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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. -
Möbius Bridges
{ Final version for JMA - Nov 2, 2017 } Möbius Bridges Carlo H. Séquin CS Division, University of California, Berkeley E-mail: [email protected] Abstract Key concepts and geometrical constraints are discussed that allow the construction of a usable bridge that is topological equivalent to a Möbius band. A multi-year search in publications and on the internet for real-world bridges that meet these requirements has not identified a single clean construction that warrants the designation “Möbius bridge,” but a few promising designs can be found. Several simple but practical designs are presented here. 1. Introduction July 2017 marks the twentieth installment of the annual Bridges conference [1], which elucidates the connections between mathematics and art, music, architecture, and many other cultural venues. This year the conference has been held in Waterloo, Canada. In its twenty-year history it has visited many places around the globe, including Seoul in South Korea, Coimbra in Portugal, Pécz in Hungary, and Leeuwarden in the Netherlands, the hometown of M.C. Escher. This conference series got started by Reza Sarhangi [2] at Southwestern College in Winfield, Kansas. After a few occurrences at this initial location, Reza Sarhangi and other core members of this conference started discussing the possibility of establishing some kind of a commemorative entity of the conference on the Winfield campus. Since Escher, Möbius, and Klein are among the heroes of this Math-Art community, suggestions included an Escher Garden, a Möbius Bridge, or a Klein Bottle House. This prompted me to study the feasibility of such entities; and over the following year, I developed some practical designs for bridges and buildings that follow the geometry of a Möbius band [3]. -
Bridges: a World Community for Mathematical Art
Accepted manuscript for The Mathematical Intelligencer, ISSN: 0343-6993 (print version) ISSN: 1866-7414 (electronic version) The final publication is available at Springer via http://link.springer.com/article/10.1007/s00283-016-9630-9 DOI 10.1007/s00283-016-9630-9 Bridges: A World Community for Mathematical Art Kristóf Fenyvesi Mathematical Art Reborn: Academic Gathering or Festival of the Arts? This is not the first time the Mathematical Communities column has featured the Bridges Organization: the 2005 conference1, in the breathtaking Canadian Rocky Mountains at Banff, was described in these pages by Doris Schattschneider [Schattschneider, 2006], a regular Bridges participant and Escher-specialist. The 2005 conference saw the debut of Delicious Rivers, Ellen Maddow’s play on the life of Robert Ammann, a postal worker who discovered a number of aperiodic tilings.2 Marjorie Senechal, The Mathematical Intelligencer’s current editor-in-chief, served as Maddow's consultant.3 A theatre premiér at a conference on mathematics? A production performed by mathematicians, moonlighting as actors? But this is Bridges. A quick look at the 2005 conference relays the “essence” of this scientific and artistic “happening” resembling a first-rate festival of the arts. True to its title, Renaissance Banff, the 2005 Bridges gave all members of its community, whether based in the sciences or the arts, the feeling that they had helped bring about a genuine rebirth. I use “community” in its most complete sense—including adults, children, artists, university professors, art lovers and local people—for the wealth of conference activities could only be accomplished through the participation of each and every individual present. -
Science • Art • Technology
SCIENCE • ART • TECHNOLOGY 24 JULY THROUGH 10 AUGUST 2008 < Rinus Roelofs, PROGRAMME OF EVENTS new design for artwork consisting of a single 24 JULY – 10 AUGUST, 2008 continuous surface! (Location: Boer) BRIDGES, an annual conference founded in 1998 and serving since then 4 metres long, 2.5 metres high, as an international platform for artists, scientists and scholars working on corten steel the interface of science, art and technology will be held this year in Leeuwarden, The Netherlands from 24 - 29 July 2008. The approximately 200 visitors to the conference from 25 different countries will be coming to Leeuwarden to participate in a broad program of mathematical connections in art, music, architecture and science. Associated with the conference is a highly varied programme Gerard Caris > Polyhedral Net of cultural activities open to the general public that will run through Structure # 1, 10 August 2008. During the Open Day held on 29 July 2008, you can 160 x 95 x 95 cm become acquainted with a number of scientists and artists whilst young and old can participate in various workshops on Grote Kerkstraat in Exhibitions in churches Leeuwarden. The winners of the Gateways to Fryslân Competition will be announced during the conference. The artists exhibiting their work have come from abstract mathematical backgrounds to create many different visual products. Some artists, such as Gerard Caris (1925), limit their oeuvre to a single theme. In his case, this is the pentagon. In the village of Zweins, this artist will be showing a selection of his work including his ‘Polyhedral Net Structure # 1’. -
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. -
Report on Bridges 2016—In Memory of Our Founder, Reza Sarhangi (1952–2016)
COMMUNICATION Report on Bridges 2016—In Memory of Our Founder, Reza Sarhangi (1952–2016) Carlo H. Séquin For the last decade, the international Bridges conference has showcased mathematical connections in art, ar- chitecture, music, and many other cultural domains. It regularly attracts a few hundred participants—artists, mathematicians, computer scientists, teachers, etc.—from dozens of coun- tries. Sample Annual Bridges Conference Sites 2014 Seoul, South Korea 2011 Coimbra, Portugal 2010 Pécs, Hungary 2009 Banff, Canada 2008 Leeuwarden, Netherlands 2006 London, United Kingdom 2003 Granada, Spain Founder Reza Sarhangi at the CrossBorderScience 2012 Conference in Kaposvár. (The photo was first published in an article by Dirk This year the annual Bridges conference Huylebrouck, “Is mathematics ‘halal’?” in the Dutch popular science was held at the beautiful University of magazine Eos, www.kennislink.nl/publicaties/is-wiskunde-halal.) Jyväskylä in Finland. The conference comprised four days of talks and in- teractions plus an optional excursion day. The formal, refereed part of the conference entailed ten plenary pre- sentations, forty regular papers, six- ty-one short papers, and seventeen “hands-on” workshops. There was also a curated art exhibition, a festi- val of short mathematical movies, a session of mathematical poetry, and an informal theatre event performed by conference participants. More- Carlo H. Séquin is a professor in the grad- uate school, EECS Computer Science, UC Berkeley. His e-mail address is sequin@ berkeley.edu. For permission to reprint this article, please Henry Segerman and his Prizewinner Judy Holdener contact: 4π camera. discussing “Immersion.” [email protected]. DOI: http://dx.doi.org/10.1090/noti1471 152 NOTICES OF THE AMS VOLUME 64, NUMBER 2 COMMUNICATION about the role of this college in the the front, from one side, and from hills above Asheville, North Caro- the bottom with two suitably placed lina, promoting a spirit and interac- mirrors. -
University of Rochester Program on The
PROCEEDINGS OF SPIE SPIEDigitalLibrary.org/conference-proceedings-of-spie Development of multidisciplinary nanotechnology undergraduate education program at the University of Rochester Integrated Svetlana G. Lukishova Nicholas P. Bigelow Paul D. D'Alessandris Downloaded From: https://www.spiedigitallibrary.org/conference-proceedings-of-spie on 9/7/2017 Terms of Use: https://spiedigitallibrary.spie.org/ss/TermsOfUse.aspx Development of multidisciplinary nanotechnology undergraduate education program at the University of Rochester Integrated Nanosystems Center Svetlana G. Lukishovaa*, Nicholas P. Bigelowa,b, Paul D. D’Alessandrisc aThe Institute of Optics, University of Rochester, Rochester NY, USA bDepartment of Physics and Astronomy, University of Rochester, Rochester NY, USA cMonroe Community College, Rochester NY, USA *E-mail: [email protected] ABSTRACT Supported by the U.S. National Science Foundation educational grant, a coherent educational program at the University of Rochester (UR) in nanoscience and nanoengineering, based on the Institute of Optics and Intergrated Nanosystems Center resources was created. The main achievements of this program are (1) developing curriculum and offering the Certificate for Nanoscience and Nanoengineering program (15 students were awarded the Certificate and approximately 10 other students are working in this direction), (2) creating a reproducible model of collaboration in nanotechnology between a university with state-of-the-art, expensive experimental facilities, and a nearby, two-year community college (CC) with participation of a local Monroe Community College (MCC). 52 MCC students carried out two labs at the UR on the atomic force microscopy and a photolithography at a clean room; (3) developing reproducible hand-on experiments on nanophotonics (“mini-labs”), learning materials and pedagogical methods to educate students with diverse backgrounds, including freshmen and non-STEM-major CC students. -
Current Practices in Quantitative Literacy © 2006 by the Mathematical Association of America (Incorporated)
Current Practices in Quantitative Literacy © 2006 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2005937262 Print edition ISBN: 978-0-88385-180-7 Electronic edition ISBN: 978-0-88385-978-0 Printed in the United States of America Current Printing (last digit): 10 9 8 7 6 5 4 3 2 1 Current Practices in Quantitative Literacy edited by Rick Gillman Valparaiso University Published and Distributed by The Mathematical Association of America The MAA Notes Series, started in 1982, addresses a broad range of topics and themes of interest to all who are in- volved with undergraduate mathematics. The volumes in this series are readable, informative, and useful, and help the mathematical community keep up with developments of importance to mathematics. Council on Publications Roger Nelsen, Chair Notes Editorial Board Sr. Barbara E. Reynolds, Editor Stephen B Maurer, Editor-Elect Paul E. Fishback, Associate Editor Jack Bookman Annalisa Crannell Rosalie Dance William E. Fenton Michael K. May Mark Parker Susan F. Pustejovsky Sharon C. Ross David J. Sprows Andrius Tamulis MAA Notes 14. Mathematical Writing, by Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts. 16. Using Writing to Teach Mathematics, Andrew Sterrett, Editor. 17. Priming the Calculus Pump: Innovations and Resources, Committee on Calculus Reform and the First Two Years, a subcomit- tee of the Committee on the Undergraduate Program in Mathematics, Thomas W. Tucker, Editor. 18. Models for Undergraduate Research in Mathematics, Lester Senechal, Editor. 19. Visualization in Teaching and Learning Mathematics, Committee on Computers in Mathematics Education, Steve Cunningham and Walter S. -
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 West Math Collection
Anaheim Meetings Oanuary 9 -13) - Page 15 Notices of the American Mathematical Society January 1985, Issue 239 Volume 32, Number 1, Pages 1-144 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to the press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society. Abstracts must be accompanied by the Sl5 processing charge. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence. Rhode Island. on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcements and the list of organizers of special sessions. -
Mathematical Sciences Employment Register
Program for the Annual Meeting in Cincinnati begins on page 20 Notices of the American Mathematical Society January 1982, Issue 215 Volume 29, Number 1, Pages 1-128 Providence, Rhode Island USA ISSN 0002-9920 CALENDAR OF AMS MEETINGS THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet· ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions.