Published - c11045_TOC.pdf
Published - i11045_INTRO.pdf
Submitted - 1211.4065.pdf
", "abstract": "Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-H\u00f6lder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations.\n\nThe construction itself\u2014an intricate algorithm with hidden symmetries\u2014mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful \"Main Lemma\"\u2014used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem\u2014has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.", "date": "2017", "date_type": "published", "publisher": "Princeton University Press", "place_of_pub": "Princeton, NJ", "id_number": "CaltechAUTHORS:20180702-123946440", "isbn": "978-0-691-17483-9", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180702-123946440", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF Graduate Research Fellowship", "grant_number": "DGE-1148900" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.48550/arXiv.1211.4065", "primary_object": { "basename": "1211.4065.pdf", "url": "https://authors.library.caltech.edu/records/3vvf9-nxe16/files/1211.4065.pdf" }, "related_objects": [ { "basename": "c11045_TOC.pdf", "url": "https://authors.library.caltech.edu/records/3vvf9-nxe16/files/c11045_TOC.pdf" }, { "basename": "i11045_INTRO.pdf", "url": "https://authors.library.caltech.edu/records/3vvf9-nxe16/files/i11045_INTRO.pdf" } ], "pub_year": "2017", "author_list": "Isett, Philip" }, { "id": "https://authors.library.caltech.edu/records/yzaqr-6fd02", "eprint_id": 66460, "eprint_status": "archive", "datestamp": "2023-08-20 09:34:48", "lastmod": "2026-03-07 04:13:43", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "title": "Overgroups of Root Groups in Classical Groups", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Finite groups, linear groups", "note": "\u00a9 2015 American Mathematical Society. \n\nPublished electronically: December 10, 2015.", "abstract": "We extend results of McLaughlin and Kantor on overgroups of long root subgroups and long root elements in finite classical groups. In particular we determine the maximal subgroups of this form. We also determine the maximal overgroups of short root subgroups in finite classical groups, and the maximal overgroups in finite orthogonal groups of c-root subgroups.", "date": "2016", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "id_number": "CaltechAUTHORS:20160425-141046633", "isbn": "978-1-4704-1845-8", "book_title": "Overgroups of root groups in classical groups", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160425-141046633", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } } ] }, "doi": "10.1090/memo/1140", "pub_year": "2016", "author_list": "Aschbacher, Michael" }, { "id": "https://authors.library.caltech.edu/records/wwmkh-2yk50", "eprint_id": 88591, "eprint_status": "archive", "datestamp": "2023-08-20 09:38:37", "lastmod": "2026-03-09 20:39:16", "type": "book", "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": "Ordinal Definability and Recursion Theory: The Cabal Seminar", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2016 Cambridge University Press.", "abstract": "The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.", "date": "2016", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180806-095451417", "isbn": "9781139519694", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-095451417", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/CBO9781139519694", "pub_year": "2016", "author_list": "Kechris, Alexander S.; L\u00f6we, Benedikt; et al." }, { "id": "https://authors.library.caltech.edu/records/6ezw4-z0n28", "eprint_id": 88588, "eprint_status": "archive", "datestamp": "2023-08-19 14:06:19", "lastmod": "2026-03-18 00:01:05", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Holden-H", "name": { "family": "Holden", "given": "Helge" } }, { "id": "Gesztesy-F", "name": { "family": "Gesztesy", "given": "Fritz" } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" }, { "id": "Teschl-G", "name": { "family": "Teschl", "given": "Gerald" } } ] }, "title": "Spectral analysis, differential equations, and mathematical physics : a festschrift in honor of Fritz Gesztesy's 60th birthday", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2013 American Mathematical Society.\n\nPublished - pspum087-endmatter.pdf
", "abstract": "[no abstract]", "date": "2013", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "id_number": "CaltechAUTHORS:20180806-091538693", "isbn": "978-0-8218-7574-2", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-091538693", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "doi": "10.1090/pspum/087", "primary_object": { "basename": "pspum087-endmatter.pdf", "url": "https://authors.library.caltech.edu/records/6ezw4-z0n28/files/pspum087-endmatter.pdf" }, "pub_year": "2013", "author_list": "Holden, Helge; Gesztesy, Fritz; et al." }, { "id": "https://authors.library.caltech.edu/records/dz6dm-kwx53", "eprint_id": 88612, "eprint_status": "archive", "datestamp": "2023-08-22 04:31:45", "lastmod": "2026-03-09 23:14:21", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Goldfeld", "given": "Dorian" } }, { "name": { "family": "Jorgenson", "given": "Jay" } }, { "name": { "family": "Jones", "given": "Peter" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" }, { "name": { "family": "Ribet", "given": "Kenneth" } }, { "name": { "family": "Tate", "given": "John" } } ] }, "title": "Number Theory, Analysis and Geometry: In Memory of Serge Lang", "ispublished": "unpub", "full_text_status": "public", "keywords": "Bessel integrals; Diophantine approximation; Gelfand's transcendence criterion; Lang-Trotter conjecture; arithmetic dimension; elliptic Einstein series; elliptic divisibility sequence; irreducibility of L-functions; quadratic reciprocity", "note": "\u00a9 2012 Springer Science+Business Media, LLC.\n\nPublished - 2012_Book_NumberTheoryAnalysisAndGeometr.pdf
", "abstract": "Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future.\n\nIn the spirit of Lang's vast contribution to mathematics, this memorial volume contains articles by prominent mathematicians in a variety of areas, namely number theory, analysis and geometry, representing Lang's own breadth of interests. A special introduction by John Tate includes a brief and engaging account of Serge Lang's life.", "date": "2012", "date_type": "published", "publisher": "Springer", "place_of_pub": "Boston, MA", "id_number": "CaltechAUTHORS:20180806-134204157", "isbn": "978-1-4614-1259-5", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180806-134204157", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "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", "name": { "family": "Ribet", "given": "Kenneth" } }, { "id": "Tate-J-T", "name": { "family": "Tate", "given": "John" } } ] }, "doi": "10.1007/978-1-4614-1260-1", "primary_object": { "basename": "2012_Book_NumberTheoryAnalysisAndGeometr.pdf", "url": "https://authors.library.caltech.edu/records/dz6dm-kwx53/files/2012_Book_NumberTheoryAnalysisAndGeometr.pdf" }, "pub_year": "2012", "author_list": "Goldfeld, Dorian; Jorgenson, Jay; et al." }, { "id": "https://authors.library.caltech.edu/records/pm2th-6kq30", "eprint_id": 88923, "eprint_status": "archive", "datestamp": "2023-08-19 08:57:25", "lastmod": "2026-03-09 20:38:08", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "name": { "family": "Steel", "given": "John R." } }, { "name": { "family": "L\u00f6we", "given": "Benedikt" } } ] }, "title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Wadge Degrees and Projective Ordinals is the second of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Wadge Degrees and Pointclasses' (Part III) and 'Projective Ordinals' (Part IV), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.", "date": "2011-12-14", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180817-104145629", "isbn": "9781139028073", "book_title": "Wadge Degrees and Projective Ordinals: The Cabal Seminar, Volume II", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180817-104145629", "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", "pub_year": "2011", "author_list": "Kechris, Alexander S.; Steel, John R.; et al." }, { "id": "https://authors.library.caltech.edu/records/esfyh-2pw10", "eprint_id": 88645, "eprint_status": "archive", "datestamp": "2023-08-22 01:40:41", "lastmod": "2026-03-09 21:40:33", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "name": { "family": "Parashar", "given": "Deepak" } } ] }, "title": "Quantum Groups and Noncommutative Spaces: Perspectives on Quantum Geometry", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Hopf algebras; Noncommutative geometry; Quantum groups; quantization; spectral triples", "note": "\u00a9 2011 Vieweg+Teubner Verlag; Springer Fachmedien Wiesbaden GmbH.", "abstract": "This book is aimed at presenting different methods and perspectives in the theory of Quantum Groups, bridging between the algebraic, representation theoretic, analytic, and differential-geometric approaches. It also covers recent developments in Noncommutative Geometry, which have close relations to quantization and quantum group symmetries. The volume collects surveys by experts which originate from an acitvity at the Max-Planck-Institute for Mathematics in Bonn.", "date": "2011", "date_type": "published", "publisher": "Springer", "place_of_pub": "Wiesbaden, Germany", "id_number": "CaltechAUTHORS:20180808-084743368", "isbn": "978-3-8348-1442-5", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180808-084743368", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" } }, { "id": "Parashar-D", "name": { "family": "Parashar", "given": "Deepak" } } ] }, "doi": "10.1007/978-3-8348-9831-9", "pub_year": "2011", "author_list": "Marcolli, Matilde and Parashar, Deepak" }, { "id": "https://authors.library.caltech.edu/records/r5359-bqa87", "eprint_id": 88625, "eprint_status": "archive", "datestamp": "2023-08-19 05:02:50", "lastmod": "2026-03-07 04:14:48", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Aschbacher-M", "name": { "family": "Aschbacher", "given": "Michael" } }, { "id": "Kessar-R", "name": { "family": "Kessar", "given": "Radha" } }, { "id": "Oliver-B", "name": { "family": "Oliver", "given": "Bob" } } ] }, "title": "Fusion Systems in Algebra and Topology", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.", "date": "2011", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180807-124803752", "isbn": "9781139003841", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180807-124803752", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "doi": "10.1017/CBO9781139003841", "pub_year": "2011", "author_list": "Aschbacher, Michael; Kessar, Radha; et al." }, { "id": "https://authors.library.caltech.edu/records/5ftfr-67n96", "eprint_id": 88638, "eprint_status": "archive", "datestamp": "2023-08-19 05:03:01", "lastmod": "2026-03-18 00:07:44", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Convexity: An Analytic Viewpoint", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Cambridge University Press.", "abstract": "Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein\u2013Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.", "date": "2011", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180808-075325457", "isbn": "9781107007314", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180808-075325457", "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": "Simon-B", "name": { "family": "Simon", "given": "Barry" } } ] }, "doi": "10.1017/CBO9780511910135", "pub_year": "2011", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/gy4ak-grz36", "eprint_id": 88632, "eprint_status": "archive", "datestamp": "2023-08-19 05:02:58", "lastmod": "2026-03-09 23:12:54", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Arthur", "given": "James" } }, { "name": { "family": "Cogdell", "given": "James W." } }, { "name": { "family": "Gelbart", "given": "Steve" } }, { "name": { "family": "Goldberg", "given": "David" } }, { "id": "Ramakrishnan-D", "name": { "family": "Ramakrishnan", "given": "Dinakar" }, "orcid": "0000-0002-0159-087X" }, { "name": { "family": "Yu", "given": "Jiu-Kang" } } ] }, "title": "On certain L-functions: conference on certain L-functions in honor of Freydoon Shahidi", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2011 by the Clay Mathematics Institute. Published by the American Mathematical Society.", "abstract": "A co-publication of the AMS and Clay Mathematics Institute. \n\nThis volume constitutes the proceedings of a conference, \"On Certain L-functions\", held July 23\u201327, 2007 at Purdue University, West Lafayette, Indiana. The conference was organized in honor of the 60th birthday of Freydoon Shahidi, widely recognized as having made groundbreaking contributions to the Langlands program. \n\nThe articles in this volume represent a snapshot of the state of the field from several viewpoints. Contributions illuminate various areas of the study of geometric, analytic, and number theoretic aspects of automorphic forms and their L-functions, and both local and global theory are addressed. \n\nTopics discussed in the articles include Langlands functoriality, the Rankin\u2013Selberg method, the Langlands\u2013Shahidi method, motivic Galois groups, Shimura varieties, orbital integrals, representations of p-adic groups, Plancherel formula and its consequences, the Gross\u2013Prasad conjecture, and more. The volume also includes an expository article on Shahidi's contributions to the field, which serves as an introduction to the subject. \n\nExperts will find this book a useful reference, and beginning researchers will be able to use it to survey major results in the Langlands program.", "date": "2011", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "id_number": "CaltechAUTHORS:20180807-133743522", "isbn": "978-0-8218-5204-0", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180807-133743522", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Arhtur-J", "name": { "family": "Arthur", "given": "James" } }, { "id": "Cogdell-J-W", "name": { "family": "Cogdell", "given": "James W." } }, { "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-Jiu-Kang", "name": { "family": "Yu", "given": "Jiu-Kang" } } ] }, "pub_year": "2011", "author_list": "Arthur, James; Cogdell, James W.; et al." }, { "id": "https://authors.library.caltech.edu/records/0na9q-jyf11", "eprint_id": 88649, "eprint_status": "archive", "datestamp": "2023-08-19 01:11:45", "lastmod": "2026-03-18 00:03:26", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Szeg\u0151's Theorem and Its Descendants: Spectral Theory for L^2 Perturbations of Orthogonal Polynomials", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2011 Princeton University Press.\n\nOther - s9377.pdf
", "abstract": "This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from G\u00e1bor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line. \n\nIn addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.", "date": "2010", "date_type": "published", "publisher": "Princeton University Press", "place_of_pub": "Princeton, NJ", "id_number": "CaltechAUTHORS:20180808-092107298", "isbn": "9780691147048", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180808-092107298", "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": "Simon-B", "name": { "family": "Simon", "given": "Barry" } } ] }, "primary_object": { "basename": "s9377.pdf", "url": "https://authors.library.caltech.edu/records/0na9q-jyf11/files/s9377.pdf" }, "pub_year": "2010", "author_list": "Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/4w487-0sy76", "eprint_id": 88797, "eprint_status": "archive", "datestamp": "2023-08-19 01:11:56", "lastmod": "2026-03-09 21:39:59", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Blanchard", "given": "Etienne" } }, { "name": { "family": "Ellwood", "given": "David" } }, { "name": { "family": "Khalkhali", "given": "Masoud" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "name": { "family": "Moscovici", "given": "Henri" } }, { "name": { "family": "Popa", "given": "Sorin" } } ] }, "title": "Quanta of Maths", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2010 by the Clay Mathematics Institute. Published by the American Mathematical Society, Providence, RI,\nfor the Clay Mathematics Institute, Cambridge, MA.\n\nPublished - cmip011c.pdf
", "abstract": "The work of Alain Connes has cut a wide swath across several areas of math- ematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics.", "date": "2010", "date_type": "published", "publisher": "American Mathematical Society", "place_of_pub": "Providence, RI", "id_number": "CaltechAUTHORS:20180814-142452298", "isbn": "9780821852033", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180814-142452298", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Blanchard-E", "name": { "family": "Blanchard", "given": "Etienne" } }, { "id": "Ellwood-D", "name": { "family": "Ellwood", "given": "David" } }, { "id": "Khalkhali-M", "name": { "family": "Khalkhali", "given": "Masoud" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" } }, { "id": "Moscovici-H", "name": { "family": "Moscovici", "given": "Henri" } }, { "id": "Popa-S", "name": { "family": "Popa", "given": "Sorin" } } ] }, "primary_object": { "basename": "cmip011c.pdf", "url": "https://authors.library.caltech.edu/records/4w487-0sy76/files/cmip011c.pdf" }, "pub_year": "2010", "author_list": "Blanchard, Etienne; Ellwood, David; et al." }, { "id": "https://authors.library.caltech.edu/records/tpzen-8fd78", "eprint_id": 88646, "eprint_status": "archive", "datestamp": "2023-08-21 23:04:18", "lastmod": "2026-03-09 21:38:42", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Ceyhan", "given": "\u00d6zg\u00fcr" } }, { "name": { "family": "Manin", "given": "Yu. I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Arithmetic and Geometry Around Quantization", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Algebra; geometric Langlands program; mirror symmetry; non-commutative geometry; quantum chaos; quantum ergodicity; quantum groups; quantum invariants; symplectic and algebraic geometry", "note": "\u00a9 2010 Birkh\u00e4user Boston.", "abstract": "In recent decades, quantization has led to interesting applications in various mathematical branches. This volume, comprised of research and survey articles, discusses key topics, including symplectic and algebraic geometry, representation theory, quantum groups, the geometric Langlands program, quantum ergodicity, and non-commutative geometry. A wide range of topics related to quantization are covered, giving a glimpse of the broad subject. The articles are written by distinguished mathematicians in the field and reflect subsequent developments following the Arithmetic and Geometry around Quantization conference held in Istanbul.", "date": "2010", "date_type": "published", "publisher": "Springer", "place_of_pub": "Boston, MA", "id_number": "CaltechAUTHORS:20180808-085720175", "isbn": "978-0-8176-4830-5", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180808-085720175", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Ceyhan-\u00d6", "name": { "family": "Ceyhan", "given": "\u00d6zg\u00fcr" } }, { "id": "Manin-Yu-I", "name": { "family": "Manin", "given": "Yu. I." } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" } } ] }, "doi": "10.1007/978-0-8176-4831-2", "pub_year": "2010", "author_list": "Ceyhan, \u00d6zg\u00fcr; Manin, Yu. I.; et al." }, { "id": "https://authors.library.caltech.edu/records/mak25-kbx66", "eprint_id": 88648, "eprint_status": "archive", "datestamp": "2023-08-21 23:04:28", "lastmod": "2026-03-09 21:40:28", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Abbaspour", "given": "Hossein" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" }, { "name": { "family": "Tradler", "given": "Thomas" } } ] }, "title": "Deformation Spaces: Perspectives on algebro-geometric moduli", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Hochschild Cohomology; algebraic geometry; algebraic topology; deformation theory; mathematical physics; noncommutative geometry; quantum field theory", "note": "\u00a9 2010 Vieweg+Teubner Verlag; Springer Fachmedien Wiesbaden GmbH.", "abstract": "The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics.\nThis volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.", "date": "2010", "date_type": "published", "publisher": "Springer", "place_of_pub": "Wiesbaden, Germany", "id_number": "CaltechAUTHORS:20180808-091119205", "isbn": "978-3-8348-1271-1", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180808-091119205", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Abbaspour-H", "name": { "family": "Abbaspour", "given": "Hossein" } }, { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" } }, { "id": "Tradler-T", "name": { "family": "Tradler", "given": "Thomas" } } ] }, "doi": "10.1007/978-3-8348-9680-3", "pub_year": "2010", "author_list": "Abbaspour, Hossein; Marcolli, Matilde; et al." }, { "id": "https://authors.library.caltech.edu/records/wdpyf-71h20", "eprint_id": 88639, "eprint_status": "archive", "datestamp": "2023-08-19 00:44:32", "lastmod": "2026-04-12 18:21:51", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" }, "orcid": "0000-0002-2045-2907" } ] }, "title": "Feynman Motives", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2010 World Scientific Publishing Co Pte Ltd.", "abstract": "This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer. \n\nTwo different approaches to the subject are described. The first, a \"bottom-up\" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of Bloch\u2013Esnault\u2013Kreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, \"top-down\" approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann\u2013Hilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry. \n\nThe text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area.", "date": "2009-12", "date_type": "published", "publisher": "World Scientific", "place_of_pub": "Singapore", "id_number": "CaltechAUTHORS:20180808-075818895", "isbn": "978-981-4271-20-2", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180808-075818895", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Marcolli-M", "name": { "family": "Marcolli", "given": "Matilde" } } ] }, "doi": "10.1142/7245", "pub_year": "2009", "author_list": "Marcolli, Matilde" }, { "id": "https://authors.library.caltech.edu/records/c5bk6-vzr94", "eprint_id": 83983, "eprint_status": "archive", "datestamp": "2023-08-22 12:46:15", "lastmod": "2026-03-09 02:37:05", "type": "book", "metadata_visibility": "show", "creators": { "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" }, "orcid": "0000-0003-3903-5158" } ] }, "title": "Homological Mirror Symmetry: New Developments and Perspectives", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Gauge theory; algebra; category theory; duality in quantum field theory; mirror manifolds; mirror symmetry; ring theory", "note": "\u00a9 2009 Springer-Verlag Berlin Heidelberg.", "abstract": "Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap in the literature by providing a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A. Kapustin, L. Katzarkov, A. Klemm, M. Kontsevich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematical aspects of quantum field theory.", "date": "2008-08-20", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "id_number": "CaltechAUTHORS:20171220-123129463", "isbn": "978-3-540-68029-1", "book_title": "Homological Mirror Symmetry", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171220-123129463", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "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", "pub_year": "2008", "author_list": "Schlesinger, Karl-Georg; Kreuzer, Maximilian; et al." }, { "id": "https://authors.library.caltech.edu/records/ckzr1-hh534", "eprint_id": 88734, "eprint_status": "archive", "datestamp": "2023-08-19 21:53:36", "lastmod": "2026-03-09 20:36:08", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" }, { "name": { "family": "L\u00f6we", "given": "Benedikt" } }, { "name": { "family": "Steel", "given": "John R." } } ] }, "title": "Games, Scales and Suslin Cardinals: The Cabal Seminar, Volume I", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2008 Cambridge University Press.", "abstract": "The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Games, Scales, and Suslin Cardinals is the first of a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics, and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'Games and Scales' (Part 1) and 'Suslin Cardinals, Partition Properties, and Homogeneity' (Part 2), each of the two sections is preceded by an introductory survey putting the papers into present context. This volume will be an invaluable reference for anyone interested in higher set theory.", "date": "2008", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180810-080825868", "isbn": "9780521899512", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-080825868", "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", "pub_year": "2008", "author_list": "Kechris, Alexander S.; L\u00f6we, Benedikt; et al." }, { "id": "https://authors.library.caltech.edu/records/5j4ax-rb476", "eprint_id": 81942, "eprint_status": "archive", "datestamp": "2023-08-19 17:07:01", "lastmod": "2026-03-09 22:11:18", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "id": "Nebe-G", "name": { "family": "Nebe", "given": "Gabriele" } }, { "id": "Rains-E-M", "name": { "family": "Rains", "given": "Eric M." }, "orcid": "0000-0002-9915-0919" }, { "id": "Sloane-N-J-A", "name": { "family": "Sloane", "given": "Neil J. A." } } ] }, "title": "Self-Dual Codes and Invariant Theory", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 2006 Springer-Verlag Berlin Heidelberg.", "abstract": "[No abstract]", "date": "2006", "date_type": "published", "publisher": "Springer", "place_of_pub": "Berlin", "id_number": "CaltechAUTHORS:20171002-101719306", "isbn": "978-3-540-30729-7", "book_title": "Self-Dual Codes and Invariant Theory", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20171002-101719306", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "id": "Cohen-A-M", "name": { "family": "Cohen", "given": "Arjeh M." } }, { "id": "Cohen-H", "name": { "family": "Cohen", "given": "Henri" } }, { "id": "Eisenbud-D", "name": { "family": "Eisenbud", "given": "David" } }, { "id": "Sturmfels-B", "name": { "family": "Sturmfels", "given": "Bernd" } } ] }, "doi": "10.1007/3-540-30731-1", "pub_year": "2006", "author_list": "Nebe, Gabriele; Rains, Eric M.; et al." }, { "id": "https://authors.library.caltech.edu/records/j2y60-rz007", "eprint_id": 88746, "eprint_status": "archive", "datestamp": "2023-08-19 10:38:45", "lastmod": "2026-03-09 20:36:28", "type": "book", "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": "Analysis and Logic", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 2003 Cambridge University Press.", "abstract": "This volume comprises articles from four outstanding researchers who work at the cusp of analysis and logic. The emphasis is on active research topics; many results are presented that have not been published before and open problems are formulated. Considerable effort has been made by the authors to integrate their articles and make them accessible to mathematicians new to the area.", "date": "2003", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180810-092445662", "isbn": "9781107360006", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-092445662", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "local_group": { "items": [ { "id": "Mathematics-Department" } ] }, "contributors": { "items": [ { "name": { "family": "Finet", "given": "Catherine" } }, { "name": { "family": "Michaux", "given": "Christian" } } ] }, "doi": "10.1017/CBO9781107360006", "pub_year": "2003", "author_list": "Henson, C. Ward; Iovino, Jos\u00e9; et al." }, { "id": "https://authors.library.caltech.edu/records/0kr1g-b2143", "eprint_id": 103117, "eprint_status": "archive", "datestamp": "2023-08-22 11:28:26", "lastmod": "2026-03-18 00:05:13", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Truhlar", "given": "Donald G." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" }, "orcid": "0000-0003-2561-8539" } ] }, "title": "Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Potential; Quantum mechanics; cluster; collision; particles; quantum system; scattering; scattering theory", "note": "\u00a9 1997 Springer-Verlag New York, Inc.", "abstract": "This IMA Volume in Mathematics and its Applications MULTIPARTICLE QUANTUM SCATTERING WITH APPLICATIONS TO NUCLEAR, ATOMIC AND MOLECULAR PHYSICS is based on the proceedings of a workshop with the same title, which was an integral part of the 1994-1995 IMA program on \"Waves and Scattering.\" We would like to thank Donald G. Truhlar and Barry Simon for their ex\u00ad cellent work as organizers of this meeting and as editors of the proceedings. We also take this opportunity to thank the National Science Foundation (NSF), the Army Research Office (ARO), and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE The workshop on Multiparticle Quantum Scattering with Applications to Nuclear, Atomic, and Molecular Physics was held June 12-16, 1995 at the Institute for Mathematics and Its Applications in the University of Min\u00ad nesota Twin Cities campus as part of the 1994-95 Program on Waves and Scattering. There were about seventy participants including the plenary lecturers whose contributions are included in this volume. The workshop was preceded by a two-day tutorial featuring lectures by Donald J. Kouri and Gian Michele Graf, and we are pleased that both Professors Graf and Kouri were able to write up their tutorials as opening chapters of this volume.", "date": "1997", "date_type": "published", "publisher": "Springer", "place_of_pub": "New York, NY", "id_number": "CaltechAUTHORS:20200512-072314011", "isbn": "978-1-4612-7318-9", "book_title": "Multiparticle Quantum Scattering With Applications to Nuclear, Atomic and Molecular Physics", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20200512-072314011", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "funders": { "items": [ { "agency": "NSF" }, { "agency": "Army Research Office (ARO)" }, { "agency": "Office of Naval Research (ONR)" } ] }, "local_group": { "items": [ { "id": "Mathematics-Department" }, { "id": "Physics-Department" } ] }, "contributors": { "items": [ { "id": "Truhlar-D-G", "name": { "family": "Truhlar", "given": "Donald G." } }, { "id": "Simon-B", "name": { "family": "Simon", "given": "Barry" } } ] }, "doi": "10.1007/978-1-4612-1870-8", "pub_year": "1997", "author_list": "Truhlar, Donald G. and Simon, Barry" }, { "id": "https://authors.library.caltech.edu/records/2eyc0-mcp07", "eprint_id": 88812, "eprint_status": "archive", "datestamp": "2023-08-20 07:00:57", "lastmod": "2026-03-09 20:41:56", "type": "book", "metadata_visibility": "show", "creators": { "items": [ { "name": { "family": "Becker", "given": "Howard" } }, { "id": "Kechris-A-S", "name": { "family": "Kechris", "given": "Alexander S." }, "orcid": "0000-0002-2226-0423" } ] }, "title": "The Descriptive Set Theory of Polish Group Actions", "ispublished": "unpub", "full_text_status": "restricted", "note": "\u00a9 1996 Cambridge University Press.", "abstract": "In this book the authors present their research into the foundations of the theory of Polish groups and the associated orbit equivalence relations. The particular case of locally compact groups has long been studied in many areas of mathematics. Non-locally compact Polish groups occur naturally as groups of symmetries in such areas as logic (especially model theory), ergodic theory, group representations, and operator algebras. Some of the topics covered here are: topological realizations of Borel measurable actions; universal actions; applications to invariant measures; actions of the infinite symmetric group in connection with model theory (logic actions); dichotomies for orbit spaces (including Silver, Glimm-Effros type dichotomies and the topological Vaught conjecture); descriptive complexity of orbit equivalence relations; definable cardinality of orbit spaces.", "date": "1996", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180815-091513340", "isbn": "9780521576055", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180815-091513340", "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", "pub_year": "1996", "author_list": "Becker, Howard and Kechris, Alexander S." }, { "id": "https://authors.library.caltech.edu/records/9v9f6-azn58", "eprint_id": 88735, "eprint_status": "archive", "datestamp": "2023-08-19 19:11:29", "lastmod": "2026-03-09 20:38:41", "type": "book", "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": "Descriptive Set Theory and the Structure of Sets of Uniqueness", "ispublished": "unpub", "full_text_status": "public", "note": "\u00a9 1987 Cambridge University Press.", "abstract": "The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the mid-nineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially self-contained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis.", "date": "1987", "date_type": "published", "publisher": "Cambridge University Press", "place_of_pub": "Cambridge", "id_number": "CaltechAUTHORS:20180810-081409898", "isbn": "9780521358118", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180810-081409898", "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." } }, { "name": { "family": "Louveau", "given": "Alain" } } ] }, "doi": "10.1017/CBO9780511758850", "pub_year": "1987", "author_list": "Kechris, Alexander S. and Louveau, Alain" }, { "id": "https://authors.library.caltech.edu/records/my4ef-an845", "eprint_id": 97883, "eprint_status": "archive", "datestamp": "2023-08-22 05:08:11", "lastmod": "2026-03-07 04:14:08", "type": "book", "metadata_visibility": "show", "creators": { "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." } } ] }, "title": "Geometries and Groups", "ispublished": "unpub", "full_text_status": "restricted", "keywords": "Area; Finite; Lie; Maxima; Morphism; Node.js; algebra; character; classification; diagrams; presentation; reflection; representation theory; set; techniques", "note": "\u00a9 1988 Springer Science+Business Media B.V.", "abstract": "The workshop was set up in order to stimulate the interaction between (finite and algebraic) geometries and groups. Five areas of concentrated research were chosen on which attention would be focused, namely: diagram geometries and chamber systems with transitive automorphism groups, geometries viewed as incidence systems, properties of finite groups of Lie type, geometries related to finite simple groups, and algebraic groups. The list of talks (cf. page iii) illustrates how these subjects were represented during the workshop. The contributions to these proceedings mainly belong to the first three areas; therefore, (i) diagram geometries and chamber systems with transitive automorphism groups, (ii) geometries viewed as incidence systems, and (iii) properties of finite groups of Lie type occur as section titles. The fourth and final section of these proceedings has been named graphs and groups; besides some graph theory, this encapsules most of the work related to finite simple groups that does not (explicitly) deal with diagram geometry. A few more words about the content: (i). Diagram geometries and chamber systems with transitive automorphism groups. As a consequence of Tits' seminal work on the subject, all finite buildings are known. But usually, in a situation where groups are to be characterized by certain data concerning subgroups, a lot less is known than the full parabolic picture corresponding to the building.", "date": "1987", "date_type": "published", "publisher": "Springer", "place_of_pub": "Dordrecht", "id_number": "CaltechAUTHORS:20190814-100149802", "isbn": "978-94-010-8282-2", "official_url": "https://resolver.caltech.edu/CaltechAUTHORS:20190814-100149802", "rights": "No commercial reproduction, distribution, display or performance rights in this work are provided.", "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", "pub_year": "1987", "author_list": "Aschbacher, M.; Cohen, A. M.; et al." } ]