Report for the Academic Year 2000-2001
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
2006 Annual Report
Contents Clay Mathematics Institute 2006 James A. Carlson Letter from the President 2 Recognizing Achievement Fields Medal Winner Terence Tao 3 Persi Diaconis Mathematics & Magic Tricks 4 Annual Meeting Clay Lectures at Cambridge University 6 Researchers, Workshops & Conferences Summary of 2006 Research Activities 8 Profile Interview with Research Fellow Ben Green 10 Davar Khoshnevisan Normal Numbers are Normal 15 Feature Article CMI—Göttingen Library Project: 16 Eugene Chislenko The Felix Klein Protocols Digitized The Klein Protokolle 18 Summer School Arithmetic Geometry at the Mathematisches Institut, Göttingen, Germany 22 Program Overview The Ross Program at Ohio State University 24 PROMYS at Boston University Institute News Awards & Honors 26 Deadlines Nominations, Proposals and Applications 32 Publications Selected Articles by Research Fellows 33 Books & Videos Activities 2007 Institute Calendar 36 2006 Another major change this year concerns the editorial board for the Clay Mathematics Institute Monograph Series, published jointly with the American Mathematical Society. Simon Donaldson and Andrew Wiles will serve as editors-in-chief, while I will serve as managing editor. Associate editors are Brian Conrad, Ingrid Daubechies, Charles Fefferman, János Kollár, Andrei Okounkov, David Morrison, Cliff Taubes, Peter Ozsváth, and Karen Smith. The Monograph Series publishes Letter from the president selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. The next volume in the series will be Ricci Flow and the Poincaré Conjecture, by John Morgan and Gang Tian. Their book will appear in the summer of 2007. In related publishing news, the Institute has had the complete record of the Göttingen seminars of Felix Klein, 1872–1912, digitized and made available on James Carlson. -
Arxiv:Math/9911264V1 [Math.NT] 1 Nov 1999
Annals of Mathematics, 150 (1999), 807–866 On explicit lifts of cusp forms from GLm to classical groups By David Ginzburg, Stephen Rallis, and David Soudry* Introduction In this paper, we begin the study of poles of partial L-functions LS(σ ⊗ τ,s), where σ ⊗ τ is an irreducible, automorphic, cuspidal, generic (i.e. with nontrivial Whittaker coefficient) representation of GA × GLm(A). G is a split classical group and A is the adele ring of a number field F . We also consider Sp2n(A) × GLm(A), where ∼ denotes the metaplectic cover. Examining LS(σ ⊗ τ,s) through the corresponding Rankin-Selberg, or Shimura-typef integrals ([G-PS-R], [G-R-S3], [G], [So]), we find that the global integral contains, in its integrand, a certain normalized Eisenstein series which is responsible for the poles. For example, if G = SO2k+1, then the Eisenstein series is on the adele points of split SO2m, induced from the Siegel parabolic s−1/2 subgroup and τ ⊗ | det ·| . If G = Sp2k (this is a convenient abuse of notation), then the Eisenstein series is on Sp2m(A), induced from the Siegel parabolic subgroup and τ ⊗ | det ·|s−1/2. Thef constant term (along the “Siegel radical”) of such a normalized Eisenstein series involves one of the L-functions LS(τ, Λ2, 2s − 1) or LS(τ, Sym2, 2s − 1). So, up to problems of normalization of intertwining operators, the only pole we expect, for Re(s) > 1/2, is at s = 1 and then τ should be self-dual. (See [J-S1], [B-G].) Thus, let us assume that τ is self-dual. -
Inflation, Large Branes, and the Shape of Space
Inflation, Large Branes, and the Shape of Space Brett McInnes National University of Singapore email: [email protected] ABSTRACT Linde has recently argued that compact flat or negatively curved spatial sections should, in many circumstances, be considered typical in Inflationary cosmologies. We suggest that the “large brane instability” of Seiberg and Witten eliminates the negative candidates in the context of string theory. That leaves the flat, compact, three-dimensional manifolds — Conway’s platycosms. We show that deep theorems of Schoen, Yau, Gromov and Lawson imply that, even in this case, Seiberg-Witten instability can be avoided only with difficulty. Using a specific cosmological model of the Maldacena-Maoz type, we explain how to do this, and we also show how the list of platycosmic candidates can be reduced to three. This leads to an extension of the basic idea: the conformal compactification of the entire Euclidean spacetime also has the topology of a flat, compact, four-dimensional space. arXiv:hep-th/0410115v2 19 Oct 2004 1. Nearly Flat or Really Flat? Linde has recently argued [1] that, at least in some circumstances, we should regard cosmological models with flat or negatively curved compact spatial sections as the norm from an Inflationary point of view. Here we wish to argue that cosmic holography, in the novel form proposed by Maldacena and Maoz [2], gives a deep new interpretation of this idea, and also sharpens it very considerably to exclude the negative case. This focuses our attention on cosmological models with flat, compact spatial sections. Current observations [3] show that the spatial sections of our Universe [as defined by observers for whom local isotropy obtains] are fairly close to being flat: the total density parameter Ω satisfies Ω = 1.02 0.02 at 95% confidence level, if we allow the imposition ± of a reasonable prior [4] on the Hubble parameter. -
Bfm:978-1-4612-2582-9/1.Pdf
Progress in Mathematics Volume 131 Series Editors Hyman Bass Joseph Oesterle Alan Weinstein Functional Analysis on the Eve of the 21st Century Volume I In Honor of the Eightieth Birthday of I. M. Gelfand Simon Gindikin James Lepowsky Robert L. Wilson Editors Birkhauser Boston • Basel • Berlin Simon Gindikin James Lepowsky Department of Mathematics Department of Mathematics Rutgers University Rutgers University New Brunswick, NJ 08903 New Brunswick, NJ 08903 Robert L. Wilson Department of Mathematics Rutgers University New Brunswick, NJ 08903 Library of Congress Cataloging-in-Publication Data Functional analysis on the eve of the 21 st century in honor of the 80th birthday 0fI. M. Gelfand I [edited) by S. Gindikin, 1. Lepowsky, R. Wilson. p. cm. -- (Progress in mathematics ; vol. 131) Includes bibliographical references. ISBN-13:978-1-4612-7590-9 e-ISBN-13:978-1-4612-2582-9 DOl: 10.1007/978-1-4612-2582-9 1. Functional analysis. I. Gel'fand, I. M. (lzraU' Moiseevich) II. Gindikin, S. G. (Semen Grigor'evich) III. Lepowsky, J. (James) IV. Wilson, R. (Robert), 1946- . V. Series: Progress in mathematics (Boston, Mass.) ; vol. 131. QA321.F856 1995 95-20760 515'.7--dc20 CIP Printed on acid-free paper d»® Birkhiiuser ltGD © 1995 Birkhliuser Boston Softcover reprint of the hardcover 1st edition 1995 Copyright is not claimed for works of u.s. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. -
Anomalies, Dualities, and Topology of D = 6 N = 1 Superstring Vacua
RU-96-16 NSF-ITP-96-21 CALT-68-2057 IASSNS-HEP-96/53 hep-th/9605184 Anomalies, Dualities, and Topology of D =6 N =1 Superstring Vacua Micha Berkooz,1 Robert G. Leigh,1 Joseph Polchinski,2 John H. Schwarz,3 Nathan Seiberg,1 and Edward Witten4 1Department of Physics, Rutgers University, Piscataway, NJ 08855-0849 2Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 3California Institute of Technology, Pasadena, CA 91125 4Institute for Advanced Study, Princeton, NJ 08540 Abstract We consider various aspects of compactifications of the Type I/heterotic Spin(32)/Z2 theory on K3. One family of such compactifications in- cludes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of arXiv:hep-th/9605184v1 25 May 1996 the heterotic E8 × E8 theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory re- cently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E8 × E8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z2 and E8 × E8 models can be demonstrated by T duality, and permit a better understanding of non- perturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/Z2 and E8 × E8 models, the strong/weak coupling duality of the (12,12) E8 × E8 model is mapped to T duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism. -
Mathematics and Materials
IAS/PARK CITY MATHEMATICS SERIES Volume 23 Mathematics and Materials Mark J. Bowick David Kinderlehrer Govind Menon Charles Radin Editors American Mathematical Society Institute for Advanced Study Society for Industrial and Applied Mathematics 10.1090/pcms/023 Mathematics and Materials IAS/PARK CITY MATHEMATICS SERIES Volume 23 Mathematics and Materials Mark J. Bowick David Kinderlehrer Govind Menon Charles Radin Editors American Mathematical Society Institute for Advanced Study Society for Industrial and Applied Mathematics Rafe Mazzeo, Series Editor Mark J. Bowick, David Kinderlehrer, Govind Menon, and Charles Radin, Volume Editors. IAS/Park City Mathematics Institute runs mathematics education programs that bring together high school mathematics teachers, researchers in mathematics and mathematics education, undergraduate mathematics faculty, graduate students, and undergraduates to participate in distinct but overlapping programs of research and education. This volume contains the lecture notes from the Graduate Summer School program 2010 Mathematics Subject Classification. Primary 82B05, 35Q70, 82B26, 74N05, 51P05, 52C17, 52C23. Library of Congress Cataloging-in-Publication Data Names: Bowick, Mark J., editor. | Kinderlehrer, David, editor. | Menon, Govind, 1973– editor. | Radin, Charles, 1945– editor. | Institute for Advanced Study (Princeton, N.J.) | Society for Industrial and Applied Mathematics. Title: Mathematics and materials / Mark J. Bowick, David Kinderlehrer, Govind Menon, Charles Radin, editors. Description: [Providence] : American Mathematical Society, [2017] | Series: IAS/Park City math- ematics series ; volume 23 | “Institute for Advanced Study.” | “Society for Industrial and Applied Mathematics.” | “This volume contains lectures presented at the Park City summer school on Mathematics and Materials in July 2014.” – Introduction. | Includes bibliographical references. Identifiers: LCCN 2016030010 | ISBN 9781470429195 (alk. paper) Subjects: LCSH: Statistical mechanics–Congresses. -
The Abel Prize 2003-2007 the First Five Years
springer.com Mathematics : History of Mathematics Holden, Helge, Piene, Ragni (Eds.) The Abel Prize 2003-2007 The First Five Years Presenting the winners of the Abel Prize, which is one of the premier international prizes in mathematics The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com . Order online at springer.com/booksellers Springer Nature Customer Service Center GmbH Springer Customer Service Tiergartenstrasse 15-17 2010, XI, 329 p. With DVD. 1st 69121 Heidelberg edition Germany T: +49 (0)6221 345-4301 [email protected] Printed book Hardcover Book with DVD Hardcover ISBN 978-3-642-01372-0 £ 76,50 | CHF 103,00 | 86,99 € | 95,69 € (A) | 93,08 € (D) Out of stock Discount group Science (SC) Product category Commemorative publication Series The Abel Prize Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one book and $ 1.00 for each additional book. Outside the US and Canada add $ 10.00 for first book, $5.00 for each additional book. -
Report Concerning Jeffrey E. Epstein's Connections to Harvard University
REPORT CONCERNING JEFFREY E. EPSTEIN’S CONNECTIONS TO HARVARD UNIVERSITY Diane E. Lopez, Harvard University Vice President and General Counsel Ara B. Gershengorn, Harvard University Attorney Martin F. Murphy, Foley Hoag LLP May 2020 1 INTRODUCTION On September 12, 2019, Harvard President Lawrence S. Bacow issued a message to the Harvard Community concerning Jeffrey E. Epstein’s relationship with Harvard. That message condemned Epstein’s crimes as “utterly abhorrent . repulsive and reprehensible” and expressed “profound[] regret” about “Harvard’s past association with him.” President Bacow’s message announced that he had asked for a review of Epstein’s donations to Harvard. In that communication, President Bacow noted that a preliminary review indicated that Harvard did not accept gifts from Epstein after his 2008 conviction, and this report confirms that as a finding. Lastly, President Bacow also noted Epstein’s appointment as a Visiting Fellow in the Department of Psychology in 2005 and asked that the review address how that appointment had come about. Following up on President Bacow’s announcement, Vice President and General Counsel Diane E. Lopez engaged outside counsel, Martin F. Murphy of Foley Hoag, to work with the Office of General Counsel to conduct the review. Ms. Lopez also issued a message to the community provid- ing two ways for individuals to come forward with information or concerns about Epstein’s ties to Harvard: anonymously through Harvard’s compliance hotline and with attribution to an email ac- count established for that purpose. Since September, we have interviewed more than 40 individu- als, including senior leaders of the University, staff in Harvard’s Office of Alumni Affairs and Development, faculty members, and others. -
Mathematisches Forschungsinstitut Oberwolfach Reflection Positivity
Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2017 DOI: 10.4171/OWR/2017/55 Reflection Positivity Organised by Arthur Jaffe, Harvard Karl-Hermann Neeb, Erlangen Gestur Olafsson, Baton Rouge Benjamin Schlein, Z¨urich 26 November – 2 December 2017 Abstract. The main theme of the workshop was reflection positivity and its occurences in various areas of mathematics and physics, such as Representa- tion Theory, Quantum Field Theory, Noncommutative Geometry, Dynamical Systems, Analysis and Statistical Mechanics. Accordingly, the program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity. Mathematics Subject Classification (2010): 17B10, 22E65, 22E70, 81T08. Introduction by the Organisers The workshop on Reflection Positivity was organized by Arthur Jaffe (Cambridge, MA), Karl-Hermann Neeb (Erlangen), Gestur Olafsson´ (Baton Rouge) and Ben- jamin Schlein (Z¨urich) during the week November 27 to December 1, 2017. The meeting was attended by 53 participants from all over the world. It was organized around 24 lectures each of 50 minutes duration representing major recent advances or introducing to a specific aspect or application of reflection positivity. The meeting was exciting and highly successful. The quality of the lectures was outstanding. The exceptional atmosphere of the Oberwolfach Institute provided the optimal environment for bringing people from different areas together and to create an atmosphere of scientific interaction and cross-fertilization. In particular, people from different subcommunities exchanged ideas and this lead to new col- laborations that will probably stimulate progress in unexpected directions. 3264 Oberwolfach Report 55/2017 Reflection positivity (RP) emerged in the early 1970s in the work of Osterwalder and Schrader as one of their axioms for constructive quantum field theory ensuring the equivalence of their euclidean setup with Wightman fields. -
Scientific Report for 2012
Scientific Report for 2012 Impressum: Eigent¨umer,Verleger, Herausgeber: The Erwin Schr¨odingerInternational Institute for Mathematical Physics - University of Vienna (DVR 0065528), Boltzmanngasse 9, A-1090 Vienna. Redaktion: Joachim Schwermer, Jakob Yngvason. Supported by the Austrian Federal Ministry of Science and Research (BMWF) via the University of Vienna. Contents Preface 3 The Institute and its Mission . 3 Scientific activities in 2012 . 4 The ESI in 2012 . 7 Scientific Reports 9 Main Research Programmes . 9 Automorphic Forms: Arithmetic and Geometry . 9 K-theory and Quantum Fields . 14 The Interaction of Geometry and Representation Theory. Exploring new frontiers. 18 Modern Methods of Time-Frequency Analysis II . 22 Workshops Organized Outside the Main Programmes . 32 Operator Related Function Theory . 32 Higher Spin Gravity . 34 Computational Inverse Problems . 35 Periodic Orbits in Dynamical Systems . 37 EMS-IAMP Summer School on Quantum Chaos . 39 Golod-Shafarevich Groups and Algebras, and the Rank Gradient . 41 Recent Developments in the Mathematical Analysis of Large Systems . 44 9th Vienna Central European Seminar on Particle Physics and Quantum Field Theory: Dark Matter, Dark Energy, Black Holes and Quantum Aspects of the Universe . 46 Dynamics of General Relativity: Black Holes and Asymptotics . 47 Research in Teams . 49 Bruno Nachtergaele et al: Disordered Oscillator Systems . 49 Alexander Fel'shtyn et al: Twisted Conjugacy Classes in Discrete Groups . 50 Erez Lapid et al: Whittaker Periods of Automorphic Forms . 53 Dale Cutkosky et al: Resolution of Surface Singularities in Positive Characteristic . 55 Senior Research Fellows Programme . 57 James Cogdell: L-functions and Functoriality . 57 Detlev Buchholz: Fundamentals and Highlights of Algebraic Quantum Field Theory . -
Dawkins on Nowak Et Al. and Kin Selection « Why Evolution Is True 25/03/2011 10:17
Big dust-up about kin selection « Why Evolution Is True 25/03/2011 10:19 Why Evolution Is True « Bummer Peregrinations » Book Links « Home Big dust-up about kin selection About the Author Search About the Book Excerpt Find » Last August I wrote about a new paper in Nature by three Harvard Research Interests biologists, Martin Nowak, Corina Tarnita, and Edward O. Wilson. Their Reviews Meta paper was, as I called it, a “misguided attack on kin selection,” referring Register Log in to the form of selection in which the reproductive success of a gene Buy the Book (usually a gene that affects behavior) is influenced not only by its effects Amazon.co.uk Links on its carrier, but also by its effects on related individuals (kin) carrying Amazon.com the same gene. This idea, introduced to evolutionary biology by George All posts Barnes & Noble All comments Price and W. D. Hamilton, has been enormously productive, explaining all Borders sorts of things from parental care and parent-offspring conflict to sex Indie Bound Email Subscription ratios in animals and, perhaps most important, the evolution of “altruism.” Nowak et al.’s paper attacked the idea that this form of Enter your email address to selection—based on a gene’s “inclusive fitness”—was important in subscribe to this blog and explaining anything; indeed, they didn’t even see kin selection as a form receive notifications of new of natural selection. My original post details most of my objections to posts by email. their paper. Now, seven months later, Nature has published a spate of objections to the Nowak et al paper: there are five critiques and a response to them by Nowak et al. -
Memories of Julian Schwinger
Memories of Julian Schwinger Edward Gerjuoy* ABSTRACT The career and accomplishments of Julian Schwinger, who shared the Nobel Prize for physics in 1965, have been reviewed in numerous books and articles. For this reason these Memories, which seek to convey a sense of Schwinger’s remarkable talents as a physicist, concentrate primarily (though not entirely) on heretofore unpuBlished pertinent recollections of the youthful Schwinger by this writer, who first encountered Schwinger in 1934 when they both were undergraduates at the City College of New York. *University of Pittsburgh Dept. of Physics and Astronomy, Pittsburgh, PA 15260. 1 Memories of Julian Schwinger Julian Seymour Schwinger, who shared the 1965 Nobel prize in physics with Richard Feynman and Sin-itiro Tomonaga, died in Los Angeles on July 16, 1994 at the age of 76. He was a remarkably talented theoretical physicist, who—through his own publications and through the students he trained—had an enormous influence on the evolution of physics after World War II. Accordingly, his life and work have been reviewed in a number of publications [1-3, inter alia]. There also have been numerous published obituaries, of course [4-5, e.g.] These Memories largely are the text of the Schwinger portion of a colloquium talk, “Recollections of Oppenheimer and Schwinger”, which the writer has given at a number of universities, and which can be found on the web [6]. The portion of the talk devoted to J. Robert Oppenheimer—who is enduringly famous as director of the Los Alamos laboratory during World War II—has been published [7], but the portion devoted to Julian is essentially unpublished; references 7-9 describe the basically trivial exceptions to this last assertion.