Science Lives: Video Portraits of Great Mathematicians
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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:1006.1489V2 [Math.GT] 8 Aug 2010 Ril.Ias Rfie Rmraigtesre Rils[14 Articles Survey the Reading from Profited Also I Article
Pure and Applied Mathematics Quarterly Volume 8, Number 1 (Special Issue: In honor of F. Thomas Farrell and Lowell E. Jones, Part 1 of 2 ) 1—14, 2012 The Work of Tom Farrell and Lowell Jones in Topology and Geometry James F. Davis∗ Tom Farrell and Lowell Jones caused a paradigm shift in high-dimensional topology, away from the view that high-dimensional topology was, at its core, an algebraic subject, to the current view that geometry, dynamics, and analysis, as well as algebra, are key for classifying manifolds whose fundamental group is infinite. Their collaboration produced about fifty papers over a twenty-five year period. In this tribute for the special issue of Pure and Applied Mathematics Quarterly in their honor, I will survey some of the impact of their joint work and mention briefly their individual contributions – they have written about one hundred non-joint papers. 1 Setting the stage arXiv:1006.1489v2 [math.GT] 8 Aug 2010 In order to indicate the Farrell–Jones shift, it is necessary to describe the situation before the onset of their collaboration. This is intimidating – during the period of twenty-five years starting in the early fifties, manifold theory was perhaps the most active and dynamic area of mathematics. Any narrative will have omissions and be non-linear. Manifold theory deals with the classification of ∗I thank Shmuel Weinberger and Tom Farrell for their helpful comments on a draft of this article. I also profited from reading the survey articles [14] and [4]. 2 James F. Davis manifolds. There is an existence question – when is there a closed manifold within a particular homotopy type, and a uniqueness question, what is the classification of manifolds within a homotopy type? The fifties were the foundational decade of manifold theory. -
Campus Profile Sept 2018.Indd
CAMPUS PROFILE AND POINTS OF DISTINCTION campus profileOCTOBER 2018 CAMPUS PROFILE AND POINTS OF DISTINCTION At the University of California San Diego, we constantly push boundaries and challenge expectations. Established in 1960, UC San Diego has been shaped by exceptional scholars who aren’t afraid to take risks and redefine conventional wisdom. Today, as one of the top 15 research universities in the world, we are driving innovation and change to advance society, propel economic growth, and make our world a better place. UC San Diego’s main campus is located near the Pacific Ocean on 1,200 acres of coastal woodland in La Jolla, California. The campus sits on land formerly inhabited by Kumeyaay tribal members, the original native inhabitants of San Diego County. UC San Diego’s rich academic portfolio includes six undergraduate colleges, five academic divisions, and five graduate and professional schools. BY THE NUMBERS • 36,624 Total campus enrollment (as of Fall 2017); • 16 Number of Nobel laureates who have taught the largest number of students among colleges on campus and universities in San Diego County. • 201 Memberships held by current and emeriti • 97,670 Total freshman applications for 2018 faculty in the National Academy of Sciences (73), National Academy of Engineering (84), • 4.13 Admitted freshman average high school GPA and National Academy of Medicine (44). • $4.7 billion Fiscal year 2016-17 revenues; • 4 Scripps Institution of Oceanography operates 20 percent of this total is revenue from contracts three research vessels and an innovative Floating and grants, most of which is from the federal Instrument Platform (FLIP), enabling faculty, government for research. -
Part III Essay on Serre's Conjecture
Serre’s conjecture Alex J. Best June 2015 Contents 1 Introduction 2 2 Background 2 2.1 Modular forms . 2 2.2 Galois representations . 6 3 Obtaining Galois representations from modular forms 13 3.1 Congruences for Ramanujan’s t function . 13 3.2 Attaching Galois representations to general eigenforms . 15 4 Serre’s conjecture 17 4.1 The qualitative form . 17 4.2 The refined form . 18 4.3 Results on Galois representations associated to modular forms 19 4.4 The level . 21 4.5 The character and the weight mod p − 1 . 22 4.6 The weight . 24 4.6.1 The level 2 case . 25 4.6.2 The level 1 tame case . 27 4.6.3 The level 1 non-tame case . 28 4.7 A counterexample . 30 4.8 The proof . 31 5 Examples 32 5.1 A Galois representation arising from D . 32 5.2 A Galois representation arising from a D4 extension . 33 6 Consequences 35 6.1 Finiteness of classes of Galois representations . 35 6.2 Unramified mod p Galois representations for small p . 35 6.3 Modularity of abelian varieties . 36 7 References 37 1 1 Introduction In 1987 Jean-Pierre Serre published a paper [Ser87], “Sur les representations´ modulaires de degre´ 2 de Gal(Q/Q)”, in the Duke Mathematical Journal. In this paper Serre outlined a conjecture detailing a precise relationship between certain mod p Galois representations and specific mod p modular forms. This conjecture and its variants have become known as Serre’s conjecture, or sometimes Serre’s modularity conjecture in order to distinguish it from the many other conjectures Serre has made. -
Roots of L-Functions of Characters Over Function Fields, Generic
Roots of L-functions of characters over function fields, generic linear independence and biases Corentin Perret-Gentil Abstract. We first show joint uniform distribution of values of Kloost- erman sums or Birch sums among all extensions of a finite field Fq, for ˆ almost all couples of arguments in Fq , as well as lower bounds on dif- ferences. Using similar ideas, we then study the biases in the distribu- tion of generalized angles of Gaussian primes over function fields and primes in short intervals over function fields, following recent works of Rudnick–Waxman and Keating–Rudnick, building on cohomological in- terpretations and determinations of monodromy groups by Katz. Our results are based on generic linear independence of Frobenius eigenval- ues of ℓ-adic representations, that we obtain from integral monodromy information via the strategy of Kowalski, which combines his large sieve for Frobenius with a method of Girstmair. An extension of the large sieve is given to handle wild ramification of sheaves on varieties. Contents 1. Introduction and statement of the results 1 2. Kloosterman sums and Birch sums 12 3. Angles of Gaussian primes 14 4. Prime polynomials in short intervals 20 5. An extension of the large sieve for Frobenius 22 6. Generic maximality of splitting fields and linear independence 33 7. Proof of the generic linear independence theorems 36 References 37 1. Introduction and statement of the results arXiv:1903.05491v2 [math.NT] 17 Dec 2019 Throughout, p will denote a prime larger than 5 and q a power of p. ˆ 1.1. Kloosterman and Birch sums. -
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. -
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. -
Arxiv:1402.0409V1 [Math.HO]
THE PICARD SCHEME STEVEN L. KLEIMAN Abstract. This article introduces, informally, the substance and the spirit of Grothendieck’s theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger historical record. 1. Introduction A scientific biography should be written in which we indicate the “flow” of mathematics ... discussing a certain aspect of Grothendieck’s work, indicating possible roots, then describing the leap Grothendieck made from those roots to general ideas, and finally setting forth the impact of those ideas. Frans Oort [60, p. 2] Alexander Grothendieck sketched his proof of the existence of the Picard scheme in his February 1962 Bourbaki talk. Then, in his May 1962 Bourbaki talk, he sketched his proofs of various general properties of the scheme. Shortly afterwards, these two talks were reprinted in [31], commonly known as FGA, along with his commentaries, which included statements of nine finiteness theorems that refine the single finiteness theorem in his May talk and answer several related questions. However, Grothendieck had already defined the Picard scheme, via the functor it represents, on pp.195-15,16 of his February 1960 Bourbaki talk. Furthermore, on p.212-01 of his February 1961 Bourbaki talk, he had announced that the scheme can be constructed by combining results on quotients sketched in that talk along with results on the Hilbert scheme to be sketched in his forthcoming May 1961 Bourbaki talk. Those three talks plus three earlier talks, which prepare the way, were also reprinted in [31]. arXiv:1402.0409v1 [math.HO] 3 Feb 2014 Moreover, Grothendieck noted in [31, p. -
Prospects in Topology
Annals of Mathematics Studies Number 138 Prospects in Topology PROCEEDINGS OF A CONFERENCE IN HONOR OF WILLIAM BROWDER edited by Frank Quinn PRINCETON UNIVERSITY PRESS PRINCETON, NEW JERSEY 1995 Copyright © 1995 by Princeton University Press ALL RIGHTS RESERVED The Annals of Mathematics Studies are edited by Luis A. Caffarelli, John N. Mather, and Elias M. Stein Princeton University Press books are printed on acid-free paper and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton Academic Press 10 987654321 Library of Congress Cataloging-in-Publication Data Prospects in topology : proceedings of a conference in honor of W illiam Browder / Edited by Frank Quinn. p. cm. — (Annals of mathematics studies ; no. 138) Conference held Mar. 1994, at Princeton University. Includes bibliographical references. ISB N 0-691-02729-3 (alk. paper). — ISBN 0-691-02728-5 (pbk. : alk. paper) 1. Topology— Congresses. I. Browder, William. II. Quinn, F. (Frank), 1946- . III. Series. QA611.A1P76 1996 514— dc20 95-25751 The publisher would like to acknowledge the editor of this volume for providing the camera-ready copy from which this book was printed PROSPECTS IN TOPOLOGY F r a n k Q u in n , E d it o r Proceedings of a conference in honor of William Browder Princeton, March 1994 Contents Foreword..........................................................................................................vii Program of the conference ................................................................................ix Mathematical descendants of William Browder...............................................xi A. Adem and R. J. Milgram, The mod 2 cohomology rings of rank 3 simple groups are Cohen-Macaulay........................................................................3 A. -
All That Math Portraits of Mathematicians As Young Researchers
Downloaded from orbit.dtu.dk on: Oct 06, 2021 All that Math Portraits of mathematicians as young researchers Hansen, Vagn Lundsgaard Published in: EMS Newsletter Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Hansen, V. L. (2012). All that Math: Portraits of mathematicians as young researchers. EMS Newsletter, (85), 61-62. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. -
Analysis in Complex Geometry
1946-4 School and Conference on Differential Geometry 2 - 20 June 2008 Analysis in Complex Geometry Shing-Tung Yau Harvard University, Dept. of Mathematics Cambridge, MA 02138 United States of America Analysis in Complex Geometry Shing-Tung Yau Harvard University ICTP, June 18, 2008 1 An important question in complex geometry is to char- acterize those topological manifolds that admit a com- plex structure. Once a complex structure is found, one wants to search for the existence of algebraic or geo- metric structures that are compatible with the complex structure. 2 Most geometric structures are given by Hermitian met- rics or connections that are compatible with the com- plex structure. In most cases, we look for connections with special holonomy group. A connection may have torsion. The torsion tensor is not well-understood. Much more research need to be done especially for those Hermitian connections with special holonomy group. 3 Karen Uhlenbeck Simon Donaldson By using the theorem of Donaldson-Uhlenbeck-Yau, it is possible to construct special holonomy connections with torsion. Their significance in relation to complex or algebraic structure need to be explored. 4 K¨ahler metrics have no torsion and their geometry is very close to that of algebraic geometry. Yet, as was demonstrated by Voisin, there are K¨ahler manifolds that are not homotopy equivalent to any algebraic manifolds. The distinction between K¨ahler and algebraic geometry is therefore rather delicate. Erich K¨ahler 5 Algebraic geometry is a classical subject and there are several natural equivalences of algebraic manifolds: bi- rational equivalence, biregular equivalence, and arith- metic equivalence.