastmod": "2026-04-23 16:35:31", "type": "article", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Convergence of regularized, renormalized perturbation series for super-renormalizable field theories", "ispublished": "pub", "full_text_status": "restricted", "keywords": "Perturbation Series; Yukawa Interaction; Disjoint Cycle; Finite Radius; Vacuum Diagram", "note": "\u00a9 Italian Society of Physics 1969. \n\n(ricevuto il 12 Agosto 1968) \n\nThis paper was written with partial support of the Air Force Research and Development Command under Contract No. AF 49(638)-1545.\n\nIt is a pleasure to thank Prof. A. S. Wightman who originally suggested the problem, for his patience, advice and aid. I should also like to thank Prof. E. R. Caianiello for an enlightening correspondence on this paper.", "abstract": "It is shown for the two-dimensional scalar Yukawa interaction, that the renormalized perturbation series has at least a finite radius of convergence when a regularized space-time and momentum space. This is accomplished by writing down the explicit renormalized series, studying some of its associated combinatorics, and applying Caianiello's standard arguments on the unrenormalized series ( 16 ). The result extends to any super-renormalizable theory of the \u03c6 \u03c8\u00af\u03c8 form.", "date": "1969-01", "date_type": "published", "publication": "Il Nuovo Cimento A Series 10", "volume": "59", "number": "1", "publisher": "Springer Nature", "pagerange": "199-214", "id_number": "CaltechAUTHORS:20181120-145801316", "issn": "0369-3546", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181120-145801316", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "AF 49(638)-1545" }, { "agency": "NSF Graduate Research Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1007/bf02756356", "pub_year": "1969", "author_list": "Simon, B." } ]