January AAAS Meeting in San Francisco to Offer Strong Mathematics Program
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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. -
Commentary on the Kervaire–Milnor Correspondence 1958–1961
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 52, Number 4, October 2015, Pages 603–609 http://dx.doi.org/10.1090/bull/1508 Article electronically published on July 1, 2015 COMMENTARY ON THE KERVAIRE–MILNOR CORRESPONDENCE 1958–1961 ANDREW RANICKI AND CLAUDE WEBER Abstract. The extant letters exchanged between Kervaire and Milnor during their collaboration from 1958–1961 concerned their work on the classification of exotic spheres, culminating in their 1963 Annals of Mathematics paper. Michel Kervaire died in 2007; for an account of his life, see the obituary by Shalom Eliahou, Pierre de la Harpe, Jean-Claude Hausmann, and Claude We- ber in the September 2008 issue of the Notices of the American Mathematical Society. The letters were made public at the 2009 Kervaire Memorial Confer- ence in Geneva. Their publication in this issue of the Bulletin of the American Mathematical Society is preceded by our commentary on these letters, provid- ing some historical background. Letter 1. From Milnor, 22 August 1958 Kervaire and Milnor both attended the International Congress of Mathemati- cians held in Edinburgh, 14–21 August 1958. Milnor gave an invited half-hour talk on Bernoulli numbers, homotopy groups, and a theorem of Rohlin,andKer- vaire gave a talk in the short communications section on Non-parallelizability of the n-sphere for n>7 (see [2]). In this letter written immediately after the Congress, Milnor invites Kervaire to join him in writing up the lecture he gave at the Con- gress. The joint paper appeared in the Proceedings of the ICM as [10]. Milnor’s name is listed first (contrary to the tradition in mathematics) since it was he who was invited to deliver a talk. -
Journal Symbolic Logic
THT, E JOURNAL : OF SYMBOLIC LOGIC •' . X , , ' V. ;'••*• • EDITED B\Y \ ' ALONZO CHURCH S. C. KLEENE ALICE A. LAZEROWITZ Managing Editor'. ALFONS BOROERS Consulting Editors'. i W. ACKERMANN ROBERT FEYS ANDRZEJ MOSTOWSKJ G. A. BAYLIS FREDERIC B. FITCH R6ZSA PETER PAUL BERNAYS CARL G. HEMPEL BARKLEY ROSSER G. D. W. BERRY LEON HENKIN THORALF SKOLEM MARTIN DAVIS JOHN G. KEMENY A. R. TURQUETTE VOLUME 19 NUMBER 4 DECEMBER 1954 1 s PUBLISHED QUARTERLY BY THE ASSOCIATION FOR SYMBOLIC LOGIC, INC. WITH THE AID OF SUBVENTIONS FROM EDWARD C. HEGELER TRUST FUND HARVARD UNIVERSITY RUTGERS UNIVERSITY INSTITUTE FOR ADVANCED STUDY SMITH COLLEGE UNIVERSITY OF MICHIGAN 1_—; , Copyright igss by the Association for Symbolic Logic, Inc. Reproduction by photostat, photo-print, microfilm, or like process by permission only r • A Downloaded from https://www.cambridge.org/core. IP address: 170.106.51.11, on 05 Oct 2021 at 08:48:31, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0022481200086618 TABLE OF CONTENTS The formalization of mathematics. By HAO WANG 24.1 The recursive irrationality of n. By R. L. GOODSTEIN 267 Distributivity and an axiom of choice. By GEORGE E. COLLINS . 275 Reviews . ! t 278 List of officers and members of the Association for Symbolic Logic . 305 The JOURNAL OF SYMBOLIC LOCIC is the official organ of the Association for Symbolic Logic, Inc., published quarterly, in the months of March, June, September, and December. The JOURNAL is published for the Association by N.V. Erven P. Noordhoff, Publishers, Gronin- gen, The Netherlands. -
Millennium Prize for the Poincaré
FOR IMMEDIATE RELEASE • March 18, 2010 Press contact: James Carlson: [email protected]; 617-852-7490 See also the Clay Mathematics Institute website: • The Poincaré conjecture and Dr. Perelmanʼs work: http://www.claymath.org/poincare • The Millennium Prizes: http://www.claymath.org/millennium/ • Full text: http://www.claymath.org/poincare/millenniumprize.pdf First Clay Mathematics Institute Millennium Prize Announced Today Prize for Resolution of the Poincaré Conjecture a Awarded to Dr. Grigoriy Perelman The Clay Mathematics Institute (CMI) announces today that Dr. Grigoriy Perelman of St. Petersburg, Russia, is the recipient of the Millennium Prize for resolution of the Poincaré conjecture. The citation for the award reads: The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincaré conjecture to Grigoriy Perelman. The Poincaré conjecture is one of the seven Millennium Prize Problems established by CMI in 2000. The Prizes were conceived to record some of the most difficult problems with which mathematicians were grappling at the turn of the second millennium; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; to emphasize the importance of working towards a solution of the deepest, most difficult problems; and to recognize achievement in mathematics of historical magnitude. The award of the Millennium Prize to Dr. Perelman was made in accord with their governing rules: recommendation first by a Special Advisory Committee (Simon Donaldson, David Gabai, Mikhail Gromov, Terence Tao, and Andrew Wiles), then by the CMI Scientific Advisory Board (James Carlson, Simon Donaldson, Gregory Margulis, Richard Melrose, Yum-Tong Siu, and Andrew Wiles), with final decision by the Board of Directors (Landon T. -
Alfred Tarski and a Watershed Meeting in Logic: Cornell, 1957 Solomon Feferman1
Alfred Tarski and a watershed meeting in logic: Cornell, 1957 Solomon Feferman1 For Jan Wolenski, on the occasion of his 60th birthday2 In the summer of 1957 at Cornell University the first of a cavalcade of large-scale meetings partially or completely devoted to logic took place--the five-week long Summer Institute for Symbolic Logic. That meeting turned out to be a watershed event in the development of logic: it was unique in bringing together for such an extended period researchers at every level in all parts of the subject, and the synergetic connections established there would thenceforth change the face of mathematical logic both qualitatively and quantitatively. Prior to the Cornell meeting there had been nothing remotely like it for logicians. Previously, with the growing importance in the twentieth century of their subject both in mathematics and philosophy, it had been natural for many of the broadly representative meetings of mathematicians and of philosophers to include lectures by logicians or even have special sections devoted to logic. Only with the establishment of the Association for Symbolic Logic in 1936 did logicians begin to meet regularly by themselves, but until the 1950s these occasions were usually relatively short in duration, never more than a day or two. Alfred Tarski was one of the principal organizers of the Cornell institute and of some of the major meetings to follow on its heels. Before the outbreak of World War II, outside of Poland Tarski had primarily been involved in several Unity of Science Congresses, including the first, in Paris in 1935, and the fifth, at Harvard in September, 1939. -
AMERICAN MATHEMATICAL SOCIETY Business Office: P.O. Box 6248, Providence, Rhode Island 02940 William J
AMERICAN MATHEMATICAL SOCIETY Business Office: P.O. Box 6248, Providence, Rhode Island 02940 William J. LeVeque, Executive Director Lincoln K. Durst, Deputy Director OFFICERS President: R. H. Bing, Dept. of Mathematics, University of Texas at Austin, Austin, TX 78712 President-elect: Peter D. Lax, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012 Vice-Presidents: William Browder, Dept. of Mathematics, Box 708, Fine Hall, Princeton University, Princeton, NJ 08540; Julia B. Robinson, 243 Lake Dr., Berkeley, CA 94708; George W. Whitehead, Dept. of Mathematics, Room 2-284, Massachusetts Institute of Technology, Cambridge, MA 02139 Secretary: Everett Pitcher, Dept. of Mathematics, Lehigh University, Bethelehem, PA 18015 Associate Secretaries: Raymond G. Ayoub, Dept. of Mathematics, 203 McAllister Building, Pennsylvania State University, University Park, PA 16802; Paul T. Bateman, Dept. of Mathematics, University of Illinois, Urbana, IL 61801; Frank T. Birtel, College of Arts and Sciences, Tulane University, New Orleans, LA 70118; Kenneth A. Ross, Dept. of Mathema tics, University of Oregon, Eugene, OR 97403 Treasurer: Franklin P. Peterson, Dept. of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139 Associate Treasurer: Steve Armentrout, Dept. of Mathematics, 230 McAllister Building, Penn sylvania State University, University Park, PA 16802 Board of Trustees: Steve Armentrout (ex officio); R. H. Bing (ex officio); Joseph J. Kohn, Dept. of Mathematics, Princeton University, Princeton, NJ 08540; Calvin C. Moore, Dept. of Mathematics, University of California, Berkeley, CA 94720; Cathleen S. Morawetz, Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012; Richard S. Palais, Dept. of Mathematics, Brandeis University, Waltham, MA 02154; Franklin P. -
Writing the History of Dynamical Systems and Chaos
Historia Mathematica 29 (2002), 273–339 doi:10.1006/hmat.2002.2351 Writing the History of Dynamical Systems and Chaos: View metadata, citation and similar papersLongue at core.ac.uk Dur´ee and Revolution, Disciplines and Cultures1 brought to you by CORE provided by Elsevier - Publisher Connector David Aubin Max-Planck Institut fur¨ Wissenschaftsgeschichte, Berlin, Germany E-mail: [email protected] and Amy Dahan Dalmedico Centre national de la recherche scientifique and Centre Alexandre-Koyre,´ Paris, France E-mail: [email protected] Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined—“chaos.” Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincar´e who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-duree´ history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincar´e to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as -
A Bibliography of Publications in American Mathematical Monthly: 1990–1999
A Bibliography of Publications in American Mathematical Monthly: 1990{1999 Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 14 October 2017 Version 1.19 Title word cross-reference NF [737]. !(n) [82]. p [619, 149, 694, 412]. P2 [357]. p ≡ 1 (mod 4) [34]. φ [674]. φ(30n + 1) [947]. Φpq(X) [618]. π 0 y − z 2 [105]. 1 [21]. (logx N) [333]. (x +1) x = 1 [845]. 0 [740, 684, 693, 950, 489]. π 2 3 [495, 1]. 1 [495, 1]. 1=p [511]. 10 [140]. 168 Qc(x)=x + c [399]. R [35, 226].p R [357].p n n R [62, 588]. S6 [315]. σ [19]. −1 [995]. 2 [538]. 2 [335]. $29.50 [792]. 2 :n! [1003]. p p p P1 n × 2 × 2 [26]. 3 [828, 583]. 4 − 2 [748]. A [435]. [473]. 2 3= 6 [257]. n=0 1=n! [619]. A∗A = B∗B [607]. AB [620]. BA [620]. 2n tan(k) z [160]. } [512]. x [859]. x=(sin x) n 0 [260]. mod5 [982]. C1 [832]. cos(2π/n) [322]. [755]. x = f(x ) [832]. x2 + ym = z2n [7]. d [844]. dy=dx [449]. ex [859]. f(x; y) [469]. x2 + ym = z2n [65]. x5 + ax + b [465]. xn =1 − [235]. Z3 [975]. -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes. -
Sinai Awarded 2014 Abel Prize
Sinai Awarded 2014 Abel Prize The Norwegian Academy of Sci- Sinai’s first remarkable contribution, inspired ence and Letters has awarded by Kolmogorov, was to develop an invariant of the Abel Prize for 2014 to dynamical systems. This invariant has become Yakov Sinai of Princeton Uni- known as the Kolmogorov-Sinai entropy, and it versity and the Landau Insti- has become a central notion for studying the com- tute for Theoretical Physics plexity of a system through a measure-theoretical of the Russian Academy of description of its trajectories. It has led to very Sciences “for his fundamen- important advances in the classification of dynami- tal contributions to dynamical cal systems. systems, ergodic theory, and Sinai has been at the forefront of ergodic theory. mathematical physics.” The He proved the first ergodicity theorems for scat- Photo courtesy of Princeton University Mathematics Department. Abel Prize recognizes contribu- tering billiards in the style of Boltzmann, work tions of extraordinary depth he continued with Bunimovich and Chernov. He Yakov Sinai and influence in the mathemat- constructed Markov partitions for systems defined ical sciences and has been awarded annually since by iterations of Anosov diffeomorphisms, which 2003. The prize carries a cash award of approxi- led to a series of outstanding works showing the mately US$1 million. Sinai received the Abel Prize power of symbolic dynamics to describe various at a ceremony in Oslo, Norway, on May 20, 2014. classes of mixing systems. With Ruelle and Bowen, Sinai discovered the Citation notion of SRB measures: a rather general and Ever since the time of Newton, differential equa- distinguished invariant measure for dissipative tions have been used by mathematicians, scientists, systems with chaotic behavior. -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
Complex Analysis (Princeton Lectures in Analysis, Volume
COMPLEX ANALYSIS Ibookroot October 20, 2007 Princeton Lectures in Analysis I Fourier Analysis: An Introduction II Complex Analysis III Real Analysis: Measure Theory, Integration, and Hilbert Spaces Princeton Lectures in Analysis II COMPLEX ANALYSIS Elias M. Stein & Rami Shakarchi PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright © 2003 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Control Number 2005274996 ISBN 978-0-691-11385-2 British Library Cataloging-in-Publication Data is available The publisher would like to acknowledge the authors of this volume for providing the camera-ready copy from which this book was printed Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 5 7 9 10 8 6 To my grandchildren Carolyn, Alison, Jason E.M.S. To my parents Mohamed & Mireille and my brother Karim R.S. Foreword Beginning in the spring of 2000, a series of four one-semester courses were taught at Princeton University whose purpose was to present, in an integrated manner, the core areas of analysis. The objective was to make plain the organic unity that exists between the various parts of the subject, and to illustrate the wide applicability of ideas of analysis to other fields of mathematics and science. The present series of books is an elaboration of the lectures that were given. While there are a number of excellent texts dealing with individual parts of what we cover, our exposition aims at a different goal: pre- senting the various sub-areas of analysis not as separate disciplines, but rather as highly interconnected.