[ { "id": "https://authors.library.caltech.edu/records/bt0x6-3b609", "eprint_status": "archive", "datestamp": "2025-09-10 15:07:42", "lastmod": "2026-03-09 02:36:40", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Isett-Philip", "name": { "family": "Isett", "given": "Philip" }, "orcid": "0000-0001-9038-5546" } ] }, "title": "Regularity of Trajectories and Smooth Observables in Rough Euler Flows", "ispublished": "pub", "full_text_status": "public", "note": "

© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG.

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\n

The author thanks V. Šverak for conversations motivating the study of smooth observables.

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\n\n

The author acknowledges the support of a Sloan Fellowship and the NSF grant DMS 2346799.

", "abstract": "

For any Euler flow that is C^α uniformly in time, we show that all particle trajectories are of class C¹/(1-α) when 1/(1-α) is not an integer. This result holds despite the ill-posedness of the Euler equations and the expected nonuniqueness of trajectories. We discuss the implications for pair dispersion of particle trajectories. We also show that the Fourier coefficients and more generally the integral of velocity against any smooth function is C(1+α)/(1-α) in time when (1+α)/(1-α) is not an integer.

", "date": "2025-08-23", "date_type": "published", "publication": "Abel Symposia", "volume": "18", "publisher": "Springer Nature Switzerland", "place_of_pub": "Cham", "pagerange": "185-204", "isbn": "978-3-031-91284-9", "issn": "2193-2808", "book_title": "Partial Differential Equations: Waves, Nonlinearities and Nonlocalities", "official_url": "https://authors.library.caltech.edu/records/bt0x6-3b609", "funders": { "items": [ { "grant_number": "DMS-2346799" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.1007/978-3-031-91282-5_9", "pub_year": "2025", "author_list": "Isett, Philip" }, { "id": "https://authors.library.caltech.edu/records/dd468-e0p67", "eprint_status": "archive", "datestamp": "2025-01-29 22:51:50", "lastmod": "2026-03-09 02:15:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "The Sharp Sobolev Inequality and Its Stability: An Introduction", "ispublished": "pub", "full_text_status": "public", "note": "

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

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© 2023 by the author. This paper may be reproduced, in its entirety, for noncommercial purposes.

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Partial support through US National Science Foundation grant DMS-1954995, as well as through the Deutsche Forschungsgemeinschaft through Germany’s Excellence Strategy EXC-2111-390814868 and through TRR 352—Project-ID 470903074 is acknowledged.

", "abstract": "These notes are an extended version of a series of lectures given at the CIME Summer School in Cetraro in June 2022. The goal is to explain questions about optimal functional inequalities on the example of the sharp Sobolev inequality and its fractional generalizations. Topics covered include compactness theorems for optimizing sequences, characterization of optimizers and quantitative stability.", "date": "2024-11-20", "date_type": "published", "publication": "Geometric and Analytic Aspects of Functional Variational Principles", "publisher": "Springer Nature Switzerland", "place_of_pub": "Cham", "pagerange": "1-64", "isbn": "978-3-031-67600-0", "official_url": "https://authors.library.caltech.edu/records/dd468-e0p67", "funders": { "items": [ { "grant_number": "DMS-1954995" }, { "grant_number": "EXC-2111-390814868" }, { "grant_number": "470903074" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/978-3-031-67601-7_1", "pub_year": "2024", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/v2j97-wx003", "eprint_status": "archive", "datestamp": "2024-10-15 23:01:51", "lastmod": "2026-03-10 03:35:05", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Topological Phases of Matter and Homotopy Theory", "ispublished": "pub", "full_text_status": "public", "note": "

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

", "abstract": "

Phases of quantum matter with a nonzero gap for local excitations are commonly referred to as topological phases of matter, because of their long-assumed relation to Topological Quantum Field Theory. While this relation is no longer believed to be true in all cases, topology, and more specifically homotopy theory, are used to define gapped phases rigorously. The connection with the homotopy theory is especially fruitful in the case of invertible gapped phases where a precise conjecture about the classification of such phases has been advanced. The topology of the space of gapped many-body systems on a lattice can be probed using higher-dimensional generalizations of the Berry phase.

", "date": "2024-10-03", "date_type": "published", "publication": "Encyclopedia of Mathematical Physics", "volume": "1", "publisher": "Elsevier", "place_of_pub": "Amsterdam", "edition": "2", "pagerange": "106-110", "isbn": "978-0-323-95706-9", "book_title": "Encyclopedia of Mathematical Physics", "official_url": "https://authors.library.caltech.edu/records/v2j97-wx003", "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1016/b978-0-323-95703-8.00048-3", "pub_year": "2024", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/qmnvz-dpz51", "eprint_status": "archive", "datestamp": "2026-01-15 00:34:46", "lastmod": "2026-03-09 22:09:55", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Jain", "given": "Vishesh" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" } ] }, "title": "Optimal thresholds for Latin squares, Steiner Triple Systems, and edge colorings", "ispublished": "pub", "full_text_status": "public", "abstract": "
Given a graph G, a random (k, n)-list assignment L for edges of G is an assignment of an independent, uniformly random set L(e) ∈ ([n]/k)of colors to each edge e and a proper L-list coloring of G is a proper edge-coloring where the color of an edge e belongs to L(e). We show that for a random (O(log n), n)-list assignment L for edges of the complete bipartite graph Kn,n, there is a an L-list coloring of Kn,n with high probability. We also prove analogous results for the thresholds of Steiner triple systems and Latin squares in random (binomial) hypergraphs. All of our results are optimal up to absolute constants, and resolve several related conjectures of Johansson, Luria-Simkin, Casselgren-Häggkvist, Simkin, and Kang-Kelly-Kühn-Methuku-Osthus.
\n
 
\n
A key contribution of our work is to show that in natural settings, the Lovász Local Lemma - a central tool in probabilistic combinatorics to establish the existence of objects with desired properties - can also be used to design optimally “spread” distributions on such objects. This is made possible by carefully exploiting the local uniformity property of the so-called Lovász Local Lemma distribution, an important observation that has recently been utilized in finding efficient algorithms for sampling approximately uniformly random solutions to constraint satisfaction problems. In conjunction with the recently proved Kahn-Kalai conjecture, this opens the door to obtaining optimal threshold results for the appearance of many interesting objects.
", "date": "2024-01", "date_type": "published", "publication": "Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "1425-1436", "official_url": "https://authors.library.caltech.edu/records/qmnvz-dpz51", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/1.9781611977912.57", "pub_year": "2024", "author_list": "Jain, Vishesh and Pham, Huy Tuan" }, { "id": "https://authors.library.caltech.edu/records/4x56w-qmn68", "eprint_status": "archive", "datestamp": "2026-01-15 00:35:29", "lastmod": "2026-03-09 22:10:02", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Anari", "given": "Nima" } }, { "name": { "family": "Jain", "given": "Vishesh" } }, { "name": { "family": "Koehler", "given": "Frederic" } }, { "id": "Pham-Huy-Tuan", "name": { "family": "Pham", "given": "Huy Tuan" }, "orcid": "0000-0003-4659-4345" }, { "name": { "family": "Vuong", "given": "Thuy-Duong" } } ] }, "title": "Universality of Spectral Independence with Applications to Fast Mixing in Spin Glasses", "ispublished": "pub", "full_text_status": "public", "abstract": "
We study Glauber dynamics for sampling from discrete distributions μ on the hypercube {±1}n. Recently, techniques based on spectral independence have successfully yielded optimal O(n) relaxation times for a host of different distributions μ. We show that spectral independence is universal: a relaxation time of O(n) implies spectral independence.
\n
We then study a notion of tractability for μ, defined in terms of smoothness of the multilinear extension of its Hamiltonian - log μ - over [— 1, +1]n. We show that Glauber dynamics has relaxation time O(n) for such μ, and using the universality of spectral independence, we conclude that these distributions are also fractionally log-concave and consequently satisfy modified log-Sobolev inequalities. We sharpen our estimates and obtain approximate tensorization of entropy and the optimal Õ(n) mixing time for random Hamiltonians, i.e. the classically studied mixed p-spin model at sufficiently high temperature. These results have significant downstream consequences for concentration of measure, statistical testing, and learning.
", "date": "2024-01", "date_type": "published", "publication": "Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)", "publisher": "Society for Industrial and Applied Mathematics", "pagerange": "5029-5056", "official_url": "https://authors.library.caltech.edu/records/4x56w-qmn68", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1137/1.9781611977912.181", "pub_year": "2024", "author_list": "Anari, Nima; Jain, Vishesh; et al." }, { "id": "https://authors.library.caltech.edu/records/dw1qz-96n28", "eprint_status": "archive", "datestamp": "2025-11-13 23:43:45", "lastmod": "2026-03-27 18:07:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Some minimization problems for mean field models with competing forces", "ispublished": "unpub", "full_text_status": "public", "keywords": "Minimization problems; mean field models; liquid drop model; swarming; Keller\u2013Segel model", "note": "

© 2023 EMS Press. This work is licensed under a CC BY 4.0 license.

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The author would like to thank the organizers of the 8th European Congress of Mathematics for the organization of the meeting and for the invitation to speak. Since the topic of his invited talk was recently and rather exhaustively
reviewed in [24], this contribution is based on a talk in a minisymposium at the congress, organized by L. Pick, to whom the author is very grateful. The results reviewed here were obtained in collaboration with many researchers and it is a pleasure to thank, in particular, José Carrillo, Matías Delgadino, Jean Dolbeault, Franca Hoffmann, Rowan Killip, Mathieu Lewin, Elliott Lieb, and Phan Thành Nam for many stimulating discussions.

\n\n

This research was supported in part by NSF grants DMS-1363432 and DMS-1954995 and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2111-390814868.

", "abstract": "

We review recent results on three families of minimization problems, defined on subsets of nonnegative functions with fixed integral. The competition between attractive and repulsive forces leads to transitions between parameter regimes, where minimizers exist and where they do not. The problems considered are generalized liquid drop models, swarming models and generalized Keller-Segel models.

", "date": "2023-07-14", "date_type": "published", "publisher": "European Mathematical Society", "place_of_pub": "Berlin, Germany", "pagerange": "277-294", "isbn": "978-3-98547-051-8", "book_title": "Eighth European Congress of Mathematics: Portoro\u017e, 20-26 June 2021", "official_url": "https://authors.library.caltech.edu/records/dw1qz-96n28", "funders": { "items": [ { "grant_number": "DMS-1363432" }, { "grant_number": "DMS-1954995" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)", "grant_number": "EXC-2111-390814868" } ] }, "local_group": { "items": [ { "id": "Division-of-Physics-Mathematics-and-Astronomy" }, { "id": "Mathematics-Department" } ] }, "doi": "10.4171/8ECM/06", "primary_object": { "basename": "978-3-98547-551-3-chapter-5197.pdf", "url": "https://authors.library.caltech.edu/records/dw1qz-96n28/files/978-3-98547-551-3-chapter-5197.pdf" }, "pub_year": "2023", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/bxbqn-1de28", "eprint_id": 115371, "eprint_status": "archive", "datestamp": "2023-08-20 08:10:48", "lastmod": "2026-03-09 23:59:16", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Huang-Wanying", "name": { "family": "Huang", "given": "Wanying" } }, { "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": "Learning in Repeated Interactions on Networks", "ispublished": "unpub", "full_text_status": "public", "keywords": "social learning", "note": "\u00a9 2022 Copyright held by the owner/author(s). \n\nPhilipp Strack was supported by a Sloan fellowship. Omer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan fellowship, a BSF award (#2018397) and a National Science Foundation CAREER award (DMS-1944153).\n\n

Published - 3490486.3538307.pdf

Submitted - 2112.14265.pdf

", "abstract": "We study how long-lived, rational, exponentially discounting agents learn in a social network. In every period, each agent observes the past actions of his neighbors, receives a private signal, and chooses an action with the objective of matching the state. Since agents behave strategically, and since their actions depend on higher order beliefs, it is difficult to characterize equilibrium behavior. Nevertheless, we show that regardless of the size and shape of the network, and the patience of the agents, the equilibrium speed of learning is bounded from above by a constant that only depends on the private signal distribution.", "date": "2022-07-11", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "325", "id_number": "CaltechAUTHORS:20220707-170550926", "isbn": "978-1-4503-9150-4", "book_title": "Proceedings of the 23rd ACM Conference on Economics and Computation", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170550926", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2018397" }, { "agency": "NSF", "grant_number": "DMS-1944153" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/3490486.3538307", "primary_object": { "basename": "2112.14265.pdf", "url": "https://authors.library.caltech.edu/records/bxbqn-1de28/files/2112.14265.pdf" }, "related_objects": [ { "basename": "3490486.3538307.pdf", "url": "https://authors.library.caltech.edu/records/bxbqn-1de28/files/3490486.3538307.pdf" } ], "pub_year": "2022", "author_list": "Huang, Wanying; Strack, Philipp; et al." }, { "id": "https://authors.library.caltech.edu/records/7pf6j-r2e27", "eprint_id": 115372, "eprint_status": "archive", "datestamp": "2023-08-20 08:10:54", "lastmod": "2026-03-09 23:59:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "He-Kevin", "name": { "family": "He", "given": "Kevin" }, "orcid": "0000-0001-5806-0370" }, { "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": "Private Private Information", "ispublished": "unpub", "full_text_status": "public", "keywords": "game theory, information design, beliefs", "note": "\u00a9 2022 Copyright held by the owner/author(s). \n\nFedor Sandomirskiy was supported by the Linde Institute at Caltech and the National Science Foundation (grant CNS\n1518941). \n\nOmer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan fellowship, a BSF award (#2018397) and a National Science Foundation CAREER award (DMS-1944153).\n\n

Published - 3490486.3538348.pdf

Submitted - 2112.14356.pdf

", "abstract": "In a private private information structure, agents' signals contain no information about the signals of their peers. We study how informative such structures can be, and characterize those that are on the Pareto frontier, in the sense that it is impossible to give more information to any agent without violating privacy. In our main application, we show how to optimally disclose information about an unknown state under the constraint of not revealing anything about a correlated variable that contains sensitive information.", "date": "2022-07-11", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "1145", "id_number": "CaltechAUTHORS:20220707-170554297", "isbn": "978-1-4503-9150-4", "book_title": "Proceedings of the 23rd ACM Conference on Economics and Computation", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220707-170554297", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Linde Institute of Economic and Management Science" }, { "agency": "NSF", "grant_number": "CNS-1518941" }, { "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": "10.1145/3490486.3538348", "primary_object": { "basename": "2112.14356.pdf", "url": "https://authors.library.caltech.edu/records/7pf6j-r2e27/files/2112.14356.pdf" }, "related_objects": [ { "basename": "3490486.3538348.pdf", "url": "https://authors.library.caltech.edu/records/7pf6j-r2e27/files/3490486.3538348.pdf" } ], "pub_year": "2022", "author_list": "He, Kevin; Sandomirskiy, Fedor; et al." }, { "id": "https://authors.library.caltech.edu/records/qks6c-x6q46", "eprint_id": 108299, "eprint_status": "archive", "datestamp": "2023-08-20 08:10:36", "lastmod": "2026-03-10 00:00:38", "type": "book_section", "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" }, "orcid": "0000-0002-7960-9243" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Monotone Additive Statistics", "ispublished": "unpub", "full_text_status": "public", "keywords": "statistics, stationary preferences, stochastic dominance", "note": "\u00a9 2022 Copyright held by the owner/author(s). \n\nPhilipp Strack was supported by a Sloan fellowship. \n\nOmer Tamuz was supported by a grant from the Simons Foundation (#419427), a Sloan fellowship, a BSF award (#2018397) and a National Science Foundation CAREER award (DMS-1944153).\n\n

Published - 3490486.3538318.pdf

Submitted - 2102.00618.pdf

", "abstract": "The expectation is an example of a descriptive statistic that is monotone with respect to stochastic dominance, and additive for sums of independent random variables. We provide a complete characterization of such statistics, and explore a number of applications to models of individual and group decision-making. These include a representation of stationary, monotone time preferences, extending the work of Fishburn and Rubinstein (1982) to time lotteries, as well as a characterization of risk-averse preferences over monetary gambles that are invariant to mean-zero background risks.", "date": "2022-07-11", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "34", "id_number": "CaltechAUTHORS:20210303-154811036", "isbn": "978-1-4503-9150-4", "book_title": "Proceedings of the 23rd ACM Conference on Economics and Computation", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210303-154811036", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Alfred P. Sloan Foundation" }, { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2018397" }, { "agency": "NSF", "grant_number": "DMS-1944153" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/3490486.3538318", "primary_object": { "basename": "3490486.3538318.pdf", "url": "https://authors.library.caltech.edu/records/qks6c-x6q46/files/3490486.3538318.pdf" }, "related_objects": [ { "basename": "2102.00618.pdf", "url": "https://authors.library.caltech.edu/records/qks6c-x6q46/files/2102.00618.pdf" } ], "pub_year": "2022", "author_list": "Mu, Xiaosheng; Pomatto, Luciano; et al." }, { "id": "https://authors.library.caltech.edu/records/th9km-0pa57", "eprint_id": 113669, "eprint_status": "archive", "datestamp": "2023-08-22 14:09:55", "lastmod": "2026-03-18 00:00:05", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "van-Enter-Aernout", "name": { "family": "van Enter", "given": "Aernout" } } ] }, "title": "Lattice Systems", "ispublished": "unpub", "full_text_status": "public", "keywords": "Ising models; Potts models; vector spin models; quantum spin models; vertex models; lattice gauge models", "note": "\u00a9 2022 John Wiley & Sons. \n\nPublished Online: 27 February 2022.", "abstract": "Lattice systems form a widely studied class of models originating in statistical mechanics, and consisting of single-site observables (functions or operators) describing \"spins,\" living on infinite lattices. They have found applications in various other fields, in physics (e.g., field theory), mathematics (dynamical systems and probability theory), and also as models for epidemics and populations. Their major interest and difference with other stochastic processes is due to the occurrence of various phase transitions, where the dependence on parameters becomes nonsmooth, and/or the number of measures associated with a certain parameter can change.", "date": "2022-02-28", "date_type": "published", "publisher": "Wiley", "place_of_pub": "New York, NY", "pagerange": "1-8", "id_number": "CaltechAUTHORS:20220301-900050000", "isbn": "9781118445112", "book_title": "Wiley StatsRef: Statistics Reference Online", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20220301-900050000", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Balakrishnan-N", "name": { "family": "Balakrishnan", "given": "N." } }, { "id": "Colton-Theodore", "name": { "family": "Colton", "given": "Theodore" } }, { "id": "Everitt-Brian", "name": { "family": "Everitt", "given": "Brian" } }, { "id": "Piegorsch-Walter", "name": { "family": "Piegorsch", "given": "Walter" } }, { "id": "Ruggeri-Fabrizio", "name": { "family": "Ruggeri", "given": "Fabrizio" } }, { "id": "Teugels-Jef", "name": { "family": "Teugels", "given": "Jef" } } ] }, "doi": "10.1002/9781118445112.stat00085.pub2", "pub_year": "2022", "author_list": "Simon, Barry and van Enter, Aernout" }, { "id": "https://authors.library.caltech.edu/records/c78xs-6qc80", "eprint_id": 112640, "eprint_status": "archive", "datestamp": "2023-08-20 04:14:24", "lastmod": "2026-03-28 21:11:20", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Topological Model of Neural Information Networks", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 Springer Nature Switzerland AG 2021. \n\nFirst Online: 14 July 2021. \n\nSupported by Foundational Questions Institute and Fetzer Franklin Fund FFF grant number FQXi-RFP-1804, SVCF grant 2018-190467 and FQXi-RFP-CPW-2014, SVCF grant 2020-224047.", "abstract": "This is a brief overview of an ongoing research project, involving topological models of neural information networks and the development of new versions of associated information measures that can be seen as possible alternatives to integrated information. Among the goals are a geometric modeling of a \"space of qualia\" and an associated mechanism that constructs and transforms representations from neural codes topologically. The more mathematical aspects of this project stem from the recent joint work of the author and Yuri Manin [18], while the neuroscience modeling aspects are part of an ongoing collaboration of the author with Doris Tsao.", "date": "2021-07-14", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham", "pagerange": "623-633", "id_number": "CaltechAUTHORS:20211222-457136400", "isbn": "9783030802080", "book_title": "Geometric Science of Information", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20211222-457136400", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Foundational Questions Institute (FQXI)", "grant_number": "FQXi-RFP-1804" }, { "agency": "Silicon Valley Community Foundation", "grant_number": "2018-190467" }, { "agency": "Foundational Questions Institute (FQXI)", "grant_number": "RFP-CPW-2014" }, { "agency": "Silicon Valley Community Foundation", "grant_number": "2020-224047" }, { "agency": "Fetzer Franklin Fund" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Nielsen-Frank", "name": { "family": "Nielsen", "given": "Frank" } }, { "id": "Barbaresco-Fr\u00e9d\u00e9ric", "name": { "family": "Barbaresco", "given": "Fr\u00e9d\u00e9ric" } } ] }, "doi": "10.1007/978-3-030-80209-7_67", "pub_year": "2021", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/x92h8-9bn53", "eprint_id": 88623, "eprint_status": "archive", "datestamp": "2023-08-22 05:38:56", "lastmod": "2026-03-29 20:45:05", "type": "book_section", "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, III. Sets Saturating Szeg\u0151, Schiefermayr, and Totik--Widom Bounds", "ispublished": "unpub", "full_text_status": "public", "keywords": "Chebyshev polynomials; Szeg\u0151 lower bound; Schiefermayr lower bound; Totik\u2013Widom upper bound", "note": "\u00a9 2020 Springer Nature Switzerland AG. \n\nFirst Online: 15 July 2020. \n\nJ. S. Christiansen's research supported in part by Project Grant DFF-4181-00502 from the Danish Council for Independent Research. B. Simon's research supported in part by NSF grants DMS-1265592 and DMS-1665526 and in part by Israeli BSF Grant No. 2014337. M. Zinchenko's research supported in part by Simons Foundation grant CGM\u2013281971.\n\n

Submitted - 1712.03482.pdf

", "abstract": "We determine which sets saturate the Szeg\u0151 and Schiefermayr lower bounds on the norms of Chebyshev Polynomials. We also discuss sets that saturate our optimal Totik\u2013Widom upper bound.", "date": "2020-07-15", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham", "pagerange": "231-246", "id_number": "CaltechAUTHORS:20180807-111909106", "isbn": "978-3-030-31530-6", "book_title": "Analysis as a Tool in Mathematical Physics: In Memory of Boris Pavlov", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180807-111909106", "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": "Simons Foundation", "grant_number": "CGM-281971" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Kurasov-P", "name": { "family": "Kurasov", "given": "Pavel" } }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } }, { "id": "Naboko-S", "name": { "family": "Naboko", "given": "Sergey" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" } } ] }, "doi": "10.1007/978-3-030-31531-3_15", "primary_object": { "basename": "1712.03482.pdf", "url": "https://authors.library.caltech.edu/records/x92h8-9bn53/files/1712.03482.pdf" }, "pub_year": "2020", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/r0r4n-zhw14", "eprint_id": 103930, "eprint_status": "archive", "datestamp": "2023-08-22 05:30:11", "lastmod": "2026-03-29 00:16:43", "type": "book_section", "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": "unpub", "full_text_status": "public", "keywords": "Bayesian updating; Bayesian games; Bayesian persuasion; splitting lemma; no-trade theorem; extreme points; social learning; joint distribution; belief hierarchy", "note": "\u00a9 2020 Copyright held by the owner/author(s). \n\nThe paper greatly benefited from multiple suggestions and comments of our colleagues. We are grateful (in alphabetic order) to Kim Border, Laura Doval, Sergiu Hart, Kevin He, Aviad Heifetz, Yuval Heller, Matthew Jackson, Benny Moldovanu, Jeffrey Mensch, Alexander Nesterov, Michael Ostrovsky, Thomas Palfrey, Luciano Pomatto, Marco Scarsini, Eilon Solan, Gabriel Ziegler, and seminar participants at Bar-Ilan Univeristy, Caltech, HSE St. Petersburg, Technion, Stanford, and UC San Diego. Itai Arieli is supported by the Ministry of Science and Technology (#2028255). Yakov Babichenko is supported by a BSF award (#2018397). Fedor Sandomirskiy is partially 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. Omer Tamuz is supported by a grant from the Simons Foundation (#419427) and by a BSF award (#2018397).\n\n

Published - 3391403.3399505.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. Our main result is that, for the two agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. For any number of agents, a related \"no trade\" condition likewise provides a characterization of feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.", "date": "2020-07", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "643", "id_number": "CaltechAUTHORS:20200615-155012317", "isbn": "978-1-4503-7975-5", "book_title": "Proceedings of the 21st ACM Conference on Economics and Computation", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200615-155012317", "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": "Binational Science Foundation (USA-Israel)", "grant_number": "2018397" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/3391403.3399505", "primary_object": { "basename": "2002.11362.pdf", "url": "https://authors.library.caltech.edu/records/r0r4n-zhw14/files/2002.11362.pdf" }, "related_objects": [ { "basename": "3391403.3399505.pdf", "url": "https://authors.library.caltech.edu/records/r0r4n-zhw14/files/3391403.3399505.pdf" } ], "pub_year": "2020", "author_list": "Arieli, Itai; Babichenko, Yakov; et al." }, { "id": "https://authors.library.caltech.edu/records/5390y-6yb83", "eprint_id": 105442, "eprint_status": "archive", "datestamp": "2023-08-19 19:18:00", "lastmod": "2026-03-09 21:40:50", "type": "book_section", "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": "Homotopy types and geometries below Spec(\u2124)", "ispublished": "unpub", "full_text_status": "public", "keywords": "Weil numbers, Bost\u2013Connes systems, zeta functions, motivic integration,\ngeometries below Spec Z, assemblers", "note": "\u00a9 2020 American Mathematical Society. \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 Inna Zakharevich for several useful suggestions that were incorporated in the final version of the article.\n\n

Submitted - 1806.10801.pdf

", "abstract": "After the first heuristic ideas about 'the field of one element' F\u2081 and 'geometry in characteristics 1' (J. Tits, C. Deninger, M. Kapranov, A. Smirnov et al.), there were developed several general approaches to the construction of 'geometries below Spec Z'. Homotopy theory and the 'the brave new algebra' were taking more and more important places in these developments, systematically explored by B. To\u00ebn and M. Vaqui\u00e9, among others.\nThis article contains a brief survey and some new results on counting problems in this context, including various approaches to zeta--functions and generalised scissors congruences.\nThe new version includes considerable extensions and revisions suggested by I. Zakharevich.", "date": "2020", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "27-56", "id_number": "CaltechAUTHORS:20200918-070725967", "isbn": "978-1-4704-5100-4", "book_title": "Dynamics: Topology and Numbers", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200918-070725967", "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" } ] }, "contributors": { "items": [ { "id": "Moree-P", "name": { "family": "Moree", "given": "Pieter" } }, { "id": "Pohl-A", "name": { "family": "Pohl", "given": "Anke" } }, { "id": "Snoha-L", "name": { "family": "Snoha", "given": "L'ubom\u00edr" } }, { "id": "Ward-T", "name": { "family": "Ward", "given": "Tom" } } ] }, "doi": "10.1090/conm/744/14978", "primary_object": { "basename": "1806.10801.pdf", "url": "https://authors.library.caltech.edu/records/5390y-6yb83/files/1806.10801.pdf" }, "pub_year": "2020", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/xx7r1-n0q03", "eprint_id": 109734, "eprint_status": "archive", "datestamp": "2023-08-19 19:18:36", "lastmod": "2026-03-09 20:36:43", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Quasi-invariant measures for continuous group actions", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "group actions, invariant measures, quasi-invariant measures, ergodic measures", "note": "\u00a9 2020 American Mathematical Society. \n\nThe author was partially supported by NSF grant DMS-1464475.", "abstract": "The class of ergodic, invariant probability Borel measure for the shift action of a countable group is a G_\u03b4 set in the compact, metrizable space of probability Borel measures. We study in this paper the descriptive complexity of the class of ergodic, quasi-invariant probability Borel measures and show that for any infinite countable group \u0393 it is \u03a0\u2070\u2083-hard, for the group Z it is \u03a0\u2070\u2083-complete, while for the free group F_\u221e with infinite, countably many generators it is \u03a0\u2070_\u03b1-complete, for some ordinal \u03b1 with 3 \u2264 \u03b1 \u2264 \u03c9 +2. The exact value of this ordinal is unknown.", "date": "2020", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "113-119", "id_number": "CaltechAUTHORS:20210707-142840752", "isbn": "978-1-4704-4332-0", "book_title": "Trends in Set Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210707-142840752", "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" } ] }, "contributors": { "items": [ { "id": "Coskey-Samuel", "name": { "family": "Coskey", "given": "Samuel" } }, { "id": "Sargsyan-Grigor", "name": { "family": "Sargsyan", "given": "Grigor" } } ] }, "doi": "10.1090/conm/752/15132", "pub_year": "2020", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/yk4qj-72d73", "eprint_id": 97611, "eprint_status": "archive", "datestamp": "2023-08-22 02:13:47", "lastmod": "2026-03-31 14:33:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Li-Wanlin", "name": { "family": "Li", "given": "Wanlin" } }, { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } }, { "id": "Pries-R", "name": { "family": "Pries", "given": "Rachel" } }, { "id": "Tang-Yunqing", "name": { "family": "Tang", "given": "Yunqing" } } ] }, "title": "Newton Polygons of Cyclic Covers of the Projective Line Branched at Three Points", "ispublished": "unpub", "full_text_status": "public", "keywords": "Curve; Cyclic cover; Jacobian; Abelian variety; Moduli space; Reduction; Supersingular; Newton polygon; p-rank; Dieudonn\u00e9 module; p-divisible group; Complex multiplication; Shimura\u2013Taniyama method", "note": "\u00a9 2019 The Author(s) and The Association for Women in Mathematics. \n\nFirst Online: 02 August 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 the referee for the valuable feedback and comments.\n\n

Submitted - 1805.04598.pdf

", "abstract": "We review the Shimura\u2013Taniyama method for computing the Newton polygon of an abelian variety with complex multiplication. We apply this method to cyclic covers of the projective line branched at three points. As an application, we produce multiple new examples of Newton polygons that occur for Jacobians of smooth curves in characteristic p. Under certain congruence conditions on p, these include: the supersingular Newton polygon for each genus g with 4\u2009\u2264\u2009g\u2009\u2264\u200911; nine non-supersingular Newton polygons with p-rank 0 with 4\u2009\u2264\u2009g\u2009\u2264\u200911; and, for all g\u2009\u2265\u20095, the Newton polygon with p-rank g\u2009\u2212\u20095 having slopes 1\u22155 and 4\u22155.", "date": "2019-08-02", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham", "pagerange": "115-132", "id_number": "CaltechAUTHORS:20190801-153624143", "isbn": "978-3-030-19477-2", "book_title": "Research Directions in Number Theory - Women in Numbers IV", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190801-153624143", "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" } ] }, "contributors": { "items": [ { "id": "Balakrishnan-J-S", "name": { "family": "Balakrishnan", "given": "Jennifer S." } }, { "id": "Folsom-A", "name": { "family": "Folsom", "given": "Amanda" } }, { "id": "Lal\u00edn-M", "name": { "family": "Lal\u00edn", "given": "Matilde" } }, { "id": "Manes-M", "name": { "family": "Manes", "given": "Michelle" } } ] }, "doi": "10.1007/978-3-030-19478-9_5", "primary_object": { "basename": "1805.04598.pdf", "url": "https://authors.library.caltech.edu/records/yk4qj-72d73/files/1805.04598.pdf" }, "pub_year": "2019", "author_list": "Li, Wanlin; Mantovan, Elena; et al." }, { "id": "https://authors.library.caltech.edu/records/b3s3s-wtn44", "eprint_id": 96021, "eprint_status": "archive", "datestamp": "2023-08-19 16:10:59", "lastmod": "2026-03-31 15:15:18", "type": "book_section", "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": "unpub", "full_text_status": "public", "note": "\u00a9 Springer Nature Switzerland AG 2019.", "abstract": "We present the highpoints of Tosio Kato's work on the mathematics behind Non-relativistic Quantum Mechanics.", "date": "2019-06-01", "date_type": "published", "publisher": "Springer International Publishing", "place_of_pub": "Cham, Switzerland", "pagerange": "353-378", "id_number": "CaltechAUTHORS:20190531-154921211", "isbn": "9783030126605", "book_title": "Analysis and Operator Theory: Dedicated in Memory of Tosio Kato's 100th Birthday", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190531-154921211", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Rassias-T-M", "name": { "family": "Rassias", "given": "Themistocles M." } }, { "id": "Zagrebnov-V-A", "name": { "family": "Zagrebnov", "given": "Valentin A." } } ] }, "doi": "10.1007/978-3-030-12661-2_16", "pub_year": "2019", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/8mk1w-9ze73", "eprint_id": 96700, "eprint_status": "archive", "datestamp": "2023-08-19 16:04:21", "lastmod": "2026-03-31 14:03:20", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Bartholdi-L", "name": { "family": "Bartholdi", "given": "Laurent" } }, { "id": "Hann-Caruthers-W", "name": { "family": "Hann-Caruthers", "given": "Wade" } }, { "id": "Josyula-M", "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": "unpub", "full_text_status": "public", "keywords": "social choice", "note": "\u00a9 2019 ACM.\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

Submitted - 1811.01227.pdf

", "abstract": "A celebrated result in social choice is May's Theorem (1952), providing 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 modification of May's symmetry assumption allows for a far richer set of rules that still treat voters equally, but have minimal winning coalitions comprising a vanishing fraction of the population. We conclude that procedural fairness can coexist with the empowerment of a small minority of individuals. Methodologically, we introduce techniques from discrete mathematics and illustrate their usefulness for the analysis of social choice questions.", "date": "2019-06", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "315", "id_number": "CaltechAUTHORS:20190625-114737785", "isbn": "978-1-4503-6792-9", "book_title": "Proceedings of the 2019 ACM Conference on Economics and Computation", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190625-114737785", "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": "10.1145/3328526.3329551", "primary_object": { "basename": "1811.01227.pdf", "url": "https://authors.library.caltech.edu/records/8mk1w-9ze73/files/1811.01227.pdf" }, "pub_year": "2019", "author_list": "Bartholdi, Laurent; Hann-Caruthers, Wade; et al." }, { "id": "https://authors.library.caltech.edu/records/7sx75-zgn87", "eprint_id": 100570, "eprint_status": "archive", "datestamp": "2023-09-15 06:26:02", "lastmod": "2026-03-31 22:15:51", "type": "book_section", "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" } } ] }, "title": "The BCS Critical Temperature in a Weak External Electric Field via a Linear Two-Body Operator", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 by the authors. This paper may be reproduced, in its entirety, for noncommercial purposes. \u00a9 2018 Springer Nature Switzerland AG. \n\nFirst Online: 27 October 2018. \n\nDedicated to Herbert Spohn on the occasion of his seventieth birthday. \n\nWe thank Edwin Langmann who initiated and coauthored our previous work [2] which forms the basis of the present paper. We further thank Robert Seiringer and Jan Philip Solovej for our long-lasting collaboration on BCS theory. Further, partial support by the U.S. National Science Foundation through grant DMS-1363432 (R.L.F.) is acknowledged.\n\n

Published - Frank-Hainzl2018_Chapter_TheBCSCriticalTemperatureInAWe.pdf

Submitted - 1809.08667.pdf

", "abstract": "We study the critical temperature of a superconductive material in a weak external electric potential via a linear approximation of the BCS functional. We reproduce a similar result as in Frank et al. (Commun Math Phys 342(1):189\u2013216, 2016, [5]) using the strategy introduced in Frank et al. (The BCS critical temperature in a weak homogeneous magnetic field, [2]), where we considered the case of an external constant magnetic field.", "date": "2018-10-27", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham", "pagerange": "29-62", "id_number": "CaltechAUTHORS:20200109-070444248", "isbn": "978-3-030-01601-2", "book_title": "Macroscopic Limits of Quantum Systems", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200109-070444248", "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" } ] }, "contributors": { "items": [ { "id": "Cadamuro-D", "name": { "family": "Cadamuro", "given": "Daniela" } }, { "id": "Duell-M", "name": { "family": "Duell", "given": "Maximilian" } }, { "id": "Dybalski-W", "name": { "family": "Dybalski", "given": "Wojciech" } }, { "id": "Simonella-S", "name": { "family": "Simonella", "given": "Sergio" } } ] }, "doi": "10.1007/978-3-030-01602-9_2", "primary_object": { "basename": "1809.08667.pdf", "url": "https://authors.library.caltech.edu/records/7sx75-zgn87/files/1809.08667.pdf" }, "related_objects": [ { "basename": "Frank-Hainzl2018_Chapter_TheBCSCriticalTemperatureInAWe.pdf", "url": "https://authors.library.caltech.edu/records/7sx75-zgn87/files/Frank-Hainzl2018_Chapter_TheBCSCriticalTemperatureInAWe.pdf" } ], "pub_year": "2018", "author_list": "Frank, Rupert L. and Hainzl, Christian" }, { "id": "https://authors.library.caltech.edu/records/am3x5-nbb28", "eprint_id": 95424, "eprint_status": "archive", "datestamp": "2023-09-15 06:18:11", "lastmod": "2026-03-31 22:18:09", "type": "book_section", "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": "A short proof of the ionization conjecture in M\u00fcller theory", "ispublished": "unpub", "full_text_status": "public", "keywords": "Maximal ionization, M\u00fcller density-matrix-functional theory", "note": "\u00a9 2019 American Mathematical Society. \n\nThe first author was supported in part by U.S. NSF Grant DMS-1363432. \n\nThe third author was supported in part by Conicyt (Chile) through CONICYT\u2013PCHA/Doctorado Nacional/2014 Project # 116\u20130856 and Iniciativa Cient\u00edfica Milenio (Chile) through Millenium Nucleus RC\u2013120002 \"F\u00edsica Matem\u00e1tica\".\n\n

Submitted - 1807.11690.pdf

", "abstract": "We prove that in M\u00fcller theory, a nucleus of charge Z can bind at most Z+C electrons for a constant C independent of Z.", "date": "2018-10-25", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "1-12", "id_number": "CaltechAUTHORS:20190513-100341402", "isbn": "978-1-4704-3681-0", "book_title": "Mathematical Problems in Quantum Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190513-100341402", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1363432" }, { "agency": "Comisi\u00f3n Nacional de Investigaci\u00f3n Cient\u00edfica y Tecnol\u00f3gica (CONICYT)", "grant_number": "116\u20130856" }, { "agency": "Iniciativa Cient\u00edfica Milenio", "grant_number": "RC-120002" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Bonetto-F", "name": { "family": "Bonetto", "given": "F." } }, { "id": "Borthwick-D", "name": { "family": "Borthwick", "given": "David" } }, { "id": "Harrell-E-M", "name": { "family": "Harrell", "given": "Evans M." } }, { "id": "Loss-M", "name": { "family": "Loss", "given": "Michael" } } ] }, "doi": "10.1090/conm/717/14437", "primary_object": { "basename": "1807.11690.pdf", "url": "https://authors.library.caltech.edu/records/am3x5-nbb28/files/1807.11690.pdf" }, "pub_year": "2018", "author_list": "Frank, Rupert L.; Nam, Phan Th\u00e0nh; et al." }, { "id": "https://authors.library.caltech.edu/records/a6azn-28e15", "eprint_id": 94296, "eprint_status": "archive", "datestamp": "2023-08-19 11:30:25", "lastmod": "2026-03-31 21:23:44", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Grayson-D-R", "name": { "family": "Grayson", "given": "Daniel R." } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Eisenstein Series of Weight One, q-Averages of the 0-Logarithm and Periods of Elliptic Curves", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 Springer Nature Switzerland AG. \n\nFirst Online: 18 September 2018. \n\nD. R. Grayson and D. Ramakrishnan Research supported by the NSF; D. Ramakrishnan supported by a Simons Fellowship.\n\n

Submitted - 1806.04925.pdf

", "abstract": "For any elliptic curve E over k \u2282 R with E(C) = C^\u00d7/q^Z, q = e^(2\u03c0iz),Im(z) >, we study the q-average D_(0,q), defined on E(C), of the function D_0(z) = Im(z/(1\u2212z)). Let \u03a9+(E) denote the real period of E. We show that there is a rational function R \u2208 Q(X_1(N)) such that for any non-cuspidal real point s \u2208 X_1(N) (which defines an elliptic curve E(s) over R together with a point P(s) of order N), \u03c0D_(0,q)(P(s)) equals \u03a9+(E(s))R(s). In particular, if s is Q-rational point of X_1(N), a rare occurrence according to Mazur, R(s) is a rational number.", "date": "2018-09-18", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "245-266", "id_number": "CaltechAUTHORS:20190329-145231143", "isbn": "978-3-319-97378-4", "book_title": "Geometry, Algebra, Number Theory, and Their Information Technology Applications", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190329-145231143", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Simons Foundation" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Akbary-A", "name": { "family": "Akbary", "given": "Amir" } }, { "id": "Gun-S", "name": { "family": "Gun", "given": "Sanoli" } } ] }, "doi": "10.1007/978-3-319-97379-1_11", "primary_object": { "basename": "1806.04925.pdf", "url": "https://authors.library.caltech.edu/records/a6azn-28e15/files/1806.04925.pdf" }, "pub_year": "2018", "author_list": "Grayson, Daniel R. and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/s2z9p-cek47", "eprint_id": 91194, "eprint_status": "archive", "datestamp": "2023-08-19 09:36:10", "lastmod": "2026-03-31 21:25:40", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Cheng-Yu", "name": { "family": "Cheng", "given": "Yu" } }, { "id": "Hann-Caruthers-W", "name": { "family": "Hann-Caruthers", "given": "Wade" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "A Deterministic Protocol for Sequential Asymptotic Learning", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 IEEE. \n\nPart of this work was done while Yu Cheng was a student at the University of Southern California. Yu Cheng was supported in part by Shang-Hua Teng's Simons Investigator Award. Omer Tamuz was supported in part by grant #419427 from the Simons Foundation.\n\n

Submitted - 1802.06871.pdf

", "abstract": "In the classic herding model, agents receive private signals about an underlying binary state of nature, and act sequentially to choose one of two possible actions, after observing the actions of their predecessors. We investigate what types of behaviors lead to asymptotic learning, where agents will eventually converge to the right action in probability. It is known that for rational agents and bounded signals, there will not be asymptotic learning. Does it help if the agents can be cooperative rather than act selfishly? This is simple to achieve if the agents are allowed to use randomized protocols. In this paper, we provide the first deterministic protocol under which asymptotic learning occurs. In addition, our protocol has the advantage of being much simpler than previous protocols.", "date": "2018-06", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "1735-1738", "id_number": "CaltechAUTHORS:20181126-153354872", "isbn": "978-1-5386-4780-6", "book_title": "2018 IEEE International Symposium on Information Theory (ISIT)", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20181126-153354872", "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": "10.1109/ISIT.2018.8437859", "primary_object": { "basename": "1802.06871.pdf", "url": "https://authors.library.caltech.edu/records/s2z9p-cek47/files/1802.06871.pdf" }, "pub_year": "2018", "author_list": "Cheng, Yu; Hann-Caruthers, Wade; et al." }, { "id": "https://authors.library.caltech.edu/records/ays2h-xav26", "eprint_id": 71939, "eprint_status": "archive", "datestamp": "2023-08-21 23:24:23", "lastmod": "2026-03-31 22:11:41", "type": "book_section", "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": "unpub", "full_text_status": "public", "keywords": "Consensus; Learning; Herding", "note": "\u00a9 2018 Copyright held by the owner/author(s). \n\nElchanan Mossel is supported by awards NSF DMS-1737944, ONR N00014-17-1-2598, and CCF 1665252. Manuel Mueller-Frank gratefully acknowledges the financial support of the Spanish Ministry of Economy and Competitiveness (Ref. ECO2015-63711-P). Omer Tamuz is supported by a grant from the Simons Foundation (#419427).\n\n

Accepted Version - 1207.5895.pdf

", "abstract": "We consider social learning settings in which a group of agents face uncertainty regarding a state of the world, observe private signals, share the same utility function, and act in a general dynamic setting. We introduce Social Learning Equilibria, a static equilibrium concept that abstracts away from the details of the given dynamics, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish strong equilibrium properties on agreement, herding, and information aggregation.", "date": "2018-06", "date_type": "published", "publisher": "Association for Computing Machinery", "place_of_pub": "New York, NY", "pagerange": "639", "id_number": "CaltechAUTHORS:20161111-104138106", "isbn": "978-1-4503-5829-3", "book_title": "Proceedings of the 2018 ACM Conference on Economics and Computation", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161111-104138106", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1737944" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-17-1-2598" }, { "agency": "NSF", "grant_number": "CCF-1665252" }, { "agency": "Ministerio de Econom\u00eda, Industria y Competitividad (MINECO)", "grant_number": "ECO2015-63711-P" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1145/3219166.3219207", "primary_object": { "basename": "1207.5895.pdf", "url": "https://authors.library.caltech.edu/records/ays2h-xav26/files/1207.5895.pdf" }, "pub_year": "2018", "author_list": "Mossel, Elchanan; Mueller-Frank, Manuel; et al." }, { "id": "https://authors.library.caltech.edu/records/8nc85-zp950", "eprint_id": 86661, "eprint_status": "archive", "datestamp": "2023-08-19 09:22:09", "lastmod": "2026-03-31 22:02:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Shu-Kevin", "name": { "family": "Shu", "given": "Kevin" } }, { "id": "Aziz-S", "name": { "family": "Aziz", "given": "Sharjeel" } }, { "id": "Huynh-Vy-Luan", "name": { "family": "Huynh", "given": "Vy-Luan" } }, { "id": "Warrick-D", "name": { "family": "Warrick", "given": "David" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Syntactic Phylogenetic Trees", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2018 Springer International Publishing AG, part of Springer Nature. \n\nFirst Online: 27 May 2018. \n\nThe first author is supported by a Summer Undergraduate Research Fellowship at Caltech. Part of this work was performed as part of the activities of the last author's Mathematical and Computational Linguistics lab and CS101/Ma191 class at Caltech. The last author is partially supported by NSF grants DMS-1201512 and PHY-1205440 and DMS-1707882.", "abstract": "In light of recent controversies surrounding the use of computational methods for the reconstruction of phylogenetic trees of language families (especially the Indo-European family), a possible approach based on syntactic information, complementing other linguistic methods, appeared as a promising possibility, largely developed in recent years in Longobardi's Parametric Comparison Method. In this paper we identify several serious problems that arise in the use of syntactic data from the SSWL database for the purpose of computational phylogenetic reconstruction. We show that the most naive approach fails to produce reliable linguistic phylogenetic trees. We identify some of the sources of the observed problems and we discuss how they may be, at least partly, corrected by using additional information, such as prior subdivision into language families and subfamilies, and a better use of the information about ancient languages. We also describe how the use of phylogenetic algebraic geometry can help in estimating to what extent the probability distribution at the leaves of the phylogenetic tree obtained from the SSWL data can be considered reliable, by testing it on phylogenetic trees established by other forms of linguistic analysis. In simple examples, we find that, after restricting to smaller language subfamilies and considering only those SSWL parameters that are fully mapped for the whole subfamily, the SSWL data match extremely well reliable phylogenetic trees, according to the evaluation of phylogenetic invariants. This is a promising sign for the use of SSWL data for linguistic phylogenetics. We also argue how dependencies and nontrivial geometry/topology in the space of syntactic parameters would have to be taken into consideration in phylogenetic reconstructions based on syntactic data. A more detailed analysis of syntactic phylogenetic trees and their algebro-geometric invariants will appear elsewhere [33].", "date": "2018-05-27", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "417-441", "id_number": "CaltechAUTHORS:20180529-110159594", "isbn": "978-3-319-64812-5", "book_title": "Foundations of Mathematics and Physics One Century After Hilbert", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180529-110159594", "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": "NSF", "grant_number": "DMS-1707882" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kouneiher-J", "name": { "family": "Kouneiher", "given": "Joseph" } } ] }, "doi": "10.1007/978-3-319-64813-2_14", "pub_year": "2018", "author_list": "Shu, Kevin; Aziz, Sharjeel; et al." }, { "id": "https://authors.library.caltech.edu/records/899h4-y2s31", "eprint_id": 99216, "eprint_status": "archive", "datestamp": "2023-08-21 22:43:35", "lastmod": "2026-03-10 00:00:15", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Vardi-S", "name": { "family": "Vardi", "given": "Shai" } }, { "id": "Ziani-Juba", "name": { "family": "Ziani", "given": "Juba" }, "orcid": "0000-0002-3324-4349" } ] }, "title": "Non-Exploitable Protocols for Repeated Cake Cutting", "ispublished": "unpub", "full_text_status": "public", "keywords": "cake cutting; fair division; dynamic fair division; repeated cake cutting; exploitability", "note": "\u00a9 2018 Association for the Advancement of Artificial Intelligence. \n\nOmer Tamuz was supported by a grant from the Simons Foundation (#419427). Shai Vardi was supported in part by the Linde Foundation and NSF grants CNS-1254169 and CNS-1518941. Juba Ziani was supported by NSF grants #1331343 and #1518941, and US-Israel Binational Science Foundation grant #201234.\n\n

Published - 17113-76573-1-PB.pdf

", "abstract": "We introduce the notion of exploitability in cut-and-choose protocols for repeated cake cutting. If a cut-and-choose protocol is repeated, the cutter can possibly gain information about the chooser from her previous actions, and exploit this information for her own gain, at the expense of the chooser. We define a generalization of cut-and-choose protocols - forced-cut protocols - in which some cuts are made exogenously while others are made by the cutter, and show that there exist non-exploitable forced-cut protocols that use a small number of cuts per day: When the cake has at least as many dimensions as days, we show a protocol that uses a single cut per day. When the cake is 1-dimensional, we show an adaptive non-exploitable protocol that uses 3 cuts per day, and a non-adaptive protocol that uses n cuts per day (where n is the number of days). In contrast, we show that no non-adaptive non-exploitable forced-cut protocol can use a constant number of cuts per day. Finally, we show that if the cake is at least 2-dimensional, there is a non-adaptive non-exploitable protocol that uses 3 cuts per day.", "date": "2018-02", "date_type": "published", "publisher": "Association for the Advancement of Artificial Intelligence", "id_number": "CaltechAUTHORS:20191010-132749128", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191010-132749128", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "419427" }, { "agency": "Linde Institute of Economic and Management Science" }, { "agency": "NSF", "grant_number": "CNS-1254169" }, { "agency": "NSF", "grant_number": "CNS-1518941" }, { "agency": "NSF", "grant_number": "CCF-1331343" }, { "agency": "NSF", "grant_number": "CNS-1518941" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2012348" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "primary_object": { "basename": "17113-76573-1-PB.pdf", "url": "https://authors.library.caltech.edu/records/899h4-y2s31/files/17113-76573-1-PB.pdf" }, "pub_year": "2018", "author_list": "Tamuz, Omer; Vardi, Shai; et al." }, { "id": "https://authors.library.caltech.edu/records/x2458-79e56", "eprint_id": 85735, "eprint_status": "archive", "datestamp": "2023-08-19 07:11:31", "lastmod": "2026-03-10 00:00:43", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kempe-D", "name": { "family": "Kempe", "given": "David" } }, { "id": "Schulman-L-J", "name": { "family": "Schulman", "given": "Leonard J." }, "orcid": "0000-0001-9901-2797" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Quasi-regular sequences and optimal schedules for security games", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 SIAM. \n\nSupported in parts by NSF grants 1619458 and 1423618. \n\nSupported in part by NSF grants 1319745, 1618795, and a EURIAS Senior Fellowship co-funded by the Marie Sk\u0142odowska-Curie Actions under the 7th Framework Programme. \n\nThis work was supported by a grant from the Simons Foundation (#419427, Omer Tamuz).\n\n

Published - p1625-kempe.pdf

Submitted - 1611.07169.pdf

", "abstract": "We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time t at a target i of value \u03b1_i, and if he leaves before the defender visits the target, his utility is t \u00b7 \u03b1_i; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc.\n\nWe show that optimal defender play for such security games, although played in continuous time, reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol i: (1) i constitutes a prescribed limiting fraction p_i of the sequence. (2) The occurrences of i are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter K. We call such sequences K-quasi-regular; a 1-quasi-regular sequence is one in which the occurrences of each symbol form an arithmetic sequence. \n\nAs we show, a 1-quasi-regular sequence ensures an optimal defender strategy for these security games: the intuition for this fact lies in the famous \"inspection paradox.\" However, as we demonstrate, for K < 2 and general p_i, K-quasi-regular sequences may not exist. Fortunately, this does not turn out to be an obstruction: we show that, surprisingly, 2-quasi-regular sequences also suffice for optimal defender play. What is more, even randomized 2-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. Thus, we can ensure optimal defender play for these security games. \n\nThe question of the least K for which deterministic K-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we proceed to show that deterministic 3-quasi-regular sequences always exist (and can be calculated efficiently). We also show that these deterministic 3-regular sequences give rise to a \u2248 1.006-approximation algorithm for the defender's optimal strategy. For 2 \u2264 K < 3 we do not know whether deterministic K-quasi-regular sequences always exist; however, when the pi are all small, improved bounds are possible, and in fact, (1 + \u220a)-quasi-regular deterministic sequences exist for any \u220a > 0 for sufficiently small p_i.", "date": "2018-01", "date_type": "published", "publisher": "Society for Industrial and Applied Mathematics", "place_of_pub": "Philadelphia, PA", "pagerange": "1625-1644", "id_number": "CaltechAUTHORS:20180410-145958889", "isbn": "978-1-6119-7503-1", "book_title": "Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180410-145958889", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1619458" }, { "agency": "NSF", "grant_number": "DMS-1423618" }, { "agency": "NSF", "grant_number": "DMS-1319745" }, { "agency": "NSF", "grant_number": "DMS-1618795" }, { "agency": "Marie Curie Fellowship" }, { "agency": "Simons Foundation", "grant_number": "419427" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Czumaj-A", "name": { "family": "Czumaj", "given": "Artur" } } ] }, "doi": "10.1137/1.9781611975031.106", "primary_object": { "basename": "1611.07169.pdf", "url": "https://authors.library.caltech.edu/records/x2458-79e56/files/1611.07169.pdf" }, "related_objects": [ { "basename": "p1625-kempe.pdf", "url": "https://authors.library.caltech.edu/records/x2458-79e56/files/p1625-kempe.pdf" } ], "pub_year": "2018", "author_list": "Kempe, David; Schulman, Leonard J.; et al." }, { "id": "https://authors.library.caltech.edu/records/5d27n-a1k66", "eprint_id": 111008, "eprint_status": "archive", "datestamp": "2023-08-19 07:05:23", "lastmod": "2026-03-09 02:34:52", "type": "book_section", "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" } ] }, "title": "Counterexamples for percolation on unimodular random graphs", "ispublished": "unpub", "full_text_status": "public", "keywords": "Unimodular random graphs, percolation, uniqueness, connectivity, nonamenable", "note": "\u00a9 2018 Omer Angel and Thomas Hutchcroft. \n\nThis was was carried out while TH was a PhD student at the University of British Columbia, during which time he was supported by a Microsoft Research PhD Fellowship.\n\n

Submitted - 1710.03003.pdf

", "abstract": "We construct an example of a bounded degree, nonamenable, unimodular random rooted graph with p_c = p_u for Bernoulli bond percolation, as well as an example of a bounded degree, unimodular random rooted graph with p_c < 1 but with an infinite cluster at criticality. These examples show that two well-known conjectures of Benjamini and Schramm are false when generalised from transitive graphs to unimodular random rooted graphs.", "date": "2018", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "11-28", "id_number": "CaltechAUTHORS:20210922-193309642", "isbn": "978-1-4704-3914-9", "book_title": "Unimodularity in randomly generated graphs", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20210922-193309642", "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" } ] }, "contributors": { "items": [ { "id": "Sobieczky-Florian", "name": { "family": "Sobieczky", "given": "Florian" }, "orcid": "0000-0001-5228-0153" } ] }, "doi": "10.1090/conm/719/14465", "primary_object": { "basename": "1710.03003.pdf", "url": "https://authors.library.caltech.edu/records/5d27n-a1k66/files/1710.03003.pdf" }, "pub_year": "2018", "author_list": "Angel, Omer and Hutchcroft, Tom" }, { "id": "https://authors.library.caltech.edu/records/g0301-tca57", "eprint_id": 79010, "eprint_status": "archive", "datestamp": "2023-08-19 05:43:47", "lastmod": "2026-04-01 07:50:40", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Park-Jeong-Joon", "name": { "family": "Park", "given": "Jeong Joon" } }, { "id": "Boettcher-R", "name": { "family": "Boettcher", "given": "Ronnel" } }, { "id": "Zhao-Andrew", "name": { "family": "Zhao", "given": "Andrew" } }, { "id": "Mun-Alex", "name": { "family": "Mun", "given": "Alex" } }, { "id": "Yuh-Kevin", "name": { "family": "Yuh", "given": "Kevin" } }, { "id": "Kumar-Vibhor", "name": { "family": "Kumar", "given": "Vibhor" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Prevalence and recoverability of syntactic parameters in sparse distributed memories", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 Springer International Publishing AG 2017. \n\nThis work was performed in 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-1201512 and PHY-1205440.\n\n

Submitted - 1510.06342.pdf

", "abstract": "We propose a new method, based on sparse distributed memory, for studying dependence relations between syntactic parameters in the Principles and Parameters model of Syntax. By storing data of syntactic structures of world languages in a Kanerva network and checking recoverability of corrupted data from the network, we identify two different effects: an overall underlying relation between the prevalence of parameters across languages and their degree of recoverability, and a finer effect that makes some parameters more easily recoverable beyond what their prevalence would indicate. The latter can be seen as an indication of the existence of dependence relations, through which a given parameter can be determined using the remaining uncorrupted data.", "date": "2017-10-24", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "265-272", "id_number": "CaltechAUTHORS:20170712-110411817", "isbn": "978-3-319-68444-4", "book_title": "Geometric Science of Information. GSI 2017", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-110411817", "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" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Nielsen-F", "name": { "family": "Nielsen", "given": "Frank" } }, { "id": "Barbaresco-F", "name": { "family": "Barbaresco", "given": "Fr\u00e9d\u00e9ric" } } ] }, "doi": "10.1007/978-3-319-68445-1_31", "primary_object": { "basename": "1510.06342.pdf", "url": "https://authors.library.caltech.edu/records/g0301-tca57/files/1510.06342.pdf" }, "pub_year": "2017", "author_list": "Park, Jeong Joon; Boettcher, Ronnel; et al." }, { "id": "https://authors.library.caltech.edu/records/t78t9-yyw71", "eprint_id": 66633, "eprint_status": "archive", "datestamp": "2023-08-21 21:28:52", "lastmod": "2026-04-01 06:44:30", "type": "book_section", "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": "Higher symmetry and gapped phases of gauge theories", "ispublished": "unpub", "full_text_status": "public", "keywords": "Symmetries; higher categories; topological phases of matter", "note": "\u00a9 2017 Springer International Publishing AG. \n\nFirst Online: 29 July 2017. \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 like to thank Scott Carnahan, Curt von Keyserlingk, 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

Submitted - 1309.4721.pdf

", "abstract": "We study topological field theory describing gapped phases of gauge theories where the gauge symmetry is partially Higgsed and partially confined. The TQFT can be formulated both in the continuum and on the lattice and generalizes Dijkgraaf\u2013Witten theory by replacing a finite group by a finite 2-group. The basic field in this TQFT is a 2-connection on a principal 2-bundle. We classify topological actions for such theories as well as loop and surface observables. When the topological action is trivial, the TQFT is related to a Dijkgraaf\u2013Witten theory by electric-magnetic duality, but in general it is distinct.We propose the existence of new phases of matter protected by higher symmetry.", "date": "2017-07-29", "date_type": "published", "publisher": "Birkh\u00e4user Verlag", "place_of_pub": "Cham, Switzerland", "pagerange": "177-202", "id_number": "CaltechAUTHORS:20160504-081444693", "isbn": "978-3-319-59938-0", "book_title": "Algebra, Geometry, and Physics in the 21st Century", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160504-081444693", "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": "PHYS-1066293" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Auroux-D", "name": { "family": "Auroux", "given": "Denis" } }, { "id": "Katzarkov-L", "name": { "family": "Katzarkov", "given": "Ludmil" } }, { "id": "Pantev-T", "name": { "family": "Pantev", "given": "Tony" } }, { "id": "Soibelman-Y", "name": { "family": "Soibelman", "given": "Yan" } }, { "id": "Tschinkel-Y", "name": { "family": "Tschinkel", "given": "Yuri" } } ] }, "doi": "10.1007/978-3-319-59939-7_5", "primary_object": { "basename": "1309.4721.pdf", "url": "https://authors.library.caltech.edu/records/t78t9-yyw71/files/1309.4721.pdf" }, "pub_year": "2017", "author_list": "Kapustin, Anton and Thorngren, Ryan" }, { "id": "https://authors.library.caltech.edu/records/4evw2-jxc52", "eprint_id": 97826, "eprint_status": "archive", "datestamp": "2023-08-19 03:06:10", "lastmod": "2026-04-01 19:46:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" }, { "id": "Dellamonica-Domingos", "name": { "family": "Dellamonica", "given": "Domingos" } }, { "id": "La-Fleur-Steven", "name": { "family": "La Fleur", "given": "Steven" } }, { "id": "R\u00f6dl-Vojt\u011bch", "name": { "family": "R\u00f6dl", "given": "Vojt\u011bch" } }, { "id": "Schacht-Mathias", "name": { "family": "Schacht", "given": "Mathias" } } ] }, "title": "A Note on Induced Ramsey Numbers", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 Springer International publishing AG 2017. \n\nFirst Online 09 May 2017. \n\nThe first author was supported by a Royal Society University Research Fellowship. The fourth author was partially supported by NSF grants DMS-1102086 and DMS-1301698. The fifth author was supported through the Heisenberg-Programme of the DFG. \n\nDedicated to the memory of Jirka Matou\u0161ek.\n\n

Submitted - 1601.01493.pdf

", "abstract": "The induced Ramsey number r_(ind)(F) of a k-uniform hypergraph F is the smallest natural number n for which there exists a k-uniform hypergraph G on n vertices such that every two-coloring of the edges of G contains an induced monochromatic copy of F. We study this function, showing that r_(ind)(F) is bounded above by a reasonable power of r(F). In particular, our result implies that r_(ind)(F) \u2264 2_(2_(ct)) for any 3-uniform hypergraph F with t vertices, mirroring the best known bound for the usual Ramsey number. The proof relies on an application of the hypergraph container method.", "date": "2017-05-09", "date_type": "published", "publisher": "Springer International Publishing", "place_of_pub": "Cham, Switzerland", "pagerange": "357-366", "id_number": "CaltechAUTHORS:20190812-162959255", "isbn": "9783319444789", "book_title": "A Journey Through Discrete Mathematics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959255", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Royal Society" }, { "agency": "NSF", "grant_number": "DMS-1102086" }, { "agency": "NSF", "grant_number": "DMS-1301698" }, { "agency": "Deutsche Forschungsgemeinschaft (DFG)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Loebl-Martin", "name": { "family": "Loebl", "given": "Martin" } }, { "id": "Ne\u0161et\u0159il-Jaroslav", "name": { "family": "Ne\u0161et\u0159il", "given": "Jaroslav" } }, { "id": "Thomas-Robin", "name": { "family": "Thomas", "given": "Robin" } } ] }, "doi": "10.1007/978-3-319-44479-6_13", "primary_object": { "basename": "1601.01493.pdf", "url": "https://authors.library.caltech.edu/records/4evw2-jxc52/files/1601.01493.pdf" }, "pub_year": "2017", "author_list": "Conlon, David; Dellamonica, Domingos; et al." }, { "id": "https://authors.library.caltech.edu/records/a92jc-dhm52", "eprint_id": 77271, "eprint_status": "archive", "datestamp": "2023-08-19 02:52:59", "lastmod": "2026-04-01 19:36:16", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "A Cayley-Hamiltonian Theorem for Periodic Finite Band Matrices", "ispublished": "unpub", "full_text_status": "public", "keywords": "Periodic Jacobi Matrices, Discriminant, Magic Formula", "note": "\u00a9 2017 EMS Publishing House. \n\nResearch supported in part by NSF grant DMS-1265592 and in part by Israeli BSF Grant No. 2014337.\n\n

Submitted - p337.pdf

", "abstract": "Let K be a doubly infinite, self-adjoint matrix which is finite band (i.e. K_(jk) = 0 if |j \u2013 k| > m) and periodic (K S^n = S^n K for some n where (Su)_j = u_(j+1)) and non-degenerate (i.e. K_(jj+m) \u2260 = 0 for all j). Then, there is a polynomial, p(x, y), in two variables with p(K, S^n) = 0. This generalizes the tridiagonal case where p(x, y) =\ny^2 - y\u0394(x) + 1 where \u0394 is the discriminant. I hope Pavel Exner will enjoy this birthday bouquet.", "date": "2017-05", "date_type": "published", "publisher": "EMS Publishing House", "place_of_pub": "Zurich, Switzerland", "pagerange": "525-529", "id_number": "CaltechAUTHORS:20170508-161208689", "isbn": "978-3-03719-175-0", "book_title": "Functional analysis and operator theory for quantum physics : Pavel Exner anniversary volume", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170508-161208689", "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": "2014337" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-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": "10.4171/175-1/25", "primary_object": { "basename": "p337.pdf", "url": "https://authors.library.caltech.edu/records/a92jc-dhm52/files/p337.pdf" }, "pub_year": "2017", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/939xq-kqn82", "eprint_id": 77111, "eprint_status": "archive", "datestamp": "2023-08-19 02:52:11", "lastmod": "2026-03-09 02:12:55", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Eigenvalues of Schr\u00f6dinger operators with complex surface potentials", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 EMS Publishing House. \n\nSupport through NSF grant DMS-1363432 is acknowledged.\n\n

Submitted - 1512.09067.pdf

", "abstract": "We consider Schr\u00f6dinger operators in R^d with complex potentials supported on a hyperplane and show that all eigenvalues lie in a disk in the complex plane with radius bounded in terms of the L^p norm of the potential with d\u22121", "date": "2017-05", "date_type": "published", "place_of_pub": "Z\u00fcrich", "pagerange": "245-259", "id_number": "CaltechAUTHORS:20170501-155923176", "isbn": "978-3-03719-175-0", "book_title": "Functional Analysis and Operator Theory for Quantum Physics: The Pavel Exner Anniversary Volume", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-155923176", "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" } ] }, "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" } }, { "id": "Exner-P", "name": { "family": "Exner", "given": "Pavel" } } ] }, "doi": "10.4171/175", "primary_object": { "basename": "1512.09067.pdf", "url": "https://authors.library.caltech.edu/records/939xq-kqn82/files/1512.09067.pdf" }, "pub_year": "2017", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/xdrzd-r5344", "eprint_id": 77096, "eprint_status": "archive", "datestamp": "2023-08-19 00:41:10", "lastmod": "2026-03-09 02:15:38", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frank-R-L", "name": { "family": "Frank", "given": "Rupert L." }, "orcid": "0000-0001-7973-4688" } ] }, "title": "Eigenvalue bounds for the fractional Laplacian: A review", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2018 Rupert L. Frank, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 License. \n\nThe author would like to thank B. Dyda, L.Geisinger, E. Lenzmann, E. Lieb, R. Seiringer and L. Silvestre for collaborations involving the fractional Laplacian. He thanks R. Ba\u00f1uelos, M. Kwa\u015bnicki, F. Maggi and R. Song for helpful comments. Partial support by U.S. National Science Foundation DMS-1363432 is acknowledged.\n\n

Published - _9783110571561_-_Recent_Developments_in_Nonlocal_Theory__Eigenvalue_Bounds_for_the_Fractional_Laplacian_A_Review.pdf

Submitted - 1603.09736.pdf

", "abstract": "We review some recent results on eigenvalues of fractional Laplacians and fractional Schr\u00f6dinger operators.We discuss, in particular, Lieb\u2013Thirring inequalities and their generalizations, as well as semi-classical asymptotics.", "date": "2017", "date_type": "published", "publisher": "De Gruyter", "place_of_pub": "Berlin", "pagerange": "210-235", "id_number": "CaltechAUTHORS:20170501-092157290", "isbn": "9783110571561", "book_title": "Recent Developments in Nonlocal Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-092157290", "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" } ] }, "contributors": { "items": [ { "id": "Palatucci-Giampiero", "name": { "family": "Palatucci", "given": "Giampiero" } }, { "id": "Kuusi-Tuomo", "name": { "family": "Kuusi", "given": "Tuomo" } } ] }, "doi": "10.1515/9783110571561-007", "primary_object": { "basename": "1603.09736.pdf", "url": "https://authors.library.caltech.edu/records/xdrzd-r5344/files/1603.09736.pdf" }, "related_objects": [ { "basename": "_9783110571561_-_Recent_Developments_in_Nonlocal_Theory__Eigenvalue_Bounds_for_the_Fractional_Laplacian_A_Review.pdf", "url": "https://authors.library.caltech.edu/records/xdrzd-r5344/files/_9783110571561_-_Recent_Developments_in_Nonlocal_Theory__Eigenvalue_Bounds_for_the_Fractional_Laplacian_A_Review.pdf" } ], "pub_year": "2017", "author_list": "Frank, Rupert L." }, { "id": "https://authors.library.caltech.edu/records/hv2fa-w5m79", "eprint_id": 81892, "eprint_status": "archive", "datestamp": "2023-08-19 00:42:20", "lastmod": "2026-03-07 04:14:13", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "The subgroup structure of finite groups", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 American Mathematical Society.", "abstract": "[No abstract]", "date": "2017", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "111-121", "id_number": "CaltechAUTHORS:20170928-081918166", "isbn": "978-1-4704-3678-0", "book_title": "Finite Simple Groups: Thirty Years of the Atlas and Beyond", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170928-081918166", "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" } ] }, "contributors": { "items": [ { "id": "Bhargava-M", "name": { "family": "Bhargava", "given": "Manjul" } }, { "id": "Guralnick-R", "name": { "family": "Guralnick", "given": "Robert" } }, { "id": "Hiss-G", "name": { "family": "Hiss", "given": "Gerhard" } }, { "id": "Lux-K", "name": { "family": "Lux", "given": "Klaus" } }, { "id": "Tiep-Pham-Huu", "name": { "family": "Tiep", "given": "Pham Huu" } } ] }, "doi": "10.1090/conm/694/13959", "pub_year": "2017", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/4c0nr-xb414", "eprint_id": 78728, "eprint_status": "archive", "datestamp": "2023-08-19 00:41:44", "lastmod": "2026-03-09 20:41:10", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Soki\u0107-M", "name": { "family": "Soki\u0107", "given": "M." } }, { "id": "Todor\u010devi\u0107-S", "name": { "family": "Todorcevic", "given": "S." } } ] }, "title": "Ramsey properties of finite measure algebras and topological dynamics of the group of measure preserving automorphisms: Some results and an open problem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2017 American Mathematical Society. \n\nA.S.K. was partially supported by NSF grants DMS-0455285, DMS-0968710 and DMS-1464475. \n\nS.T. was partially supported by grants from NSERC and CNRS.\n\n

Accepted Version - KechrisSokicTodorcevic01.pdf

", "abstract": "We study in this paper ordered finite measure algebras from the point of view of Fra\u00efss\u00e9 and Ramsey theory. We also propose an open problem, which is a homogeneous version of the Dual Ramsey Theorem of Graham-Rothschild, and derive consequences of a positive answer to the study of the\ntopological dynamics of the automorphism group of a standard probability space and also the group of measure preserving homeomorphisms of the Cantor space.", "date": "2017", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "69-85", "id_number": "CaltechAUTHORS:20170630-111205546", "isbn": "978-1-4704-2256-1", "book_title": "Foundations of Mathematics: Logic at Harvard: Essays in Honor of W. Hugh Woodin's 60th Birthday", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170630-111205546", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0455285" }, { "agency": "NSF", "grant_number": "DMS-0968710" }, { "agency": "NSF", "grant_number": "DMS-1464475" }, { "agency": "Natural Sciences and Engineering Research Council of Canada (NSERC)" }, { "agency": "Centre National de la Recherche Scientifique (CNRS)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Caicedo-A-E", "name": { "family": "Caicedo", "given": "Andr\u00e9s Eduardo" } }, { "id": "Cummings-J", "name": { "family": "Cummings", "given": "James" } }, { "id": "Koellner-P", "name": { "family": "Koellner", "given": "Peter" } }, { "id": "Larson-P-B", "name": { "family": "Larson", "given": "Paul B." } } ] }, "doi": "10.1090/conm/690", "primary_object": { "basename": "KechrisSokicTodorcevic01.pdf", "url": "https://authors.library.caltech.edu/records/4c0nr-xb414/files/KechrisSokicTodorcevic01.pdf" }, "pub_year": "2017", "author_list": "Kechris, A. S.; Soki\u0107, M.; et al." }, { "id": "https://authors.library.caltech.edu/records/evfd1-z5c19", "eprint_id": 78238, "eprint_status": "archive", "datestamp": "2023-08-19 00:02:19", "lastmod": "2026-04-02 06:27:32", "type": "book_section", "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": "Fivebranes and 4-Manifolds", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Springer International Publishing Switzerland. \n\nWe thank F. Quinn, D. Roggenkamp, C. Schweigert, A. Stipsicz, and P. Teichner for patient and extremely helpful explanations.We also thank T. Dimofte, Y. Eliashberg, A. Kapustin, T. Mrowka, W. Neumann, T. Okazaki, E. Sharpe, C. Vafa, J. Walcher, and E. Witten, among others, for a wide variety of helpful 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. 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

Submitted - 1306.4320.pdf

", "abstract": "We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2)N=(0,2) theories, we obtain a number of results, which include new 3d N=2N=2 theories T[M 3] associated with rational homology spheres and new results for Vafa\u2013Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0,\u20092) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines/walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2)N=(0,2) theories and 3d N=2N=2 theories, respectively.", "date": "2016-11-13", "date_type": "published", "publisher": "Springer", "place_of_pub": "New York, NY", "pagerange": "155-245", "id_number": "CaltechAUTHORS:20170615-083539862", "isbn": "978-3-319-43646-3", "book_title": "Arbeitstagung Bonn 2013", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170615-083539862", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Department of Energy (DOE)", "grant_number": "DE-FG02-92-ER40701" }, { "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 Postdoctoral Fellowship" } ] }, "other_numbering_system": { "items": [ { "id": "68-2904", "name": "CALT" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Ballmann-W", "name": { "family": "Ballmann", "given": "Werner" } }, { "id": "Blohmann-C", "name": { "family": "Blohmann", "given": "Christian" } }, { "id": "Faltins-G", "name": { "family": "Faltins", "given": "Gerd" } }, { "id": "Teichner-P", "name": { "family": "Teichner", "given": "Peter" } }, { "id": "Zagier-D", "name": { "family": "Zagier", "given": "Don" } } ] }, "doi": "10.1007/978-3-319-43648-7_7", "primary_object": { "basename": "1306.4320.pdf", "url": "https://authors.library.caltech.edu/records/evfd1-z5c19/files/1306.4320.pdf" }, "pub_year": "2016", "author_list": "Gadde, Abhijit; Gukov, Sergei; et al." }, { "id": "https://authors.library.caltech.edu/records/sg4gy-p6629", "eprint_id": 71907, "eprint_status": "archive", "datestamp": "2023-08-20 13:56:38", "lastmod": "2026-03-09 23:59:23", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mossel-E", "name": { "family": "Mossel", "given": "Elchanan" }, "orcid": "0000-0001-7812-7886" }, { "id": "Olsman-N", "name": { "family": "Olsman", "given": "Noah" }, "orcid": "0000-0002-4351-3880" }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Efficient Bayesian Learning in Social Networks with Gaussian Estimators", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 IEEE. \n\nDate of Conference: 27-30 Sept. 2016. Date Added to IEEE Xplore: 13 February 2017. \n\nThis work is an extension of an unpublished manuscript by Mossel and Tamuz. \n\nWe thank Shachar Kariv for introducing us to the literature on learning on networks and for fascinating discussions. Thanks go to Marcus M\u00f6bius for an interesting discussion and for directing us to the work of DeMarzo et al., after a draft of this note had been circulated. We also thank Grant Schoenebeck, Rafael M. Frongillo and Adam Kalai for interesting discussions regarding follow-up work. We thank Ashwin Ganesan for a lesson on distance-transitive graphs. Finally, we are indebted to Yaron Singer for much support and helpful suggestions on writing the results.\n\n

Submitted - 1002.0747.pdf

", "abstract": "We consider a group of Bayesian agents who try to estimate a state of the world \u03b8 through interaction on a social\nnetwork. Each agent v initially receives a private measurement of \u03b8: a number S_v picked from a Gaussian distribution with mean \u03b8 and standard deviation one. Then, in each discrete time iteration, each reveals its estimate of \u03b8 to its neighbors, and, observing its neighbors' actions, updates its belief using Bayes' Law. This process aggregates information efficiently, in the sense that all the agents converge to the belief that they would have,\nhad they access to all the private measurements. We show that this process is computationally efficient, so that each agent's calculation can be easily carried out. We also show that on any graph the process converges after at most 2N \u00b7 D steps, where N is the number of agents and D is the diameter of the network. Finally, we show that on trees and on distance transitive-graphs the process converges after D steps, and that it preserves privacy, so that agents learn very little about the private signal of most other agents, despite the efficient aggregation of information. Our results extend those in an unpublished manuscript of the first and last authors.", "date": "2016-09-30", "date_type": "published", "publisher": "IEEE", "place_of_pub": "Piscataway, NJ", "pagerange": "425-432", "id_number": "CaltechAUTHORS:20161110-074103834", "isbn": "978-1-5090-4551-8", "book_title": "54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2016", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-074103834", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1109/ALLERTON.2016.7852341", "primary_object": { "basename": "1002.0747.pdf", "url": "https://authors.library.caltech.edu/records/sg4gy-p6629/files/1002.0747.pdf" }, "pub_year": "2016", "author_list": "Mossel, Elchanan; Olsman, Noah; et al." }, { "id": "https://authors.library.caltech.edu/records/6ert3-r4y12", "eprint_id": 56958, "eprint_status": "archive", "datestamp": "2023-08-20 13:54:34", "lastmod": "2026-04-02 05:49:10", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Caraiani-A", "name": { "family": "Caraiani", "given": "Ana" } }, { "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": "p-adic q-expansion principles on unitary Shimura varieties", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Springer International Publishing Switzerland.\n\nFirst Online: 27 September 2016.\n\nAna Caraiani's research is partially supported by NSF Postdoctoral Fellowship DMS-1204465 and NSF Grant DMS-1501064.\nEllen Eischen's research is partially supported by NSF Grants NSF DMS-1249384 and DMS-1559609.\nJessica Fintzen's research is partially supported by the Studienstiftung des deutschen Volkes.\nElena Mantovan's research is partially supported by NSF Grant DMS-1001077.\nIla Varma's research is partially supported by a National Defense Science and Engineering Fellowship. \n\nWe are grateful to L. Long, R. Pries, and K. Stange for organizing the Women in Numbers 3 workshop and facilitating this collaboration. We would like to thank the referee for carefully reading the paper and providing many helpful comments, including suggestions for how to improve the introduction. We would also like to thank M. Harris, H. Hida, and K.-W. Lan for answering questions about q-expansion principles. We are grateful to the Banff International Research Station for creating an ideal working environment.\n\n

Submitted - 1411.4350.pdf

", "abstract": "We formulate and prove certain vanishing theorems for p-adic automorphic forms on unitary groups of arbitrary signature. The p-adic q-expansion principle for p-adic modular forms on the Igusa tower says that if the coefficients of (sufficiently many of) the q-expansions of a p-adic modular form f are zero, then f vanishes everywhere on the Igusa tower. There is no p-adic q-expansion principle for unitary groups of arbitrary signature in the literature. By replacing q-expansions with Serre\u2013Tate expansions (expansions in terms of Serre\u2013Tate deformation coordinates) and replacing modular forms with automorphic forms on unitary groups of arbitrary signature, we prove an analogue of the p-adic q-expansion principle. More precisely, we show that if the coefficients of (sufficiently many of) the Serre\u2013Tate expansions of a p-adic automorphic form f on the Igusa tower (over a unitary Shimura variety) are zero, then f vanishes identically on the Igusa tower.This paper also contains a substantial expository component. In particular, the expository component serves as a complement to Hida's extensive work on p-adic automorphic forms.", "date": "2016-09-27", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham", "pagerange": "197-243", "id_number": "CaltechAUTHORS:20150424-124825553", "isbn": "978-3-319-30974-3", "book_title": "Directions in Number Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150424-124825553", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Postdoctoral Fellowship", "grant_number": "DMS-1204465" }, { "agency": "NSF", "grant_number": "DMS-1501064" }, { "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" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Eischen-E-E", "name": { "family": "Eischen", "given": "Ellen E." } }, { "id": "Long-Ling", "name": { "family": "Long", "given": "Ling" } }, { "id": "Pries-R", "name": { "family": "Pries", "given": "Rachel" } }, { "id": "Stange-K-E", "name": { "family": "Stange", "given": "Katherine E." } } ] }, "doi": "10.1007/978-3-319-30976-7_7", "primary_object": { "basename": "1411.4350.pdf", "url": "https://authors.library.caltech.edu/records/6ert3-r4y12/files/1411.4350.pdf" }, "pub_year": "2016", "author_list": "Caraiani, Ana; Eischen, Ellen; et al." }, { "id": "https://authors.library.caltech.edu/records/vy2pb-qbm80", "eprint_id": 78999, "eprint_status": "archive", "datestamp": "2023-08-20 12:43:58", "lastmod": "2026-04-02 16:08:12", "type": "book_section", "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": "Moduli Operad over F_1", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 EMS Publishing House. \n\nThe second author acknowledges support and hospitality of the Max Planck Institute and the Mathematical Sciences Research Institute and support from NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440. We thank Paolo Aluffi, Tom Graber and Oliver Lorscheid for constructive criticism, useful comments and discussions.\n\n

Submitted - 1302.6526.pdf

", "abstract": "In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad {M_(0,n+1)} can be endowed with natural descent data that allow it to be considered as the lift to Spec Z of an operad over F_1. The relevant descent data are based on a notion of constructible sets and constructible functions over F_1, which describes suitable differences of torifications with a positivity condition on the class in the Grothendieck ring. More generally, we do the same for the operads {T_(d,n+1)} (whose components were) introduced in [5]. Finally, we describe a blueprint structure on {M_(0,n)} and we discuss from this perspective the genus zero boundary modular operad {M^0_(g,n+1)}.", "date": "2016-07", "date_type": "published", "publisher": "European Mathematical Society", "place_of_pub": "Z\u00fcrich", "pagerange": "331-361", "id_number": "CaltechAUTHORS:20170712-091753130", "isbn": "978-3-03719-157-6", "book_title": "Absolute arithmetic and F1-geometry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-091753130", "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-1201512" }, { "agency": "NSF", "grant_number": "PHY-1205440" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Thas-K", "name": { "family": "Thas", "given": "Koen" } } ] }, "doi": "10.4171/157-1/7", "primary_object": { "basename": "1302.6526.pdf", "url": "https://authors.library.caltech.edu/records/vy2pb-qbm80/files/1302.6526.pdf" }, "pub_year": "2016", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/xqrv2-ffb73", "eprint_id": 67542, "eprint_status": "archive", "datestamp": "2023-08-20 11:12:52", "lastmod": "2026-04-02 16:26:21", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Information Algebras and Their Applications", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2015 Springer International Publishing Switzerland.", "abstract": "In this lecture we will present joint work with Ryan Thorngren on thermodynamic semirings and entropy operads, with Nicolas Tedeschi on Birkhoff factorization in thermodynamic semirings, ongoing work with Marcus Bintz on tropicalization of Feynman graph hypersurfaces and Potts model hypersurfaces, and their thermodynamic deformations, and ongoing work by the author on applications of thermodynamic semirings to models of morphology and syntax in Computational Linguistics.", "date": "2016-04-03", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham", "pagerange": "271-276", "id_number": "CaltechAUTHORS:20160601-111532492", "isbn": "978-3-319-25039-7", "book_title": "Geometric Science of Information", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160601-111532492", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Nielsen-F", "name": { "family": "Nielsen", "given": "Frank" } }, { "id": "Barbaresco-F", "name": { "family": "Barbaresco", "given": "Fr\u00e9d\u00e9ric" } } ] }, "doi": "10.1007/978-3-319-25040-3_30", "pub_year": "2016", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/tkqn1-sq294", "eprint_id": 68877, "eprint_status": "archive", "datestamp": "2023-08-20 09:35:18", "lastmod": "2026-03-09 23:14:14", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Martin-K", "name": { "family": "Martin", "given": "Kimball" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "A comparison of automorphic and Artin L-series of GL(2)-type agreeing at degree one primes", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 American Mathematical Society. \n\nThe first author was partially supported by Simons Collaboration Grant 240605. \n\nThe second author was partially supported by NSF grant DMS-1001916.\n\n

Submitted - 1502.04175v1.pdf

", "abstract": "Let F/k be a cyclic extension of number fields of prime degree. Let \u03c1 be an irreducible 2-dimensional representation of Artin type of the absolute Galois group of F, and \u03c0 a cuspidal automorphic representation of GL_2(A_F), such that the L-functions L(s,\u03c1_v) and L(s,\u03c0_v) agree at all (but finitely many of) the places v of degree one over k. We prove in this case that we have the global identity L(s,\u03c1)=L(s,\u03c0), with \u03c1_v\u2194\u03c0_v being given by the local Langlands correspondence at all v. In particular, \u03c0 is tempered and L(s,\u03c1) is entire.", "date": "2016", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "339-350", "id_number": "CaltechAUTHORS:20160707-080856277", "isbn": "978-1-4704-1709-3", "book_title": "Advances in the theory of automorphic forms and their L-functions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160707-080856277", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Simons Foundation", "grant_number": "240605" }, { "agency": "NSF", "grant_number": "DMS-1001916" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cogdell-J-W", "name": { "family": "Cogdell", "given": "James W." } }, { "id": "Jiang-Dihua", "name": { "family": "Jiang", "given": "Dihua" } }, { "id": "Shahidi-F", "name": { "family": "Shahidi", "given": "Freydoon" } }, { "id": "Soudry-D", "name": { "family": "Soudry", "given": "David" } } ] }, "doi": "10.48550/arXiv.1502.04175", "primary_object": { "basename": "1502.04175v1.pdf", "url": "https://authors.library.caltech.edu/records/tkqn1-sq294/files/1502.04175v1.pdf" }, "pub_year": "2016", "author_list": "Martin, Kimball and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/j19aa-kf757", "eprint_id": 88590, "eprint_status": "archive", "datestamp": "2023-08-20 09:38:34", "lastmod": "2026-03-09 20:36:26", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On Spector classes", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Cambridge University Press.", "abstract": "[no abstract]", "date": "2016", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "390-423", "id_number": "CaltechAUTHORS:20180806-093515411", "isbn": "9781139519694", "book_title": "Ordinal Definability and Recursion Theory: The Cabal Seminar", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-093515411", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9781139519694.013", "pub_year": "2016", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/4bfne-24b32", "eprint_id": 88592, "eprint_status": "archive", "datestamp": "2023-08-20 09:38:40", "lastmod": "2026-03-09 20:36:39", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "title": "Preface", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Cambridge University Press.", "abstract": "This book continues the series of volumes containing reprints of the papers in the original Cabal Seminar volumes of the Springer Lecture Notes in Mathematics series [Cabal i, Cabal ii, Cabal iii, Cabal iv], unpublished material, and new papers. The first volume, [Cabal I], contained papers on games, scales and Suslin cardinals. The second volume, [Cabal II], contained papers on Wadge degrees and pointclasses and projective ordinals. In this volume, we continue with Parts V and VI of the project: Ordinal definability in models of determinacy and Recursion theory. As in our first two volumes, each of the parts contains an introductory survey (written by John Steel for Part V and by Leo Harrington and Ted Slaman for Part VI) putting the papers into a present-day context.\n\nIn addition to the reprinted papers, this volume contains a paper by Kechris and Martin (On the theory of \u03a0^1_3 sets of reals, II) that dates back to the period of the original Cabal publications but was not included in the old volumes. Neeman contributed a new paper, An inner models proof of the Kechris\u2013Martin theorem, related to this paper. Steel and Woodin contributed two new papers (A theorem of Woodin on mouse sets, authored by Steel, and HOD as a core model, jointly) with recent results that fit well with the topics of Part V. There is also a new paper by Marks, Slaman and Steel (Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations) that contains earlier, unpublished, as well as new results related to the theme of Part VI. Table 1 gives an overview of the papers in this volume with their original references.\n\nAs emphasized in our first two volumes, our project is not to be understood as a historical edition of old papers. In the retyping process, we uniformized and modernized notation and numbering of sections and theorems. As a consequence, references to papers in the old Cabal volumes will not always agree with references to their reprinted versions. In this volume, references to papers that already appeared in reprinted form will use the new numbering. In order to help the reader to easily cross-reference old and new numberings, we provide a list of changes after the preface.", "date": "2016", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "vii-x", "id_number": "CaltechAUTHORS:20180806-100030179", "isbn": "9781139519694", "book_title": "Ordinal Definability and Recursion Theory: The Cabal Seminar", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-100030179", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9781139519694.001", "pub_year": "2016", "author_list": "Kechris, Alexander S.; L\u00f6we, Benedikt; et al." }, { "id": "https://authors.library.caltech.edu/records/awjpx-r2a62", "eprint_id": 88593, "eprint_status": "archive", "datestamp": "2023-08-20 09:38:43", "lastmod": "2026-03-09 20:35:12", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Solovay-R-M", "name": { "family": "Solovay", "given": "Robert M." } } ] }, "title": "Introduction to Q-theory", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Cambridge University Press.", "abstract": "[no abstract]", "date": "2016", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "126-199", "id_number": "CaltechAUTHORS:20180806-100432570", "isbn": "9781139519694", "book_title": "Ordinal Definability and Recursion Theory: The Cabal Seminar", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-100432570", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9781139519694.006", "pub_year": "2016", "author_list": "Kechris, Alexander S.; Martin, Donald A.; et al." }, { "id": "https://authors.library.caltech.edu/records/6b3nx-xsc69", "eprint_id": 88589, "eprint_status": "archive", "datestamp": "2023-08-20 09:38:32", "lastmod": "2026-03-09 20:31:52", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } } ] }, "title": "On the theory of \u03a013 sets of reals, II", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Cambridge University Press.", "abstract": "[no abstract]", "date": "2016", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "200-219", "id_number": "CaltechAUTHORS:20180806-092249394", "isbn": "9781139519694", "book_title": "Ordinal Definability and Recursion Theory: The Cabal Seminar", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-092249394", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9781139519694.007", "pub_year": "2016", "author_list": "Kechris, Alexander S. and Martin, Donald A." }, { "id": "https://authors.library.caltech.edu/records/qnq5a-eh607", "eprint_id": 66603, "eprint_status": "archive", "datestamp": "2023-08-22 17:06:19", "lastmod": "2026-03-09 02:33:27", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" }, { "id": "Saberi-Ingmar-A", "name": { "family": "Saberi", "given": "Ingmar" } } ] }, "title": "Lectures on Knot Homology and Quantum Curves", "ispublished": "unpub", "full_text_status": "public", "keywords": "Knot invariants; quantization; categorification; Chern-Simons theory", "note": "\u00a9 2017 American Mathematical Society. \n\nThis survey was presented in a series of lectures first at University of Notre Dame (2012 summer school on Topology and Field Theories at the Center for Mathematics), then at Stanford (summer school on Holomorphic curves and low-dimensional topology), and in other versions in Hamburg, Oberwolfach, Lisbon, and Heidelberg.\n\n

Submitted - 1211.6075.pdf

", "abstract": "Besides offering a friendly introduction to knot homologies and quantum curves, the goal of these lectures is to review some of the concrete predictions that follow from the physical interpretation of knot homologies. In particular, this interpretation allows one to pose questions that would not have been asked otherwise, such as, \"Is there a direct relation between Khovanov homology and the A-polynomial of a knot?\" We will explain that the answer to this question is \"yes,\" and introduce a certain deformation of the planar algebraic curve defined by the zero locus of the A-polynomial. This novel deformation leads to a categorified version of the Generalized Volume Conjecture that completely describes the \"color behavior\" of the colored sl(2) knot homology, and eventually to a similar version for the colored HOMFLY homology. Furthermore, this deformation is strong enough to distinguish mutants, and its most interesting properties include relations to knot contact homology and knot Floer homology.", "date": "2016", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "59-97", "id_number": "CaltechAUTHORS:20160503-081755071", "isbn": "978-1-4704-1459-7", "book_title": "Physics and Mathematics of Link Homology", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-081755071", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" } }, { "id": "Khovanov-M", "name": { "family": "Khovanov", "given": "Mikhail" } }, { "id": "Walcher-J", "name": { "family": "Walcher", "given": "Johannes" } } ] }, "doi": "10.1090/conm/680/13700", "primary_object": { "basename": "1211.6075.pdf", "url": "https://authors.library.caltech.edu/records/qnq5a-eh607/files/1211.6075.pdf" }, "pub_year": "2016", "author_list": "Gukov, Sergei and Saberi, Ingmar" }, { "id": "https://authors.library.caltech.edu/records/th675-h6y10", "eprint_id": 53751, "eprint_status": "archive", "datestamp": "2023-08-20 09:07:11", "lastmod": "2026-04-04 21:22:49", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Surface Operators", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 Springer International Publishing Switzerland.\n\n

Submitted - 1412.7127v1.pdf

", "abstract": "We give an introduction and a broad survey of surface operators in 4d gauge theories, with a particular emphasis on aspects relevant to AGT correspondence. One of the main goals is to highlight the boundary between what we know and what we don't know about surface operators. To this end, the survey contains many open questions and suggests various directions for future research. Although this article is mostly a review, we did include a number of new results, previously unpublished.", "date": "2015-11-18", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "223-259", "id_number": "CaltechAUTHORS:20150114-205456566", "isbn": "978-3-319-18768-6", "book_title": "New Dualities of Supersymmetric Gauge Theories", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20150114-205456566", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "2014-170", "name": "CALT-TH" } ] }, "local_group": { "items": [ { "id": "Walter-Burke-Institute-for-Theoretical-Physics" }, { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Teschner-J", "name": { "family": "Teschner", "given": "J\u00f6rg" } } ] }, "doi": "10.1007/978-3-319-18769-3_8", "primary_object": { "basename": "1412.7127v1.pdf", "url": "https://authors.library.caltech.edu/records/th675-h6y10/files/1412.7127v1.pdf" }, "pub_year": "2015", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/7tq4m-xda06", "eprint_id": 97833, "eprint_status": "archive", "datestamp": "2023-08-20 07:10:57", "lastmod": "2026-04-04 05:55:24", "type": "book_section", "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": "Recent developments in graph Ramsey theory", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 Cambridge University Press. \n\nPrint publication year 2015; online publication date July 2015. \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\nThe authors would like to thank the anonymous referee for a number of useful comments.\n\n

Published - recent_developments_in_graph_ramsey_theory.pdf

Submitted - 1501.02474.pdf

", "abstract": "Given a graph H, the Ramsey number r(H) is the smallest natural number N such that any two-colouring of the edges of K_N contains a monochromatic copy of H. The existence of these numbers has been known since 1930 but their quantitative behaviour is still not well understood. Even so, there has been a great deal of recent progress on the study of Ramsey numbers and their variants, spurred on by the many advances across extremal combinatorics. In this survey, we will describe some of this progress.", "date": "2015-07", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge, United Kingdom", "pagerange": "49-118", "id_number": "CaltechAUTHORS:20190812-162959899", "isbn": "9781316106853", "book_title": "Surveys in Combinatorics 2015", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-162959899", "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" } ] }, "contributors": { "items": [ { "id": "Czumaj-A", "name": { "family": "Czumaj", "given": "Artur" } }, { "id": "Georgakopoulos-A", "name": { "family": "Georgakopoulos", "given": "Agelos" } }, { "id": "Kr\u00e1l-D", "name": { "family": "Kr\u00e1l", "given": "Daniel" } }, { "id": "Lozin-V", "name": { "family": "Lozin", "given": "Vadim" } }, { "id": "Pikhurko-O", "name": { "family": "Pikhurko", "given": "Oleg" } } ] }, "doi": "10.1017/cbo9781316106853.003", "primary_object": { "basename": "recent_developments_in_graph_ramsey_theory.pdf", "url": "https://authors.library.caltech.edu/records/7tq4m-xda06/files/recent_developments_in_graph_ramsey_theory.pdf" }, "related_objects": [ { "basename": "1501.02474.pdf", "url": "https://authors.library.caltech.edu/records/7tq4m-xda06/files/1501.02474.pdf" } ], "pub_year": "2015", "author_list": "Conlon, David; Fox, Jacob; et al." }, { "id": "https://authors.library.caltech.edu/records/gsya8-zeq05", "eprint_id": 62231, "eprint_status": "archive", "datestamp": "2023-08-20 04:11:38", "lastmod": "2026-03-09 21:44:06", "type": "book_section", "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": "Unconditional noncommutative motivic Galois groups", "ispublished": "unpub", "full_text_status": "public", "keywords": "Motivic Galois groups, motives, noncommutative algebraic geometry", "note": "\u00a9 2015 American Mathematical Society. \n\nMarcolli was partially supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. G. Tabuada was partially supported by the NEC Award-2742738. \n\nThe authors are very grateful to the organizers of the conference \"Hodge Theory and Classical Algebraic Geometry\" for the opportunity to present this work. \n\nThe authors are grateful to Michael Artin, Eric Friedlander, Steven Kleiman, and Yuri Manin for useful discussions and motivating questions.\n\n

Submitted - 1112.5422v2.pdf

", "abstract": "In this short note we introduce the unconditional noncommutative motivic Galois groups and relate them with those of Andre-Kahn.", "date": "2015", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "109-115", "id_number": "CaltechAUTHORS:20151119-101540033", "isbn": "978-1-4704-0990-6", "book_title": "Hodge Theory and Classical Algebraic Geometry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151119-101540033", "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" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kennedy-Gary", "name": { "family": "Kennedy", "given": "Gary" } }, { "id": "Caib\u00e1r-M", "name": { "family": "Caib\u00e1r", "given": "Mirel" } }, { "id": "Castravet-A-M", "name": { "family": "Castravet", "given": "Ana-Maria" } }, { "id": "Macri-E", "name": { "family": "Macri", "given": "Emanuele" } } ] }, "doi": "10.48550/arXiv.1112.5422", "primary_object": { "basename": "1112.5422v2.pdf", "url": "https://authors.library.caltech.edu/records/gsya8-zeq05/files/1112.5422v2.pdf" }, "pub_year": "2015", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/b8fy6-qjj49", "eprint_id": 78252, "eprint_status": "archive", "datestamp": "2023-08-20 04:17:08", "lastmod": "2026-03-09 21:38:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "The Wolf and the Street: Narrative Encounters with Mathematics", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2015 Springer. \n\nDate: 12 November 2014.", "abstract": "I was invited to this conference to present the results of an old experiment, a twenty year old exploration of narrative and mathematics, in the form of a collection of fairy tales. I began writing the stories of Racconti per il lupo (Tales for the Wolf) in 1986, when I was a 16 year old student of the Liceo Classico, more occupied with ancient Greek texts and philosophy than with mathematics. I finished the collection when I was about to graduate in Theoretical Physics, at the University of Milano, in 1993. Those few years spanned enormous transformations, at the personal level, going through the passage from late adolescence to adulthood, and from being a student of classical languages to a professional physicist, as well as on the larger scale of society and the world: those were the years that marked \"the end of the short century\", with all the upheaval, excitement and anxiety that came with it. In their minuscule cameo scale, the mathematical stories I was putting together, act as a small fragmented mirror of larger events. The stories, written in Italian, and illustrated by a series of collages I prepared in the style of Max Ernst, are now available online at the publisher Lulu.com, along with some of my more recent writings. In this presentation, I will try to describe the main ideas behind that old attempt at conveying in a narrative form some mathematical concepts, and I will contrast the spirit of that early encounter with mathematics, with the very different spirit in which I came to see the mathematical profession nowadays, after twenty years of experience. The latter is best represented in some of my more recent writings, especially the lyric prose collection Street Science, composed in 2013, illustrated by mathematical street art graffiti, also available online from the same publisher.", "date": "2015", "date_type": "published", "publisher": "Springer", "place_of_pub": "New York, NY", "pagerange": "225-234", "id_number": "CaltechAUTHORS:20170615-124503245", "isbn": "978-3-319-01230-8", "book_title": "Imagine Math 3", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170615-124503245", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Emmer-M", "name": { "family": "Emmer", "given": "Matilde" } } ] }, "doi": "10.1007/978-3-319-01231-5_16", "pub_year": "2015", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/z8r8e-kt167", "eprint_id": 88586, "eprint_status": "archive", "datestamp": "2023-08-20 04:18:40", "lastmod": "2026-03-09 23:11:11", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Paranjape-K", "name": { "family": "Paranjape", "given": "Kapil" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Modular forms and Calabi-Yau varieties", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 Cambridge University Press.", "abstract": "[no abstract]", "date": "2015", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "351-372", "id_number": "CaltechAUTHORS:20180806-085816292", "isbn": "9781107462540", "book_title": "Arithmetic and Geometry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-085816292", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Dieulefait-L", "name": { "family": "Dieulefait", "given": "Luis" } }, { "id": "Faltings-G", "name": { "family": "Faltings", "given": "Gerd" } }, { "id": "Heath-Brown-D-R", "name": { "family": "Heath-Brown", "given": "D. R." } }, { "id": "Manin-Yu-V", "name": { "family": "Manin", "given": "Yu. V." } }, { "id": "Moroz-B-Z", "name": { "family": "Moroz", "given": "B. Z." } }, { "id": "Wintenberger-J-P", "name": { "family": "Wintenberger", "given": "Jean-Pierre" } } ] }, "doi": "10.1017/CBO9781316106877.019", "pub_year": "2015", "author_list": "Paranjape, Kapil and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/jxgvy-0ra15", "eprint_id": 63135, "eprint_status": "archive", "datestamp": "2023-08-20 04:12:10", "lastmod": "2026-03-08 18:14:34", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Demirel-Frank-S", "name": { "family": "Demirel-Frank", "given": "Semra" } } ] }, "title": "Spectral Inequalities for Quantum Graphs", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2015 Springer International Publishing Switzerland. \n\nThe author is grateful to Evans Harrell with whom the results reviewed in Sect. 2 were obtained and to Timo Weidl who suggested that there might be an alternative proof of the trace inequality. Many thanks to Delio Mugnolo for organizing the wonderful conference \"Mathematical Technology of Networks\".", "abstract": "We review our joint work with Evans Harrell on semiclassical and universal inequalities for quantum graphs. The proofs of these inequalities are based on an abstract trace inequality for commutators of operators. In this article we give a new proof of this abstract trace inequality. Another ingredient in proving semiclassical and universal inequalities is an appropriate choice of operators in this trace inequality. We provide a new approximation method for such a choice.", "date": "2015", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "65-80", "id_number": "CaltechAUTHORS:20151222-103336784", "isbn": "978-3-319-16618-6", "book_title": "Mathematical Technology of Networks", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151222-103336784", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Mugnolo-D", "name": { "family": "Mugnolo", "given": "Delio" } } ] }, "doi": "10.1007/978-3-319-16619-3_6", "pub_year": "2015", "author_list": "Demirel-Frank, Semra" }, { "id": "https://authors.library.caltech.edu/records/1zced-pkb20", "eprint_id": 79024, "eprint_status": "archive", "datestamp": "2023-08-20 04:18:20", "lastmod": "2026-03-09 21:44:24", "type": "book_section", "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 and their applications", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 Mathematical Sciences Research Institute. \n\nMarcolli was partially supported by the grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. 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 UID/MAT/00297/2013 (Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es). \n\n\nThe authors are very grateful to the organizers Michael Artin, Victor Ginzburg, Catharina Stroppel, Toby Stafford, Michel Van den Bergh, and Efim Zelmanov for kindly giving us the opportunity to present our recent work. They would like also to thank the anonymous referee for comments and corrections.\n\n

Published - 150122-Marcolli.pdf

Submitted - 1311.2867.pdf

", "abstract": "This survey is based on lectures given by the authors during the program \"Noncommutative algebraic geometry and representation theory\" at the MSRI in the Spring 2013. It covers the recent work [44, 45, 46, 47, 48, 49, 50] on noncommutative motives and their applications, and is intended for a broad mathematical audience. In Section 1 we recall the main features of Grothendieck's theory of motives. In Sections 2 and 3 we introduce several categories of noncommutative motives and describe their relation with the classical commutative counterparts. In Section 4 we formulate the noncommutative analogues of Grothendieck's standard conjectures of type C and D, of Voevodsky's smash-nilpotence conjecture, and of Kimura-O'Sullivan finite-dimensionality conjecture. Section 5 is devoted to recollections of the (super-)Tannakian formalism. In Section 6 we introduce the noncommutative motivic Galois (super-)groups and their unconditional versions. In Section 7 we explain how the classical theory of (intermediate) Jacobians can be extended to the noncommutative world. Finally, in Section 8 we present some applications to motivic decompositions and to Dubrovin's conjecture.", "date": "2015", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "191-214", "id_number": "CaltechAUTHORS:20170712-143931835", "isbn": "978-1-107-06562-8", "book_title": "Commutative algebra and noncommutative algebraic geometry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170712-143931835", "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": "NSF", "grant_number": "DMS-1350472" }, { "agency": "Funda\ufffd\ufffdo para a Ci\ufffdncia e a Tecnologia (FCT)", "grant_number": "UID/MAT/00297/2013" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Eisenbud-D", "name": { "family": "Eisenbud", "given": "David" } }, { "id": "Iyengar-S-B", "name": { "family": "Iyengar", "given": "Srikanth B." } }, { "id": "Singh-A-K", "name": { "family": "Singh", "given": "Anurag K." } }, { "id": "Stafford-J-J", "name": { "family": "Stafford", "given": "J. Joby" } }, { "id": "Van-de-Bergh-M", "name": { "family": "Van de Bergh", "given": "Michel" } } ] }, "doi": "10.48550/arXiv.1311.2867", "primary_object": { "basename": "1311.2867.pdf", "url": "https://authors.library.caltech.edu/records/1zced-pkb20/files/1311.2867.pdf" }, "related_objects": [ { "basename": "150122-Marcolli.pdf", "url": "https://authors.library.caltech.edu/records/1zced-pkb20/files/150122-Marcolli.pdf" } ], "pub_year": "2015", "author_list": "Marcolli, Matilde and Tabuada, Gon\u00e7alo" }, { "id": "https://authors.library.caltech.edu/records/02am0-hba28", "eprint_id": 62441, "eprint_status": "archive", "datestamp": "2023-08-20 04:11:43", "lastmod": "2026-03-09 21:40:08", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Delaney-C-R", "name": { "family": "Delaney", "given": "Colleen" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Dyson-Schwinger equations in the theory of computation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 American Mathematical Society.\n\nThe first author was supported for this project by the Summer Undergraduate Research Fellowship (SURF) program of Caltech, through a Herbert J. Ryser fellowship. The second author is partially supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, and PHY-1205440. The second author acknowledges MSRI for hospitality and support. The authors are especially grateful to Joachim Kock for many helpful comments and suggestions that significantly improved the paper.\n\n

Submitted - 1302.5040v2.pdf

", "abstract": "Following Manin's approach to renormalization in the theory of computation, we investigate Dyson-Schwinger equations on Hopf algebras, operads and properads of flow charts, as a way of encoding self-similarity structures in the theory of algorithms computing primitive and partial recursive functions and in the halting problem.", "date": "2015", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "79-107", "id_number": "CaltechAUTHORS:20151130-084148729", "isbn": "978-1-4704-2247-9", "book_title": "Feynman Amplitudes, Periods and Motives", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151130-084148729", "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" } ] }, "contributors": { "items": [ { "id": "\u00c1lvarez-C\u00f3nsul-L", "name": { "family": "\u00c1lvarez-C\u00f3nsul", "given": "Luis" } }, { "id": "Burgos-Gil-J-I", "name": { "family": "Burgos-Gil", "given": "Jos\u00e9 Ignacio" } }, { "id": "Ebrahimi-Fard-K", "name": { "family": "Ebrahimi-Fard", "given": "Kurusch" } } ] }, "doi": "10.48550/arXiv.1302.5040", "primary_object": { "basename": "1302.5040v2.pdf", "url": "https://authors.library.caltech.edu/records/02am0-hba28/files/1302.5040v2.pdf" }, "pub_year": "2015", "author_list": "Delaney, Colleen and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/t02a8-a7n29", "eprint_id": 64408, "eprint_status": "archive", "datestamp": "2023-08-20 04:12:44", "lastmod": "2026-03-09 23:11:13", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Recovering Cusp Forms on GL(2) from Symmetric Cubes", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2015 American Mathematical Society. \n\nThis article is dedicated to Ram Murty, a friend whose works I have long read with interest.\n\n

Submitted - 1503.08242v1.pdf

", "abstract": "Suppose \u03c0, \u03c0\u2032 are cusp forms on GL(2), not of solvable polyhedral type, such that they have the same symmetric cubes. Then we show that either \u03c0, \u03c0\u2032 are twist equivalent, or else a certain degree 36 L-function associated to the pair has a pole at s=1. If we further assume that the symmetric fifth power of \u03c0 is automorphic, then in the latter case, \u03c0 is icosahedral in a suitable sense, agreeing with the usual notion when there is an associated Galois representation.", "date": "2015", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "id_number": "CaltechAUTHORS:20160211-083113741", "isbn": "978-1-4704-1457-3", "book_title": "SCHOLAR\u2014a Scientific Celebration Highlighting Open Lines of Arithmetic Research", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160211-083113741", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cojocaru-A-C", "name": { "family": "Cojocaru", "given": "A. C." } }, { "id": "David-C", "name": { "family": "David", "given": "C." } }, { "id": "Pappalardi-F", "name": { "family": "Pappalardi", "given": "F." } } ] }, "doi": "10.1090/conm/655/13205", "primary_object": { "basename": "1503.08242v1.pdf", "url": "https://authors.library.caltech.edu/records/t02a8-a7n29/files/1503.08242v1.pdf" }, "pub_year": "2015", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/q15jw-18d37", "eprint_id": 88534, "eprint_status": "archive", "datestamp": "2023-08-20 02:49:02", "lastmod": "2026-04-06 00:05:16", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Ed Nelson's Work in Quantum Theory", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2014 Princeton University Press.", "abstract": "It is a pleasure to contribute to this celebration of Ed Nelson's scientific work, not only because of the importance of that work but because it allows me an opportunity to express my gratitude and acknowledge my enormous debt to Ed. He and Arthur Wightman were the key formulative influences on my education, not only as a graduate student but during my early postdoctoral years. Thanks, Ed!", "date": "2014-09", "date_type": "published", "publisher": "Princeton University Press", "place_of_pub": "Princeton, NJ", "pagerange": "75-94", "id_number": "CaltechAUTHORS:20180802-142924769", "isbn": "978-1-4008-6525-3", "book_title": "Diffusion, Quantum Theory, and Radically Elementary Mathematics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180802-142924769", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Faris-W-G", "name": { "family": "Faris", "given": "William G." } } ] }, "doi": "10.1515/9781400865253.75", "pub_year": "2014", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/29gfk-tr108", "eprint_id": 78664, "eprint_status": "archive", "datestamp": "2023-08-20 02:24:08", "lastmod": "2026-04-05 16:48:52", "type": "book_section", "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": "Quantum Statistical Mechanics, L-Series and Anabelian Geometry I: Partition Functions", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2014 Springer International Publishing Switzerland. \n\nFirst Online: 02 August 2014.\n\n

Submitted - 1009.0736.pdf

", "abstract": "The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical (QSM) system, built from abelian class field theory.\n\nWe introduce a general notion of isomorphism of QSM-systems and prove that it preserves (extremal) KMS equilibrium states.\n\nWe prove that two number fields with isomorphic quantum statistical mechanical systems are arithmetically equivalent, i.e., have the same zeta function. If one of the fields is normal over \u211a, this implies that the fields are isomorphic. Thus, in this case, isomorphism of QSM-systems is the same as isomorphism of number fields, and the noncommutative space built from the abelianized Galois group can replace the anabelian absolute Galois group from the theorem of Neukirch and Uchida.\n\nThis paper is an updated version of part of [9]. We have split the original preprint into various parts, depending on the methods that are used in them. In the current part, these belong mainly to mathematical physics.", "date": "2014-08-02", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "47-57", "id_number": "CaltechAUTHORS:20170628-141113183", "isbn": "978-3-319-05253-3", "book_title": "Trends in Contemporary Mathematics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170628-141113183", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Ancona-V", "name": { "family": "Ancona", "given": "Vincenzo" } }, { "id": "Strickland-E", "name": { "family": "Strickland", "given": "Elisabetta" } } ] }, "doi": "10.1007/978-3-319-05254-0_4", "primary_object": { "basename": "1009.0736.pdf", "url": "https://authors.library.caltech.edu/records/29gfk-tr108/files/1009.0736.pdf" }, "pub_year": "2014", "author_list": "Cornelissen, Gunther and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/jra4q-hch51", "eprint_id": 88575, "eprint_status": "archive", "datestamp": "2023-08-20 02:22:41", "lastmod": "2026-03-09 20:29:32", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Katz-N-H", "name": { "family": "Katz", "given": "Nets Hawk" }, "orcid": "0000-0002-6239-5429" } ] }, "title": "The flecnode polynomial: a central object in incidence geometry", "ispublished": "unpub", "full_text_status": "public", "keywords": "Incidence theory, flecnodes, ruled surfaces.", "note": "\u24d2 2014 Seoul ICM Organizing Committee. The Seoul ICM Organizing Committee, the legal copyright owner of the articles in the proceedings, hearby grants unlimited noncommercial download and use of the articles. \n\nThe author was partially supported by NSF grant DMS 1266104.\n\n

Published - Katz-ICM2014.pdf

Submitted - 1404.3412

", "abstract": "Recently there has been a lot of progress in point/line incidence theory in three dimension real affine spaces. Generally, this progress all happens where the lines and points lie in a ruled surface. Conversely, in many related problems we are yet unable to touch, we are just outside the threshold where the ruled condition can be enforced. This puts the celebrated flecnode polynomial of Cayley and Salmon at the center of the action.", "date": "2014-08", "date_type": "published", "publisher": "Kyung Moon SA", "place_of_pub": "Seoul, Korea", "pagerange": "303-314", "id_number": "CaltechAUTHORS:20180803-153657345", "isbn": "9788961058063", "book_title": "Seoul ICM Proceedings", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180803-153657345", "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": "10.48550/arXiv.1404.3412", "primary_object": { "basename": "Katz-ICM2014.pdf", "url": "https://authors.library.caltech.edu/records/jra4q-hch51/files/Katz-ICM2014.pdf" }, "related_objects": [ { "basename": "1404.3412", "url": "https://authors.library.caltech.edu/records/jra4q-hch51/files/1404.3412" } ], "pub_year": "2014", "author_list": "Katz, Nets Hawk" }, { "id": "https://authors.library.caltech.edu/records/zmh6w-mv829", "eprint_id": 78793, "eprint_status": "archive", "datestamp": "2023-08-20 01:31:43", "lastmod": "2026-04-05 23:24:23", "type": "book_section", "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": "unpub", "full_text_status": "restricted", "note": "\u00a9 2014 Springer International Publishing Switzerland. \n\nFirst Online: 24 June 2014. \n\nIt is pleasure to thank Vincent Bouchard, Tudor Dimofte, Nathan Dunfield, Bertrand Eynard, Maxim Kontsevich, and Don Zagier for helpful discussions and correspondence. 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 and the European Commission under the Marie-Curie International Outgoing Fellowship Programme. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies.", "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 \u210f\u21920, and becomes non-commutative or \"quantum\" away from this limit. For a classical curve defined by the zero locus of a polynomial A(x,\u2009y), we provide a construction of its non-commutative counterpart A^(x^,y^) using the technique of the topological recursion. This leads to a powerful and systematic algorithm for computing A^ that, 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 geometry,\" their non-commutative counterparts can be determined just from the first few steps of the topological recursion. We also propose a K-theory 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. The material contained in this chapter was presented at the conference Mirror Symmetry and Tropical Geometry in Cetraro (July 2011) and is based on the work: Gukov and Su\u0142kowski, \"A-polynomial, B-model, and quantization\", JHEP 1202 (2012) 070.", "date": "2014-06-24", "date_type": "published", "publisher": "Springer", "place_of_pub": "Cham, Switzerland", "pagerange": "87-151", "id_number": "CaltechAUTHORS:20170706-082515229", "isbn": "978-3-319-06513-7", "book_title": "Homological Mirror Symmetry and Tropical Geometry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170706-082515229", "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": "Marie Curie Fellowship" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Castano-Bernard-R", "name": { "family": "Castano-Bernard", "given": "Ricardo" } }, { "id": "Catanese-F", "name": { "family": "Catanese", "given": "Fabrizio" } }, { "id": "Kontsevich-M", "name": { "family": "Kontsevich", "given": "Maxim" } }, { "id": "Pantev-T", "name": { "family": "Pantev", "given": "Tony" } }, { "id": "Soibelman-Y", "name": { "family": "Soibelman", "given": "Yan" } }, { "id": "Zharkov-I", "name": { "family": "Zharkov", "given": "Ilia" } } ] }, "doi": "10.1007/978-3-319-06514-4_4", "pub_year": "2014", "author_list": "Gukov, Sergei and Su\u0142kowski, Piotr" }, { "id": "https://authors.library.caltech.edu/records/hgwzf-ttf17", "eprint_id": 70983, "eprint_status": "archive", "datestamp": "2023-08-20 00:50:18", "lastmod": "2026-04-16 01:40:23", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Eisentr\u00e4ger-K", "name": { "family": "Eisentr\u00e4ger", "given": "Kirsten" } }, { "id": "Hallgren-S", "name": { "family": "Hallgren", "given": "Sean" } }, { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Song-Fang", "name": { "family": "Song", "given": "Fang" } } ] }, "title": "A quantum algorithm for computing the unit group of an arbitrary degree number field", "ispublished": "unpub", "full_text_status": "public", "keywords": "Algorithms, Theory, Quantum Algorithms, Unit Group, Computational Algebraic Number Theory", "note": "Copyright is held by the owner/author(s). \n\nPartially supported by National Science Foundation grant DMS-1056703 and by the National Security Agency (NSA) under Army Research Office (ARO) contract number W911NF-12-1-0522. Part of this work was done while the first author was visiting Harvard University and MIT. \n\nPartially supported by National Science Foundation awards CCF-0747274 and CCF-1218721, and by the National Security Agency (NSA) under Army Research Office (ARO) contract number W911NF-12-1-0522. Part of this work was done while visiting MIT.\n\n

Published - p293-eisentrager.pdf

", "abstract": "Computing the group of units in a field of algebraic numbers\nis one of the central tasks of computational algebraic number theory. It is believed to be hard classically, which is of interest for cryptography. In the quantum setting, efficient algorithms were previously known for fields of constant degree. We give a quantum algorithm that is polynomial in the degree of the field and the logarithm of its discriminant. This is achieved by combining three new results. The first is a classical algorithm for computing a basis for certain ideal lattices with doubly exponentially large generators. The second shows that a Gaussian-weighted superposition of lattice points, with an appropriate encoding, can be used to provide a unique representation of a real-valued lattice. The third is an extension of the hidden subgroup problem to continuous groups and a quantum algorithm for solving the HSP over the group \u211d^n.", "date": "2014-05", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "293-302", "id_number": "CaltechAUTHORS:20161010-172823440", "isbn": "978-1-4503-2710-7", "book_title": "STOC '14 Proceedings of the 46th Annual ACM Symposium on Theory of Computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161010-172823440", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-1056703" }, { "agency": "Army Research Office (ARO)", "grant_number": "W911NF-12-1-0522" }, { "agency": "NSF", "grant_number": "CCF-0747274" }, { "agency": "NSF", "grant_number": "CCF-1218721" }, { "agency": "National Security Agency" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Shmoys-D", "name": { "family": "Shmoys", "given": "David" } } ] }, "doi": "10.1145/2591796.2591860", "primary_object": { "basename": "p293-eisentrager.pdf", "url": "https://authors.library.caltech.edu/records/hgwzf-ttf17/files/p293-eisentrager.pdf" }, "pub_year": "2014", "author_list": "Eisentr\u00e4ger, Kirsten; Hallgren, Sean; et al." }, { "id": "https://authors.library.caltech.edu/records/9zq9z-rcg96", "eprint_id": 52148, "eprint_status": "archive", "datestamp": "2023-08-19 22:57:25", "lastmod": "2026-03-09 21:44:03", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Noncommutative geometry models for particle physics", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Noncommutative geometry, particle models", "note": "\u00a9 2014 World Scientific Publishing.", "abstract": "This is a writeup of part of a series of lectures delivered at the Villa de\nLeyva summer school \"Geometric, Algebraic and Topological Methods for\nQuantum Field Theory\".\nI am very grateful to Sylvi Paycha for the invitation and to the organizers and the participants for the very friendly\nand nice atmosphere and the very lively and useful discussions. This paper\nfollows the same format of the lectures and the same very informal style,\nbut we refer the reader, wherever needed, to more detailed references for\nadditional material and a more rigorous treatment. The lectures originally\ncovered both the particle physics applications and some recent applications\nto cosmology, along the lines of the work. This writeup\nonly deals with the particle physics part, while the cosmology part of the\nlectures will be written up elsewhere.", "date": "2014-01", "date_type": "published", "publisher": "World Scientific Publishing", "place_of_pub": "Hackensack, NJ", "pagerange": "189-223", "id_number": "CaltechAUTHORS:20141125-125438021", "isbn": "9789814460057", "book_title": "Geometric, algebraic and topological methods for quantum field theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141125-125438021", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cardona-A", "name": { "family": "Cardona", "given": "Alexander" } } ] }, "doi": "10.1142/9789814460057_0005", "pub_year": "2014", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/6xzh8-1ca79", "eprint_id": 98056, "eprint_status": "archive", "datestamp": "2023-08-19 22:49:50", "lastmod": "2026-03-08 03:20:33", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Conlon-David", "name": { "family": "Conlon", "given": "David" }, "orcid": "0000-0001-5899-1829" } ] }, "title": "Combinatorial theorems relative to a random set", "ispublished": "unpub", "full_text_status": "public", "keywords": "Extremal combinatorics, random graphs", "note": "\u00a9 2014 by SEOUL ICM 2014 Organizing Committee. \n\nThis research was supported by a Royal Society University Research Fellowship. I would like to thank Jacob Fox, Tim Gowers, Rob Morris, Wojtek Samotij, Mathias Schacht, Benny Sudakov and Yufei Zhao for helpful discussions on the topics in this paper. Particular thanks are due to Wojtek Samotij for a number of detailed comments on the manuscript.\n\n

Submitted - 1404.3324.pdf

", "abstract": "We describe recent advances in the study of random analogues of combinatorial theorems.", "date": "2014", "date_type": "published", "publisher": "Kyung Moon Sa Co. Ltd.", "place_of_pub": "Seoul, Korea", "pagerange": "303-327", "id_number": "CaltechAUTHORS:20190820-164721413", "isbn": "9788961058070", "book_title": "Proceedings of the International Congress of Mathematicians", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190820-164721413", "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" } ] }, "contributors": { "items": [ { "id": "Jang-Sun-Young", "name": { "family": "Jang", "given": "Sun Young" } }, { "id": "Kim-Young-Rock", "name": { "family": "Kim", "given": "Young Rock" } }, { "id": "Lee-Dae-Woong", "name": { "family": "Lee", "given": "Dae-Woong" } }, { "id": "Yie-Ikkwon", "name": { "family": "Yie", "given": "Ikkwon" } } ] }, "doi": "10.48550/arXiv.1404.3324", "primary_object": { "basename": "1404.3324.pdf", "url": "https://authors.library.caltech.edu/records/6xzh8-1ca79/files/1404.3324.pdf" }, "pub_year": "2014", "author_list": "Conlon, David" }, { "id": "https://authors.library.caltech.edu/records/5tph9-ha980", "eprint_id": 51138, "eprint_status": "archive", "datestamp": "2023-08-19 21:43:24", "lastmod": "2026-03-18 00:02:26", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "B." }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Spectral Theory of Orthogonal Polynomials", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "OPRL, OPUC, potential theory", "note": "\u00a9 2013 World Scientific Publishing Co.\n\nIt is a pleasure to thank the Poincare Prize Committee for their honor, including\nthe opportunity to give this talk, and Arne Jensen and the rest of the organizing\ncommittees (local and scientific) for a stimulating conference.\nThe author was supported in part by NSF grant DMS-0968856 and by U.S.-Israel\nBinational Science Foundation (BSF) grant 2010348.", "abstract": "This is a summary of a talk given at ICMP 2012. It discusses some recent results in\nspectral theory through the prism of a new-found synergy between the spectral theory\nand OP communities.", "date": "2013-10", "date_type": "published", "publisher": "World Scientific Publishing", "place_of_pub": "Hackensack, NJ", "pagerange": "217-228", "id_number": "CaltechAUTHORS:20141031-135217196", "isbn": "9789814449243", "book_title": "XVIIth International Congress on Mathematical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141031-135217196", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0968856" }, { "agency": "Binational Science Foundation (USA-Israel)", "grant_number": "2010348" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Jensen-A", "name": { "family": "Jensen", "given": "Arne" } } ] }, "doi": "10.1142/9789814449243_0012", "pub_year": "2013", "author_list": "Simon, B." }, { "id": "https://authors.library.caltech.edu/records/kk69w-7xs20", "eprint_id": 97850, "eprint_status": "archive", "datestamp": "2023-08-19 20:39:33", "lastmod": "2026-03-08 18:14:05", "type": "book_section", "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": "Graph removal lemmas", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2013 Cambridge University Press. \n\nPrint publication year 2013; online publication date July 2013. \n\nConlon supported by a Royal Society University Research Fellowship. Fox supported by a Simons Fellowship and NSF Grant DMS-1069197. \n\nThe authors would like to thank Noga Alon, Zoltan F\u00fcredi, Vojta R\u00f6dl and Terry Tao for helpful comments regarding the history of the removal lemma.\n\n

Submitted - 1211.3487.pdf

", "abstract": "The graph removal lemma states that any graph on n vertices with o(n^h) copies of a fixed graph H on h vertices may be made H-free by removing o(n^2) edges. Despite its innocent appearance, this lemma and its extensions have several important consequences in number theory, discrete geometry, graph theory and computer science. In this survey we discuss these lemmas, focusing in particular on recent improvements to their quantitative aspects.", "date": "2013-07", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge, United Kingdom", "pagerange": "1-50", "id_number": "CaltechAUTHORS:20190812-163001516", "isbn": "9781139506748", "book_title": "Surveys in Combinatorics 2013", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190812-163001516", "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" } ] }, "contributors": { "items": [ { "id": "Blackburn-S-R", "name": { "family": "Blackburn", "given": "Simon R." } }, { "id": "Gerke-S", "name": { "family": "Gerke", "given": "Stefanie" } }, { "id": "Wildon-M", "name": { "family": "Wildon", "given": "Mark" } } ] }, "doi": "10.1017/cbo9781139506748.002", "primary_object": { "basename": "1211.3487.pdf", "url": "https://authors.library.caltech.edu/records/kk69w-7xs20/files/1211.3487.pdf" }, "pub_year": "2013", "author_list": "Conlon, David and Fox, Jacob" }, { "id": "https://authors.library.caltech.edu/records/61kqx-axk09", "eprint_id": 77091, "eprint_status": "archive", "datestamp": "2023-08-22 08:02:33", "lastmod": "2026-03-09 02:11:33", "type": "book_section", "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": "Derivation of Ginzburg-Landau theory for a one-dimensional system with contact interaction", "ispublished": "unpub", "full_text_status": "public", "keywords": "Ginzburg\u2013Landau theory; BCS theory; semiclassical analysis; superfluidity; superconductivity", "note": "\u00a9 2013 Springer Basel. \n\nFirst Online: 12 December 2012. \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. Financial support via U.S. NSF grants DMS-0800906 (C.H.) and PHY-0845292 (R.S.) and a grant from the Danish council for independent research (J.P.S.) is gratefully acknowledged.\n\n

Submitted - 1103.1866.pdf

", "abstract": "In a recent paper [7] we give the first rigorous derivation of the celebrated Ginzburg-Landau (GL)the ory, starting from the microscopic Bardeen- Cooper-Schrieffer (BCS)mo del. Here we present our results in the simplified case of a one-dimensional system of particles interacting via a \u03b4-potential.", "date": "2013", "date_type": "published", "publisher": "Springer", "place_of_pub": "Basel", "pagerange": "57-88", "id_number": "CaltechAUTHORS:20170501-083839909", "isbn": "978-3-0348-0531-5", "book_title": "Operator Methods in Mathematical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-083839909", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0800906" }, { "agency": "NSF", "grant_number": "PHY-0845292" }, { "agency": "Danish Council for Independent Research" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Janas-J", "name": { "family": "Janas", "given": "Jan" } }, { "id": "Kurasov-P", "name": { "family": "Kurasov", "given": "Pavel" } }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } }, { "id": "Naboko-S", "name": { "family": "Naboko", "given": "Sergei" } } ] }, "doi": "10.1007/978-3-0348-0531-5_3", "primary_object": { "basename": "1103.1866.pdf", "url": "https://authors.library.caltech.edu/records/61kqx-axk09/files/1103.1866.pdf" }, "pub_year": "2013", "author_list": "Frank, Rupert L.; Hainzl, Christian; et al." }, { "id": "https://authors.library.caltech.edu/records/qsdk4-86q79", "eprint_id": 44363, "eprint_status": "archive", "datestamp": "2023-08-19 14:02:19", "lastmod": "2026-03-17 23:59:57", "type": "book_section", "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: A review", "ispublished": "unpub", "full_text_status": "public", "keywords": "Isospectral torus, Orthogonal polynomials, Szeg\u00f6's theorem, Szeg\u00f6 asymptotics, Lieb-Thirring bounds.", "note": "\u00a9 2013 American Mathematical Society. The first and third authors would like to thank Caltech for its hospitality where\nthis manuscript was written. The first author was supported in part by a Steno Research Grant (09-064947) from the Danish Research Council for Nature and Universe. The second author was supported in part by NSF grant DMS-0968856.\nThe third author was supported in part by NSF grant DMS-0965411.\n\n

Submitted - 1301.5073v2.pdf

", "abstract": "Perhaps the most common theme in Fritz Gesztesy's broad opus is the study of problems with periodic or almost periodic finite gap differential and difference equations, especially those connected to integrable systems. The present paper reviews recent progress in the understanding of finite gap Jacobi matrices and their perturbations. We'd like to acknowledge our debt to Fritz as a collaborator and\nfriend. We hope Fritz enjoys this birthday bouquet!", "date": "2013", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, Rhode Island", "pagerange": "87-103", "id_number": "CaltechAUTHORS:20140317-145017007", "isbn": "978-0821875742", "book_title": "Spectral Analysis, Differential Equations and Mathematical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140317-145017007", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Danish Research Council for Nature and Universe Steno Reseach Grant", "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" } ] }, "contributors": { "items": [ { "id": "Holden-H", "name": { "family": "Holden", "given": "Helge" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" } }, { "id": "Teschl-G", "name": { "family": "Teschl", "given": "Gerald" } } ] }, "doi": "10.48550/arXiv.1301.5073", "primary_object": { "basename": "1301.5073v2.pdf", "url": "https://authors.library.caltech.edu/records/qsdk4-86q79/files/1301.5073v2.pdf" }, "pub_year": "2013", "author_list": "Christiansen, Jacob S.; Simon, Barry; et al." }, { "id": "https://authors.library.caltech.edu/records/d2wb1-23129", "eprint_id": 88576, "eprint_status": "archive", "datestamp": "2023-08-19 11:37:46", "lastmod": "2026-03-09 20:40:51", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Dynamics of non-archimedean Polish groups", "ispublished": "unpub", "full_text_status": "public", "keywords": "Non-archimedean groups, Fra\u00efss\u00e9 theory, Ramsey theory, ample genericity, automatic continuity, unique ergodicity, spatial realizations, unitary representations", "note": "\u00a9 2014 EMS Publishing House. \n\nWork on this paper was partially supported by NSF Grant DMS-0968710. I would like to thank J. Melleray, L. Nguyen Van Th\u00e9, C. Rosendal, M. Soki\u0107, S. Solecki, S. Thomas and T. Tsankov for many helpful comments on an earlier draft of this paper\n\n

Accepted Version - nonarchimedean01.pdf

", "abstract": "A topological group G is Polish if its topology admits a compatible separable complete metric. Such a group is non-archimedean if it has a basis at the identity that consists of open subgroups. This class of Polish groups includes the profinite groups and (\u211a_p, +)\nbut our main interest here will be on non-locally compact groups. \n\nIn recent years there has been considerable activity in the study of the dynamics of Polish non-archimedean groups and this has led to interesting interactions between logic, finite combinatorics, group theory, topological dynamics, ergodic theory and representation theory. In this paper I will give a survey of some of the main directions in this area of research.", "date": "2012-07", "date_type": "published", "publisher": "European Mathematical Society", "place_of_pub": "Zurich, Switzerland", "pagerange": "375-397", "id_number": "CaltechAUTHORS:20180803-160520242", "isbn": "978-3-03719-120-0", "book_title": "European Congress of Mathematics, Krak\u00f3w, 2-7 July, 2012", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180803-160520242", "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" } ] }, "contributors": { "items": [ { "id": "Lata\u0142a-R", "name": { "family": "Lata\u0142a", "given": "Rafa\u0142" } }, { "id": "Ruci\u0144ski-A", "name": { "family": "Ruci\u0144ski", "given": "Andrzej" } }, { "id": "Strzelecki-P", "name": { "family": "Strzelecki", "given": "Pawe\u0142" } }, { "id": "\u015awi\u0105tkowski-J", "name": { "family": "\u015awi\u0105tkowski", "given": "Jacek" } }, { "id": "Wrzosek-D", "name": { "family": "Wrzosek", "given": "Dariusz" } }, { "id": "Zakrzewski-P", "name": { "family": "Zakrzewski", "given": "Piotr" } } ] }, "doi": "10.4171/120", "primary_object": { "basename": "nonarchimedean01.pdf", "url": "https://authors.library.caltech.edu/records/d2wb1-23129/files/nonarchimedean01.pdf" }, "pub_year": "2012", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/arwxv-qn786", "eprint_id": 71975, "eprint_status": "archive", "datestamp": "2023-08-19 09:18:25", "lastmod": "2026-03-09 23:59:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Sivan-S", "name": { "family": "Sivan", "given": "Balasubramanian" } }, { "id": "Syrgkanis-V", "name": { "family": "Syrgkanis", "given": "Vasilis" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Lower Bounds on Revenue of Approximately Optimal Auctions", "ispublished": "unpub", "full_text_status": "public", "keywords": "Revenue, Auction, Geometric expectation, Single posted\nprice", "note": "\u00a9 2012 Springer-Verlag Berlin Heidelberg. \n\nThis work was done while the author was an intern at Microsoft Research. Part of this work was done while the author was an intern at Microsoft Research. Supported in part by ONR grant N00014-98-1-0589 and a Simons Graduate Fellowship. Part of this work was done while the author was a visitor at Microsoft Research. Supported in part by a Google Europe fellowship in Social Computing.\n\n

Submitted - 1210.0275.pdf

", "abstract": "We obtain revenue guarantees for the simple pricing mechanism of a single posted price, in terms of a natural parameter of the distribution of buyers' valuations. Our revenue guarantee applies to the single item n buyers setting, with values drawn from an arbitrary joint distribution. Specifically, we show that a single price drawn from the distribution of the maximum valuation v_(max)\u2009= \u2009max{V_1,V_2,\u2026,V_n} achieves a revenue of at least a 1/e fraction of the geometric expectation of v_(max). This generic bound is a measure of how revenue improves/degrades as a function of the concentration/spread of v_(max).\n\nWe further show that in absence of buyers' valuation distributions, recruiting an additional set of identical bidders will yield a similar guarantee on revenue. Finally, our bound also gives a measure of the extent to which one can simultaneously approximate welfare and revenue in terms of the concentration/spread of v_(max).", "date": "2012", "date_type": "published", "publisher": "Springer Verlag", "place_of_pub": "New York, NY", "pagerange": "526-531", "id_number": "CaltechAUTHORS:20161114-082632264", "isbn": "978-3-642-35310-9", "book_title": "Internet and Network Economics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161114-082632264", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-98-1-0589" }, { "agency": "Simons Foundation" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Goldberg-P-W", "name": { "family": "Goldberg", "given": "Paul W." } } ] }, "doi": "10.1007/978-3-642-35311-6_42", "primary_object": { "basename": "1210.0275.pdf", "url": "https://authors.library.caltech.edu/records/arwxv-qn786/files/1210.0275.pdf" }, "pub_year": "2012", "author_list": "Sivan, Balasubramanian; Syrgkanis, Vasilis; et al." }, { "id": "https://authors.library.caltech.edu/records/beqdn-6wr67", "eprint_id": 33160, "eprint_status": "archive", "datestamp": "2023-08-19 09:10:10", "lastmod": "2026-03-09 22:01:37", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ooguri-H", "name": { "family": "Ooguri", "given": "Hirosi" }, "orcid": "0000-0001-6021-3778" } ] }, "title": "Chapter 6. Lectures on Topological String Theory", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2012 Springer. \n\nI would like to thank the organizers of the summer school \"Strings and Fundamental Physics\" for the opportunity to give this set of lectures and for their hospitality. I am also grateful to Michael Kay and Daniel Plencner for helping with this manuscript.", "abstract": "In string theory, one typically studies em beddings of the string worldsheet E (which is a Riemann surface) into a 10-dimensional manifold of the form X : \u03a3 \u2192 R^(1,3) \u00d7 M,\nwith M a compact 6-dimensional manifold. In the following, we will restrict our attention to the study of supersymmetric sigma models onto the 6 compact dimensions.\nIn particular, we will assume M to be a Calabi-Yau threefold so that the theory possesses N = (2, 2) worldsheet superconformal symmetry.", "date": "2012", "date_type": "published", "publisher": "Springer", "pagerange": "233-263", "id_number": "CaltechAUTHORS:20120814-102100151", "isbn": "978-3-642-25946-3", "book_title": "Strings and Fundamental Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120814-102100151", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Baumgartl-M", "name": { "family": "Baumgartl", "given": "Marco" } }, { "id": "Brunner-I", "name": { "family": "Brunner", "given": "Illka" } }, { "id": "Haack-M", "name": { "family": "Haack", "given": "Michael" } } ] }, "doi": "10.1007/978-3-642-25947-0_6", "pub_year": "2012", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/7we1n-jk031", "eprint_id": 31987, "eprint_status": "archive", "datestamp": "2023-08-22 04:28:42", "lastmod": "2026-03-09 23:12:49", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Michel-P", "name": { "family": "Michel", "given": "Philippe" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Consequences of the Gross\u2013Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p", "ispublished": "unpub", "full_text_status": "public", "keywords": "Average L-values; Gross\u2013Zagier formulae; Non-vanishing; Subconvexity; Stability", "note": "\u00a9 2012 Springer. In memory of Serge Lang. Serge Lang always conveyed infectious excitement about mathematics to anyone he came into contact with, and he will be missed. He was quite interested in the values of L-functions and in the divisibility properties of arithmetic invariants, and\nit is a pleasure to dedicate this article to him. We would like to thank B. Gross for discussions concerning the occurrence of a factorial in Theorems 5.5, 5.6 of [11],\nand also M. Flach, H. Hida, K. Prasanna, V. Vatsal, and D. Whitehouse for helpful conversations concerning parts of the paper. Thanks are also due to Paul Nelson and\nthe anonymous referee for reading the paper carefully and finding a number of typos and small inaccuracies.\nThe first author would like to thank Caltech for its hospitality during the preparation of this work, and acknowledge the partial support he received from\nthe ERC advanced research grant no. 228304. The second author was partially supported by the National Science Foundation through the grants DMS-0402044 and DMS-0701089.\n\n

Submitted - 0709.4668.pdf

", "abstract": "Applying the celebrated results of Gross and Zagier for central values of L-series of holomorphic forms of prime level, we deduce an exact average formula for suitable twists of such L-values, with a relation to the class number of associated imaginary quadratic fieds, thereby strengthening a result of Duke. We also obtain a stability result, as well as subconvexity (in this setting), and certain non-vanishing assertions.", "date": "2012", "date_type": "published", "publisher": "Springer", "place_of_pub": "New York", "pagerange": "437-459", "id_number": "CaltechAUTHORS:20120620-113738336", "isbn": "978-1-4614-1259-5", "book_title": "Number Theory, Analysis and Geometry: In Memory of Serge Lang", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120620-113738336", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "European Research Council (ERC)", "grant_number": "228304" }, { "agency": "NSF", "grant_number": "DMS-0402044" }, { "agency": "NSF", "grant_number": "DMS-0701089" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Goldfeld-D", "name": { "family": "Goldfeld", "given": "Dorian" } }, { "id": "Jorgenson-J", "name": { "family": "Jorgenson", "given": "Jay" } }, { "id": "Jones-P", "name": { "family": "Jones", "given": "Peter" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" } }, { "id": "Ribet-K-A", "name": { "family": "Ribet", "given": "Kenneth A." } }, { "id": "Tate-J", "name": { "family": "Tate", "given": "John" } } ] }, "doi": "10.1007/978-1-4614-1260-1_20", "primary_object": { "basename": "0709.4668.pdf", "url": "https://authors.library.caltech.edu/records/7we1n-jk031/files/0709.4668.pdf" }, "pub_year": "2012", "author_list": "Michel, Philippe and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/8rxb0-07b70", "eprint_id": 88766, "eprint_status": "archive", "datestamp": "2023-08-19 09:19:02", "lastmod": "2026-03-09 20:34:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "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": "The complexity of classification problems in ergodic theory", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2012 Cambridge University Press.", "abstract": "The twelfth Appalachian Set Theory workshop was held at Vanderbilt University in Nashville on October 30, 2010. The lecturer was Alexander S. Kechris. As a graduate student Robin D. Tucker-Drob assisted in writing this chapter, which is based on the workshop lectures. \n\nDedicated to the memory of Greg Hjorth (1963\u20132011) \n\nThe last two decades have seen the emergence of a theory of set theoretic complexity of classification problems in mathematics. In these lectures we will discuss recent developments concerning the application of this theory to classification problems in ergodic theory. \n\nThe first lecture will be devoted to a general introduction to this area. The next two lectures will give the basics of Hjorth's theory of turbulence, a mixture of topological dynamics and descriptive set theory, which is a basic tool for proving strong non-classification theorems in various areas of mathematics. \n\nIn the last three lectures, we will show how these ideas can be applied in proving a strong non-classification theorem for orbit equivalence. Given a countable group \u0393, two free, measure-preserving, ergodic actions of \u0393 on standard probability spaces are called orbit equivalent if, roughly speaking, they have the same orbit spaces. More precisely this means that there is an isomorphism of the underlying measure spaces that takes the orbits of one action to the orbits of the other. A remarkable result of Dye and Ornstein-Weiss asserts that any two such actions of amenable groups are orbit equivalent.", "date": "2012", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "265-300", "id_number": "CaltechAUTHORS:20180810-151353411", "isbn": "9781139843065", "book_title": "Appalachian Set Theory: 2006-2012", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-151353411", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cummings-J", "name": { "family": "Cummings", "given": "James" } }, { "id": "Schimmerling-E", "name": { "family": "Schimmerling", "given": "Ernest" } } ] }, "doi": "10.1017/CBO9781139208574.010", "pub_year": "2012", "author_list": "Kechris, Alexander S. and Tucker-Drob, Robin D." }, { "id": "https://authors.library.caltech.edu/records/dymh4-e3754", "eprint_id": 36876, "eprint_status": "archive", "datestamp": "2023-08-19 09:13:03", "lastmod": "2026-03-09 21:43:48", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Motivic structures in quantum field theory", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2012 American Mathematical Society.\n\n

Published - Marcolli_2012p173.pdf

", "abstract": "This is a writeup of the lecture given by the author at the String-Math\n2011 conference in Philadelphia. It gives an overview of recent work of\nthe author, in collaboration with Aluffi and with Ceyhan, on some aspects of\nthe occurrence of motivic structures in perturbative quantum field theory.", "date": "2012", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "173-190", "id_number": "CaltechAUTHORS:20130212-112112394", "isbn": "9780821872956", "book_title": "String-Math 2011", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130212-112112394", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Block-J", "name": { "family": "Block", "given": "Jonathan" } }, { "id": "Distler-J", "name": { "family": "Distler", "given": "Jacques" } }, { "id": "Donagi-R", "name": { "family": "Donagi", "given": "Ron" } }, { "id": "Sharpe-E", "name": { "family": "Sharpe", "given": "Eric" } } ] }, "primary_object": { "basename": "Marcolli_2012p173.pdf", "url": "https://authors.library.caltech.edu/records/dymh4-e3754/files/Marcolli_2012p173.pdf" }, "pub_year": "2012", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/f16jr-nw068", "eprint_id": 36874, "eprint_status": "archive", "datestamp": "2023-08-19 09:12:59", "lastmod": "2026-03-09 02:17:36", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "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": "Homological algebra of knots and BPS states", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2012 American Mathematical Society. \n\nWe would like to thank S. Cautis, M. Marino, K. Schaeffer,\nY. Soibelman, C. Stroppel, C. Vafa, J. Walcher, and E. Witten for valuable discussions. The work of SG is supported in part by DOE Grant DE-FG03-92-ER40701\nand 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.\nMS was partially supported by the Portuguese Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia through ISR/IST plurianual funding and through the project number PTDC/MAT/101503/2008, New Geometry and Topology. MS was also partially supported by the Ministry of Science of Serbia, project no. 174012.\n\n

Published - Gukov_2012p125.pdf

Submitted - 1112.0030v2.pdf

", "abstract": "It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves wall crossing\nphenomena, algebras of closed BPS states acting on spaces of open BPS states, and deformations of Landau-Ginzburg models.\nOne important application to knot homologies is the existence of \"colored differentials\" that relate homological invariants of knots colored by different\nrepresentations. Based on this structure, we formulate a list of properties of the colored HOMFLY homology that categorifies the colored HOMFLY polynomial. By calculating the colored HOMFLY homology for symmetric and anti-symmetric representations, we find a remarkable \"mirror symmetry\" between these triply-graded theories.", "date": "2012", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "125-171", "id_number": "CaltechAUTHORS:20130212-111358154", "isbn": "9780821872956", "book_title": "String-Math 2011", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130212-111358154", "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": "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": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Block-J", "name": { "family": "Block", "given": "Jonathan" } }, { "id": "Distler-J", "name": { "family": "Distler", "given": "Jacques" } }, { "id": "Donagi-R", "name": { "family": "Donagi", "given": "Ron" } }, { "id": "Sharpe-E", "name": { "family": "Sharpe", "given": "Eric" } } ] }, "doi": "10.1090/pspum/085", "primary_object": { "basename": "Gukov_2012p125.pdf", "url": "https://authors.library.caltech.edu/records/f16jr-nw068/files/Gukov_2012p125.pdf" }, "related_objects": [ { "basename": "1112.0030v2.pdf", "url": "https://authors.library.caltech.edu/records/f16jr-nw068/files/1112.0030v2.pdf" } ], "pub_year": "2012", "author_list": "Gukov, Sergei and Sto\u0161i\u0107, Marko" }, { "id": "https://authors.library.caltech.edu/records/83ckw-tkz28", "eprint_id": 77085, "eprint_status": "archive", "datestamp": "2023-08-22 04:31:36", "lastmod": "2026-03-09 02:16:19", "type": "book_section", "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 new, rearrangement-free proof of the sharp Hardy-Littlewood-Sobolev inequality", "ispublished": "unpub", "full_text_status": "public", "keywords": "Sharp constants; Sobolev inequality; Hardy\u2013Littlewood\u2013Sobolev inequality", "note": "\u00a9 2012 Springer Basel AG. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nFirst Online: 11 October 2011. \n\nSupport by U.S. NSF grant PHY 0965859 (E.H.L.) is acknowledged. \n\nWe thank Richard Bamler for valuable help with Appendix B. \n\nThe published version of this paper contains a typo in the following boxed formula (1.3), which has been corrected here. We thank T. Weth for pointing this out to us.\n\n

Updated - 1010.5821.pdf

", "abstract": "We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on rearrangement inequalities; it is the first one to do so for the whole parameter range.", "date": "2012", "date_type": "published", "publisher": "Springer", "place_of_pub": "Basel", "pagerange": "55-67", "id_number": "CaltechAUTHORS:20170501-075729792", "isbn": "978-3-0348-0263-5", "book_title": "Spectral Theory, Function Spaces and Inequalities", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-075729792", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0965859" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Brown-B-M", "name": { "family": "Brown", "given": "B. Malcolm" } }, { "id": "Lang-Jan", "name": { "family": "Lang", "given": "Jan" } }, { "id": "Wood-I-G", "name": { "family": "Wood", "given": "Ian G." } } ] }, "doi": "10.1007/978-3-0348-0263-5_4", "primary_object": { "basename": "1010.5821.pdf", "url": "https://authors.library.caltech.edu/records/83ckw-tkz28/files/1010.5821.pdf" }, "pub_year": "2012", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/s7r86-ceg31", "eprint_id": 88905, "eprint_status": "archive", "datestamp": "2023-08-19 08:57:02", "lastmod": "2026-03-09 20:40:20", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "title": "Preface", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "This book continues the series of volumes containing reprints of the papers in the original Cabal Seminar volumes of the Springer Lecture Notes in Mathematics series [Cabal i, Cabal ii, Cabal iii, Cabal iv], unpublished material, and new papers. The first volume, [Cabal I], contained papers on games, scales and Suslin cardinals. In this volume, we continue with Parts III and IV of the project: Wadge degrees and pointclasses and Projective ordinals. As in our first volume, each of the parts contains an introductory survey (written by Alessandro Andretta and Alain Louveau for Part III and by Steve Jackson for Part IV) putting the papers into a present-day context. \n\nIn addition to the reprinted papers, this volume contains papers by Steel (More measures from AD) and Martin (Projective sets and cardinal numbers) that date back to the period of the original Cabal publications but were not included in the old volumes. Jackson contributed a new paper Regular cardinals without the weak partition property with recent results that fit well with the topic of Part IV. The paper Early investigations of the degrees of Borel sets by Wadge is a historical overview of the process of the development of the basic theory of the Wadge degrees. Table 1 gives an overview of the papers in this volume with their original references. \n\nAs emphasized in our first volume, our project is not to be understood as a historical edition of old papers. In the retyping process, we uniformized and modernized notation and numbering of sections and theorems.", "date": "2011-12-14", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "ix-xii", "id_number": "CaltechAUTHORS:20180817-104143981", "isbn": "9781139028073", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143981", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Schmid-B", "name": { "family": "Schmid", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9781139028073.001", "pub_year": "2011", "author_list": "Kechris, Alexander S.; L\u00f6we, Benedikt; et al." }, { "id": "https://authors.library.caltech.edu/records/ywh08-x3k15", "eprint_id": 88902, "eprint_status": "archive", "datestamp": "2023-08-19 08:56:58", "lastmod": "2026-03-09 20:36:37", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "title": "Original Numbering", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "[no abstract]", "date": "2011-12-14", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "xiii-xxii", "id_number": "CaltechAUTHORS:20180817-104143730", "isbn": "9781139028073", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143730", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9781139028073.021", "pub_year": "2011", "author_list": "Kechris, Alexander S.; L\u00f6we, Benedikt; et al." }, { "id": "https://authors.library.caltech.edu/records/8mahr-21p13", "eprint_id": 88880, "eprint_status": "archive", "datestamp": "2023-08-19 08:56:51", "lastmod": "2026-03-09 20:31:42", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Homogeneous trees and projective scales", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "date": "2011-12-14", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "270-303", "id_number": "CaltechAUTHORS:20180816-160145289", "isbn": "9781139028073", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145289", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9781139028073.014", "pub_year": "2011", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/8k8fg-wre98", "eprint_id": 88898, "eprint_status": "archive", "datestamp": "2023-08-19 08:56:55", "lastmod": "2026-03-09 20:40:56", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "A note on Wadge degrees", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "[no abstract]", "date": "2011-12-14", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "43-46", "id_number": "CaltechAUTHORS:20180817-104143314", "isbn": "9781139028073", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143314", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9781139028073.004", "pub_year": "2011", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/p4eqg-25p92", "eprint_id": 71914, "eprint_status": "archive", "datestamp": "2023-08-19 08:49:54", "lastmod": "2026-04-10 21:02:31", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Frongillo-R-M", "name": { "family": "Frongillo", "given": "Rafael M." } }, { "id": "Schoenebeck-G", "name": { "family": "Schoenebeck", "given": "Grant" } }, { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" } ] }, "title": "Social Learning in a Changing World", "ispublished": "unpub", "full_text_status": "public", "keywords": "social networks, Bayesian agents, social learning", "note": "\u00a9 2011 Springer-Verlag Berlin Heidelberg. \n\nSupported by the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program. This work was supported by Simons Foundation Postdoctoral Fellowship and National Science Foundation Graduate Fellowship. 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 - 1109.5482.pdf

", "abstract": "We study a model of learning on social networks in dynamic environments, describing a group of agents who are each trying to estimate an underlying state that varies over time, given access to weak signals and the estimates of their social network neighbors.\n\nWe study three models of agent behavior. In the fixed response model, agents use a fixed linear combination to incorporate information from their peers into their own estimate. This can be thought of as an extension of the DeGroot model to a dynamic setting. In the best response model, players calculate minimum variance linear estimators of the underlying state.\n\nWe show that regardless of the initial configuration, fixed response dynamics converge to a steady state, and that the same holds for best response on the complete graph. We show that best response dynamics can, in the long term, lead to estimators with higher variance than is achievable using well chosen fixed responses.\n\nThe penultimate prediction model is an elaboration of the best response model. While this model only slightly complicates the computations required of the agents, we show that in some cases it greatly increases the efficiency of learning, and on complete graphs is in fact optimal, in a strong sense.", "date": "2011-12", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin Heidelberg", "pagerange": "146-157", "id_number": "CaltechAUTHORS:20161110-121844664", "isbn": "978-3-642-25509-0", "book_title": "Internet and Network Economics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-121844664", "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": "Simons Foundation" }, { "agency": "NSF" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "Google" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Chen-Ning", "name": { "family": "Chen", "given": "Ning" } }, { "id": "Elkind-E", "name": { "family": "Elkind", "given": "Edith" } }, { "id": "Koutsoupias-E", "name": { "family": "Koutsoupias", "given": "Elias" } } ] }, "doi": "10.1007/978-3-642-25510-6_13", "primary_object": { "basename": "1109.5482.pdf", "url": "https://authors.library.caltech.edu/records/p4eqg-25p92/files/1109.5482.pdf" }, "pub_year": "2011", "author_list": "Frongillo, Rafael M.; Schoenebeck, Grant; et al." }, { "id": "https://authors.library.caltech.edu/records/qq6jx-pzf63", "eprint_id": 71912, "eprint_status": "archive", "datestamp": "2023-08-19 07:23:43", "lastmod": "2026-04-10 20:46:36", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Tamuz-O", "name": { "family": "Tamuz", "given": "Omer" }, "orcid": "0000-0002-0111-0418" }, { "id": "Liu-Ce", "name": { "family": "Liu", "given": "Ce" } }, { "id": "Belongie-S", "name": { "family": "Belongie", "given": "Serge" }, "orcid": "0000-0002-0388-5217" }, { "id": "Shamir-O", "name": { "family": "Shamir", "given": "Ohad" } }, { "id": "Kalai-A-T", "name": { "family": "Kalai", "given": "Adam Tauman" } } ] }, "title": "Adaptively Learning the Crowd Kernel", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 by the author(s)/owner(s). \n\nWe thank Sham Kakade and Varun Kanade for helpful discussions. Serge Belongie's research is partly funded by ONR MURI Grant N00014-08-1-0638 and NSF Grant AGS-0941760.\n\n

Published - ICML2011Tamuz_395.pdf

Submitted - 1105.1033.pdf

", "abstract": "We introduce an algorithm that, given n objects, learns a similarity matrix over all n^2 pairs, from crowdsourced data alone. The algorithm samples responses to adaptively chosen triplet-based relative-similarity queries. Each query has the form \"is object a more similar to b or to c?\" and is chosen to be maximally informative given the preceding responses. The output is an embedding of\nthe objects into Euclidean space (like MDS); we refer to this as the \"crowd kernel.\" SVMs reveal that the crowd kernel captures prominent and subtle features across a number of domains, such as \"is striped\" among neckties\nand \"vowel vs. consonant\" among letters.", "date": "2011-07", "date_type": "published", "publisher": "ACM", "place_of_pub": "New York, NY", "pagerange": "673-680", "id_number": "CaltechAUTHORS:20161110-102619803", "isbn": "978-1-4503-0619-5", "book_title": "International Conference on Machine Learning", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-102619803", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Office of Naval Research (ONR)", "grant_number": "N00014-08-1-0638" }, { "agency": "NSF", "grant_number": "AGS-0941760" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Getoor-L", "name": { "family": "Getoor", "given": "Lise" } }, { "id": "Scheffer-T", "name": { "family": "Scheffer", "given": "Tobias" } } ] }, "doi": "10.48550/arXiv.1105.1033", "primary_object": { "basename": "1105.1033.pdf", "url": "https://authors.library.caltech.edu/records/qq6jx-pzf63/files/1105.1033.pdf" }, "related_objects": [ { "basename": "ICML2011Tamuz_395.pdf", "url": "https://authors.library.caltech.edu/records/qq6jx-pzf63/files/ICML2011Tamuz_395.pdf" } ], "pub_year": "2011", "author_list": "Tamuz, Omer; Liu, Ce; et al." }, { "id": "https://authors.library.caltech.edu/records/y19yb-rnv59", "eprint_id": 77808, "eprint_status": "archive", "datestamp": "2023-08-19 05:55:08", "lastmod": "2026-04-10 23:31:47", "type": "book_section", "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": "Seiringer-R", "name": { "family": "Seiringer", "given": "Robert" } } ] }, "title": "A sharp bound on eigenvalues of Schr\u00f6edinger operators on the half-line with complex-valued potentials", "ispublished": "unpub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator, complex potential, eigenvalue bounds", "note": "\u00a9 2011 Springer Basel AG. \n\nFirst Online: 21 March 2011. \n\nSupport through DFG grant FR 2664/1-1 (R.F.) and U.S. National Science Foundation grants PHY 0652854 (R.F.) and PHY 0652356 (R.S.) is gratefully acknowledged.\n\n

Submitted - 0903.2053.pdf

", "abstract": "We derive a sharp bound on the location of non-positive eigenvalues of Schr\u00f6edinger operators on the halfline with complex-valued potentials.", "date": "2011-03-21", "date_type": "published", "publisher": "Springer", "place_of_pub": "Basel", "pagerange": "39-44", "id_number": "CaltechAUTHORS:20170526-100635987", "isbn": "9783764399948", "book_title": "Spectral Theory and Analysis", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-100635987", "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": "NSF", "grant_number": "PHY-0652356" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Janas-J", "name": { "family": "Janas", "given": "Jan" } }, { "id": "Kurasov-P", "name": { "family": "Kurasov", "given": "Pavel" } }, { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } }, { "id": "Naboko-S", "name": { "family": "Naboko", "given": "Sergei" } }, { "id": "Stolz-G", "name": { "family": "Stolz", "given": "G\u00fcnter" } } ] }, "doi": "10.1007/978-3-7643-9994-8_3", "primary_object": { "basename": "0903.2053.pdf", "url": "https://authors.library.caltech.edu/records/y19yb-rnv59/files/0903.2053.pdf" }, "pub_year": "2011", "author_list": "Frank, Rupert L.; Laptev, Ari; et al." }, { "id": "https://authors.library.caltech.edu/records/458yg-fnj69", "eprint_id": 77080, "eprint_status": "archive", "datestamp": "2023-08-19 05:02:09", "lastmod": "2026-03-09 02:15:13", "type": "book_section", "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": "Spherical reflection positivity and the Hardy-Littlewood-Sobolev inequality", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 American Mathematical Society. \n\nSupport through U.S. NSF grant PHY 0652854 is gratefully acknowledged.\n\n

Submitted - 1003.5248.pdf

", "abstract": "We introduce the concept of spherical (as distinguished from planar) reflection positivity and use it to obtain a new proof of the sharp constants in certain cases of the HLS and the logarithmic HLS inequality. Our proofs relies on an extension of a work by Li and Zhu which characterizes the minimizing functions of the type (1+|x|^2)^(\u2212p).", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "89-102", "id_number": "CaltechAUTHORS:20170501-070506766", "isbn": "978-0-8218-4971-2", "book_title": "Concentration, Functional Inequalities and Isoperimetry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-070506766", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0652854" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Houdr\u00e9-C", "name": { "family": "Houdr\u00e9", "given": "Christian" } }, { "id": "Ledoux-M", "name": { "family": "Ledoux", "given": "Michel" } }, { "id": "Milman-E", "name": { "family": "Milman", "given": "Emanuel" } }, { "id": "Milman-M", "name": { "family": "Milman", "given": "Mario" } } ] }, "doi": "10.48550/arXiv.1003.5248", "primary_object": { "basename": "1003.5248.pdf", "url": "https://authors.library.caltech.edu/records/458yg-fnj69/files/1003.5248.pdf" }, "pub_year": "2011", "author_list": "Frank, Rupert L. and Lieb, Elliott H." }, { "id": "https://authors.library.caltech.edu/records/t31jv-7jn38", "eprint_id": 81813, "eprint_status": "archive", "datestamp": "2023-08-19 05:02:24", "lastmod": "2026-03-09 22:11:39", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "Elliptic Analogues of the Macdonald and Koornwinder Polynomials", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Macdonald polynomials, elliptic curves, special functions", "note": "\u00a9 2011 Hindustan Book Agency. \n\nPartially supported by the NSF, grant no. DMS-0401387.", "abstract": "Perhaps the nicest multivariate orthogonal polynomials are the Macdonald and Koornwinder polynomials, respectively 2-parameter deformations of Schur functions and 6-parameter deformations of orthogonal and symplectic characters,\nsatisfying a trio of nice properties known as the Macdonald \"conjectures\". In recent work, the author has constructed elliptic analogues: a family of multivariate\nfunctions on an elliptic curve satisfying analogues of the Macdonald conjectures, and degenerating to Macdonald and Koornwinder polynomials under suitable limits. This article will discuss the two main constructions for these functions, focusing on the more algebraic/combinatorial of the two approaches.", "date": "2011", "date_type": "published", "publisher": "Hindustan Book Agency", "place_of_pub": "New Delhi, India", "pagerange": "2530-2554", "id_number": "CaltechAUTHORS:20170925-124323959", "isbn": "9789814324304", "book_title": "Proceedings of the International Congress of Mathematicians : Hyderabad, August 19-27, 2010", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-124323959", "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" } ] }, "contributors": { "items": [ { "id": "Bhatia-R", "name": { "family": "Bhatia", "given": "Rajendra" } }, { "id": "Pal-A", "name": { "family": "Pal", "given": "Arup" } }, { "id": "Rangarajan-G", "name": { "family": "Rangarajan", "given": "G." } }, { "id": "Srinivas-V", "name": { "family": "Srinivas", "given": "V." } }, { "id": "Vanninathan-M", "name": { "family": "Vanninathan", "given": "M." } } ] }, "doi": "10.1142/9789814324359_0157", "pub_year": "2011", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/1j6aw-wxs82", "eprint_id": 23983, "eprint_status": "archive", "datestamp": "2023-08-19 04:51:47", "lastmod": "2026-03-09 21:42:19", "type": "book_section", "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": "Feynman motives and deletion-contraction relations", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 American Mathematical Society. \n\nThe results in this article were catalyzed by a question posed to the first author by Michael Falk during the Jaca 'Lib60ber' conference, in June 2009. We thank him and the organizers of the conference, and renew our best wishes to Anatoly Libgober. We thank Friedrich Hirzebruch for pointing out Remark 5.4 to us, thereby triggering the thoughts leading to much of the material in \u00a76. We also thank Don Zagier for a useful conversation on divisibility sequences and generating functions. The second author is partially supported by NSF grants DMS-0651925 and DMS-0901221. This work was carried out during a stay of the\nauthors at the Max Planck Institute in July 2009.\n\n

Published - Aluffi2011p14060.pdf

", "abstract": "We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic Feynman rules under the operation of multiplying edges in a graph and we compare it with similar formulae for the Tutte polynomial of graphs, both being specializations of the same universal recursive relation. We obtain similar recursions for outerplanar graphs (given in full for chains of polygons) and for graphs obtained by replacing an edge by a chain of triangles. We show that the deletion-contraction relation can be lifted to the level of the category of mixed motives in the form of a distinguished triangle, similarly to what happens in categorfications of graph invariants.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "21-64", "id_number": "CaltechAUTHORS:20110613-094812678", "isbn": "978-0-8218-4890-6", "book_title": "Topology of Algebraic Varieties and Singularities", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110613-094812678", "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" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Libgober-A", "name": { "family": "Libgober", "given": "A." } }, { "id": "Cogolludo-Agust\u00edn-J-I", "name": { "family": "Cogolludo-Agust\u00edn", "given": "Jos\u00e9 Ignacio" } }, { "id": "Hironaka-E", "name": { "family": "Hironaka", "given": "Eriko" } } ] }, "doi": "10.48550/arXiv.0907.3225", "primary_object": { "basename": "Aluffi2011p14060.pdf", "url": "https://authors.library.caltech.edu/records/1j6aw-wxs82/files/Aluffi2011p14060.pdf" }, "pub_year": "2011", "author_list": "Aluffi, Paolo and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/csrxr-6vg78", "eprint_id": 24336, "eprint_status": "archive", "datestamp": "2023-08-19 04:52:38", "lastmod": "2026-03-09 02:33:10", "type": "book_section", "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": "Quantum Field Theory and the Volume Conjecture", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 American Mathematical Society. \n\nSubmitted on 25 Mar 2010 (v1), last revised 26 Mar 2010 (this version, v2). T\n\nhe 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. Opinions and conclusions expressed here are those of the authors and do not necessarily reflect the views of funding agencies. We would like to thank Edward Witten, Don Zagier, and Jonatan Lenells for enlightening\ndiscussions on subjects considered in these notes. We would also like to thank the organizers of the workshop Interactions Between Hyperbolic Geometry, Quantum Topology, and Knot Theory and Columbia University for their generous\nsupport, accommodations, and collaborative working environment.\n\n

Published - Dimofte2011p14335Interactions_Between_Hyperbolic_Geometry_Quantum_Topology_And_Number_Theory.pdf

", "abstract": "The volume conjecture states that for a hyperbolic knot K in the three-sphere S^3 the asymptotic growth of the colored Jones polynomial of K is governed by the hyperbolic volume of the knot complement S^3\\K. The conjecture relates two topological invariants, one combinatorial and one geometric, in a very nonobvious, nontrivial manner. The goal of the present lectures is to review the original statement of the volume conjecture and its recent extensions and generalizations, and to show how, in the most general context, the conjecture can be understood in terms of topological quantum field theory. In particular, we consider: a) generalization of the volume conjecture to families of incomplete hyperbolic metrics; b) generalization that involves not only the leading (volume) term, but the entire asymptotic expansion in 1/N; c) generalization to quantum group invariants for groups of higher rank; and d) generalization to arbitrary links in arbitrary three-manifolds.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "41-67", "id_number": "CaltechAUTHORS:20110707-110110717", "isbn": "978-0-8218-4960-6", "book_title": "Interactions between hyperbolic geometry, quantum topology, and number theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110707-110110717", "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" } ] }, "contributors": { "items": [ { "id": "Champanerkar-A", "name": { "family": "Champanerkar", "given": "A." } }, { "id": "Dasbach-O", "name": { "family": "Dasbach", "given": "O." } }, { "id": "Kalfagianni-E", "name": { "family": "Kalfagianni", "given": "E." } }, { "id": "Kofman-I", "name": { "family": "Kofman", "given": "I." } }, { "id": "Neumann-W", "name": { "family": "Neumann", "given": "W." } }, { "id": "Stoltzfus-N", "name": { "family": "Stoltzfus", "given": "N." } } ] }, "doi": "10.1090/conm/541/10678", "primary_object": { "basename": "Dimofte2011p14335Interactions_Between_Hyperbolic_Geometry_Quantum_Topology_And_Number_Theory.pdf", "url": "https://authors.library.caltech.edu/records/csrxr-6vg78/files/Dimofte2011p14335Interactions_Between_Hyperbolic_Geometry_Quantum_Topology_And_Number_Theory.pdf" }, "pub_year": "2011", "author_list": "Dimofte, Tudor and Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/t0w2e-xpe36", "eprint_id": 77084, "eprint_status": "archive", "datestamp": "2023-08-22 01:40:26", "lastmod": "2026-03-08 19:57:04", "type": "book_section", "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": "Binding, Stability, and Non-binding of Multi-polaron Systems", "ispublished": "unpub", "full_text_status": "public", "keywords": "Polaron; binding energies; stability; Coulomb system; Lieb-Thirring inequality", "note": "\u00a9 2010 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nPartial financial support from the U.S. National Science Foundation through grants PHY-0965859 (E.L.) 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 - 9789814350365_0002.pdf

Submitted - 1010.0737.pdf

", "abstract": "The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U = 2\u0251, where U is the electronic Coulomb repulsion and \u0251 is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large \u0251. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.", "date": "2011", "date_type": "published", "publisher": "World Scientific", "place_of_pub": "Singapore", "pagerange": "21-32", "id_number": "CaltechAUTHORS:20170501-075001254", "isbn": "9789814350365", "book_title": "Mathematical Results in Quantum Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-075001254", "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": "University of British Columbia" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Exner-P", "name": { "family": "Exner", "given": "Pavel" } } ] }, "doi": "10.1142/9789814350365_0002", "primary_object": { "basename": "1010.0737.pdf", "url": "https://authors.library.caltech.edu/records/t0w2e-xpe36/files/1010.0737.pdf" }, "related_objects": [ { "basename": "9789814350365_0002.pdf", "url": "https://authors.library.caltech.edu/records/t0w2e-xpe36/files/9789814350365_0002.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/n5697-t5b91", "eprint_id": 25212, "eprint_status": "archive", "datestamp": "2023-08-19 04:53:45", "lastmod": "2026-03-09 23:11:38", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Icosahedral Fibres of the Symmetric Cube and Algebraicity", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Dinakar Ramakrishnan. Partly supported by the NSF grant DMS-0701089.\n\n

Submitted - 0812.4787v2_1_.pdf

", "abstract": "For any number field F, call a cusp form \u03c0 = \u03c0_\u221e\u2297\u03c0f on GL(2)/F special icosahedral, or just s-icosahedral for short, if \u03c0 is not solvable polyhedral, and for a\nsuitable \"conjugate\" cusp form \u03c0' on GL(2)/F, sym^3(\u03c0) is isomorphic to sym^3(\u03c0'), and the symmetric fifth power L-series of \u03c0 equals the Rankin-Selberg L-function\nL(s, sym^2(\u03c0') \u00d7 \u03c0) (up to a finite number of Euler factors). Then the point of this Note is to obtain the following result: Let \u03c0 be s-icosahedral (of trivial central character). Then \u03c0 f is algebraic without local components of Steinberg type, \u03c0 \u221e is of Galois type, and \u03c0_v is tempered every-where. Moreover, if \u03c0' is also of trivial central character, it is s-icosahedral, and the\nfield of rationality Q(\u03c0f) (of \u03c0f) is K := Q[\u221a5], with \u03c0'\n_f being the Galois conjugate of \u03c0f under the non-trivial automorphism of K. There is an analogue in the case of non-trivial central character \u03c9, with the conclusion that \u03c0 is algebraic when \u03c9 is, and when \u03c9 has finite order, Q(\u03c0f) is contained in a cyclotomic field.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "483-499", "id_number": "CaltechAUTHORS:20110902-114949812", "isbn": "0-8218-5204-3", "book_title": "On certain L-functions: conference in honor of Freydoon Shahidi on certain L-functions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110902-114949812", "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" } ] }, "contributors": { "items": [ { "id": "Arthur-J", "name": { "family": "Arthur", "given": "James" } }, { "id": "Shahidi-F", "name": { "family": "Shahidi", "given": "Freydoon" } }, { "id": "Gelbart-S", "name": { "family": "Gelbart", "given": "Steve" } }, { "id": "Goldberg-D", "name": { "family": "Goldberg", "given": "David" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" } }, { "id": "Yu-J-K", "name": { "family": "Yu", "given": "Jiu-Kang" } } ] }, "doi": "10.48550/arXiv.0812.4787v2", "primary_object": { "basename": "0812.4787v2_1_.pdf", "url": "https://authors.library.caltech.edu/records/n5697-t5b91/files/0812.4787v2_1_.pdf" }, "pub_year": "2011", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/n2xft-jzr11", "eprint_id": 32382, "eprint_status": "archive", "datestamp": "2023-08-19 04:57:41", "lastmod": "2026-03-09 21:40:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Carey-A", "name": { "family": "Carey", "given": "Alan" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "id": "Rennie-A", "name": { "family": "Rennie", "given": "Adam" } } ] }, "title": "Modular Index Invariants of Mumford Curves", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Johns Hopkins University Press.\n\n

Submitted - 0905.3157v1.pdf

", "abstract": "We continue an investigation initiated by Consani-Marcolli of the relation between the algebraic geometry of p-adic Mumford curves and the noncommutative geometry of graph C*-algebras associated to the action of the uniformizing p-adic Schottky group on the Bruhat-Tits tree. We reconstruct invariants of Mumford curves related to valuations of generators of the associated Schottky group, by developing a graphical theory for KMS weights on the associated graph C*-algebra, and using modular index theory for KMS weights. We give explicit examples of the construction of graph weights for low genus Mumford curves. We then show that the theta functions of Mumford curves, and the induced currents on the Bruhat-Tits tree, define functions that generalize the graph weights. We show that such inhomogeneous graph weights can be constructed from spectral flows, and that one can reconstruct theta functions from such graphical data.", "date": "2011", "date_type": "published", "publisher": "Johns Hopkins University Press", "place_of_pub": "Baltimore", "pagerange": "31-73", "id_number": "CaltechAUTHORS:20120712-101547699", "isbn": "9781421403526", "book_title": "Noncommutative geometry, arithmetic, and related topics: proceedings of the Twenty-first Meeting of the Japan-U.S. Mathematics Institute", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120712-101547699", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Consani-C", "name": { "family": "Consani", "given": "Caterina" } }, { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } } ] }, "doi": "10.48550/arXiv.0905.3157", "primary_object": { "basename": "0905.3157v1.pdf", "url": "https://authors.library.caltech.edu/records/n2xft-jzr11/files/0905.3157v1.pdf" }, "pub_year": "2011", "author_list": "Carey, Alan; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/28cek-jqe96", "eprint_id": 29571, "eprint_status": "archive", "datestamp": "2023-08-22 01:39:08", "lastmod": "2026-03-09 02:38:35", "type": "book_section", "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": "Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory", "ispublished": "unpub", "full_text_status": "public", "keywords": "High Energy Physics - Theory (hep-th); Quantum Algebra (math.QA)", "note": "\u00a9 2011 American Mathematical Society.\n\n

Submitted - Kapustin_2010.pdf

", "abstract": "We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The algebraic properties of the resulting 2d RCFT, such as the classification of symmetry-preserving boundary conditions, are expressed in terms of properties of the surface operator. We show that to every surface operator one may attach a Morita-equivalence class of symmetric Frobenius algebras in the ribbon category of bulk line operators. This provides a simple interpretation of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs from Frobenius algebras. We also show that every topological boundary condition in a 3d TFT gives rise to a commutative Frobenius algebra in the category of bulk line operators. We illustrate these general considerations by studying in detail surface operators in abelian Chern-Simons theory.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "175-198", "id_number": "CaltechAUTHORS:20120302-140549797", "isbn": "978-0-8218-5195-1", "book_title": "Mathematical Foundations of Quantum Field Theory and Perturbative String Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120302-140549797", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Caltech-Theory" }, { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Sati-H", "name": { "family": "Sati", "given": "Hisham" } }, { "id": "Schreiber-U", "name": { "family": "Schreiber", "given": "Urs" } } ] }, "doi": "10.48550/arXiv.1012.0911", "primary_object": { "basename": "Kapustin_2010.pdf", "url": "https://authors.library.caltech.edu/records/28cek-jqe96/files/Kapustin_2010.pdf" }, "pub_year": "2011", "author_list": "Kapustin, Anton and Saulina, Natalia" }, { "id": "https://authors.library.caltech.edu/records/5w8at-7mn11", "eprint_id": 29262, "eprint_status": "archive", "datestamp": "2023-08-19 04:56:16", "lastmod": "2026-03-09 21:51:38", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ni-Yi", "name": { "family": "Ni", "given": "Yi" } } ] }, "title": "Thurston norm and cosmetic surgeries", "ispublished": "unpub", "full_text_status": "public", "keywords": "Thurston norm, cosmetic surgeries, Heegaard Floer homology", "note": "\u00a9 2011 American Mathematical Society.\nThe author is partially supported by an AIM Five-Year Fellowship and NSF grant number\nDMS-0805807\n\n

Submitted - 1001.3926v1.pdf

", "abstract": "Two Dehn surgeries on a knot are called cosmetic if they yield\nhomeomorphic manifolds. For a null-homologous knot with certain conditions\non the Thurston norm of the ambient manifold, if the knot admits cosmetic\nsurgeries, then the surgery coefficients are equal up to sign.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "53-63", "id_number": "CaltechAUTHORS:20120213-133917658", "isbn": "9780821852354", "book_title": "Low-dimensional and Symplectic Topology", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120213-133917658", "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" } ] }, "contributors": { "items": [ { "id": "Usher-M", "name": { "family": "Usher", "given": "Michael" } } ] }, "doi": "10.48550/arXiv.1001.3926", "primary_object": { "basename": "1001.3926v1.pdf", "url": "https://authors.library.caltech.edu/records/5w8at-7mn11/files/1001.3926v1.pdf" }, "pub_year": "2011", "author_list": "Ni, Yi" }, { "id": "https://authors.library.caltech.edu/records/s0b8s-tmq68", "eprint_id": 23655, "eprint_status": "archive", "datestamp": "2023-08-19 04:50:55", "lastmod": "2026-03-09 21:31:01", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Mantovan-E", "name": { "family": "Mantovan", "given": "Elena" } } ] }, "title": "l-Adic \u00c9tale Cohomology of PEL Type Shimura Varieties with Non-Trivial Coefficients", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 American Mathematical Society.\nPartially supported by the National Science Foundation under Grant DMS-0701310.\nI would like to thank R. Taylor, M. Harris, and S.W. Shin\nfor their interest in my work and for stimulating discussions, and the referee for\nhelpful comments and useful suggestions.\n\n

Published - Mantovan2011p13778Win_-_Women_In_Numbers_Research_Directions_In_Number_Theory.pdf

", "abstract": "Given a Shimura datum (G, h) of PEL type, let p be an odd prime at which G is unramified. In [13], we established a formula computing the l-adic cohomology of the associated Shimura varieties (regarded as a representation of the acidic points of G and of the local Weil group at p) in terms of that of their local models at p (the associated Rapoport-Zink spaces) and of the corresponding Igusa varieties. In this paper we extend those results (which are for cohomology with constant l-adic coefficients) to the general case of coefficients in a lisse \u00e9tale sheaf attached to a finite dimensional l-adic representation of the group G.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "61-83", "id_number": "CaltechAUTHORS:20110512-135514802", "isbn": "978-0-8218-5226-2", "book_title": "Win- Women in Numbers: Research Directions in Number Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110512-135514802", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0701310" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cojocaru-A-C", "name": { "family": "Cojocaru", "given": "Alina Carmen" } } ] }, "primary_object": { "basename": "Mantovan2011p13778Win_-_Women_In_Numbers_Research_Directions_In_Number_Theory.pdf", "url": "https://authors.library.caltech.edu/records/s0b8s-tmq68/files/Mantovan2011p13778Win_-_Women_In_Numbers_Research_Directions_In_Number_Theory.pdf" }, "pub_year": "2011", "author_list": "Mantovan, Elena" }, { "id": "https://authors.library.caltech.edu/records/03hke-k0r77", "eprint_id": 88758, "eprint_status": "archive", "datestamp": "2023-08-19 05:03:09", "lastmod": "2026-03-09 20:31:53", "type": "book_section", "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." } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "title": "The axiom of determinacy and the prewellordering property", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2011", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "118-140", "id_number": "CaltechAUTHORS:20180810-140140332", "isbn": "9780521762038", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-140140332", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9781139028073.008", "pub_year": "2011", "author_list": "Kechris, Alexander S.; Solovay, Robert M.; et al." }, { "id": "https://authors.library.caltech.edu/records/fv1ds-kq837", "eprint_id": 77088, "eprint_status": "archive", "datestamp": "2023-08-22 01:40:33", "lastmod": "2026-03-09 02:14:35", "type": "book_section", "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": "Two-term spectral asymptotics for the Dirichlet Laplacian on a bounded domain", "ispublished": "unpub", "full_text_status": "public", "keywords": "Dirichlet Laplace operator; Semiclassical limit; Weyl's law", "note": "\u00a9 2010 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes.\n\n

Published - 9789814350365_0012.pdf

Submitted - 1105.5182.pdf

", "abstract": "Let \u2212\u0394 denote the Dirichlet Laplace operator on a bounded open set in Rd. We study the sum of the negative eigenvalues of the operator \u2212h^2\u0394 \u2212 1 in the semiclassical limit h \u2192 0+. We give a new proof that yields not only the first term of the asymptotic formula but also the second term involving the surface area of the boundary of the set. The proof is valid under weak smoothness assumptions on the boundary.", "date": "2011", "date_type": "published", "publisher": "World Scientific", "place_of_pub": "Singapore", "pagerange": "138-147", "id_number": "CaltechAUTHORS:20170501-080935483", "isbn": "9789814350365", "book_title": "Mathematical Results in Quantum Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170501-080935483", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Exner-P", "name": { "family": "Exner", "given": "Pavel" } } ] }, "doi": "10.1142/9789814350365_0012", "primary_object": { "basename": "1105.5182.pdf", "url": "https://authors.library.caltech.edu/records/fv1ds-kq837/files/1105.5182.pdf" }, "related_objects": [ { "basename": "9789814350365_0012.pdf", "url": "https://authors.library.caltech.edu/records/fv1ds-kq837/files/9789814350365_0012.pdf" } ], "pub_year": "2011", "author_list": "Frank, Rupert L. and Geisinger, Leander" }, { "id": "https://authors.library.caltech.edu/records/eyg3y-28z07", "eprint_id": 88740, "eprint_status": "archive", "datestamp": "2023-08-19 05:03:05", "lastmod": "2026-03-09 20:34:37", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "AD and projective ordinals", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "[no abstract]", "date": "2011", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "304-345", "id_number": "CaltechAUTHORS:20180810-084248820", "isbn": "9780521762038", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-084248820", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9781139028073.015", "pub_year": "2011", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/xf64a-qg632", "eprint_id": 79068, "eprint_status": "archive", "datestamp": "2023-08-19 04:27:34", "lastmod": "2026-04-11 22:08:28", "type": "book_section", "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": "The Weil Proof and the Geometry of the Adel\u00e8s Class Space", "ispublished": "unpub", "full_text_status": "public", "keywords": "noncommutative geometry, cyclic homology, thermodynamics,\nfactors, Riemann zeta function, correspondences, Lefschetz trace formula, ad\u00e8les, id\u00e8les, Frobenius", "note": "\u00a9 2009 Springer Science+Business Media, LLC. \n\nFirst Online: 21 November 2010. \n\nDedicated to Yuri Manin on the occasion of his 70th birthday.\n\n

Submitted - 0703392.pdf

", "abstract": "This paper explores analogies between the Weil proof of the Riemann hypothesis for function fields and the geometry of the ad\u00e8les class space, which is the noncommutative space underlying Connes' spectral realization of the zeros of the Riemann zeta function. We consider the cyclic homology of the cokernel (in the abelian category of cyclic modules) of the \"restriction map\" defined by the inclusion of the id\u00e8les class group of a global field in the noncommutative ad\u00e8les class space. Weil's explicit formula can then be formulated as a Lefschetz trace formula for the induced action of the id\u00e8les class group on this cohomology. In this formulation the Riemann hypothesis becomes equivalent to the positivity of the relevant trace pairing. This result suggests a possible dictionary between the steps in the Weil proof and corresponding notions involving the noncommutative geometry of the ad\u00e8les class space, with good working notions of correspondences, degree, and codegree etc. In particular, we construct an analog for number fields of the algebraic points of the curve for function fields, realized here as classical points (low temperature KMS states) of quantum statistical mechanical systems naturally associated to the periodic orbits of the action of the id\u00e8les class group, that is, to the noncommutative spaces on which the geometric side of the trace formula is supported.", "date": "2010-11-21", "date_type": "published", "publisher": "Springer", "place_of_pub": "Boston, MA", "pagerange": "339-405", "id_number": "CaltechAUTHORS:20170713-091114280", "isbn": "978-0-8176-4744-5", "book_title": "Algebra, Arithmetic, and Geometry. Volume I: In Honor of Yu. I. Manin", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170713-091114280", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Tschinkel-Y", "name": { "family": "Tschinkel", "given": "Yuri" } }, { "id": "Zarhin-Y", "name": { "family": "Zarhin", "given": "Yuri" } } ] }, "doi": "10.1007/978-0-8176-4745-2_8", "primary_object": { "basename": "0703392.pdf", "url": "https://authors.library.caltech.edu/records/xf64a-qg632/files/0703392.pdf" }, "pub_year": "2010", "author_list": "Connes, Alain; Consani, Caterina; et al." }, { "id": "https://authors.library.caltech.edu/records/bxnny-r5798", "eprint_id": 66625, "eprint_status": "archive", "datestamp": "2023-08-19 03:24:09", "lastmod": "2026-03-09 02:37:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Topological Field Theory, Higher Categories, and Their Applications", "ispublished": "unpub", "full_text_status": "public", "keywords": "Topological field theory, 2-categories, monoidal categories, derived category of coherent sheaves, geometric Langlands duality", "note": "\u00a9 2010 Hindustan Book Agency. \n\nSubmitted on 14 Apr 2010 (v1), last revised 22 Apr 2010 this version, (v2). \n\nI would like to thank David Ben-Zvi, Dmitri Orlov, and Lev Rozansky for comments on the draft of the talk.\n\n

Published - icm2010.3.2021.2043.pdf

Submitted - 1004.2307.pdf

", "abstract": "It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories\nwith n > 1. Recently the physical meaning of these higher categorical structures has been recognized and concrete examples of Extended TFTs have been constructed. Some\nof these examples, like the Rozansky-Witten model, are of geometric nature, while others are related to representation theory. I outline two application of higher-dimensional TFTs. One is related to the problem of classifying monoidal deformations of the derived\ncategory of coherent sheaves, and the other one is geometric Langlands duality.", "date": "2010-08", "date_type": "published", "publisher": "Hindustan Book Agency", "place_of_pub": "New Delhi", "pagerange": "2021-2043", "id_number": "CaltechAUTHORS:20160503-151154407", "isbn": "9789814324335", "book_title": "ICM Proceedings", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160503-151154407", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Bhatia-R", "name": { "family": "Bhatia", "given": "Rajendra" } } ] }, "doi": "10.48550/arXiv.1004.2307", "primary_object": { "basename": "1004.2307.pdf", "url": "https://authors.library.caltech.edu/records/bxnny-r5798/files/1004.2307.pdf" }, "related_objects": [ { "basename": "icm2010.3.2021.2043.pdf", "url": "https://authors.library.caltech.edu/records/bxnny-r5798/files/icm2010.3.2021.2043.pdf" } ], "pub_year": "2010", "author_list": "Kapustin, Anton" }, { "id": "https://authors.library.caltech.edu/records/61nva-56f13", "eprint_id": 77815, "eprint_status": "archive", "datestamp": "2023-08-21 23:32:38", "lastmod": "2026-04-11 22:19:39", "type": "book_section", "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": "Equivalence of Sobolev inequalities and Lieb-Thirring inequalities", "ispublished": "unpub", "full_text_status": "public", "keywords": "Schr\u00f6dinger operator; Sobolev inequality; bound states; stability of matter", "note": "\u00a9 2010 World Scientific Publishing Co Pte Ltd. This paper may be reproduced, in its entirety, for non-commercial purposes. \n\nThis work was partially supported by U.S. NSF grants PHY-0652854 (R.L.F. and E.H.L.) and PHY-0652356 (R.S.).\n\n

Submitted - 0909.5449.pdf

", "abstract": "We show that, under very general definitions of a kinetic energy operator T, the Lieb\u2013Thirring inequalities for sums of eigenvalues of T - V can be derived from the Sobolev inequality appropriate to that choice of T.", "date": "2010-03", "date_type": "published", "publisher": "World Scientific", "place_of_pub": "Singapore", "pagerange": "523-535", "id_number": "CaltechAUTHORS:20170526-125941569", "isbn": "978-981-4304-62-7", "book_title": "XVIth International Congress on Mathematical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-125941569", "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-0652356" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Exner-P", "name": { "family": "Exner", "given": "Pavel" } } ] }, "doi": "10.1142/9789814304634_0045", "primary_object": { "basename": "0909.5449.pdf", "url": "https://authors.library.caltech.edu/records/61nva-56f13/files/0909.5449.pdf" }, "pub_year": "2010", "author_list": "Frank, Rupert L.; Lieb, Elliott H.; et al." }, { "id": "https://authors.library.caltech.edu/records/ny2y1-hs438", "eprint_id": 20066, "eprint_status": "archive", "datestamp": "2023-08-19 00:59:44", "lastmod": "2026-03-09 21:40:15", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Feynman integrals and motives", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2009 European Mathematical Society.\nSubmitted on 2 Jul 2009.\nA large part of what I described in this paper is based on recent joint\nwork with Paolo Aluffi and on previous joint work with Alain Connes, whom I thank for\ntheir essential contributions to the development of these ideas and results. Although parts of\nthis article reflect the content of the lecture I delivered at the ECM in the summer of 2008,\nnew material developed in the intervening time was included for completeness and the actual\nwriting was carried out in the winter 2009, during a stay at MSRI: I thank the institute for\nthe hospitality and for support. An informal discussion with Nikolai Reshetikhin and a talk\nI gave in Yongbin Ruan's seminar helped finalizing the form of this exposition. The topics\ncovered in this survey will appear in extended form in the book [50] based on a course given\nat Caltech in the fall 2008.\n\n

Submitted - Marcolli2010p11402.pdf

", "abstract": "This article gives an overview of recent results on the relation between quantum\nfield theory and motives, with an emphasis on two different approaches: a \"bottom-up\"\napproach based on the algebraic geometry of varieties associated to Feynman graphs, and\na \"top-down\" approach based on the comparison of the properties of associated categorical\nstructures. This survey is mostly based on joint work of the author with Paolo Aluffi, along\nthe lines of the first approach, and on previous work of the author with Alain Connes on\nthe second approach.", "date": "2010", "date_type": "published", "publisher": "European Mathematical Society", "id_number": "CaltechAUTHORS:20100921-095023951", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100921-095023951", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.0907.0321", "primary_object": { "basename": "Marcolli2010p11402.pdf", "url": "https://authors.library.caltech.edu/records/ny2y1-hs438/files/Marcolli2010p11402.pdf" }, "pub_year": "2010", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/z3h4g-72d62", "eprint_id": 19066, "eprint_status": "archive", "datestamp": "2023-08-21 22:59:26", "lastmod": "2026-03-18 00:07:17", "type": "book_section", "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: A Progress Report", "ispublished": "unpub", "full_text_status": "public", "keywords": "Orthogonal polynomials; clock behavior; Poisson process", "note": "\u00a9 2010 American Mathematical Society.\nSupported in part by NSF grant DMS-0652919.\n\n

Published - Simon2010p11240.pdf

", "abstract": "We consider the asymptotics of zeros of OPRL and POPUC as n \u2192 \u221e, focusing on the structure on a scale in x of order 1/n. We discuss three recent results (on Poisson behavior in the random case, clock on the a.c. case, and beta-distribution in between) and open questions and speculations.", "date": "2010", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "241-254", "id_number": "CaltechAUTHORS:20100715-092306403", "isbn": "978-0-8218-4803-6", "book_title": "Recent Trends in Orthogonal Polynomials and Approximation Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100715-092306403", "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" } ] }, "primary_object": { "basename": "Simon2010p11240.pdf", "url": "https://authors.library.caltech.edu/records/z3h4g-72d62/files/Simon2010p11240.pdf" }, "pub_year": "2010", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/ge6ta-6sf05", "eprint_id": 71908, "eprint_status": "archive", "datestamp": "2023-08-19 01:11:07", "lastmod": "2026-03-10 00:00:28", "type": "book_section", "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": "Truthful Fair Division", "ispublished": "unpub", "full_text_status": "public", "keywords": "Fair division cake cutting truthful mechanisms", "note": "\u00a9 2010 Springer-Verlag Berlin Heidelberg. \n\nSupported by NSF Career Award (DMS 054829) by ISF grant 1300/08 and by a Minerva grant. Supported by ISF grant 1300/08.\n\n

Submitted - 1003.5480.pdf

", "abstract": "We address the problem of fair division, or cake cutting, with the goal of finding truthful mechanisms. In the case of a general measure space (\"cake\") and non-atomic, additive individual preference measures - or utilities - we show that there exists a truthful \"mechanism\" which ensures that each of the k players gets at least 1/k of the cake. This mechanism also minimizes risk for truthful players. Furthermore, in the case where there exist at least two different measures we present a different truthful mechanism which ensures that each of the players gets more than 1/k of the cake.\n\nWe then turn our attention to partitions of indivisible goods with bounded utilities and a large number of goods. Here we provide similar mechanisms, but with slightly weaker guarantees. These guarantees converge to those obtained in the non-atomic case as the number of goods goes to infinity.", "date": "2010", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin Heidelberg", "pagerange": "288-299", "id_number": "CaltechAUTHORS:20161110-075056609", "isbn": "978-3-642-16169-8", "book_title": "Algorithmic Game Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161110-075056609", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-054829" }, { "agency": "Israel Science Foundation", "grant_number": "1300/08" }, { "agency": "MINERVA (Israel)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kontogiannis-S", "name": { "family": "Kontogiannis", "given": "S." } }, { "id": "Koutsoupias-E", "name": { "family": "Koutsoupias", "given": "Elias" } }, { "id": "Spirakis-P-G", "name": { "family": "Spirakis", "given": "P. G." } } ] }, "doi": "10.1007/978-3-642-16170-4_25", "primary_object": { "basename": "1003.5480.pdf", "url": "https://authors.library.caltech.edu/records/ge6ta-6sf05/files/1003.5480.pdf" }, "pub_year": "2010", "author_list": "Mossel, Elchanan and Tamuz, Omer" }, { "id": "https://authors.library.caltech.edu/records/0nnbr-rds46", "eprint_id": 23086, "eprint_status": "archive", "datestamp": "2023-08-19 01:02:56", "lastmod": "2026-03-09 21:40:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Motivic renormalization and singularities", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 American Mathematical Society.\n\n

Submitted - Marcolli2010p13199.pdf

", "abstract": "We consider parametric Feynman integrals and their dimensional regularization from the point of view of differential forms on hypersurface complements and the approach to mixed Hodge structures via oscillatory integrals. We consider restrictions to linear subspaces that slice the singular locus, to handle the presence\nof non-isolated singularities. In order to account for all possible choices of slicing, we encode this extra datum as an enrichment of the Hopf algebra of Feynman graphs.\nWe introduce a new regularization method for parametric Feynman integrals, which is based on Leray coboundaries and, like dimensional regularization, replaces a divergent\nintegral with a Laurent series in a complex parameter. The Connes\u2013Kreimer formulation of renormalization can be applied to this regularization method. We relate the\ndimensional regularization of the Feynman integral to the Mellin transforms of certain Gelfand\u2013Leray forms and we show that, upon varying the external momenta, the\nFeynman integrals for a given graph span a family of subspaces in the cohomological Milnor fibration. We show how to pass from regular singular Picard\u2013Fuchs equations\nto irregular singular flat equisingular connections. In the last section, which is more speculative in nature, we propose a geometric model for dimensional regularization in\nterms of logarithmic motives and motivic sheaves.", "date": "2010", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "409-458", "id_number": "CaltechAUTHORS:20110324-084219567", "isbn": "978-0-8218-5203-3", "book_title": "Quanta of Maths: Conference in Honor of Alain Connes", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110324-084219567", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Connes-A", "name": { "family": "Connes", "given": "Alain" } }, { "id": "Blanchard-E", "name": { "family": "Blanchard", "given": "Etienne" } } ] }, "doi": "10.48550/arXiv.0804.4824v3", "primary_object": { "basename": "Marcolli2010p13199.pdf", "url": "https://authors.library.caltech.edu/records/0nnbr-rds46/files/Marcolli2010p13199.pdf" }, "pub_year": "2010", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/sy5ss-j9b17", "eprint_id": 77816, "eprint_status": "archive", "datestamp": "2023-08-19 01:11:39", "lastmod": "2026-03-09 02:13:48", "type": "book_section", "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": "Sharp Fractional Hardy Inequalities in Half-Spaces", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 Springer Science+Business Media, LLC. \n\nAcknowledgments. Support through DFG grant FR 2664/1-1 (R.F.) and U.S. NSF grants PHY-0652854 (R.F.) and PHY-0652356 (R.S.) is gratefully acknowledged.\n\n

Submitted - 0906.1561.pdf

", "abstract": "We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a nonlinear and nonlocal version of the ground state representation.", "date": "2010", "date_type": "published", "publisher": "Springer New York", "pagerange": "161-167", "id_number": "CaltechAUTHORS:20170526-131557265", "isbn": "978-1-4419-1340-1", "book_title": "Around the Research of Vladimir Maz'ya I", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170526-131557265", "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": "NSF", "grant_number": "PHY-0652356" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Laptev-A", "name": { "family": "Laptev", "given": "Ari" } } ] }, "doi": "10.1007/978-1-4419-1341-8_6", "primary_object": { "basename": "0906.1561.pdf", "url": "https://authors.library.caltech.edu/records/sy5ss-j9b17/files/0906.1561.pdf" }, "pub_year": "2010", "author_list": "Frank, Rupert L. and Seiringer, Robert" }, { "id": "https://authors.library.caltech.edu/records/a3rqk-qcv02", "eprint_id": 23175, "eprint_status": "archive", "datestamp": "2023-08-19 01:04:18", "lastmod": "2026-03-10 00:02:04", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "The proportion of various graphs in graph-designs", "ispublished": "unpub", "full_text_status": "public", "keywords": "Graph designs, complete graph, decompositions", "note": "\u00a9 2010 American Mathematical Society.\nThe author was supported in part by NSF Grant #0555755.\n\n

Published - Wilson2010p12879Automorphic_Forms_And_L-Functions_I._Global_Aspects.pdf

", "abstract": "Let G be a family of simple graphs. A G-design on n points is a decomposition of the edges of K_n into copies of graphs in G. In case that G consists of complete graphs K_k with k in some set K of positive integers, such a G-design is called a pairwise balanced design (PBD) on n points with block sizes from K. Here we are concerned with the possible proportions of the numbers of copies of graphs G \u2208 G that appear in decompositions for large n. We extend a result of Colbourn and Rodl on PBDs to G-designs, and give a further result on the possible numbers of copies of G in a G-design containing each vertex of the complete graph K_n.", "date": "2010", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "251-255", "id_number": "CaltechAUTHORS:20110330-093452534", "isbn": "978-0-8218-4865-4", "book_title": "Combinatorics and Graphs", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110330-093452534", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "0555755" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Brualdi-R-A", "name": { "family": "Brualdi", "given": "Richard A." } } ] }, "primary_object": { "basename": "Wilson2010p12879Automorphic_Forms_And_L-Functions_I._Global_Aspects.pdf", "url": "https://authors.library.caltech.edu/records/a3rqk-qcv02/files/Wilson2010p12879Automorphic_Forms_And_L-Functions_I._Global_Aspects.pdf" }, "pub_year": "2010", "author_list": "Wilson, Richard M." }, { "id": "https://authors.library.caltech.edu/records/zytbp-15b77", "eprint_id": 18207, "eprint_status": "archive", "datestamp": "2023-08-20 01:42:50", "lastmod": "2026-04-16 01:40:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" } ] }, "title": "Periodic table for topological insulators and superconductors", "ispublished": "unpub", "full_text_status": "public", "keywords": "phase transitions, localised states, fermion systems, Dirac equation, matrix algebra, superconducting materials", "note": "\u00a9 2009 American Institute of Physics.\n\nIssue Date: 14 May 2009.\n\nI am grateful to Andreas Ludwig and Shinsey Ryu for\nteaching me about ^(3)He-5 and (p_x + ip_y)\u2191 + (_Px - iP_y)\u2193\nand helping to fit these phases into the periodic table. I\nalso thank John Preskill, Michael Freedman, John Roe,\nCharles Kane, and Grigori Volovik for stimulating discussions. This research is supported in part by NSF under\ngrant No. PHY-0456720.\n\n

Published - Kitaev2009p8192Advances_In_Theoretical_Physics.pdf

", "abstract": "Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.", "date": "2009-05-14", "date_type": "published", "publisher": "American Institute of Physics", "place_of_pub": "New York, NY", "pagerange": "22-30", "id_number": "CaltechAUTHORS:20100510-100944960", "isbn": "978-0-7354-0671-1", "book_title": "Advances In Theoretical Physics: Landau Memorial Conference Chernogolokova (Russia), 22\u201326 June 2008", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100510-100944960", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "PHY-0456720" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Lebedev-V", "name": { "family": "Lebedev", "given": "Vladimir" } }, { "id": "Feigel'man-M", "name": { "family": "Feigel'man", "given": "Mikhail" } } ] }, "doi": "10.1063/1.3149495", "primary_object": { "basename": "Kitaev2009p8192Advances_In_Theoretical_Physics.pdf", "url": "https://authors.library.caltech.edu/records/zytbp-15b77/files/Kitaev2009p8192Advances_In_Theoretical_Physics.pdf" }, "pub_year": "2009", "author_list": "Kitaev, Alexei" }, { "id": "https://authors.library.caltech.edu/records/tatkw-q7h44", "eprint_id": 81812, "eprint_status": "archive", "datestamp": "2023-08-20 00:32:36", "lastmod": "2026-04-13 03:43:54", "type": "book_section", "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" }, { "id": "Vanderbei-R-J", "name": { "family": "Vanderbei", "given": "Robert J." } } ] }, "title": "The Kruskal Count", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2009 Springer-Verlag Berlin Heidelberg.\n\n

Submitted - 0110143.pdf

", "abstract": "The Kruskal Count is a card trick invented by Martin D. Kruskal (who is well known for his work on solitons) which is described in Fulves and Gardner (1975) and Gardner (1978, 1988). In this card trick a magician \"guesses\" one card in a deck of cards which is determined by a subject using a special counting procedure that we call Kruskal's counting procedure. The magician has a strategy which with high probability will identify the correct card, explained below.\n\nKruskal's counting procedure goes as follows. The subject shuffles a deck of cards as many times as he likes. He mentally chooses a (secret) number between one and ten. The subject turns the cards of the deck face up one at a time, slowly, and places them in a pile. As he turns up each card he decreases his secret number by one and he continues to count this way till he reaches zero. The card just turned up at the point when the count reaches zero is called the first key card and its value is called the first key number. Here the value of an Ace is one, face cards are assigned the value five, and all other cards take their numerical value. The subject now starts the count over, using the first key number to determine where to stop the count at the second key card. He continues in this fashion, obtaining successive key cards until the deck is exhausted. The last key card encountered, which we call the tapped card, is the card to be \"guessed\" by the magician.", "date": "2009", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "371-391", "id_number": "CaltechAUTHORS:20170925-112254500", "isbn": "978-3-540-79127-0", "book_title": "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter C. Fishburn", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170925-112254500", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Brams-S-J", "name": { "family": "Brams", "given": "Steven J." } }, { "id": "Gehrlein-W-V", "name": { "family": "Gehrlein", "given": "William V." } }, { "id": "Roberts-F-S", "name": { "family": "Roberts", "given": "Fred S." } } ] }, "doi": "10.1007/978-3-540-79128-7_23", "primary_object": { "basename": "0110143.pdf", "url": "https://authors.library.caltech.edu/records/tatkw-q7h44/files/0110143.pdf" }, "pub_year": "2009", "author_list": "Lagarias, Jeffrey C.; Rains, Eric; et al." }, { "id": "https://authors.library.caltech.edu/records/z6j4s-kxr53", "eprint_id": 66695, "eprint_status": "archive", "datestamp": "2023-08-20 00:31:18", "lastmod": "2026-04-12 14:03:33", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Gukov-S", "name": { "family": "Gukov", "given": "Sergei" }, "orcid": "0000-0002-9486-1762" } ] }, "title": "Surface Operators and Knot Homologies", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2009 Springer Science + Business Media B.V.\n\nI would like to thank N. Dunfield, T. Hausel, A. Kapustin, M. Khovanov, M. Mari\u00f1o, T. Mrowka, J. Roberts, and C. Vafa for clarifying discussions and comments. I am specially indebted to E. Witten for many useful discussions and for his observations on a preliminary version of this paper. This work is supported in part by DOE grant DE-FG03-92-ER40701, in part by RFBR grant 07-02-00645, and in part by the grant for support of scientific schools NSh-8004.2006.2.\nThis paper is an extended version of the talk delivered at the International Congress on Mathematical Physics 2006 (Rio de Janeiro) and at the RTN workshop \"Constituents, Fundamental Forces and Symmetries of the Universe\" (Napoli). I am very grateful to the organizers for the opportunity to participate in these meetings and to all the participants for providing a stimulating environment.\n\n

Submitted - 0706.2369.pdf

", "abstract": "Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli space. This action plays a key role in the construction of homological knot invariants. We illustrate the general construction with examples based on surface operators in N=2 and N=4 twisted gauge theories which lead to a categorification of the Alexander polynomial, the equivariant knot signature, and certain analogs of the Casson invariant.", "date": "2009", "date_type": "published", "publisher": "Springer Netherlands", "place_of_pub": "Berlin Heidelberg", "pagerange": "313-343", "id_number": "CaltechAUTHORS:20160505-120947331", "isbn": "978-90-481-2809-9", "book_title": "New Trends in Mathematical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160505-120947331", "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": "07-02-00645" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Sidoravi\u010dius-V", "name": { "family": "Sidoravi\u010dius", "given": "V." } } ] }, "doi": "10.1007/978-90-481-2810-5_22", "primary_object": { "basename": "0706.2369.pdf", "url": "https://authors.library.caltech.edu/records/z6j4s-kxr53/files/0706.2369.pdf" }, "pub_year": "2009", "author_list": "Gukov, Sergei" }, { "id": "https://authors.library.caltech.edu/records/5kcvq-rg285", "eprint_id": 18747, "eprint_status": "archive", "datestamp": "2023-08-20 00:20:33", "lastmod": "2026-03-09 23:12:56", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Murre-J", "name": { "family": "Murre", "given": "Jacob" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Local Galois Symbols on E \u00d7 E", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2009 American Mathematical Society.\n\nPartially supported by the NSF.\n\n

Published - Murre2009p7077.pdf

", "abstract": "This article studies the Albanese kernel T_F(E x E), for an\nelliptic curve E over a p-adic field F. The main result furnishes information, for any odd prime p, about the kernel and image of the Galois symbol map from T_F(E x E)/p to the Galois cohomology group H^2 (F,E[P] \u2297 E[P]), for E/F ordinary, without requiring that the p-torsion points are F-rational, or even that the Galois module E[P] is semisimple. A key step is to show that the image is zero when the finite Galois module E[P] is acted on non-trivially by the pro-p-inertia group I_p. Non-trivial classes in the image are also constructed when\nE[P] is suitably unramified. A forthcoming sequel will deal with global questions.", "date": "2009", "date_type": "published", "publisher": "American Mathematical Society", "pagerange": "257-291", "id_number": "CaltechAUTHORS:20100621-111547961", "isbn": "978-0-8218-4494-6", "book_title": "Motives and algebraic cycles : a celebration in honour of Spencer J. Bloch", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100621-111547961", "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": "10.48550/arXiv.0808.1129", "primary_object": { "basename": "Murre2009p7077.pdf", "url": "https://authors.library.caltech.edu/records/5kcvq-rg285/files/Murre2009p7077.pdf" }, "pub_year": "2009", "author_list": "Murre, Jacob and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/8kgpe-kdr68", "eprint_id": 39687, "eprint_status": "archive", "datestamp": "2023-08-19 23:34:43", "lastmod": "2026-03-09 20:34:43", "type": "book_section", "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": "The equivalence of partition properties and determinacy", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2008 Association for Symbolic Logic.\nPreparation of this paper is partially supported by NSF Grants DMS-0455285 (A.S.K.) and\nDMS-0355334 (W.H.W.).", "abstract": "This paper was circulated in handwritten form in March\n1982 and contained Sections 1-4 below. There is an additional Section 5\ncontaining information about the solution of a problem mentioned in the last\nparagraph of Section I.", "date": "2008-09", "date_type": "published", "publisher": "Association for Symbolic Logic", "place_of_pub": "Chicago, IL", "pagerange": "355-378", "id_number": "CaltechAUTHORS:20130731-151623397", "isbn": "9780521899512", "book_title": "The Cabal Seminar. Volume I - Games, Scales, and Suslin Cardinals", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130731-151623397", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0455285" }, { "agency": "NSF", "grant_number": "DMS-0355334" } ] }, "other_numbering_system": { "items": [ { "id": "2463618", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "pub_year": "2008", "author_list": "Kechris, Alexander S. and Woodin, W. Hugh" }, { "id": "https://authors.library.caltech.edu/records/dbhn2-1d867", "eprint_id": 39686, "eprint_status": "archive", "datestamp": "2023-08-19 23:34:36", "lastmod": "2026-03-09 21:10:14", "type": "book_section", "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": "Generic codes for uncountable ordinals, partition properties, and elementary embeddings", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2008 Association for Symbolic Logic.\nPreparation of this paper is partially supported by NSF Grants DMS-0455285 (A.S.K.) and\nDMS-0355334 (W.H.W).", "abstract": "This paper was circulated in handwritten form in December 1980 and contained Sections 1-7 below. There are two additionalSections 8 and 9 here that contain further material and comments.", "date": "2008-09", "date_type": "published", "publisher": "Association for Symbolic Logic", "place_of_pub": "Chicago, IL", "pagerange": "379-397", "id_number": "CaltechAUTHORS:20130731-150603194", "isbn": "9780521899512", "book_title": "The Cabal Seminar. Volume I - Games, Scales, and Suslin Cardinals", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130731-150603194", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0455285" }, { "agency": "NSF", "grant_number": "DMS-0355334" } ] }, "other_numbering_system": { "items": [ { "id": "2463619", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "pub_year": "2008", "author_list": "Kechris, Alexander S. and Woodin, W. Hugh" }, { "id": "https://authors.library.caltech.edu/records/a1q2f-esb32", "eprint_id": 18199, "eprint_status": "archive", "datestamp": "2023-08-19 23:30:04", "lastmod": "2026-04-12 14:13:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "A. N." }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Springer-Verlag Berlin Heidelberg. \n\nFirst Online: 20 August 2008. \n\nThis work was supported in part by the DOE grant DE-FG03-92-ER40701.\n\n

Submitted - 0811.3264v1.pdf

", "abstract": "I provide an introduction to the recent work on the Montonen-Olive duality of N = 4 super-Yang-Mills theory and the Geometric Langlands Program.", "date": "2008-08-20", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "103-124", "id_number": "CaltechAUTHORS:20100507-151819865", "isbn": "978-3-540-68029-1", "book_title": "Homological Mirror Symmetry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100507-151819865", "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" } ] }, "contributors": { "items": [ { "id": "Schlesinger-K-G", "name": { "family": "Schlesinger", "given": "Karl-Georg" } }, { "id": "Kreuzer-M", "name": { "family": "Kreuzer", "given": "Maximilian" } }, { "id": "Kapustin-A", "name": { "family": "Kapustin", "given": "Anton" } } ] }, "doi": "10.1007/978-3-540-68030-7_4", "primary_object": { "basename": "0811.3264v1.pdf", "url": "https://authors.library.caltech.edu/records/a1q2f-esb32/files/0811.3264v1.pdf" }, "pub_year": "2008", "author_list": "Kapustin, A. N." }, { "id": "https://authors.library.caltech.edu/records/gst1n-3qv43", "eprint_id": 88535, "eprint_status": "archive", "datestamp": "2023-08-19 23:24:20", "lastmod": "2026-03-07 04:14:04", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "On a question of Farjoun", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Walter de Gruyter GmbH.", "abstract": "[no abstract]", "date": "2008-08", "date_type": "published", "publisher": "De Gruyter", "place_of_pub": "Berlin", "pagerange": "1-28", "id_number": "CaltechAUTHORS:20180802-143851994", "isbn": "978-3-11-019812-6", "book_title": "Finite Groups 2003 : Proceedings of the Gainesville Conference on Finite Groups", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180802-143851994", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Ho-Chat-Yin", "name": { "family": "Ho", "given": "Chat Yin" } }, { "id": "Sin-Peter", "name": { "family": "Sin", "given": "Peter" } }, { "id": "Tiep-P-H", "name": { "family": "Tiep", "given": "Pham Huu" } }, { "id": "Turull-A", "name": { "family": "Turull", "given": "Alexandre" } } ] }, "doi": "10.1515/9783110198126.1", "pub_year": "2008", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/9a9bg-hfq33", "eprint_id": 22054, "eprint_status": "archive", "datestamp": "2023-08-19 23:00:17", "lastmod": "2026-04-16 01:39:13", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kitaev-A", "name": { "family": "Kitaev", "given": "Alexei" }, "orcid": "0000-0002-5777-642X" }, { "id": "Laumann-C", "name": { "family": "Laumann", "given": "Christopher" } } ] }, "title": "Topological phases and quantum computation", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 Oxford University Press. \n\nNotes written by C. Laumann.\n\n

Submitted - 0904.2771.pdf

", "abstract": "The basic building block of quantum computation is the qubit, a system with two (nearly)\ndegenerate states that can be used to encode quantum information. Real systems typically\nhave a full spectrum of excitations that are considered illegal from the point of view of a\ncomputation, and lead to decoherence if they couple too strongly into the qubit states during\nsome process (see Fig. 4.1). The essential problem, then, is to preserve the quantum state of\nthe qubit as long as possible to allow time for computations to take place.", "date": "2008-07", "date_type": "published", "publisher": "Oxford University Press", "place_of_pub": "Oxford", "pagerange": "101-125", "id_number": "CaltechAUTHORS:20110207-134954371", "isbn": "0-19-957461-8", "book_title": "Exact methods in low-dimensional statistical physics and quantum computing", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110207-134954371", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Jacobsen-J", "name": { "family": "Jacobsen", "given": "Jesper" } } ] }, "doi": "10.48550/arXiv.0904.2771", "primary_object": { "basename": "0904.2771.pdf", "url": "https://authors.library.caltech.edu/records/9a9bg-hfq33/files/0904.2771.pdf" }, "pub_year": "2008", "author_list": "Kitaev, Alexei and Laumann, Christopher" }, { "id": "https://authors.library.caltech.edu/records/4zqa3-gb520", "eprint_id": 88899, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:46", "lastmod": "2026-03-09 20:40:25", "type": "book_section", "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": "Notes on the theory of scales", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "[no abstract]", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "28-74", "id_number": "CaltechAUTHORS:20180817-104143442", "isbn": "9780511546488", "book_title": "Games, Scales and Suslin Cardinals: The Cabal Seminar, Volume I", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143442", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9780511546488.003", "pub_year": "2008", "author_list": "Kechris, Alexander S. and Moschovakis, Yiannis N." }, { "id": "https://authors.library.caltech.edu/records/mqm5j-zxy26", "eprint_id": 79069, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:24", "lastmod": "2026-03-09 21:42:44", "type": "book_section", "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": "Modular shadows and the Levy-Mellin \u221e-adic transform", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press. \n\nPrint publication year: 2008. Online publication date: October 2009.\n\n

Submitted - 0703718.pdf

", "abstract": "This paper continues the study of the structures induced on the \"invisible boundary\" of the modular tower and extends some results of [MaMar1]. We start with a systematic formalism of pseudo\u2013measures generalizing the well\u2013known theory of modular symbols for SL(2). These pseudo\u2013measures, and the related integral formula which we call the L\u00e9vy\u2013Mellin transform, can be considered as an \"\u221e\u2013adic\" version of Mazur's p\u2013adic measures that have been introduced in the seventies in the theory of p\u2013adic interpolation of the Mellin transforms of cusp forms, cf. [Ma2]. A formalism of iterated L\u00e9vy\u2013Mellin transform in the style of [Ma3] is sketched. Finally, we discuss the invisible boundary from the perspective of non\u2013commutative geometry.", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "189-238", "id_number": "CaltechAUTHORS:20170713-091711317", "isbn": "9780521493543", "book_title": "Modular Forms on Schiermonnikoog", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170713-091711317", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Edixhoven-B", "name": { "family": "Edixhoven", "given": "Bas" } }, { "id": "van-der-Geer-G", "name": { "family": "van der Geer", "given": "Gerard" } }, { "id": "Moonen-B", "name": { "family": "Moonen", "given": "Ben" } } ] }, "doi": "10.1017/CBO9780511543371.012", "primary_object": { "basename": "0703718.pdf", "url": "https://authors.library.caltech.edu/records/mqm5j-zxy26/files/0703718.pdf" }, "pub_year": "2008", "author_list": "Manin, Yuri I. and Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/58ecr-dha68", "eprint_id": 88906, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:49", "lastmod": "2026-03-09 20:40:58", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "title": "Preface", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "This is the first of four volumes containing reprints of the papers in the original Cabal Seminar volumes of the Springer Lecture Notes in Mathematics series [cabal i, cabal ii, cabal iii, cabal iv], unpublished material, and new papers. We have grouped the papers of the original Cabal Seminar volumes according to their topics. This volume contains the papers on \"Games and Scales\" (Part I) and \"Suslin Cardinals, Partition Properties, Homogeneity\" (Part II). Each of the parts contains an introductory survey (written by John Steel and Steve Jackson, respectively) putting the papers into a present-day context. Table 1 gives an overview of the papers in this volume with their original references. \n\nThis volume must not be understood as a historical edition of old papers. In the 1980s, there were a number of results obtained by the researchers associated with the Cabal Seminar, some of which were intended for a fifth Cabal volume that was never published. We include some of these papers in this volume, together with papers reporting on new developments related to the research of the Cabal Seminar. These papers are Steel's \"Scales in K(\u211d)\" and \"The Length-\u03c91 Open Game Quantifier Propagates Scales\" in Part Iand \"The Equivalence of Partition Properties and Determinacy\" and \"Generic Codes for Uncountable Ordinals, Partition Properties, and Elementary Embeddings\" by Kechris and Woodin, \"The Tree of a Moschovakis Scale is Homogeneous\" by Martin and Steel, and \"Weakly Homogeneous Trees\" by Martin and Woodin in Part II.", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "ix-xi", "id_number": "CaltechAUTHORS:20180817-104144069", "isbn": "9780511546488", "book_title": "Games, Scales and Suslin Cardinals: The Cabal Seminar, Volume I", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144069", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9780511546488.001", "pub_year": "2008", "author_list": "Kechris, Alexander S.; L\u00f6we, Benedikt; et al." }, { "id": "https://authors.library.caltech.edu/records/fer92-yx674", "eprint_id": 88911, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:53", "lastmod": "2026-03-09 20:38:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Suslin cardinals, k-Suslin sets, and the scale property in the hyperprojective hierarchy", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "[no abstract]", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "314-332", "id_number": "CaltechAUTHORS:20180817-104144489", "isbn": "9780511546488", "book_title": "Games, Scales and Suslin Cardinals: The Cabal Seminar, Volume I", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144489", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/cbo9780511546488.016", "pub_year": "2008", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/rj56p-qfv15", "eprint_id": 88754, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:40", "lastmod": "2026-03-09 20:31:45", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "A coding theorem for measures", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "[no abstract]", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "398-403", "id_number": "CaltechAUTHORS:20180810-133923114", "isbn": "9780521899512", "book_title": "Games, Scales and Suslin Cardinals: The Cabal Seminar, Volume I", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-133923114", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9780511546488.020", "pub_year": "2008", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/6h1q9-t1a76", "eprint_id": 88759, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:43", "lastmod": "2026-03-09 20:40:30", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Kleinber-E-M", "name": { "family": "Kleinber", "given": "Eugene M." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } }, { "id": "Woodin-W-H", "name": { "family": "Woodin", "given": "W. Hugh" } } ] }, "title": "The axiom of determinacy, strong partition properties, and nonsingular measures", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "[no abstract]", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "333-354", "id_number": "CaltechAUTHORS:20180810-141457603", "isbn": "9780521899512", "book_title": "Games, Scales and Suslin Cardinals: The Cabal Seminar, Volume I", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-141457603", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "L\u00f6we-B", "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1017/CBO9780511546488.017", "pub_year": "2008", "author_list": "Kechris, Alexander S.; Kleinber, Eugene M.; et al." }, { "id": "https://authors.library.caltech.edu/records/88rh7-k3q37", "eprint_id": 19145, "eprint_status": "archive", "datestamp": "2023-08-22 10:13:43", "lastmod": "2026-03-09 23:11:07", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Irreducibility and Cuspidality", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "irreducibility; Galois representations; cuspidality; automorphic representations; general linear group; symplectic group; regular algebraic representations", "note": "\u00a9 2008 Birkh\u00e4user Boston. \n\nPartially supported by the NSF through the grant DMS-0402044.", "abstract": "Suppose \u03c1 is an n-dimensional representation of the absolute Galois group of Q\nwhich is associated, via an identity of L-functions, with an automorphic representation \u03c0 of\nGL(n) of the adele ring of Q. It is expected that \u03c0 is cuspidal if and only if \u03c1 is irreducible,\nthough nothing much is known in either direction in dimensions > 2. The object of this article\nis to show for n < 6 that the cuspidality of a regular algebraic \u03c0 is implied by the irreducibility\nof \u03c1. For n < 5, it suffices to assume that \u03c0 is semi-regular.", "date": "2007-10-10", "date_type": "published", "publisher": "Birkh\u00e4user", "place_of_pub": "Boston", "pagerange": "1-27", "id_number": "CaltechAUTHORS:20100721-134623343", "isbn": "978-0-8176-4505-2", "book_title": "Representation theory and automorphic forms", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20100721-134623343", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-0402044" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1007/978-0-8176-4646-2_1", "pub_year": "2007", "author_list": "Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/gxepa-b0081", "eprint_id": 21640, "eprint_status": "archive", "datestamp": "2023-08-19 19:15:46", "lastmod": "2026-04-14 02:14:11", "type": "book_section", "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: A Review", "ispublished": "unpub", "full_text_status": "public", "keywords": "Orthogonal polynomials", "note": "\u00a9 2007 World Scientific Publishing Co. \nWork partially supported by NSF grant DMS-0140592. \n\nIt is a pleasure to thank Andreas Ruffing for Herculean efforts in organizing\nwhat was a very successful conference.\n\n

Published - Simon2007p8417Difference_Equations_Special_Functions_And_Orthogonal_Polynomials.pdf

", "abstract": "We review recent work on zeros of orthogonal polynomials.", "date": "2007", "date_type": "published", "publisher": "World Scientific Publishing Co.", "place_of_pub": "Singapore", "pagerange": "636-653", "id_number": "CaltechAUTHORS:20110107-080243062", "isbn": "9789812706430", "book_title": "Proceedings of the international conference, difference equations, special functions and orthogonal polynomials : Munich, Germany, 25-30 July 2005", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110107-080243062", "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" } ] }, "contributors": { "items": [ { "id": "Elaydi-S", "name": { "family": "Elaydi", "given": "S." } } ] }, "doi": "10.1142/9789812770752_0055", "primary_object": { "basename": "Simon2007p8417Difference_Equations_Special_Functions_And_Orthogonal_Polynomials.pdf", "url": "https://authors.library.caltech.edu/records/gxepa-b0081/files/Simon2007p8417Difference_Equations_Special_Functions_And_Orthogonal_Polynomials.pdf" }, "pub_year": "2007", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/vw2yt-a4678", "eprint_id": 21641, "eprint_status": "archive", "datestamp": "2023-08-22 07:56:41", "lastmod": "2026-03-18 00:08:47", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Orthogonal polynomials with exponentially decaying recursion coefficients", "ispublished": "unpub", "full_text_status": "public", "keywords": "Spectral Theory (math.SP); Classical Analysis and ODEs (math.CA)", "note": "\u00a9 2007 Barry Simon.\nThis is the final form of the paper.\n\nDedicated to S. Molchanov on his 65th birthday.\nSubmitted to the Proceedings of S. Molchanov's 65th Birthday Conference.\nThis work is supported in part by NSF grant DMS-0140592.\n\n

Published - Simon2007p9109Probability_And_Mathematical_Physics_A_Volume_In_Honor_Of_Stanislav_Molchanov.pdf

", "abstract": "We review recent results on necessary and sufficient conditions for\nmeasures on R and \u2202D to yield exponential decay of the recursion coefficients of\nthe corresponding orthogonal polynomials. We include results on the relation\nof detailed asymptotics of the recursion coefficients to detailed analyticity of\nthe measures. We present an analog of Carmona's formula for OPRL. A major\nrole is played by the Szeg\u00f6 and Jost functions.", "date": "2007", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "453-463", "id_number": "CaltechAUTHORS:20110107-081647098", "isbn": "9780821840894", "book_title": "Probability and mathematical physics : a volume in honor of Stanislav Molchanov", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110107-081647098", "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" } ] }, "contributors": { "items": [ { "id": "Molchanov-S-A", "name": { "family": "Molchanov", "given": "S. A." } }, { "id": "Dawson-D-A", "name": { "family": "Dawson", "given": "Donald Andrew" } }, { "id": "Jak\u0161i\u0107-V", "name": { "family": "Jak\u0161i\u0107", "given": "Vojkan" } }, { "id": "Va\u012dnberg-B-R", "name": { "family": "Va\u012dnberg", "given": "B. R." } } ] }, "doi": "10.48550/arXiv.0603099", "primary_object": { "basename": "Simon2007p9109Probability_And_Mathematical_Physics_A_Volume_In_Honor_Of_Stanislav_Molchanov.pdf", "url": "https://authors.library.caltech.edu/records/vw2yt-a4678/files/Simon2007p9109Probability_And_Mathematical_Physics_A_Volume_In_Honor_Of_Stanislav_Molchanov.pdf" }, "pub_year": "2007", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/bdxy9-t0x39", "eprint_id": 98167, "eprint_status": "archive", "datestamp": "2023-08-22 05:08:23", "lastmod": "2026-04-13 17:15:25", "type": "book_section", "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-E", "name": { "family": "Thirring", "given": "Walter" } } ] }, "title": "Approximate Neutrality of Large-Z Ions", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Classical Energy; Pauli Principle; Hartree Equation; Schrodinger Operator; Classical Potential Theory", "note": "\u00a9 Springer-Verlag Berlin Heidelberg New York 2005. \n\nReceived December 7, 1987. \n\nCommunicated by A. Jaffe. \n\nResearch partially supported by the NSERC under Grant NA 7901 and by the USNSF under Grants DMS-8416049 and PHY 85-15288-A01. \n\nThis work was begun while I.S. was at the Weizmann Institute, and B.S. would like to thank H. Dym and I. Sigal for the hospitality of that Institute. W.T. would like to thank E. Lieb for the hospitality of Princeton University, and M. Goldberger and R. Vogt for the hospitality of Caltech. An announcement appeared in [8].", "abstract": "Let N(Z) denote the number of electrons which a nucleus of charge Z can bind in non-relativistic quantum mechanics (assuming that electrons are fermions). We prove that N(Z)/Z \u2192 1 as Z \u2192 \u221e.", "date": "2006-02-08", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin/Heidelberg", "pagerange": "103-112", "id_number": "CaltechAUTHORS:20190823-105107387", "isbn": "354022212X", "book_title": "The Stability of Matter: From Atoms to Stars: Selecta of Elliott H. Lieb", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190823-105107387", "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": "NA 7901" }, { "agency": "NSF", "grant_number": "DMS-8416049" }, { "agency": "NSF", "grant_number": "PHY 85-15288-A01" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Thirring-W-E", "name": { "family": "Thirring", "given": "Walter" } } ] }, "doi": "10.1007/3-540-27056-6_9", "pub_year": "2006", "author_list": "Lieb, Elliott H.; Sigal, Israel M.; et al." }, { "id": "https://authors.library.caltech.edu/records/yp24e-vgb65", "eprint_id": 82253, "eprint_status": "archive", "datestamp": "2023-08-19 17:07:17", "lastmod": "2026-03-09 22:49:00", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "A difference-integral representation of Koornwinder polynomials", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2006 American Mathematical Society. \n\nThis paper is based on a talk the author gave at the Workshop on Jack, Hall-Littlewood and Macdonald Polynomials held at the International Centre for Mathematical Sciences, September 23 through 26, 2003. The author would like to thank the organizers for inviting him to that stimulating meeting, as well as the other participants for making the meeting stimulating.\n\n

Submitted - 0409437.pdf

", "abstract": "We construct new families of (q-) difference and (contour) integral operators having nice actions on Koornwinder's multivariate orthogonal polynomials. We further show that the Koornwinder polynomials can be constructed by suitable sequences of these operators applied to the constant polynomial 1, giving the difference-integral representation of the title. Macdonald's conjectures (as proved by van Diejen and Sahi) for the principal specialization and norm follow immediately, as does a Cauchy-type identity of Mimachi.", "date": "2006", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "319-333", "id_number": "CaltechAUTHORS:20171010-105435263", "isbn": "978-0-8218-3683-5", "book_title": "Jack, Hall-Littlewood and Macdonald Polynomials", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171010-105435263", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kuznetsov-V-B", "name": { "family": "Kuznetsov", "given": "Vadim B." } }, { "id": "Sahi-S", "name": { "family": "Sahi", "given": "Siddhartha" } } ] }, "doi": "10.1090/conm/417/07929", "primary_object": { "basename": "0409437.pdf", "url": "https://authors.library.caltech.edu/records/yp24e-vgb65/files/0409437.pdf" }, "pub_year": "2006", "author_list": "Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/jyge0-sx626", "eprint_id": 98303, "eprint_status": "archive", "datestamp": "2023-08-19 16:06:43", "lastmod": "2026-04-14 20:54:44", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Sturm Oscillation and Comparison Theorems", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 Birkh\u00e4user Verlag Basel/Switzerland 2005. \n\nSupported in part by NSF grant DMS-0140592. \n\nIt is a pleasure to thank W. Amrein for the invitation to give this talk and for organizing an interesting conference, Y. Last and G. Kilai for the hospitality of Hebrew University where this paper was written, and F. Gesztesy for useful comments.\n\n

Submitted - math0311049.pdf

", "abstract": "This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.", "date": "2005-07-20", "date_type": "published", "publisher": "Birkh\u00e4user-Verlag", "place_of_pub": "Basel", "pagerange": "29-43", "id_number": "CaltechAUTHORS:20190828-102318098", "isbn": "3764370661", "book_title": "Sturm-Liouville Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190828-102318098", "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" } ] }, "contributors": { "items": [ { "id": "Amrein-W-O", "name": { "family": "Amrein", "given": "W. O." } }, { "id": "Hinz-A-M", "name": { "family": "Hinz", "given": "A. M." } }, { "id": "Pearson-D-P", "name": { "family": "Pearson", "given": "D. P." } } ] }, "doi": "10.1007/3-7643-7359-8_2", "primary_object": { "basename": "math0311049.pdf", "url": "https://authors.library.caltech.edu/records/jyge0-sx626/files/math0311049.pdf" }, "pub_year": "2005", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/hr825-0v920", "eprint_id": 101477, "eprint_status": "archive", "datestamp": "2023-08-22 02:57:10", "lastmod": "2026-03-09 23:12:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Paranjape-K", "name": { "family": "Paranjape", "given": "Kapil" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" } ] }, "title": "Quotients of E^n by a_(n+1) and Calabi-Yau manifolds", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "elliptic curve; Kummer surface; Calabi-Yau manifold; representations; alternating group; dual variety; crepant resolution", "note": "\u00a9 2005 Hindustan Book Agency.", "abstract": "We give a simple construction, for n \u2265 2, of an n-dimensional Calabi-Yau variety of Kummer type by studying the quotient Y of an n-fold self-product of an elliptic curve E by a natural action of the alternating group a_(n+1) (in n + 1 variables). The vanishing of H^m (Y, O_Y) for 0 < m < n follows from the lack of existence of (non-zero) fixed points in certain representations of a_(n+1). For n \u2264 3 we provide an explicit (crepant) resolution X in characteristics different from 2, 3. The key point is that Y can be realized as a double cover of \u2119^n branched along a hypersurface of degree 2(n + 1).", "date": "2005", "date_type": "published", "publisher": "Hindustan Book Agency", "place_of_pub": "Gurgaon", "pagerange": "90-98", "id_number": "CaltechAUTHORS:20200221-155530980", "isbn": "978-81-85931-57-9", "book_title": "Algebra and Number Theory: Proceedings of the Silver Jubilee Conference University of Hyderabad", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200221-155530980", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Tandon-R", "name": { "family": "Tandon", "given": "Rajat" } } ] }, "doi": "10.1007/978-93-86279-23-1_6", "pub_year": "2005", "author_list": "Paranjape, Kapil and Ramakrishnan, Dinakar" }, { "id": "https://authors.library.caltech.edu/records/6nmmy-xhv73", "eprint_id": 99231, "eprint_status": "archive", "datestamp": "2023-08-19 12:50:11", "lastmod": "2026-04-16 01:40:53", "type": "book_section", "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": "unpub", "full_text_status": "public", "note": "\u00a9 2004 Springer-Verlag Berlin Heidelberg. \n\nDiscussions with Sergey Bravyi and Frank Verstraete are gratefully acknowledged. JK is 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, and by DARPA and Air Force Laboratory, Air Force Materiel Command, USAF, under agreement number F30602-01-2-0524, and by DARPA and the\nOffice of Naval Research under grant number 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. AK is supported in part by the National Science Foundation\nunder grant EIA-0086038. OR is supported by an Alon Fellowship and the Army Research Office grant DAAD19-03-1-0082. Part of this work was carried out during a visit of OR at LRI, Universit\u00e9 de Paris-Sud and he thanks his hosts for their hospitality and acknowledges partial support by ACI S\u00e9curit\u00e9 Informatique, 2003-n24, projet \"R\u00e9seaux Quantiques\".\n\n

Submitted - 0406180.pdf

", "abstract": "The k-Local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX- k -SAT, which is NP-complete for k \u2265 2. It was known that the problem is QMA-complete for any k \u2265 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 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. The second proof uses elementary linear algebra only. Using our techniques we also show that adiabatic computation with two-local interactions on qubits is equivalent to standard quantum computation.", "date": "2004", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "372-383", "id_number": "CaltechAUTHORS:20191011-072647725", "isbn": "978-3-540-24058-7", "book_title": "FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20191011-072647725", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "ACI S\u00e9curit\u00e9 Informatique", "grant_number": "ACI-CR 2002-40" }, { "agency": "European Union", "grant_number": "RESQ IST-2001-37559" }, { "agency": "Defense Advanced Research Projects Agency (DARPA)" }, { "agency": "Air Force Office of Scientific Research (AFOSR)", "grant_number": "F30602-01-2-0524" }, { "agency": "Office of Naval Research (ONR)", "grant_number": "FDN-00014-01-1-0826" }, { "agency": "NSF", "grant_number": "EIA-0086038" }, { "agency": "Tel-Aviv University" }, { "agency": "Army Research Office (ARO)", "grant_number": "DAAD19-03-1-0082" } ] }, "local_group": { "items": [ { "id": "IQIM" }, { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Lodaya-K", "name": { "family": "Lodaya", "given": "Kamal" } }, { "id": "Mahajan-M", "name": { "family": "Mahajan", "given": "Meena" } } ] }, "doi": "10.1007/978-3-540-30538-5_31", "primary_object": { "basename": "0406180.pdf", "url": "https://authors.library.caltech.edu/records/6nmmy-xhv73/files/0406180.pdf" }, "pub_year": "2004", "author_list": "Kempe, Julia; Kitaev, Alexei; et al." }, { "id": "https://authors.library.caltech.edu/records/4fg28-3pc95", "eprint_id": 38909, "eprint_status": "archive", "datestamp": "2023-08-19 10:44:15", "lastmod": "2026-03-09 20:39:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Actions of Polish Groups and Classification Problems", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2002 Cambridge University Press. Publication date: January 2003. Research and preparation of this paper have been\npartially supported by NSF Grants DMS 96-19880 and DMS 99-87437.\n\n

Published - Kechris_2002p115.pdf

", "abstract": "We will discuss in this paper some aspects of a general program whose goal is the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This work is motivated by basic foundational questions, like understanding the nature of complete classification of mathematical objects up to some notion of equivalence by invariants, and creating a mathematical framework for\nmeasuring the complexity of such classification problems. This theory, which has been growing rapidly over the last few years, is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of the broad scope of this theory, there are natural interactions of it with other areas of mathematics, such as the theory of topological groups, topological dynamics, ergodic theory and its relationships with the theory of operator algebras, model theory, and recursion theory.", "date": "2003-01", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "115-187", "id_number": "CaltechAUTHORS:20130612-095807587", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-095807587", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS 96-19880" }, { "agency": "NSF", "grant_number": "DMS 99-87437" } ] }, "other_numbering_system": { "items": [ { "id": "MR1967835", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Henson-W-C", "name": { "family": "Henson", "given": "Ward C." } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } }, { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "primary_object": { "basename": "Kechris_2002p115.pdf", "url": "https://authors.library.caltech.edu/records/4fg28-3pc95/files/Kechris_2002p115.pdf" }, "pub_year": "2003", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/3a566-2z615", "eprint_id": 88738, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:38", "lastmod": "2026-03-09 20:31:49", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Actions of the Infinite Symmetric Group", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "133-136", "id_number": "CaltechAUTHORS:20180810-082937079", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-082937079", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.022", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/ap14y-xbw77", "eprint_id": 88820, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:11", "lastmod": "2026-03-09 20:36:45", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "The General Glimm-Effros Dichotomy", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "120-122", "id_number": "CaltechAUTHORS:20180815-101343549", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180815-101343549", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.018", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/a13d8-j4n92", "eprint_id": 88736, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:32", "lastmod": "2026-03-09 20:34:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Actions of Locally Compact Groups", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "131-132", "id_number": "CaltechAUTHORS:20180810-081922189", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-081922189", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.021", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/q9tk3-c2q65", "eprint_id": 88904, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:51", "lastmod": "2026-03-09 20:40:24", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Positive Bounded Formulas", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "In this chapter we introduce the key ingredients of the logic for normed space structures that is described in this paper. These are the positive bounded formulas and the concept of approximate satisfaction of such formulas in normed space structures. \n\nLet L be a signature for a normed space structure \u2133 based on (M^(s) \u2223 s \u2208 S). Recall that S has a distinguished element s = S_\u211d for which M^(s) = \u211d is the sort of real numbers.\n\nWe begin considering \u2133 from the model theoretic point of view, introducing a formal language based on L and a semantics according to which this language is interpreted in \u2133. In addition to the symbols of the signature L, we also need for each element s of the sort index set S, a countable set of symbols called the variables of sort s. \n\nWe begin defining the formal language by introducing the set of terms of L, or L-terms. Each term is a finite string of symbols, each of which may be a variable or a function symbol of L, or one of the symbols (or, which are used for punctuation. In this many-sorted context, each term is associated with a unique sort which indicates its range. The formal definition is recursive. \n\nDefinition. An L-term with range of sort s is a string which can be obtained by finitely many applications of the following rules of formation: \n\nIf x is a variable of L of sort s, then x is a term with range of sort s. \n\n[\u2026]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "21-30", "id_number": "CaltechAUTHORS:20180817-104143887", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143887", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.007", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/d63ag-h8e78", "eprint_id": 88921, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:22", "lastmod": "2026-03-09 20:36:52", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Types", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "96-106", "id_number": "CaltechAUTHORS:20180817-104145409", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145409", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.016", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/rjbbe-mby02", "eprint_id": 88917, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:09", "lastmod": "2026-03-09 20:41:02", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Turbulence IV: Some Examples", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "150-151", "id_number": "CaltechAUTHORS:20180817-104145011", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145011", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.026", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/vx1d9-tnt24", "eprint_id": 88883, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:27", "lastmod": "2026-03-09 20:35:14", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Introduction", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "The articles in this book had their origins in three mini-courses offered at the conference \"Analyse & Logique\" held August 25\u201329, 1997, at the University of Mons-Hainaut in M\u00f6ns, Belgium. For a long time there have been rich connections between analysis and logic; these articles bear witness that this relationship is still very active, and continues to be important for both areas. \n\nHere we briefly describe these three articles; each one has a more detailed Introduction as its first chapter.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "xi-xiv", "id_number": "CaltechAUTHORS:20180816-160145519", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145519", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.002", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/wdhyt-nf903", "eprint_id": 88922, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:26", "lastmod": "2026-03-09 20:38:12", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Ultrapowers of Normed Space Structures", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "17-20", "id_number": "CaltechAUTHORS:20180817-104145503", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145503", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.006", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/9q2qp-vhe34", "eprint_id": 88919, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:15", "lastmod": "2026-03-09 20:40:28", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Turbulence VI: The First Main Theorem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "157-162", "id_number": "CaltechAUTHORS:20180817-104145215", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145215", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.028", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/gd1r7-a4b67", "eprint_id": 88742, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:41", "lastmod": "2026-03-09 20:35:09", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Alternative Formulations of the Theory", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "72-74", "id_number": "CaltechAUTHORS:20180810-085559683", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-085559683", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.013", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/5ttz2-yka90", "eprint_id": 88763, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:58", "lastmod": "2026-03-09 20:31:05", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Basic Model Theory I", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "31-33", "id_number": "CaltechAUTHORS:20180810-150243521", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-150243521", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.008", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/t4ch5-78634", "eprint_id": 88750, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:48", "lastmod": "2026-03-09 20:40:37", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Background material: The 60's and 70's", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "194-207", "id_number": "CaltechAUTHORS:20180810-103955912", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-103955912", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.032", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/st8kc-pcq29", "eprint_id": 88885, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:33", "lastmod": "2026-03-09 20:35:20", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Introduction", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "The ideas and methods of model theory are being applied today in nearly all parts of mathematics. Here we concentrate on a framework for applications in functional analysis. Model theory has already provided several tools for the research analyst, of which the most important are: (a) the Banach space ultraproduct and nonstandard hull constructions in functional analysis; (b) spaces of (model-theoretic) types as used in the geometry of Banach spaces; and (c) Loeb measure spaces in stochastic analysis and its applications. In this paper we explain a systematic model theoretic framework within which these tools (especially (a) and (b)) are naturally situated. Our main intended audience consists of analysts who are familiar with the ultraproduct construction, and this perspective has strongly influenced our presentation of the material. We expect that many model theorists will also find something of interest in this subject. In particular, we indicate the initial steps of a program for introducing the key ideas and methods of model theory into functional analysis in a systematic and comprehensive way. \n\nApplications of model theory in functional analysis have been pursued since the mid 1960s, beginning with the introduction of Banach space ultraproducts by Bretagnolle, Dacunha-Castelle, and Krivine [BDCK66] [Kri67] [DCK72] and nonstandard hulls by Luxemburg [Lux69b]. These two constructions Avere first used at about the same time and they are essentially the same; however, these initial steps led to largely independent lines of research that have still not been fully integrated.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "3-9", "id_number": "CaltechAUTHORS:20180816-160145668", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145668", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.003", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/m3qfe-dr555", "eprint_id": 88767, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:04", "lastmod": "2026-03-09 20:41:38", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Concluding remarks", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "Summary: We have not addressed certain important problems that remain unsolved after many years concerning the classical Banach spaces themselves. (Q13) Let K be a compact metric space. Is every complemented sub-space of C(K) isomorphic to C(L) for some compact metric space L?\nIt is known that if K is uncountable then C(K) is isomorphic to C[0,1]. If if is countable then C(K) is isomorphic to C(\u03c9^(\u03c9\u03b1)) for some \u03b1 < \u03c9_1. Every complemented subspace of c_0 (isomorphic to C (\u03c9)) is either finite dimensional or isomorphic to c_0 ([Pel]). If X is complemented in C[0,1] and X* is nonseparable then X is isomorphic to C[0,1] [R6]. Every quotient of c0 embeds isomorphically into c0 but this does not hold in general for C(\u03c9^(\u03c9\u03b1)). A discussion of these and related results may be found in [A1, A2, A3, A4], [Gal, Ga2], [Bo2].\nThe isomorphism types of the complemented subspaces of L_1[0,1] remain unclassified.\n(Q14) Let X be a complemented (infinite dimensional) subspace of L_1[0,1]. Is X isomorphic to L_1 or l_1?\nEvery X which is complemented in l_p (1 \u2264 p < \u221e) or c_0 is isomorphic to l_p or c_0. There are known to be uncountably many mutually nonisomorphic complemented subspaces of L_p[0,1] (1 < p < \u221e, p \u2260 2) [BRS] and all are known to have a basis [JRZ]. These spaces have been classified as \u2112_p spaces ([LP], [LR]), provided they are not Hilbert spaces.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "254-256", "id_number": "CaltechAUTHORS:20180810-151926459", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-151926459", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.039", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/z6qr5-nee80", "eprint_id": 88918, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:12", "lastmod": "2026-03-09 20:41:54", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Turbulence V: Calmness", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "152-156", "id_number": "CaltechAUTHORS:20180817-104145112", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145112", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.027", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/htjz5-56n45", "eprint_id": 88886, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:37", "lastmod": "2026-03-09 20:40:35", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Isomorphic Ultrapowers", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "In this chapter we prove isomorphism theorems for ultrapowers and ultraproducts of normed space structures. These results show that there is a very tight connection between (a) properties that are preserved under the ultraproduct construction and (b) properties that are expressible using the logic for normed space structures that is described in this paper. \n\nLet L be a signature and let \u2133 and N be two normed space L-structures. If \u2133 and N have isomorphic ultrapowers, by Corollary 9.4 they must be approximately elementarily equivalent. Theorem 10.7 below gives the converse (in a strong form). Together these results show that ultrapower equivalence of \u2133 and N is the same as approximate elementary equivalence. (See the discussion of this issue in the Introduction.) \n\nTheorem 10.8 below is a similar result for ultraproducts. Among other things, it shows that the ultrafilter guaranteed by Theorem 10.7 can be chosen in a highly uniform way and that the ultrapowers in question can be taken to be highly saturated. The uniformity will be exploited in Chapter 12 to prove the existence of ultrapowers that are highly homogeneous (in addition to being highly saturated). \n\nThe results in this chapter are analogous to the Keisler-Shelah Theorem in ordinary model theory. (See [She71] and Chapter 6 in [CK90].) Moreover, our proof follows a similar line of argument, with adjustments appropriate to the handling of positive bounded formulas and their approximations.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "55-71", "id_number": "CaltechAUTHORS:20180816-160145747", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145747", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.012", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/yaajk-0wk55", "eprint_id": 88878, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:17", "lastmod": "2026-03-09 20:41:21", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "The homogeneous Banach space problem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "We cannot end before at least briefly discussing one other spectacular result of the 90's.\n\nWe recall that the homogeneous Banach space problem (P5) is: If X is isomorphic to all Y \u2286 X, is X isomorphic to l2? This was solved by combining two beautiful pieces of work, Gowers' dichotomy theorem (Theorem 3.1) and the following theorem of Komorowski and Tomczak-Jaegermann [KT1, KT2]. A nice exposition somewhat simplifying the argument appears in [TJ1].", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "252-253", "id_number": "CaltechAUTHORS:20180816-160145154", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145154", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Chritian" } } ] }, "doi": "10.1017/cbo9781107360006.038", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/m2cg8-pbh82", "eprint_id": 88881, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:23", "lastmod": "2026-03-09 20:35:44", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Introduction", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "We will discuss in this paper some aspects of a general program whose goal is the development of the theory of definable actions of Polish groups, the structure and classification of their orbit spaces, and the closely related study of definable equivalence relations. This work is motivated by basic foundational questions, like understanding the nature of complete classification of mathematical objects up to some notion of equivalence by invariants, and creating a mathematical framework for measuring the complexity of such classification problems. This theory, which has been growing rapidly over the last few years, is developed within the context of descriptive set theory, which provides the basic underlying concepts and methods. On the other hand, in view of the broad scope of this theory, there are natural interactions of it with other areas of mathematics, such as the theory of topological groups, topological dynamics, ergodic theory and its relationships with the theory of operator algebras, model theory, and recursion theory. \n\nClassically, in various branches of dynamics one studies actions of the groups of integers \u2124, reals \u211d, Lie groups, or even more generally (second countable) locally compact groups. One of the goals of the theory is to expand this scope by considering the more comprehensive class of Polish groups (separable completely metrizable topological groups), which seems to be the widest class of well-behaved (for our purposes) groups and which includes practically every type of topological group we are interested in.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "117-119", "id_number": "CaltechAUTHORS:20180816-160145363", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145363", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.017", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/m6d1f-n8p96", "eprint_id": 88757, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:54", "lastmod": "2026-03-09 20:36:12", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Actions of Countable Groups", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "Let G be a countable group and X a Borel G-space. Then it is clear that is a Borel equivalence relation and every one of its equivalence class is countable.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "126-130", "id_number": "CaltechAUTHORS:20180810-135928044", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-135928044", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.020", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/1c9tj-t2y51", "eprint_id": 88916, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:05", "lastmod": "2026-03-09 21:10:04", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Turbulence III: Induced Actions", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "146-149", "id_number": "CaltechAUTHORS:20180817-104144921", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144921", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.025", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/wzw19-68k90", "eprint_id": 88924, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:29", "lastmod": "2026-03-09 20:41:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Ultraproducts of Normed Space Structures", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "38-42", "id_number": "CaltechAUTHORS:20180817-104145709", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145709", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.010", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/btb5z-qfg46", "eprint_id": 88756, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:51", "lastmod": "2026-03-09 20:53:30", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Asymptotic structure", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "233-243", "id_number": "CaltechAUTHORS:20180810-135054931", "isbn": "9780521648615", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-135054931", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006.036", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/473k1-9z653", "eprint_id": 88884, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:30", "lastmod": "2026-03-09 20:35:17", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Introduction", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "The most outstanding problems in the theory of infinite dimensional Banach spaces, those that were central to the study of the general structure of a Banach space, finally yielded their secrets in the 1990's. In this survey we shall discuss these problems and their solutions and more. For many years researchers have been aware of deep connections between both the theorems and ideas of logic and set theory and Banach space theory. We shall try to illuminate these connections as well.\n\nFor example the ideas of Ramsey theory played a key role in H. Rosenthal's magnificent l_1-theorem in 1974 [R1]. But there is also a less direct connection with the Banach space question as to whether or not separable infinite dimensional Hilbert space, l_2, is distortable. This is equivalent to the following approximate Ramsey problem. Let S_(l2) = {x \u2208 l_2: \u2225x\u2225 = 1} be the unit sphere of l_2. Finitely color the sphere by colors C_1,\u2026, C_k and let \u03b5 > 0. Does there exist an i_0 and an infinite dimensional closed linear subspace X of l_2 so that the unit sphere of X, S_X, is a subset of (C_(i0))_\u03b5 = {y \u2208 S_(l2) : \u2225y \u2212 x\u2225 < \u03b5 for some x \u2208 C_(i0)}? It suffices to let (e_i) be an orthonormal basis for l_2 and confine the search to block subspaces \u2014 those spanned by block bases of (e_i) (these terms are defined precisely below).", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "191-193", "id_number": "CaltechAUTHORS:20180816-160145605", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145605", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.031", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/nepa8-sy522", "eprint_id": 88915, "eprint_status": "archive", "datestamp": "2023-08-19 10:40:02", "lastmod": "2026-03-09 20:41:46", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. Ward" } }, { "id": "Iovino-J", "name": { "family": "Iovino", "given": "Jos\u00e9" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Odell-E", "name": { "family": "Odell", "given": "Edward" } } ] }, "title": "Turbulence II: Basic Facts", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "[no abstract]", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "143-145", "id_number": "CaltechAUTHORS:20180817-104144833", "isbn": "9781107360006", "book_title": "Analysis and Logic", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144833", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Finet-C", "name": { "family": "Finet", "given": "Catherine" } }, { "id": "Michaux-C", "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/cbo9781107360006.024", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/sa1wa-twg11", "eprint_id": 88887, "eprint_status": "archive", "datestamp": "2023-08-19 10:39:40", "lastmod": "2026-03-09 20:29:46", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Henson-C-W", "name": { "family": "Henson", "given": "C. 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Published - forrester.pdf

Submitted - 9907008.pdf

", "abstract": "We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate eigenvalues from the corresponding orthogonal ensemble form a symplectic ensemble, and similarly classify those weights for which alternate eigenvalues from a union of two orthogonal ensembles forms a unitary ensemble. Also considered are the k-point distributions for the decimated orthogonal ensembles.", "date": "2001", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "171-207", "id_number": "CaltechAUTHORS:20170926-090553813", "isbn": "9780521802093", "book_title": "Random Matrix Models and Their Applications", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-090553813", "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" } ] }, "contributors": { "items": [ { "id": "Bleher-P", "name": { "family": "Bleher", "given": "Pavel" } }, { "id": "Its-A", "name": { "family": "Its", "given": "Alexander" } } ] }, "doi": "10.48550/arXiv.9907008", "primary_object": { "basename": "9907008.pdf", "url": "https://authors.library.caltech.edu/records/9ddmw-j3z48/files/9907008.pdf" }, "related_objects": [ { "basename": "forrester.pdf", "url": "https://authors.library.caltech.edu/records/9ddmw-j3z48/files/forrester.pdf" } ], "pub_year": "2001", "author_list": "Forrester, Peter J. and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/dcn12-7zh50", "eprint_id": 81862, "eprint_status": "archive", "datestamp": "2023-08-19 07:03:52", "lastmod": "2026-03-09 23:04:00", "type": "book_section", "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": "Symmetrized Random Permutations", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2001 Mathematical Sciences Research Institute. \n\n\nThe authors thank the organizers of the workshop on Random Matrix Models and their Applications for their invitations.\n\n

Published - baik.pdf

Submitted - 9910019.pdf

", "abstract": "Selecting N random points in a unit square corresponds to selecting a random permutation. By putting 5 types of symmetry restrictions on the points, we obtain subsets of permutations : involutions, signed permutations and signed involutions. We are interested in the statistics of the length of the longest up/right path of random points selections in each symmetry type as the number of points increases to infinity. The limiting distribution functions are expressed in terms of Painlev\u00e9 II equation. Some of them are Tracy-Widom distributions in random matrix theory, while there are two new classes of distribution functions interpolating GOE and GSE, and GUE and GOE^2 Tracy-Widom distribution functions. Also some applications and related topics are discussed.", "date": "2001", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "1-19", "id_number": "CaltechAUTHORS:20170926-160331200", "isbn": "9780521802093", "book_title": "Random Matrix Models and Their Applications", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170926-160331200", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Bleher-P", "name": { "family": "Bleher", "given": "Pavel" } }, { "id": "Its-A", "name": { "family": "Its", "given": "Alexander" } } ] }, "doi": "10.48550/arXiv.9910019", "primary_object": { "basename": "9910019.pdf", "url": "https://authors.library.caltech.edu/records/dcn12-7zh50/files/9910019.pdf" }, "related_objects": [ { "basename": "baik.pdf", "url": "https://authors.library.caltech.edu/records/dcn12-7zh50/files/baik.pdf" } ], "pub_year": "2001", "author_list": "Baik, Jinho and Rains, Eric M." }, { "id": "https://authors.library.caltech.edu/records/p9dz3-69j53", "eprint_id": 39684, "eprint_status": "archive", "datestamp": "2023-08-19 05:50:46", "lastmod": "2026-03-09 20:36:50", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Descriptive Dynamics", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2000 Cambridge University Press.\n\nThis paper is based on the text of a series of lectures\nthat I was scheduled to give at the International Workshop on Descriptive Set\nTheory and Dynamical Systems, CIRM, Luminy, July 1-5, 1996. Unfortunately,\nat the last moment, a family emergency prevented me from attending\nthe meeting, but A. Louveau has kindly stepped in and delivered these lectures.\n(Except for Lecture IV for which there was not sufficient time.) I\nwould like to thank him for taking over this, despite his heavy load of duties\nduring this meeting. Research and preparation of this paper were partially\nsupported by NSF Grant DMS 96-19880.\n\n

Published - Kechris_2000p231.pdf

", "abstract": "The purpose of the following informal lectures is to give a brief introduction to\ndescriptive dynamics, which I understand here to be the descriptive theory of\nPolish group actions. I will concentrate on the foundations, and hopefully at\na level accessible to anyone with a basic knowledge of descriptive set theory.\nI will illustrate some of the main methods used in this area, including Baire\ncategory arguments and various implementations of the \"changing the topology\"\ntechnique. A general reference for the results discussed in this paper is\nBecker-Kechris [1996].", "date": "2000-06", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "New York", "pagerange": "231-258", "id_number": "CaltechAUTHORS:20130731-144914781", "isbn": "9780521786447", "book_title": "Descriptive set theory and dynamical systems", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130731-144914781", "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": "1774428", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Foreman-M", "name": { "family": "Foreman", "given": "M." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "A." } }, { "id": "Weiss-B", "name": { "family": "Weiss", "given": "B." } } ] }, "primary_object": { "basename": "Kechris_2000p231.pdf", "url": "https://authors.library.caltech.edu/records/p9dz3-69j53/files/Kechris_2000p231.pdf" }, "pub_year": "2000", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/b031b-a6m60", "eprint_id": 88552, "eprint_status": "archive", "datestamp": "2023-08-19 05:43:46", "lastmod": "2026-03-10 00:02:06", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "Richard M." } } ] }, "title": "Existence of Steiner systems that admit automorphisms with large cycles", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2000 by Walter de Gruyter GmbH.", "abstract": "For every integer k \u2265 2, we construct infinite families of Steiner systems S(2, k, \u03bd) that have (1) an automorphism that permutes the v points in a single-cycle of length \u03bd, (2) an automorphism that fixes one point and permutes the remaining \u03bd \u2013 1 points in a single cycle, or (3) an automorphism that fixes one point and permutes the remaining points in two cycles, of lengths r = (\u03bd - 1)/(k \u2013 1) and \u03bd \u2013 r \u2013 1. The designs we construct with property (2) are also resolvable.", "date": "2000-05", "date_type": "published", "publisher": "De Gruyter", "place_of_pub": "Berlin", "pagerange": "305-312", "id_number": "CaltechAUTHORS:20180802-155215256", "isbn": "9783110198119", "book_title": "Codes and Designs: Proceedings of a conference honoring Professor Dijen K. Ray-Chaudhuri on the occasion of his 65th birthday", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180802-155215256", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Arasu-K-T", "name": { "family": "Arasu", "given": "K. T." } }, { "id": "Seress-A", "name": { "family": "Seress", "given": "Akos" } } ] }, "doi": "10.1515/9783110198119.305", "pub_year": "2000", "author_list": "Wilson, Richard M." }, { "id": "https://authors.library.caltech.edu/records/pz5er-rys37", "eprint_id": 39054, "eprint_status": "archive", "datestamp": "2023-08-19 05:04:16", "lastmod": "2026-03-09 20:41:04", "type": "book_section", "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": "How Many Turing Degrees are There?", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2000 American Mathematical Society.\n\nThe first author was partially supported by NSF Grant DMS 9158092.\nThe second author was partially supported by NSF Grant DMS 9619880.\n\n

Published - Kechris_2000p83.pdf

", "abstract": "A Borel equivalence relation on a Polish space is countable if all\nof its equivalence classes are countable. Standard examples of countable Borel\nequivalence relations (on the space of subsets of the integers) that occur in\nrecursion theory are: recursive isomorphism, Turing equivalence, arithmetic\nequivalence, etc. There is a canonical hierarchy of complexity of countable\nBorel equivalence relations imposed by the notion of Borel reducibility. We\nwill survey results and conjectures concerning the problem of identifying the\nplace in this hierarchy of these equivalence relations from recursion theory and\nalso discuss some of their implications.", "date": "2000", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "83-94", "id_number": "CaltechAUTHORS:20130624-113819994", "isbn": "9780821819227", "book_title": "Computability theory and its applications: current trends and open problems", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130624-113819994", "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-9619880" } ] }, "other_numbering_system": { "items": [ { "id": "MR1770736", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cholak-P", "name": { "family": "Cholak", "given": "Peter" } } ] }, "doi": "10.1090/conm/257", "primary_object": { "basename": "Kechris_2000p83.pdf", "url": "https://authors.library.caltech.edu/records/pz5er-rys37/files/Kechris_2000p83.pdf" }, "pub_year": "2000", "author_list": "Dougherty, Randall and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/yd8at-ym210", "eprint_id": 82239, "eprint_status": "archive", "datestamp": "2023-08-19 05:09:20", "lastmod": "2026-03-09 22:49:04", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Odlyzko-A-M", "name": { "family": "Odlyzko", "given": "A. M." } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "E. M." }, "orcid": "0000-0002-9915-0919" } ] }, "title": "On longest increasing subsequences in random permutations", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2000 American Mathematical Society. \n\nWe thank Craig Tracy for providing the numerical data about asymptotic distribution of L_n that is used in Table 1 and Figure 1 and Jim Reeds for help with the random number generator programs. We also thank David Aldous, Harry Kesten, Anatoly Vershik, and Ofer Zeitouni for their comments.", "abstract": "The expected value of L_n, the length of the longest increasing subsequence of a random permutation of {1, ... , n}, has been studied extensively. This paper presents the results of both Monte Carlo and exact computations that explore the finer structure of the distribution of L_n. The results suggested that several of the conjectures that had been made about L_n were incorrect, and led to new conjectures, some of which have been proved recently by Jinho Baik, Percy Deift, and Kurt Johansson. In particular, the standard deviation of L_n is of order n^(1/6), contrary to earlier conjectures.\n\nThis paper also explains some regular patterns in the distribution of L_n.", "date": "2000", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "439-451", "id_number": "CaltechAUTHORS:20171009-160133131", "isbn": "978-0-8218-1148-1", "book_title": "Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171009-160133131", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Grinberg-E-L", "name": { "family": "Grinberg", "given": "E. L." } }, { "id": "Berhanu-S", "name": { "family": "Berhanu", "given": "S." } }, { "id": "Knopp-M", "name": { "family": "Knopp", "given": "M." } }, { "id": "Mendoza-G", "name": { "family": "Mendoza", "given": "G." } }, { "id": "Quinto-E-T", "name": { "family": "Quinto", "given": "E. T." } } ] }, "doi": "10.1090/conm/251/03886", "pub_year": "2000", "author_list": "Odlyzko, A. M. and Rains, E. M." }, { "id": "https://authors.library.caltech.edu/records/jnnq0-9fe41", "eprint_id": 81526, "eprint_status": "archive", "datestamp": "2023-08-19 03:49:01", "lastmod": "2026-03-18 00:03:13", "type": "book_section", "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 the determination of a potential from three spectra", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Inverse spectral theory, Schrodinger operators, Weyl-Titchmarsh m-functions", "note": "\u00a9 1999 American Mathematical Society. \n\nThe work of the first-named author was partially supported by the National Science Foundation under Grant No. DMS-9623121.", "abstract": "We prove that under suitable circumstances, the spectra of a\nSchrodinger operator on the three intervals [O, 1], [O, \u0251], and [\u0251, 1] for some \u0251 \u0454 (0, 1) uniquely determine the potential q on [O, 1].", "date": "1999", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Province", "pagerange": "85-92", "id_number": "CaltechAUTHORS:20170918-110240939", "isbn": "978-0-8218-1387-4", "book_title": "Differential Operators and Spectral Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170918-110240939", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9623121" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Buslaev-V", "name": { "family": "Buslaev", "given": "V." } }, { "id": "Solomyak-M", "name": { "family": "Solomyak", "given": "M." } }, { "id": "Yafaev-D", "name": { "family": "Yafaev", "given": "D." } } ] }, "doi": "10.1090/trans2/189", "pub_year": "1999", "author_list": "Gesztesy, Fritz and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/g57yg-2jx07", "eprint_id": 103124, "eprint_status": "archive", "datestamp": "2023-08-22 12:28:23", "lastmod": "2026-03-07 04:14:15", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Quasithin Groups", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Finite Group; Simple Group; Borel Subgroup; Cartan Subgroup; Finite Simple Group", "note": "\u00a9 1998 Springer Science+Business Media Dordrecht. \n\nThis work was partially supported by NSF-9622843.", "abstract": "The treatment of quasithin groups of characteristic 2 was one of the last steps in the Classification of the finite simple groups. Geoff Mason [12] announced a classification of these groups in about 1980, but never published his work. A few people have a copy of a large manuscript containing his efforts, but because it was distributed slowly, section by section, it was only during the last few years that it was realized that Mason's manuscript is incomplete in various ways. A few years ago I wrote up a treatment which begins where Mason's manuscript ends and finishes the problem assuming the results he says he proves. I have only read Mason's manuscript superficially, but it appears there are missing lemmas even for the part of the problem the theorems in his manuscript cover. I do believe however that he has seriously addressed the issues involved and that he could turn his manuscript into a proof with enough work. However Mason is now involved with Moonshine and has no interest in completing or publishing his manuscript.", "date": "1998", "date_type": "published", "publisher": "Springer", "place_of_pub": "Dordrecht", "pagerange": "321-340", "id_number": "CaltechAUTHORS:20200512-081608756", "isbn": "978-0-7923-5292-1", "book_title": "Algebraic Groups and their Representations", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-081608756", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9622843" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Carter-R-W", "name": { "family": "Carter", "given": "R. W." } }, { "id": "Saxl-J", "name": { "family": "Saxl", "given": "J." } } ] }, "doi": "10.1007/978-94-011-5308-9_18", "pub_year": "1998", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/ytern-gd019", "eprint_id": 103132, "eprint_status": "archive", "datestamp": "2023-08-22 12:28:31", "lastmod": "2026-03-07 16:33:15", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael G." } }, { "id": "Smith-S-D", "name": { "family": "Smith", "given": "Stephen D." } } ] }, "title": "Quasithin Groups", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Finite Group; Weyl Group; Uniqueness Theorem; Finite Simple Group; Subnormal Subgroup", "note": "\u00a9 1998 Birkhiiuser Verlag Basel/Switzerland. \n\nPartially supported by NSF grants DMS-91-01237 and 96-22843. \n\nPartially supported by NSA grant MDA 904-93-H-3039.", "abstract": "Geoff Mason announced in about 1980 the classifcication of quasithin groups of characteristic 2; but never published this step in the classification of the finite simple groups. In January 1996, the authors began work toward a new and more general classification of quasithin groups; the paper gives an exposition of the approach and considerable progress to date.", "date": "1998", "date_type": "published", "publisher": "Springer", "place_of_pub": "Basel", "pagerange": "1-7", "id_number": "CaltechAUTHORS:20200512-100004286", "isbn": "978-3-0348-9785-3", "book_title": "Groups and Geometries", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-100004286", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-91-01237" }, { "agency": "NSF", "grant_number": "DMS-96-22843" }, { "agency": "National Security Agency", "grant_number": "MDA 904-93-H-3039" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "di-Martino-L", "name": { "family": "di Martino", "given": "Lino" } }, { "id": "Kantor-W-M", "name": { "family": "Kantor", "given": "William M." } }, { "id": "Lunardon-G", "name": { "family": "Lunardon", "given": "Guglielmo" } }, { "id": "Pasini-A", "name": { "family": "Pasini", "given": "Antonio" } }, { "id": "Tamburini-M-C", "name": { "family": "Tamburini", "given": "Maria Clara" } } ] }, "doi": "10.1007/978-3-0348-8819-6_1", "pub_year": "1998", "author_list": "Aschbacher, Michael G. and Smith, Stephen D." }, { "id": "https://authors.library.caltech.edu/records/71r71-7n935", "eprint_id": 38625, "eprint_status": "archive", "datestamp": "2023-08-19 02:10:37", "lastmod": "2026-03-09 20:36:00", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The descriptive classification of some classes of C\u2217-algebras", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1998 World Scientific.\nWe would like to thank E. Effros for many\nvaluable conversations about this subject.\nResearch and preparation of this paper were partially supported by\nNSF Grants DMS-9317509 and 9619880.", "abstract": "We introduce here a parametrization of separable C*-algebras by a\nstandard Borel space and study the descriptive complexity of various canonical\nclasses of C*-algebras in this parametrization. This can be viewed as\nproviding an analog of the corresponding classification of classes of von Neumann\nalgebras (acting on a fixed separable Hilbert space) in the Effros Borel\nspace of von Neumann algebras (see for example Nielsen [13]). However, in\ncontrast with the von Neumann case, where most interesting classes (like:\nfactors, type I, II, III, hyperfinite) turn out to be Borel, in the C*-algebra\ncase many important classes turn out to be co-analytic but not Borel. This\nmakes the situation more interesting from the set-theoretic point of view,\nand leads to further questions, like the construction of canonical co-analytic\nnorms, which we also address here. Finally, we relate the above to work of\nSutherland [17] on parametrization of Polish groups and indicate how one\nmight be able to show that various familiar classes of (second countable)\nlocally compact groups are non-Borel as well.", "date": "1998", "date_type": "published", "publisher": "World Scientific", "place_of_pub": "River Edge, NJ", "pagerange": "121-149", "id_number": "CaltechAUTHORS:20130522-083928827", "isbn": "9789810234324", "book_title": "Proceedings of the Sixth Asian Logic Conference", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130522-083928827", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9317509" }, { "agency": "NSF", "grant_number": "DMS-9619880" } ] }, "other_numbering_system": { "items": [ { "id": "MR1789734", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Chong-C-T", "name": { "family": "Chong", "given": "C. -T." } } ] }, "pub_year": "1998", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/5qe0p-g3v80", "eprint_id": 88739, "eprint_status": "archive", "datestamp": "2023-08-20 07:00:42", "lastmod": "2026-03-09 20:38:05", "type": "book_section", "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": "Actions with Borel Orbit Equivalence Relations", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1996 Cambridge University Press.\n\n

Published - actions_with_borel_orbit_equivalence_relations.pdf

", "abstract": "If G is a Polish group and (X, \u03b1) a Borel G-space, then the associated equivalence relation E_\u03b1 is analytic but in general not Borel, even when X is a Polish G-space (see 3.2). We study in this section various questions concerning the Borelness of such E_\u03b1.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "98-115", "id_number": "CaltechAUTHORS:20180810-083346365", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-083346365", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.010", "primary_object": { "basename": "actions_with_borel_orbit_equivalence_relations.pdf", "url": "https://authors.library.caltech.edu/records/5qe0p-g3v80/files/actions_with_borel_orbit_equivalence_relations.pdf" }, "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/6aem8-0j159", "eprint_id": 88867, "eprint_status": "archive", "datestamp": "2023-08-20 07:01:10", "lastmod": "2026-03-09 20:35:58", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Becker-H-S", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Polish Groups", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press.", "abstract": "We will survey here some basic facts from the theory of Polish groups.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "3-12", "id_number": "CaltechAUTHORS:20180816-134913115", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-134913115", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H-S", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.004", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/tvcy4-gz126", "eprint_id": 88726, "eprint_status": "archive", "datestamp": "2023-08-20 07:00:38", "lastmod": "2026-03-09 20:55:12", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Becker-H-S", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Better topologies", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 H. Becker & A.S. Kechris 1996.", "abstract": "This section of the book contains several results, all of which are about changing the topology on a G\u2013space X. Given an action a : G \u00d7 X \u2192 X by a Polish group G, we would like to put a new topology t on X such that: (X,t) is \"nice\", e.g., metrizable or Polish; a is continuous with respect to t; and some given a\u2013invariant set I \u2286 X is t\u2013open (or closed or clopen). We have two different types of theorems, one type which says that there is a new topology which makes the action continuous, the other type which says that given a continuous action, there is a new, finer topology in which the action is still continuous and which makes an invariant set open. We have already seen an instance of such a result in 2.6.6, from which it follows that if G is Polish and X a Borel G\u2013space, then we can put on X a separable metrizable topology having the same Borel structure in which the action is continuous. \n\nIn \u00a75.1, 5.2 we consider the most important case, that of Borel\u2013measurable actions and Borel invariant sets. In \u00a75.3, 5.4 we consider more general actions and invariant sets.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "53-81", "id_number": "CaltechAUTHORS:20180809-161147539", "isbn": "9780511735264", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180809-161147539", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/cbo9780511735264.008", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/brfgs-28861", "eprint_id": 88932, "eprint_status": "archive", "datestamp": "2023-08-20 07:01:23", "lastmod": "2026-03-09 20:38:30", "type": "book_section", "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": "Preface", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press. \n\nThe authors would also like to acknowledge the financial support of the National Science Foundation, through grants DMS-9206922 and DMS-9317509, and the help of the Mathematics Department at Caltech in the preparation of this book. We particularly thank J. Cassidy for typing the manuscript.", "abstract": "This book contains the results of the research of the authors in the foundations of the theory of definable actions of Polish groups and the associated orbit equivalence relations. It is addressed to graduate students and researchers in this area as well as to mathematicians in other fields, whose work comes in contact with this subject.\n\nThe reader will also find some new theorems which are attributed to someone other than the authors. Many people have helped in one way or another to improve this book: by allowing us to include these new theorems; by simplifying some of our proofs; by bringing to our attention some work we were unaware of; or by reading earlier versions of this book \u2013 or parts of it \u2013 and suggesting improvements in the exposition. We thank all of them: G. Cherlin, W. Comfort, R. Dougherty, G. Hjorth, A. Louveau, M. Megrelishvili, M. G. Nadkarni, R. Sami, S. Solecki, S. Thomas, and an anonymous referee.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "vii", "id_number": "CaltechAUTHORS:20180817-132523681", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-132523681", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-9206922" }, { "agency": "NSF", "grant_number": "DMS-9317509" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.001", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/tefar-hsx94", "eprint_id": 88964, "eprint_status": "archive", "datestamp": "2023-08-20 07:01:31", "lastmod": "2026-03-09 20:38:17", "type": "book_section", "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": "Invariant Measures and Paradoxical Decompositions", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press.", "abstract": "We will combine here a theorem of Nadkarni [90] with the results proved in \u00a72 to obtain an application to the theory of paradoxical decompositions. Our general reference for this subject is Wagon [93]. The results in \u00a74 are not used in the rest of the book.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "44-52", "id_number": "CaltechAUTHORS:20180821-074806630", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180821-074806630", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.007", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/n9n01-6p391", "eprint_id": 88768, "eprint_status": "archive", "datestamp": "2023-08-20 07:00:49", "lastmod": "2026-03-09 20:41:19", "type": "book_section", "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": "Actions of Polish Groups", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press.", "abstract": "In \u00a72.1 - 2.5, we survey some basic facts about Polish group actions, particularly continuous and Borel measurable actions on Polish spaces and standard Borel spaces, respectively. In \u00a72.6 we establish the existence of universal actions for any Polish group, extending a result of Mackey and Varadarajan from the locally compact case. Finally, \u00a72.7 is concerned with universal actions for S\u221e and its closed subgroups.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "13-32", "id_number": "CaltechAUTHORS:20180810-154314089", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-154314089", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.005", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/2gx5k-zp413", "eprint_id": 88893, "eprint_status": "archive", "datestamp": "2023-08-20 07:01:17", "lastmod": "2026-03-09 20:53:26", "type": "book_section", "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": "Introduction", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press.", "abstract": "A Polish space (group) is a separable, completely metrizable topological space (group). This book is about actions of Polish groups, in connection with \u2013 or from the point of view of \u2013 the subject of descriptive set theory. Descriptive set theory is the study of definable sets and functions in Polish spaces. The basic classes of definable sets are the classes of Borel, analytic and co\u2013analytic sets, and these certainly constitute the main topic of the book, but at times we also consider other classes of definable sets.\n\nThe structure of Borel actions of Polish locally compact, i.e., second countable locally compact, topological groups has long been studied in ergodic theory, operator algebras and group representation theory. See, for example, Auslander\u2013Moore [66], Feldman\u2013Hahn\u2013Moore [78], Glimm [61], Kechris [92a], Mackey [57, 62, 89], Moore [82], Ramsay [82, 85], Sinai [89], Varadarajan [63], Vershik\u2013Fedorov [87], Zimmer [84] for a sample of this work. This is closely related to the subject matter of this book. More recently, there has been increasing interest in an extension of the above: studying the structure of Borel actions of arbitrary, not necessarily locally compact, Polish groups.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "viii-xii", "id_number": "CaltechAUTHORS:20180817-094122252", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-094122252", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.002", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/c84aj-kqp16", "eprint_id": 88861, "eprint_status": "archive", "datestamp": "2023-08-20 07:01:03", "lastmod": "2026-03-09 20:36:06", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Becker-H-S", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Model Theory and the Vaught Conjecture", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press.", "abstract": "The Vaught Conjecture is a notorious open problem in mathematical logic. A number of stronger conjectures have subsequently been proposed, some of which are conjectures about the descriptive set theory of Polish group actions. These later conjectures are known (collectively) as the Topological Vaught Conjecture. In \u00a76.1 we give some background on the Vaught Conjecture. This section is written primarily for non-logicians, and contains\nnothing that is not well known to specialists. \u00a76.2 contains a number of results, some new, about the Topological Vaught Conjecture. Our new results are of two types: First, that various conjectures imply - or are equivalent to - various other conjectures, and, second, that certain even stronger conjectures are false. There are few things to be proved in \u00a76.2; the results here are mostly corollaries of theorems in earlier parts of this book. In \u00a76.3 we prove a theorem about atomic models (which has nothing to do with the Vaught Conjecture). More connections between group actions and logic will be discussed in \u00a77.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "82-97", "id_number": "CaltechAUTHORS:20180816-125320670", "isbn": "9780521576055", "book_title": "The Descriptive Set Theory of Polish Group Actions", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-125320670", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Becker-H-S", "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } } ] }, "doi": "10.1017/CBO9780511735264.009", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/wcxdz-pkj80", "eprint_id": 106760, "eprint_status": "archive", "datestamp": "2023-08-20 02:11:38", "lastmod": "2026-04-20 19:10:11", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Janwa-H", "name": { "family": "Janwa", "given": "H." } }, { "id": "Wilson-R-M", "name": { "family": "Wilson", "given": "R. M." } } ] }, "title": "Hyperplane sections of fermat varieties in P\u00b3 in char. 2 and some applications to cyclic codes", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Singular Point, Irreducible Component, Cyclic Code, Minimal Polynomial, Primitive Element", "note": "\u00a9 Springer-Verlag Berlin Heidelberg 1993. \n\nThe authors wish to thank Gary McGuire for discussions leading to improvements in the exposition. Much of the work on this article was done while the author was a Bateman Research Instructor at Caltech from 1987\u20131989. This work was supported in part by NSF Grant DMS-8703898-02.", "abstract": "We consider the cyclic codes C\u2083\u207d\u1d57\u207e of length 2\u00b3\u22121 generated by m\u2081(X)mnt(X) where m\u1d62(X) is the minimal polynomial of a primitive element of GF(2\u00b3), and ask when these codes have minimum distance \u2265 5. Words of weight \u2264 4 in these codes are directly related to rational points in GF(2\u00b3) on the curves corresponding to the polynomials X\u1d57+Y\u1d57+Z\u1d57+(X+Y+Z)\u1d57 over the algebraic closure of GF(2). Study of the singularities and absolutely irreducible components of these polynomials leads to results on the minimum distance of the codes.", "date": "1993", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin, Heidelberg", "pagerange": "180-194", "id_number": "CaltechAUTHORS:20201120-120816991", "isbn": "9783540566861", "book_title": "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201120-120816991", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "Harry Bateman Research Instructorship, Caltech" }, { "agency": "NSF", "grant_number": "DMS-8703898-02" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cohen-G\u00e9rard", "name": { "family": "Cohen", "given": "G\u00e9rard" } }, { "id": "Mora-Teo", "name": { "family": "Mora", "given": "Teo" } }, { "id": "Moreno-Oscar", "name": { "family": "Moreno", "given": "Oscar" } } ] }, "doi": "10.1007/3-540-56686-4_43", "pub_year": "1993", "author_list": "Janwa, H. and Wilson, R. M." }, { "id": "https://authors.library.caltech.edu/records/bgsv5-tdz48", "eprint_id": 73097, "eprint_status": "archive", "datestamp": "2023-08-20 02:10:09", "lastmod": "2026-04-20 19:17:32", "type": "book_section", "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": "unpub", "full_text_status": "public", "note": "\u00a9 1993 Springer Science+Business Media New York.", "abstract": "We study 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, so long as the surface is non-degenerate. We propose a set of factorization conditions on the amplitudes which singles out a solution associated to triangulations of S^3.", "date": "1993", "date_type": "published", "publisher": "Springer", "place_of_pub": "Boston, MA", "pagerange": "51-71", "id_number": "CaltechAUTHORS:20161221-134133670", "isbn": "978-1-4899-1614-3", "book_title": "Low-Dimensional Topology and Quantum Field Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20161221-134133670", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Osborn-H", "name": { "family": "Osborn", "given": "Hugh" } } ] }, "doi": "10.1007/978-1-4899-1612-9_4", "pub_year": "1993", "author_list": "Ooguri, Hirosi" }, { "id": "https://authors.library.caltech.edu/records/1np55-jtn67", "eprint_id": 38549, "eprint_status": "archive", "datestamp": "2023-08-20 00:44:22", "lastmod": "2026-03-09 20:35:03", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The structure of Borel equivalence relations in Polish spaces", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1992 Springer-Verlag.\n\nResearch supported in party by NSF Grant DMS-8718847.", "abstract": "An exposition of recent work on Borel equivalence relations in Polish spaces is presented. This includes a general Glimm-Effros dichotomy for Borel equivalence relations and a study of countable Borel equivalence relations and their classification into subclasses such as smooth, hyperfinite, amenable, treeable etc.", "date": "1992", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "New York", "pagerange": "89-102", "id_number": "CaltechAUTHORS:20130516-154155660", "isbn": "978-1-4613-9756-4", "book_title": "Set theory of the continuum", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130516-154155660", "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" } ] }, "contributors": { "items": [ { "id": "Judah-H", "name": { "family": "Judah", "given": "Haim" } }, { "id": "Just-W", "name": { "family": "Just", "given": "Winfried" } }, { "id": "Woodin-H", "name": { "family": "Woodin", "given": "Hugh" } } ] }, "doi": "10.1007/978-1-4613-9754-0_7", "pub_year": "1992", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/akb20-gxm28", "eprint_id": 39107, "eprint_status": "archive", "datestamp": "2023-08-19 22:08:10", "lastmod": "2026-03-09 20:36:31", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Classification of Hyperfinite Borel Equivalence Relations", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1991 Universit\u00e9 Pierre et Marie Curie.\n\nThe above results will appear in a forthcoming paper by the author entitled The structure of hyperfinite Borel equivalence relations.\n\n

Published - Kechris_p22-2.pdf

", "abstract": "Let X be a standard Borel space and E a Borel equivalence relation on X. We call E hyperfinite if there is a Borel automorphism T of X such that xEy \u21d4 \u2203 n \u0404 \u2124(T^nx = y).\nFor Borel equivalence relations E,F on X, Y resp. we write\nE \u2291 F \u21d4 3 \u0192 : X \u2192 Y(\u0192 Borel, injective with E = \u0192^(-1)[F]) \nE \u2248 F \u21d4 E \u2291 F and F \u2291 E E \u2245 F \u21d4 \u2203 \u0192 :X \u2192 Y(\u0192 a Borel isomorphism with E= \u0192^(-1)[F]) A Borel equivalence relation E on X is called smooth if there is a Borel map \u0192: X \u2192 Y (Y\nsome standard Borel space) with xEy \u21d4 \u0192(x) = \u0192(y).", "date": "1990", "date_type": "published", "publisher": "Universit\u00e9 Pierre et Marie Curie", "id_number": "CaltechAUTHORS:20130626-124718433", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130626-124718433", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "other_numbering_system": { "items": [ { "id": "MR1217322", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Choquet-G", "name": { "family": "Choquet", "given": "G." } }, { "id": "Godefroy-G", "name": { "family": "Godefroy", "given": "G." } }, { "id": "Rogalski-M", "name": { "family": "Rogalski", "given": "M." } }, { "id": "Saint-Raymond-J", "name": { "family": "Saint Raymond", "given": "J." } } ] }, "primary_object": { "basename": "Kechris_p22-2.pdf", "url": "https://authors.library.caltech.edu/records/akb20-gxm28/files/Kechris_p22-2.pdf" }, "pub_year": "1990", "author_list": "Kechris, A. S." }, { "id": "https://authors.library.caltech.edu/records/cbnmb-yzm17", "eprint_id": 38688, "eprint_status": "archive", "datestamp": "2023-08-19 20:45:49", "lastmod": "2026-03-09 20:38:20", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Descriptive Set Theory of \u03c3-Ideals of Compact Sets", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1989 Elsevier Science Publishers B.V. (North-Holland).\n\nResearch partially supported by NSF Grant.", "abstract": "We present here a survey of the definability theory of \u03c3-ideals of closed sets in compact metric spaces and its structural implications. We also include proofs of\nsome recent results in this area.", "date": "1988-08", "date_type": "published", "publisher": "Elsevier Science", "place_of_pub": "Amsterdam", "pagerange": "117-138", "id_number": "CaltechAUTHORS:20130528-105652249", "isbn": "978-0-444-87455-9", "book_title": "Logic Colloquium 1988: Proceedings of the Colloquium", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-105652249", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "other_numbering_system": { "items": [ { "id": "MR1015324", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Ferro-R", "name": { "family": "Ferro", "given": "R." } }, { "id": "Bonotto-C", "name": { "family": "Bonotto", "given": "C." } }, { "id": "Valentini-S", "name": { "family": "Valentini", "given": "S." } }, { "id": "Zanardo-A", "name": { "family": "Zanardo", "given": "S." } } ] }, "pub_year": "1988", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/kj462-ey512", "eprint_id": 38898, "eprint_status": "archive", "datestamp": "2023-08-19 20:02:54", "lastmod": "2026-04-21 03:49:19", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "\"AD + uniformization\" is equivalent to \"half ad_R\"", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1988 Springer. Research partially supported by NSF Grant DMS-8416349.", "abstract": "Let w be the set of natural numbers and R = 2^\u03c9 the set of \"reals\" . As usual AD is the assertion that every game on \u03c9 is determined and AD_R is the assertion that every game on R\nis determined. Let us also consider an intermediate principle AD^(1/2)_R, which is the assertion that every game in which one of the players plays in \u03c9 and the other in R is determined. Such games appear often in applications instead of full games on R, see for instance [K].", "date": "1988", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "98-102", "id_number": "CaltechAUTHORS:20130612-072000863", "isbn": "978-3-540-50020-9", "book_title": "Cabal Seminar 81-85", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-072000863", "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" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1007/BFb0084971", "pub_year": "1988", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/efe7x-yvd92", "eprint_id": 105682, "eprint_status": "archive", "datestamp": "2023-08-19 20:11:40", "lastmod": "2026-04-20 21:28:29", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Some Multilinear Forms with Large Isometry Groups", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 D. Reidel Publishing Company 1988. \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 is 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", "date_type": "published", "publisher": "Springer Netherlands", "place_of_pub": "Dordrecht", "pagerange": "417-465", "id_number": "CaltechAUTHORS:20200930-113055093", "isbn": "9789401082822", "book_title": "Geometries and Groups", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200930-113055093", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "M." } }, { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "A. M." } }, { "id": "Kantor-W-M", "name": { "family": "Kantor", "given": "W. M." } } ] }, "doi": "10.1007/978-94-009-4017-8_15", "pub_year": "1988", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/ydkxr-ean17", "eprint_id": 38904, "eprint_status": "archive", "datestamp": "2023-08-19 20:03:10", "lastmod": "2026-04-21 08:21:22", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Subsets of \u2135_1 constructible from a real", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1988 Springer. Research partially supported by NSF Grants MCS-8117804 and DMS-8416349.", "abstract": "The purpose of this paper is to give a necessary and sufficient condition for a subset of \u2135_1 to be constructible from a real in terms of structural properties of the code set of A, valid under the condition that an appropriate measurable cardinal exists. This can be combined with recent results of Woodin to provide upper bounds for the consistency strength, of theories of the form\nZFC + \u2200x \u0404 \u03c9^\u03c9(x^# exists)+ \"every subset of \u2135_1 with code set in \u0413 is constructible from a real,\" for various pointclasses \u0413.", "date": "1988", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "110-116", "id_number": "CaltechAUTHORS:20130612-090419888", "isbn": "978-3-540-50020-9", "book_title": "Cabal Seminar 81-85", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-090419888", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-8117804" }, { "agency": "NSF", "grant_number": "DMS-8416349" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1007/BFb0084973", "pub_year": "1988", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/bbn7y-77b26", "eprint_id": 38899, "eprint_status": "archive", "datestamp": "2023-08-19 20:03:03", "lastmod": "2026-04-21 03:55:26", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "A coding theorem for measures", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1988 Springer. Research partially supported by NSF Grants MCS-8117804 and DMS-8416349.", "abstract": "Assuming ZF + DC + AD Moschovakis (see [Ml]) has shown that if there is a surjection \u03c0 : R \u2192 \u03bb from the reals (R = \u03c9^\u03c9 in this paper) onto an ordinal \u03bb, then\nthere is a surjection \u03c0^* : R \u2192 p(\u03bb) from the reals onto the power set of \u03bb. Let us denote by \u03b2(\u03bb) the set of ultrafilters on \u03bb. The question was raised whether there is an analog of Moschovakis' Theorem for \u03b2(\u03bb), i.e. if there is a surjection from R onto \u03bb, is there one from R onto \u03b2(\u03bb)? Martin showed that this cannot be proved in ZF + DC + AD alone because if V = L(R) and \u03bb= ol, there is no surjection of R onto \u03b2(\u03bb).", "date": "1988", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "103-109", "id_number": "CaltechAUTHORS:20130612-074122964", "isbn": "978-3-540-50020-9", "book_title": "Cabal Seminar 81\u201385", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130612-074122964", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-8117804" }, { "agency": "NSF", "grant_number": "DMS-8416349" } ] }, "other_numbering_system": { "items": [ { "id": "MR0960898", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "doi": "10.1007/BFb0084972", "pub_year": "1988", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/6gk44-p3162", "eprint_id": 88908, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:59", "lastmod": "2026-03-09 20:38:24", "type": "book_section", "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": "Sets of resolution and synthesis", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "328-348", "id_number": "CaltechAUTHORS:20180817-104144223", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144223", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.013", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/sqt4p-3bw38", "eprint_id": 88903, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:52", "lastmod": "2026-03-09 20:40:22", "type": "book_section", "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 Piatetski-Shapiro hierarchy of U-sets", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "139-192", "id_number": "CaltechAUTHORS:20180817-104143805", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104143805", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.008", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/7fr4h-wj069", "eprint_id": 88909, "eprint_status": "archive", "datestamp": "2023-08-19 19:12:02", "lastmod": "2026-03-09 21:10:09", "type": "book_section", "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 shrinking method, the theorem of K\u00f6rner and Kaufman, and the solution to the Borel basis problem for U", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "231-265", "id_number": "CaltechAUTHORS:20180817-104144307", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144307", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.010", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/b8fmw-7d663", "eprint_id": 88907, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:56", "lastmod": "2026-03-09 20:41:40", "type": "book_section", "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": "Preface", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "This book grew out of a set of notes prepared during the course of a joint Caltech-UCLA Seminar in Descriptive Set Theory and Harmonic Analysis, organized by the authors during the academic year 1985\u201386. We appreciate very much the help as well as the patience of the participants in this seminar. \n\nWe are grateful to G. Debs, R. Dougherty, S. Jackson, R. Kaufman, R. Lyons, and J. Saint Raymond for many valuable comments and suggestions. The first author is indebted to S. Pichorides for introducing him to the subject of uniqueness for trigonometric series. We would like also to thank N. O'Connor for her efficiency, care and patience in typing the manuscript. \n\nThe work of A. S. Kechris has been partially supported by NSF Gratnt DMS84-16349. A. Louveau has been supported by CNRS, France and by UCLA during his visit in the academic year 1985\u201386. He takes this opportunity to thank the Mathematics Department for its hospitality.", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "vii", "id_number": "CaltechAUTHORS:20180817-104144144", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144144", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "DMS-8416349" }, { "agency": "Centre National de la Recherche Scientifique (CNRS)" }, { "agency": "UCLA" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.001", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/dxph5-twm07", "eprint_id": 88751, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:36", "lastmod": "2026-03-09 20:36:04", "type": "book_section", "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": "Classification of the Complexity of U", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "104-138", "id_number": "CaltechAUTHORS:20180810-104404521", "isbn": "9780521358118", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-104404521", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/CBO9780511758850.007", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/zmh2d-r4j45", "eprint_id": 38894, "eprint_status": "archive", "datestamp": "2023-08-19 19:03:13", "lastmod": "2026-03-09 20:40:07", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Complexity of Antidifferentiation, Denjoy Totalization, and Hyperarithmetic Reals", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 International Congress of Mathematicians. Research partially supported by National Science Foundation Grant DMS-8416349.\n\n

Published - Kechris_1987p307.pdf

", "abstract": "We consider real functions on the interval [0, 1]. Denote by \u0394 the set of derivatives; i.e., \u0394 = {\u0192:\u0192 is a derivative}\n= {\u0192 : \u2203F: [0,1]\u2192 R {F is differentiable and \u0192 = F')}.\nIf \u0192 \u0454 \u0394, any F with F' = \u0192 is a primitive of \u0192 and is uniquely determined up to a constant. To normalize, we denote by F(x) = \u0283^x)0 \u0192 the unique primitive of \u0192 with F(0) = 0. This is the original Newtonian concept of integration as the inverse operation of differentiation, i.e., antidifferentiation.", "date": "1987", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "307-313", "id_number": "CaltechAUTHORS:20130611-134802777", "isbn": "978-0-8218-0110-9", "book_title": "Proceedings of the International Congress of Mathematicians", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130611-134802777", "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": "MR0934228", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Gleason-A-M", "name": { "family": "Gleason", "given": "Andrew M." } } ] }, "primary_object": { "basename": "Kechris_1987p307.pdf", "url": "https://authors.library.caltech.edu/records/zmh2d-r4j45/files/Kechris_1987p307.pdf" }, "pub_year": "1987", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/nenak-zhc89", "eprint_id": 88913, "eprint_status": "archive", "datestamp": "2023-08-19 19:12:09", "lastmod": "2026-03-09 20:37:01", "type": "book_section", "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": "Trigonometric series and sets of uniqueness", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "21-50", "id_number": "CaltechAUTHORS:20180817-104144661", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144661", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.004", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/ygy5y-rxg23", "eprint_id": 88882, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:49", "lastmod": "2026-03-09 20:35:50", "type": "book_section", "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": "Introduction", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "1-16", "id_number": "CaltechAUTHORS:20180816-160145462", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180816-160145462", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.002", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/sej0z-a1476", "eprint_id": 88811, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:43", "lastmod": "2026-03-09 20:35:56", "type": "book_section", "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": "Decomposing U-Sets into Simpler Sets", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "193-230", "id_number": "CaltechAUTHORS:20180815-091126114", "isbn": "9780521358118", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180815-091126114", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/CBO9780511758850.009", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/ygvzf-qam22", "eprint_id": 88912, "eprint_status": "archive", "datestamp": "2023-08-19 19:12:06", "lastmod": "2026-03-09 21:10:07", "type": "book_section", "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": "Symmetric perfect sets and the Salem-Zygmund theorem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "80-103", "id_number": "CaltechAUTHORS:20180817-104144571", "isbn": "9780511758850", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104144571", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/cbo9780511758850.006", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/bhcwx-3xn71", "eprint_id": 88741, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:33", "lastmod": "2026-03-09 20:34:39", "type": "book_section", "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 Algebra A of Functions with Absolutely Convergent Fourier Series, Pseudofunctions and Pseudomeasures", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "51-79", "id_number": "CaltechAUTHORS:20180810-084749723", "isbn": "9780521358118", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-084749723", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/CBO9780511758850.005", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/frge6-mhe67", "eprint_id": 88818, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:46", "lastmod": "2026-03-09 20:39:59", "type": "book_section", "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": "Extended Uniqueness Sets", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "266-308", "id_number": "CaltechAUTHORS:20180815-100650741", "isbn": "9780521358118", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180815-100650741", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/CBO9780511758850.011", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/vxfkq-ezn09", "eprint_id": 88765, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:39", "lastmod": "2026-03-09 20:34:06", "type": "book_section", "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": "Characterizing Rajchman Measures", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "[no abstract]", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "pagerange": "309-327", "id_number": "CaltechAUTHORS:20180810-150902218", "isbn": "9780521358118", "book_title": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-150902218", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Louveau-A", "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/CBO9780511758850.012", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/rddsk-b2514", "eprint_id": 105732, "eprint_status": "archive", "datestamp": "2023-08-22 04:38:34", "lastmod": "2026-04-20 21:29:19", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Finite simple groups and their subgroups", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Finite Group; Simple Group; Maximal Subgroup; Finite Simple Group; Permutation Representation", "note": "\u00a9 Springer-Verlag 1986.\n\nThe author would like to thank the organizers of the Peking Symposium, particularly Professor Hsio-Fu Tuan, for all their efforts which made the conference and this article possible. \n\nThe author's work is partially supported by the National Science Foundation.", "abstract": "The material in this article corresponds roughly to the contents of six lectures given at the International Symposium on Group Theory at Peking University in September 1984. \n\nIn essence the article describes the beginnings of a theory of permutation representations of finite groups based on the classifications of the finite simple groups. Chapter 3 is devoted to an outline of the Classification, with emphasis on recent efforts to improve the proof of the Classification Theorem. Chapters, 1, 2, and 6 discuss finite groups themselves, a notion of geometry due to J. Tits, and a class of group theoretical techniques introduced by B. Fischer. Each of these topics plays a role in the theory of permutation representations under discussion. The heart of the theory is the study of the subgroup structure of the finite simple groups. Certain results on this structure are described in Chapter 4 and 5.", "date": "1986", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin, Heidelberg", "pagerange": "1-57", "id_number": "CaltechAUTHORS:20201001-145810955", "isbn": "9783540164562", "book_title": "Group Theory, Beijing 1984", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201001-145810955", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Hsio-Fu-Tuan", "name": { "family": "Hsio-Fu", "given": "Tuan" } } ] }, "doi": "10.1007/bfb0076170", "pub_year": "1986", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/c2w35-3pm59", "eprint_id": 38685, "eprint_status": "archive", "datestamp": "2023-08-19 17:23:55", "lastmod": "2026-04-21 08:19:38", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Sets of everywhere singular functions", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1985 Springer-Verlag. \n\nResearch partially supported by NSF Grant.", "abstract": "In this paper we present a simple general\nmethod for demonstrating that in certain function spaces various sets\nconsisting of functions that exhibit at every point a prescribed kind\nof singularity form a coanalytic but not Borel set. We illustrate this\nmethod by providing new proofs that the set of nowhere differential\ncontinuous functions on [0,1] is (coanalytic but) not Borel and similarly\nfor the set of continuous functions on [0,1] which fail everywhere\nto have a unilateral derivative (including \u00b1 \u221e) -- the so called\nBesicovitch functions. These results were originally proved by Mauldin,\n[Mau] and unpublished, respectively. We also give a new example of a\ncoanalytic not Borel set, namely the set of integrable functions with\neverywhere divergent Fourier series. Finally, we formulate an abstract\ntheorem, which includes as simple instances all the above and other\nsimilar examples.", "date": "1985", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "233-244", "id_number": "CaltechAUTHORS:20130528-102414726", "isbn": "978-3-540-15673-4", "book_title": "Recursion theory week", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-102414726", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Ebbinghaus-H-D", "name": { "family": "Ebbinghaus", "given": "Heinz-Dieter" } }, { "id": "M\u00fcller-G-H", "name": { "family": "M\u00fcller", "given": "G. H." } }, { "id": "Sacks-G-E", "name": { "family": "Sacks", "given": "Gerald E." } } ] }, "doi": "10.1007/BFb0076223", "pub_year": "1985", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/jk8py-pmg80", "eprint_id": 106074, "eprint_status": "archive", "datestamp": "2023-10-03 22:29:50", "lastmod": "2026-04-20 21:33:25", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Some aspects of the theory of Schr\u00f6dinger operators", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Discrete Spectrum; Essential Spectrum; Periodic Potential; Schrodinger Equation; Pure Point Spectrum", "note": "\u00a9 Springer-Verlag Berlin Heidelberg 1985. \n\nResearch partially supported by USNSF grant MCS-81-20833.", "abstract": "In these notes, we will survey a part of theory of the operator -\u0394 + V. More extensive surveys can be found in [1,2,3] and in [4].", "date": "1985", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin, Heidelberg", "pagerange": "177-203", "id_number": "CaltechAUTHORS:20201014-153714086", "isbn": "9783540160359", "book_title": "Schr\u00f6dinger Operators", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201014-153714086", "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" } ] }, "contributors": { "items": [ { "id": "Graffi-S", "name": { "family": "Graffi", "given": "Sandro" } } ] }, "doi": "10.1007/bfb0080333", "pub_year": "1985", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/g4q2z-jzn28", "eprint_id": 38892, "eprint_status": "archive", "datestamp": "2023-08-19 17:24:00", "lastmod": "2026-03-09 21:25:30", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Determinacy and the Structure of L(R)", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1985 American Mathematical Society. Research partially supported by NSF Grant MCS81-17804\n\n

Published - Kechris_1985p271.pdf

", "abstract": "Let \u03c9 = {0, 1, 2, ... } be the set of natural numbers and R = \u03c9^\u03c9 the set of all infinite sequences from \u03c9, or for simplicity reals. To each set A \u2286 R we associate a two-person infinite game, in which players I and II alternatively play natural numbers I x(0) x(2) II x(1) x(3)...x(O), x(l), x(2), ... and if x is the real they eventually produce, then I wins iff x \u0454 A. The notion of a winning strategy for player I or II is defined in the usual\nway, and we call A determined if either player I or player II has a winning strategy in the above game. For a collection \u2308 of sets of reals let \u2308-DET be the statement\nthat all sets A \u0454 \u2308 are determined. Finally AD (The Axiom of Determinacy) is the\nstatement that all sets of reals are determined.", "date": "1985", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "271-283", "id_number": "CaltechAUTHORS:20130611-130509199", "isbn": "978-0-8218-1447-5", "book_title": "Recursion Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130611-130509199", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS81-17804" } ] }, "other_numbering_system": { "items": [ { "id": "MR0791063", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Nerode-A", "name": { "family": "Nerode", "given": "Anil" } }, { "id": "Shore-R-A", "name": { "family": "Shore", "given": "Richard A." } } ] }, "doi": "10.1090/pspum/042", "primary_object": { "basename": "Kechris_1985p271.pdf", "url": "https://authors.library.caltech.edu/records/g4q2z-jzn28/files/Kechris_1985p271.pdf" }, "pub_year": "1985", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/x2f6s-mqc03", "eprint_id": 38891, "eprint_status": "archive", "datestamp": "2023-08-19 16:28:04", "lastmod": "2026-03-09 20:36:18", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Becker-H-S", "name": { "family": "Becker", "given": "Howard S." } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Sets of ordinals constructible from trees and the third Victoria Delfino problem", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1984 American Mathematical Society. \n\nResearch partially supported by NSF Grant MCS 82-11328. Research partially supported by NSF Grant MCS 81-17804.\n\n

Published - Kechris_1984p13.pdf

", "abstract": "A very important part of the structure theory of \u03a3^1_2 sets of reals is based on their close interrelationship with the G\u00f6del constructible universe L. The fundamental fact underlying this connection is the theorem of Shoenfield\nwhich asserts that every \u03a3^1_2 set of reals is Souslin over L. This means that given any \u03a3^1_2 subset of the reals (=\u03c9^\u03c9 in this paper), there is a tree T on \u03c9 x \u03bb (\u03bb some ordinal, which can be taken to be \u2135_l here) such that T \u0454 L and A = p[T] = {\u0251 \u0454 \u03c9^\u03c9: : \u2203f \u0454 \u03bb^\u03c9 \u2200n(\u0251\u21ben,f\u21ben) \u0454 T}.", "date": "1984", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "pagerange": "13-29", "id_number": "CaltechAUTHORS:20130611-104220186", "isbn": "978-0-8218-5026-8", "book_title": "Axiomatic Set Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130611-104220186", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 82-11328" }, { "agency": "NSF", "grant_number": "MCS 81-17804" } ] }, "other_numbering_system": { "items": [ { "id": "MR0763889", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Baumgartner-J-E", "name": { "family": "Baumgartner", "given": "James E." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Shelah-S", "name": { "family": "Shelah", "given": "Saharon" } } ] }, "doi": "10.1090/conm/031", "primary_object": { "basename": "Kechris_1984p13.pdf", "url": "https://authors.library.caltech.edu/records/x2f6s-mqc03/files/Kechris_1984p13.pdf" }, "pub_year": "1984", "author_list": "Becker, Howard S. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/gnmzt-mg363", "eprint_id": 38738, "eprint_status": "archive", "datestamp": "2023-08-19 15:33:05", "lastmod": "2026-04-21 04:58:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Solovay-R-M", "name": { "family": "Solovay", "given": "Robert M." } } ] }, "title": "Introduction to Q-Theory", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1983 Springer. Research partially supported by NSF Grant MCS81-17804. The author is an A. P. Sloan Foundation Fellow.\nResearch partially supported by NSF Grant MCS78-02989.\nResearch partially supported by NSF Grant.", "abstract": "Working in the context of Projective Determinacy (PD), we introduce and study in this paper a countable \u220f^1_(2n+1) set of reals Q_(2n+l) and an associated real y^0_(2n+l) for each n \u2265 0 (real means element of \u03c9^\u03c9 in this paper). Our theory has analytical (descriptive set theoretic) as well as set theoretic aspects, strongly interrelated with each other.", "date": "1983", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "199-282", "id_number": "CaltechAUTHORS:20130531-151329535", "isbn": "978-3-540-12688-1", "book_title": "Cabal Seminar 79-81", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-151329535", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS81-17804" }, { "agency": "NSF", "grant_number": "MCS78-02989" }, { "agency": "NSF", "grant_number": "MCS79-06077" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "D. A." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0071702", "pub_year": "1983", "author_list": "Kechris, Alexander S.; Martin, Donald A.; et al." }, { "id": "https://authors.library.caltech.edu/records/v7eg0-07r27", "eprint_id": 38737, "eprint_status": "archive", "datestamp": "2023-08-19 14:39:19", "lastmod": "2026-04-21 03:02:21", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Effective Ramsey Theorems in the Projective Hierarchy", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1982 North-Holland Publishing Company. Published by Elsevier B.V. The author is an A. P. Sloan Foundation Fellow. NSF Grant MCS79-20465. Research partially supported by NSF Grant MCS79-20465.", "abstract": "This chapter discusses Ramsey theorems that are effective in the projective hierarchy. The application of Q-theory is quite elementary; it will bring out some of its essential ideas and methods that can be basic ingredients in more elaborate uses and applications of this theory. The chapter proves the main theorem and discusses results related results on \u0394^1_(2n+l)- and Q_(2n+l)- encodability, and discusses some related open problems. One of the proof uses Mathias forcing over an appropriate inner model of ZFC.", "date": "1982", "date_type": "published", "publisher": "Elsevier", "place_of_pub": "Amsterdam", "pagerange": "179-187", "id_number": "CaltechAUTHORS:20130531-145645449", "isbn": "9780444864178", "book_title": "Proceedings of the Herbrand Symposium", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-145645449", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS79-20465" } ] }, "other_numbering_system": { "items": [ { "id": "MR0757028", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Stern-J", "name": { "family": "Stern", "given": "Jacques" } }, { "id": "Herbrand-J", "name": { "family": "Herbrand", "given": "Jacques" } } ] }, "doi": "10.1016/S0049-237X(08)71883-4", "pub_year": "1982", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/pf4hr-27909", "eprint_id": 105863, "eprint_status": "archive", "datestamp": "2023-10-03 22:29:32", "lastmod": "2026-04-21 06:56:35", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Almost periodic Schr\u00f6der operators: A review", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 Springer-Verlag 1982.", "abstract": "We review the recent rigorous literature on the one dimensional Sch\u00f6rdinger equation, H=\u2212d\u00b2/dx\u00b2+V(x)\nwith V(x) al most periodic and the discrete (= tight binding) analogy, i. e. the doubly infinite Jacobi matrix, h_(ij) = \u03c3_(i,j+1) + \u03c3_(i,j\u22121) + v_(i\u03c3i,j) with v_i almost periodic on the integers.\n\nTwo 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 anamalous long time behaviour. We give a theorem of Avron-Simn, Chulasvsky and Moser that for a generic sequence with \u03a3|a_n| < \u221e, the continuum operator with V(x) = \u03a3 a_n cos(x/2^n) has a Cantor spectrum.\n\nThe 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 occurende of point spectrum. We sketch the proof of Avron-Simon that for the discrete case with V_n = \u03bbcos(2\u03c0\u03b1_n + \u03b8) if \u03bb > 2 and \u03b1 is a Lionville number, then for a.e. \u03b8, h has purely singular continuous spectrum.", "date": "1982", "date_type": "published", "publisher": "Springer Berlin Heidelberg", "place_of_pub": "Berlin, Heidelberg", "pagerange": "157", "id_number": "CaltechAUTHORS:20201007-081705982", "isbn": "9783540111924", "book_title": "Mathematical Problems in Theoretical Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201007-081705982", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Schrader-R", "name": { "family": "Schrader", "given": "R." } }, { "id": "Seiler-R", "name": { "family": "Seiler", "given": "R." } }, { "id": "Uhlenbrock-D-A", "name": { "family": "Uhlenbrock", "given": "D. A." } } ] }, "doi": "10.1007/3-540-11192-1_30", "pub_year": "1982", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/kbpn3-d4360", "eprint_id": 38597, "eprint_status": "archive", "datestamp": "2023-08-19 14:39:10", "lastmod": "2026-03-09 20:36:47", "type": "book_section", "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": "Ordinal games and their applications", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1982 North-Holland Publishing Co.\n\nWork partially supported by NSF Grant MCS 76-17254 AO1. The author is an A. P.\nSloan Foundation Fellow.\n\nWe would like to thank Ramez Sami for many illuminating discussions\non the topics discussed here.", "abstract": "In this paper we give a survey of certain results on the determinacy of\ngames on ordinals and its various applications. A more comprehensive\ntreatment including more detailed versions, extensions and proofs of the\ntheorems mentioned here, will appear in a forthcoming paper by the\nauthors.", "date": "1982", "date_type": "published", "publisher": "North-Holland Publishing Co.", "place_of_pub": "Amsterdam", "pagerange": "273-277", "id_number": "CaltechAUTHORS:20130521-101019031", "isbn": "0-444-85423-1", "book_title": "Logic, methodology, and philosophy of science VI", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130521-101019031", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 76-17254 AO1" } ] }, "other_numbering_system": { "items": [ { "id": "MR0682419", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cohen-L-J", "name": { "family": "Cohen", "given": "L. Jonathan" } } ] }, "pub_year": "1982", "author_list": "Harrington, Leo A. and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/0sc9r-yb091", "eprint_id": 38736, "eprint_status": "archive", "datestamp": "2023-08-19 13:42:21", "lastmod": "2026-04-21 03:41:00", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Souslin cardinals, \u03ba-souslin sets and the scale property in the hyperprojective hierarchy", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1981 Springer. Research partially supported by NSF Grant MCS79-20465. The author is an A. P. Sloan Foundation Fellow.", "abstract": "Let \u0398 = sup{\u03be : \u03be is the length of a prewellordering of the set of reals R(= \u03c9^\u03c9)}. Let K < \u0398 be an infinite cardinal. The class \u00a7(k) of k-Souslin sets has some well-known closure properties, i.e. it is closed under continuous substitutions , countable intersections and unions, and existential quantification over R.", "date": "1981", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "127-146", "id_number": "CaltechAUTHORS:20130531-144033005", "isbn": "978-3-540-10288-5", "book_title": "Cabal Seminar 77-79", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-144033005", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS79-20465" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0090238", "pub_year": "1981", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/y8ge7-nvp84", "eprint_id": 38732, "eprint_status": "archive", "datestamp": "2023-08-19 13:41:58", "lastmod": "2026-04-21 06:00:58", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Homogeneous trees and projective scales", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1981 Springer. The preparation of this paper was partially supported by NSF Grant MCS 76-17254 A01. The author is an A.P. Sloan Foundation Fellow. We would like to thank Y. N. Moschovakis for making a number of valuable suggestions\nfor improving the presentation of this paper.", "abstract": "This exposition is a sequel to Kechris [1978]. Its main purpose is to show how set theoretical techniques, among them infinite exponent partition relations can be used to produce homogeneous trees for projective sets. The work here is again understood as being carried completely within L[R], with the hypothesis that AD+DC holds in this model.", "date": "1981", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "33-73", "id_number": "CaltechAUTHORS:20130531-110245492", "isbn": "978-3-540-10288-5", "book_title": "Cabal Seminar 77-79", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-110245492", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 76-17254 A01" } ] }, "other_numbering_system": { "items": [ { "id": "MR0611167", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0090235", "pub_year": "1981", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/4ftxr-8eb09", "eprint_id": 38734, "eprint_status": "archive", "datestamp": "2023-08-19 13:42:13", "lastmod": "2026-04-21 05:13:16", "type": "book_section", "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." } }, { "id": "Steel-J-R", "name": { "family": "Steel", "given": "John R." } } ] }, "title": "The axiom of determinacy and the prewellordering property", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1981 Springer. Partially supported by NSF Grant MCS79-20465. Tbe author is an A.P. Sloan Foundation Fellow.\nPartially supported by NSF Grant MCS77-01640. Partially supported by NSF Grant MCS78-02989.", "abstract": "Let \u03c9 = (0,1,2,...) be the set of natural numbers and R = \u03c9^\u03c9 the set of all functions from \u03c9 into \u03c9, or for simplicity reals. A product space is of the form\nX = X_1 x X_2 x ... x X_k, where X_1 = \u03c9 or R. Subsets of these product spaces are called pointsets. A boldface pointclass is a class of pointsets closed under continuous preimages and containing all clopen pointsets (in all product spaces).", "date": "1981", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "101-125", "id_number": "CaltechAUTHORS:20130531-131451792", "isbn": "978-3-540-10288-5", "book_title": "Cabal Seminar 77-79", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-131451792", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS79-20465" }, { "agency": "NSF", "grant_number": "MCS77-01640" }, { "agency": "NSF", "grant_number": "MCS78-02989" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0090237", "pub_year": "1981", "author_list": "Kechris, Alexander S.; Solovay, Robert M.; et al." }, { "id": "https://authors.library.caltech.edu/records/hayep-6ny35", "eprint_id": 38733, "eprint_status": "archive", "datestamp": "2023-08-19 13:42:06", "lastmod": "2026-04-20 22:56:14", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "id": "Kleinberg-E-M", "name": { "family": "Kleinberg", "given": "Eugene M." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } }, { "id": "Woodin-W-H", "name": { "family": "Woodin", "given": "W. Hugh" } } ] }, "title": "The axiom of determinacy, strong partition properties and nonsingular measures", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1981 Springer. Research partially supported by NSF Grant MCS79-20465. The author is an A. P. Sloan Foundation Fellow.\nResearch partially supported by NSF Grant MCS78-03744.\nResearch partially supported by NSF Grant MCS78-02989.", "abstract": "In this paper we study the relationship between AD and strong partition properties of cardinals as well as some consequences of these properties themselves.", "date": "1981", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "75-99", "id_number": "CaltechAUTHORS:20130531-114321828", "isbn": "978-3-540-10288-5", "book_title": "Cabal Seminar 77-79", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-114321828", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS79-20465" }, { "agency": "NSF", "grant_number": "MCS78-03744" }, { "agency": "NSF", "grant_number": "MCS78-02989" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Kleinberg-E-M", "name": { "family": "Kleinberg", "given": "Eugene M." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0090236", "pub_year": "1981", "author_list": "Kechris, Alexander S.; Kleinberg, Eugene M.; et al." }, { "id": "https://authors.library.caltech.edu/records/y5yry-bxe69", "eprint_id": 38707, "eprint_status": "archive", "datestamp": "2023-08-19 13:41:50", "lastmod": "2026-04-21 08:01:07", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "A note on Wadge degrees", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1981 Springer-Verlag.\nResearch partially supported by NSF Grant MCS-17254 A01. The author\nis an A.P. Sloan Foundation Fellow.", "abstract": "For pertinent definitions see published works of the Cabal Seminar. It has been shown by D. A. Martin that under the assumption of AD, Wadge degrees are well ordered; for Wadge degrees of \u0394^(1)_(2n) sets \u0394^(1)_(2n)-determinacy suffices. Martin has also proved (using AD) that the length of the well ordering of \u0394^(1)_(2n) Wadge degrees is exactly \u03b4^(1)_(2n+1). The author gives an alternate proof of this fact, using only \u0394^(1)_(2n)-determinacy.", "date": "1981", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "165-168", "id_number": "CaltechAUTHORS:20130529-162228399", "isbn": "978-3-540-38422-9", "book_title": "Cabal Seminar 77-79", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130529-162228399", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS-17254 A01" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." } }, { "id": "Martin-D-A", "name": { "family": "Martin", "given": "Donald A." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0090240", "pub_year": "1981", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/chgah-wa551", "eprint_id": 38731, "eprint_status": "archive", "datestamp": "2023-08-19 12:52:57", "lastmod": "2026-03-09 20:34:10", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Recent Advances in the Theory of Higher Level Projective Sets", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1980 North-Holland Publishing Company. Published by Elsevier B.V. \nDedicated to Professor S. C. Kleene on the occasion of his 70th birthday. Preparation of this paper was partially supported by NSF Grant MCS76-17254 A01. The author is an A. P. Sloan Foundation Fellow.", "abstract": "An outline is given of certain aspects of the current theory of higher level projective sets, especially concentrating on the structure theory of II^1_3 sets, from determinacy hypotheses. Some of the key open problems in this area are also discussed.", "date": "1980", "date_type": "published", "publisher": "Elsevier", "place_of_pub": "Amsterdam", "pagerange": "149-166", "id_number": "CaltechAUTHORS:20130531-104437708", "isbn": "978-0-444-85345-5", "book_title": "The Kleene Symposium", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-104437708", "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": "MR0591880", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Barwise-J", "name": { "family": "Barwise", "given": "J." } }, { "id": "Keisler-H-J", "name": { "family": "Keisler", "given": "H. J." } }, { "id": "Kunen-K", "name": { "family": "Kunen", "given": "K." } } ] }, "doi": "10.1016/S0049-237X(08)71258-8", "pub_year": "1980", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/tfk12-c4354", "eprint_id": 38708, "eprint_status": "archive", "datestamp": "2023-08-19 11:04:07", "lastmod": "2026-04-22 19:45:41", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On Transfinite Sequences of Projective Sets with an Application to \u2211^1_2 Equivalence Relations", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1978 North-Holland Publishing Company. Published by Elsevier B.V. Research and preparation for this paper were partially supported by NSF Grants MPS75-07562 and MCS76-17254.", "abstract": "This chapter focuses on transfinite sequences of projective sets with an application to \u03a3^1_(\u223c2n) equivalence relations. From the full axiom of determinacy (AD), the chapter demonstrates that the class of \u03a3^1_(\u223c2n) sets is closed under well ordered unions. This result is then applied to compute the maximum length of transfinite 1\u20131 sequences of ^1_(\u223c2n) sets, from AD again. As a further application, the chapter demonstrates that in the real world, every \u03a3^1_2 equivalence relation has either \u2264_\u05d01k, or 2_0^\u05d0 equivalence classes. In addition, the cardinality of the maximum length of a transfinite sequence of ^1_(\u223c2n) sets without repetitions is computed in the chapter.", "date": "1978", "date_type": "published", "publisher": "North Holland Publishing Company", "place_of_pub": "Amsterdam", "pagerange": "155-160", "id_number": "CaltechAUTHORS:20130530-070413635", "isbn": "9780444851789", "book_title": "Logic Colloquium '77", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130530-070413635", "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": "MR0519810", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Macintyre-A", "name": { "family": "Macintyre", "given": "Angus" } }, { "id": "Pacholski-L", "name": { "family": "Pacholski", "given": "Leszek" } }, { "id": "Paris-J", "name": { "family": "Paris", "given": "Jeff" } } ] }, "doi": "10.1016/S0049-237X(08)71998-0", "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/bw5br-9vb69", "eprint_id": 38695, "eprint_status": "archive", "datestamp": "2023-08-19 11:04:00", "lastmod": "2026-04-21 18:29:10", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "AD and projective ordinals", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1978 Springer-Verlag. \n\nPreparation for this paper was partially supported by NSF Grant MCS 76-17254. The author would like to thank R. M. Solovay for many interesting and helpful discussions on the topics presented in this paper.", "abstract": "This is an unpolished exposition of some work in the theory of projective ordinals\nunder the hypothesis of definable determinacy. This is understood here as the\nhypothesis that every set of reals in L[R] is determined. Since the projective\nordinals are absolute between the real world and L[R] we carry this study entirely\nwithin L[R]. Thus we will use the full Axiom of Determinacy (AD) together with\nZF + DC (DC is of course the only choice principle that is preserved under this\ntransition to L[R]).", "date": "1978", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "91-132", "id_number": "CaltechAUTHORS:20130528-134758796", "isbn": "978-3-540-09086-1", "book_title": "Cabal Seminar 76-77", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-134758796", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 76-17254" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "A. S." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0069296", "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/8v9kx-cf045", "eprint_id": 38683, "eprint_status": "archive", "datestamp": "2023-08-19 11:03:44", "lastmod": "2026-04-21 15:10:13", "type": "book_section", "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": "Notes on the Theory of Scales", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1978 Springer. \n\nMoschovakis is a Sloan Foundation Fellow. During the preparation of this manuscript both authors were partially supported by NSF Grant #GP-27964.", "abstract": "It is the purpose of these notes to give an informal exposition of several recent results in Descriptive Set Theory, all centering around the notion of a scale. This was first isolated explicitly in the generalization of the Uniformization Theorem on the hypothesis of projective determinacy [14], but is surely implicit in some of the classical proofs. It has turned out that scales have many applications beyond the Uniformization Theorem, both in producing new results and in providing more elegant proofs of known results.", "date": "1978", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "1-53", "id_number": "CaltechAUTHORS:20130528-094742588", "isbn": "978-3-540-09086-1", "book_title": "Cabal Seminar 76\u201377", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-094742588", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "GP-27964" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0069294", "pub_year": "1978", "author_list": "Kechris, Alexander S. and Moschovakis, Yiannis N." }, { "id": "https://authors.library.caltech.edu/records/t1egj-qk440", "eprint_id": 38718, "eprint_status": "archive", "datestamp": "2023-08-19 11:04:15", "lastmod": "2026-04-23 16:39:09", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "On Spector classes", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1978 Springer. Preparation of this paper was partially supported by NSF Grant MCS 76-17254. We would like to thank L. Kirousis and P. Kolaitis for many valuable comments and\nsuggestions on an earlier draft of this paper.", "abstract": "This paper contains an exposition of certain aspects of the theory of Spector classes. The general plan is as follows: In Section 1 we present a review of the structure theory, mainly developed in Chapter 9 of Moschovakis [1]. In Section 2 we give a comprehensive list of examples from various areas of definability theory. Finally, in Section 3, we deal with characterization and representation theorems.", "date": "1978", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "pagerange": "245-277", "id_number": "CaltechAUTHORS:20130531-074153858", "isbn": "9783540090861", "book_title": "Cabal Seminar 76\u201377", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-074153858", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MCS 76-17254" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." } }, { "id": "Moschovakis-Y-N", "name": { "family": "Moschovakis", "given": "Yiannis N." } } ] }, "doi": "10.1007/BFb0069303", "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/3f73d-4qr63", "eprint_id": 38721, "eprint_status": "archive", "datestamp": "2023-08-19 11:04:23", "lastmod": "2026-04-21 15:09:07", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Forcing in analysis", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1977 Springer. Research and preparation of this paper were partially supported by NSF Grants MPS-07562 and MGS 76-17254 resp.", "abstract": "In this paper we develop a method for applying \"forcing techniques\" (or equivalently \"category arguments\") in the analytical hierarchy. We present here the basic general theory and some simple applications. In a subsequent publication, which is in preparation, further and technically more complicated applications will be given,\nincluding perfect set forcing and in particular the results in the circulated note [Ke 1], which are summarized in Section 6.", "date": "1978", "date_type": "published", "publisher": "Springer-Verlag", "place_of_pub": "Berlin", "pagerange": "277-302", "id_number": "CaltechAUTHORS:20130531-091303529", "isbn": "978-3-540-08926-1", "book_title": "Higher Set Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130531-091303529", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MPS-07562" }, { "agency": "NSF", "grant_number": "MGS 76-17254" } ] }, "other_numbering_system": { "items": [ { "id": "MR0520191", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "M\u00fcller-G-H", "name": { "family": "M\u00fcller", "given": "Gert H." } }, { "id": "Scott-D-S", "name": { "family": "Scott", "given": "Dana S." } } ] }, "doi": "10.1007/BFb0103105", "pub_year": "1978", "author_list": "Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/w3qp7-s7w16", "eprint_id": 38684, "eprint_status": "archive", "datestamp": "2023-08-19 11:03:51", "lastmod": "2026-03-09 20:35:24", "type": "book_section", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "Spector second order classes and reflection", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1978 North-Holland Pub. Co.\nResearch and preparation for this paper were partially supported\nby NSF Grant MGS 16-17254.", "abstract": "The purpose of this paper, which grew out of a series of lectures (short course)\ndelivered at the Oslo Conference, is to give a survey of the theory of reflection\nin the context of Spector second order classes. We have mainly aimed at presenting\na global view of a rather extensive part of definability theory and at the\nsame time illustrate how the main concepts and results to be presented below unify\na large number of diverse areas in this theory and also clarify many of its important\naspects.", "date": "1978", "date_type": "published", "publisher": "North-Holland Publishing Company", "place_of_pub": "Amsterdam", "pagerange": "147-183", "id_number": "CaltechAUTHORS:20130528-100408397", "isbn": "9780444851635", "book_title": "Generalized recursion theory II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20130528-100408397", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF", "grant_number": "MGS 16-17254" } ] }, "other_numbering_system": { "items": [ { "id": "MR0516935", "name": "MathSciNet Review" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Fenstad-J-E", "name": { "family": "Fenstad", "given": "Jens Erik" } }, { "id": "Gandy-R-O", "name": { "family": "Gandy", "given": "R. O." } }, { "id": "Sacks-G-E", "name": { "family": "Sacks", "given": "Gerald E." } } ] }, "pub_year": "1978", "author_list": "Kechris, Alexander S." } ]