April 1997 Council Minutes
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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. -
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. -
Landon T. Clay Professor of Mathematics And
ARTHUR JAFFE WEB SITE: WWW.ARTHURJAFFE.NET Current Activities: Landon T. Clay Professor of Mathematics and Theoretical Science, Harvard University Chair of the Board, Dublin Institute for Advanced Study, School of Theoretical Physics Member of the Council, Dublin Institute for Advanced Study Member U.S. National Committee for Mathematics Member Science Board, Santa Fe Institute Member of the International Advisory Board, Center for Mathematical Physics, Hamburg Member of the Advisory Board, Pennsylvania State University Department of Mathematics Member Board of Directors, Jacobs University Bremen, Foundation of America Member Board of Directors, Institute for Schools of the Future Communication in Mathematical Physics, Advisory Board Reviews in Mathematical Physics, Associate Editor Letters in Mathematical Physics, Editorial Board Education: AB in Chemistry, Princeton University 1959 BA in Mathematics, Cambridge University 1961 PhD in Physics, Princeton University 1966 Memberships, Etc: Honorary Member of the Royal Irish Academy Member US National Academy of Sciences Fellow American Academy of Arts and Sciences Fellow American Association for the Advancement of Science Fellow of the Society of Industrial and Applied Mathematicians Fellow American Physical Society Medal from the Collège de France Dannie Heineman Prize in Mathematical Physics (APS and AIP) Prize in Mathematics and Physics (New York Academy of Science) Some Prior Activities: Co-Founder, Member, Director, and President: The Clay Mathematics Institute, 1998–2002 President, -
Stochastic PDE, Reflection Positivity, and Quantum Fields Arxiv
Stochastic PDE, Reflection Positivity, and Quantum Fields Arthur Jaffe Harvard University, Cambridge, MA 02138, USA arthur jaff[email protected] February 3, 2015 Abstract We investigate stochastic quantization as a method to go from a classical PDE (with stochastic time λ) to a corresponding quantum theory in the limit λ ! 1. We test the method for a linear PDE satisfied by the free scalar field. We begin by giving some background about the importance of establishing the property of reflection positivity for the limit λ ! 1. We then prove that the measure determined through stochastic quantization of the free scalar field violates reflection positivity (with respect to reflection of the physical time) for every λ < 1. If a non-linear perturbation of the linear equation is continuous in the perturbation parameter, the same result holds for small perturbations. For this reason, one needs to find a modified procedure for stochastic quantization, in order to use that method to obtain a quantum theory. Contents I Quantum Theory 2 arXiv:1411.2964v3 [math.PR] 2 Feb 2015 I.1 Quantization by SPDE . .2 I.2 The Measure dµλ(Φ) ...................................3 I.3 The Linear (Free-Field) Case . .4 I.4 The Measure dµλ(Φ) for the Free Field . .4 II Reflection Positivity 5 III The Main Result: dµλ(Φ) is Not Reflection Positive 7 III.1 The Case d = 1 .....................................8 III.1.1 A Numerical Check . 10 III.1.2 The Proof . 10 III.2 The Case 1 < d and λ, m2 < 1 ............................ 11 2 Arthur Jaffe I Quantum Theory Let x = (~x;t) 2 Rd denote a space-time point and denote time reflection by the map #x = (~x; −t), d 0 d and let R+ denote the subspace with 0 6 t. -
The 1999 Notices Index, Volume 46, Number 11
index.qxp 10/15/99 11:17 AM Page 1480 The 1999 Notices Index Index Section Page Number The AMS 1480 Meetings Information 1489 Announcements 1481 Memorial Articles 1490 Authors of Articles 1482 New Publications Offered by the AMS 1490 Reference and Book List 1420 Officers and Committee Members 1490 Deaths of Members of the Society 1483 Opinion 1490 Education 1484 Opportunities 1490 Feature Articles 1484 Prizes and Awards 1491 Forum 1485 Articles on the Profession 1492 Letters to the Editor 1486 Reviews 1492 Mathematicians 1487 Surveys 1493 Mathematics Articles 1489 Tables of Contents 1493 Mathematics History 1489 About the Cover, 26, 245, 318, 420, 534, 658, 781, 918, AMS Meeting in August 2000, 355 1073, 1208, 1367 AMS Menger Awards at the 1999 Intel-International Science and Engineering Fair, 912 Acknowledgment of Contributions, 947 AMS Officers and Committee Members, 1271 AMS Participates in Capitol Hill Exhibition, 918 The AMS AMS Participates in Faculty Preparation Program, 1072 1998 Election Results, 266 AMS Short Courses, 1171 1998 Report of the Committee on Meetings and Confer- AMS Standard Cover Sheet, 60, 270, 366, 698, 972, 1102, ences, 810 1282, 1428 1999 AMS Centennial Fellowships Awarded, 684 (The) Birth of an AMS Meeting, 1029 1999 AMS Election, 58, 267 Bylaws of the American Mathematical Society, 1252 1999 AMS-MAA-SIAM Morgan Prize, 469 Call for Proposals for 2001 Conferences, 1177, 1331 1999 Arnold Ross Lectures, 692 Conference Announced (Summer Mathematics Experience: 1999 Bôcher Prize, 463 A Working Conference on Summer -
Landon T. Clay Professor of Mathematics and Theoretical Science, Harvard University WEB SITE
ARTHUR JAFFE Landon T. Clay Professor of Mathematics and Theoretical Science, Harvard University WEB SITE: WWW.ARTHURJAFFE.NET University Education: AB in Chemistry, Princeton University 1959 BA in Mathematics, Cambridge University 1961 PhD in Physics, Princeton University 1966 Current Activities: Chairman of the Board, Dublin Institute for Advanced Study, School of Theoretical Physics Member of the Science Board, Santa Fe Institute Member of the Advisory Board, Communication in Mathematical Physics Member of the Editorial Board, Annals of Functional Analysis (AFA) Member of the International Advisory Board, Center for Mathematical Physics, Hamburg Member of the Board of Directors, Jacobs University Bremen Foundation of America Memberships/Recognition: Honorary Member of the Royal Irish Academy 2009 Member of the US National Academy of Sciences 2000 Member of the American Academy of Arts and Sciences 1978 Fellow of the American Mathematical Society Fellow of the American Association for the Advancement of Science Fellow of the Society of Industrial and Applied Mathematicians Fellow of the American Physical Society Medal from the Collège de France 1990 Dannie Heineman Prize in Mathematical Physics (APS and AIP) 1980 Prize in Mathematics and Physics (New York Academy of Science) 1979 Alfred P. Sloan Foundation Faculty Fellow John Simon Guggenheim Foundation Fellow (two appointments) National Research Council Post-doctoral Fellow National Science Foundation Pre-doctoral Fellow Marshall Scholar Some Prior Activities: Co-Founder, Member, Director, -
May 1998 Council Minutes
AMERICAN MATHEMATICAL SOCIETY COUNCIL MINUTES Detroit, Michigan 16 May 1998 Abstract The Council of the Society met at 7:00 PM on Saturday, 16 May 1998, at the Detroit Airport Marriott, Detroit Metropolitan Airport. These are minutes for the meeting. Several items were discussed in Executive Session and are reported in these open minutes 1 2 CONTENTS Contents IMINUTES 4 1CALLTOORDER. 4 1.1 Opening of the Meeting and Introductions. .................. 4 1.2 1997 Elections. ................................... 4 2 MINUTES. 5 2.1MinutesoftheJanuary98Council............................. 5 2.2MinutesofBusinessbyMail................................ 5 3 CONSENT AGENDA. 5 4 REPORTS OF BOARDS AND STANDING COMMITTEES. 5 4.1 Editorial Boards Committee (EBC). ......................... 5 4.1.1 Mathematical Reviews Editorial Committee. .................. 5 4.1.2 Bulletin Editorial Committee. ......................... 6 4.1.3 Transactions and Memoirs Editorial Committee. ........... 6 4.2 Nominating Committee. ......................... 6 4.2.1 VicePresident.................................... 6 4.2.2 MemberatLargeoftheCouncil.......................... 6 4.2.3 Trustee. ................................... 6 4.3 Executive Committee and Board of Trustees (ECBT). ........... 6 4.3.1 Dues......................................... 6 4.3.2 Recommendationsforappointmentofofficers................... 7 4.4 Committee on Education (COE). ......................... 7 4.5 Committee on the Profession (CPROF). ......................... 8 4.5.1 StatementonTenure............................... -
2008 Annual Report
Contents Clay Mathematics Institute 2008 Letter from the President James A. Carlson, President 2 Annual Meeting Clay Research Conference 3 Recognizing Achievement Clay Research Awards 6 Researchers, Workshops, Summary of 2008 Research Activities 8 & Conferences Profile Interview with Research Fellow Maryam Mirzakhani 11 Feature Articles A Tribute to Euler by William Dunham 14 The BBC Series The Story of Math by Marcus du Sautoy 18 Program Overview CMI Supported Conferences 20 CMI Workshops 23 Summer School Evolution Equations at the Swiss Federal Institute of Technology, Zürich 25 Publications Selected Articles by Research Fellows 29 Books & Videos 30 Activities 2009 Institute Calendar 32 2008 1 smooth variety. This is sufficient for many, but not all applications. For instance, it is still not known whether the dimension of the space of holomorphic q-forms is a birational invariant in characteristic p. In recent years there has been renewed progress on the problem by Hironaka, Villamayor and his collaborators, Wlodarczyck, Kawanoue-Matsuki, Teissier, and others. A workshop at the Clay Institute brought many of those involved together for four days in September to discuss recent developments. Participants were Dan Letter from the president Abramovich, Dale Cutkosky, Herwig Hauser, Heisuke James Carlson Hironaka, János Kollár, Tie Luo, James McKernan, Orlando Villamayor, and Jaroslaw Wlodarczyk. A superset of this group met later at RIMS in Kyoto at a Dear Friends of Mathematics, workshop organized by Shigefumi Mori. I would like to single out four activities of the Clay Mathematics Institute this past year that are of special Second was the CMI workshop organized by Rahul interest. -
ED347063.Pdf
DOCUMENT RESUME ED 347 063 SE 052 129 TITLE Renewing U.S. Mathematics: A Plan for the 1990s. INSTITUTION Nationaa Academy of Sciences- National Research Council, Washington, DC. Commission of Physical Sciences, Mathematics, and Applications. REPORT NO IS8N-0-309-0428-3 PUB DATE Apr 90 Cfw-RACT DMS-8821296 143p. AVAILABLE FPOM Nationaa Academy Press, 2101Constitution Avenue, NU, Washington, DC 20418 ($15.00United States; $18.00 overseas). PUB TYPE Reports - Descriptive (141)-- Reports - Evaluative/Feasibility (142) EDRS PRICE MF01 Plus Postage. PC Nat Available from EDRS. DESCRIPTOR.; 'College Mathematics; Educational Improvement; Educational Needs; Iducational Objectives; Excellence in Education; Federal Aid; Federal Programs; "Financial Support; Governnent Role; *Government School Relationship; Higher Education; 'Mathematics Education; National Programs; Postsecondary Education; Public Agencies; Public Policy; Public Support; Research Opportunities; "Research Utilization; Scientific Research IDENTIFIERS 'Research amd Graduate Training Facilities; Research Curriculum; Research Integration; Research Priorities ABSTRACT As requested by the National Science Foundation (NSF) and the Interagency committee for ExtranuraaMathematics Programs (ICEMAP), this report updates the 1984 Report knownas the "David Report." Specifically, the charge directedthe committee to (1) update that report, describing the infrascruccure andsupport for U.S. mathenatical sciences research; (2)assess trends and progress over the intervening five years against the recommendationsof the 1984 Report; (3) brieflyassess the field scientifically and identify significant opportunities for research, includingcross-disciplinary collaboration; and (4) make appropriate recoamendatiousdea4ned to ensure that U.S. mathematical sciences research will meet national needs in coming years. Of the severalComponents of the mathematical sciences community requiring action, its welispring--university research departments--is the primary focus of thisreport. -
Spring 2013 Fine Letters
Spring 2013, Issue 2 Department of Mathematics Princeton University Department Chair’s letter Nobel Prize for This was a great year, though one of major loved Department Manager of 25 an alumnus transition. Our department welcomed two years transitioned to Special Proj- outstanding young stars to the senior fac- ects Manager. We hired Kathy Lloyd Shapley *53, ulty; Sophie Morel who arrived in Septem- Applegate, our fourth Depart- won the 2012 Nobel Prize ber and Mihalis Dafermos *01 in January. ment Manager in almost 80 years. in economics for work he In addition Sucharit Sarkar *09, Vlad Vicol, As many of you know, Chairs in did in collaboration with and Alexander Sodin joined us as assistant our department come and go but another of our alumni, professors, Mihai Fulger, Niels Moller, it is the Department Manager David Gale *49. Both Oana Pocovnicu, and Bart Vandereycken who de facto represents the de- were graduate students in as instructors, and Stefanos Aretakis and partment to the outside world. the mathematics depart- Nicholas Sheridan as Veblen Research In- It’s clear that we made a terrific choice and ment at Princeton at a time when the field structors. the department is in excellent hands. of Game Theory was emerging and some of John Conway and Ed Nelson will retire at Josko Plazonic, our remarkable Systems its greatest names were here. the end of the academic year joining Bill Manager of 12 years, moved next door to Shapley, currently a professor Browder *58 and Eli Stein who became PICsciE. Our long time business manager emeritus of economics and emeritus last year. -
Max Dehn and the Origins of Topology and Infinite Group Theory
Max Dehn and the Origins of Topology and Infinite Group Theory David Peifer Abstract. This article provides a brief history of the life, work, and legacy of Max Dehn. The emphasis is put on Dehn’s papers from 1910 and 1911. Some of the main ideas from these papers are investigated, including Dehn surgery, the word problem, the conjugacy problem, the Dehn algorithm, and Dehn diagrams. A few examples are included to illustrate the impact that Dehn’s work has had on subsequent research in logic, topology, and geometric group theory. 1. INTRODUCTION. It is now one hundred years since Max Dehn published his papers On the Topology of Three-Dimensional Spaces (1910) [9] and On Infinite Dis- continuous Groups (1911) [10]. At that time, topology was in its infancy. Group theory was also new and the study of general infinite groups had only just begun. Dehn’s pa- pers mark the beginning of two closely related research areas: the study of 3-manifolds in topology, and the study of infinite groups given by presentations in algebra. In these papers, Dehn brought together important ideas from the late 1800’s concerning hyper- bolic geometry, group theory, and topology. These papers are beautifully written and exhibit Dehn’s gifted ability to use simple combinatorial diagrams to illustrate founda- tional connections between algebra and geometry. In the years since Dehn’s passing, mathematicians have gone back to these two papers again and again to draw motiva- tion and inspiration. This article is written as a celebration of these two papers and of Max Dehn’s influence on one hundred years of mathematics. -
2014 Annual Report
CLAY MATHEMATICS INSTITUTE www.claymath.org ANNUAL REPORT 2014 1 2 CMI ANNUAL REPORT 2014 CLAY MATHEMATICS INSTITUTE LETTER FROM THE PRESIDENT Nicholas Woodhouse, President 2 contents ANNUAL MEETING Clay Research Conference 3 The Schanuel Paradigm 3 Chinese Dragons and Mating Trees 4 Steenrod Squares and Symplectic Fixed Points 4 Higher Order Fourier Analysis and Applications 5 Clay Research Conference Workshops 6 Advances in Probability: Integrability, Universality and Beyond 6 Analytic Number Theory 7 Functional Transcendence around Ax–Schanuel 8 Symplectic Topology 9 RECOGNIZING ACHIEVEMENT Clay Research Award 10 Highlights of Peter Scholze’s contributions by Michael Rapoport 11 PROFILE Interview with Ivan Corwin, Clay Research Fellow 14 PROGRAM OVERVIEW Summary of 2014 Research Activities 16 Clay Research Fellows 17 CMI Workshops 18 Geometry and Fluids 18 Extremal and Probabilistic Combinatorics 19 CMI Summer School 20 Periods and Motives: Feynman Amplitudes in the 21st Century 20 LMS/CMI Research Schools 23 Automorphic Forms and Related Topics 23 An Invitation to Geometry and Topology via G2 24 Algebraic Lie Theory and Representation Theory 24 Bounded Gaps between Primes 25 Enhancement and Partnership 26 PUBLICATIONS Selected Articles by Research Fellows 29 Books 30 Digital Library 35 NOMINATIONS, PROPOSALS AND APPLICATIONS 36 ACTIVITIES 2015 Institute Calendar 38 1 ach year, the CMI appoints two or three Clay Research Fellows. All are recent PhDs, and Emost are selected as they complete their theses. Their fellowships provide a gener- ous stipend, research funds, and the freedom to carry on research for up to five years anywhere in the world and without the distraction of teaching and administrative duties.