Progress in Mathematics Volume 269
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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. -
The Weil Proof and the Geometry of the Adèles Class Space
The Weil Proof and the Geometry of the Adèles Class Space Alain Connes,1 Caterina Consani,2 and Matilde Marcolli3 1 Collège de France, 3, rue d’Ulm, Paris, F-75005 France [email protected] 2 Mathematics Department, Johns Hopkins University, Baltimore, MD 21218 USA [email protected] 3 Department of Mathematics, California Institute of Technology 1200 E California Blvd, Pasadena, CA 91101, USA [email protected] Dedicated to Yuri Manin on the occasion of his 70th birthday O simili o dissimili che sieno questi mondi non con minor raggione sarebe bene a l’uno l’essere che a l’altro Giordano Bruno – De l’infinito, universo e mondi Summary. This paper explores analogies between the Weil proof of the Riemann hypothesis for function fields and the geometry of the adèles class space, which is the noncommutative space underlying Connes’ spectral realization of the zeros of the Riemann zeta function. We consider the cyclic homology of the cokernel (in the abelian category of cyclic modules) of the “restriction map” defined by the inclu- sion of the idèles class group of a global field in the noncommutative adèles class space. Weil’s explicit formula can then be formulated as a Lefschetz trace formula for the induced action of the idèles class group on this cohomology. In this formu- lation the Riemann hypothesis becomes equivalent to the positivity of the relevant trace pairing. This result suggests a possible dictionary between the steps in the Weil proof and corresponding notions involving the noncommutative geometry of the adèles class space, with good working notions of correspondences, degree, and codegree etc. -
Caterina Consani – Curriculum Vitæ
3900 N. Charles St. 1303 Baltimore, MD 21218 USA T +1 410 599-4686 Caterina Consani H +39 348 0328694 B [email protected] Curriculum Vitæ Í www.math.jhu.edu/~kc Personal Data Name Caterina Surname Consani Place and date of birth Chiavari (Genoa) Italy, January 9, 1963 Nationality Italian Residence United States of America Languages English (fluent), French (fluent), Italian. Studies 1993-96 Ph.D in Mathematics Department of Mathematics, University of Chicago (USA) Research in: arithmetic geometry, algebraic number theory. Thesis title: “Double complexes and Euler L-factors on degenerations of algebraic varieties”. Thesis adviser: Prof. Spencer Bloch 1988-92 Dottorato di Ricerca in Matematica (Ph.D in Mathematics) Universities of Genoa and Turin, Italy. Research in: algebraic geometry and algebraic K-theory. Thesis title: “Teoria dell’ intersezione e K-teoria su varietà singolari”. Thesis adviser: Prof. Claudio Pedrini 1981-86 Laurea in Matematica (Bachelor Degree in Mathematics) Department of Mathematics, University of Genoa (Italy) Graduation Grade: 110/110 Summa cum Laude. University Curriculum 2008-today Full Professor (tenured) Department of Mathematics, The Johns Hopkins University (USA) 2005-08 Associate Professor (tenured) Department of Mathematics, The Johns Hopkins University (USA) 2003-05 Associate Professor (tenured) Department of Mathematics, University of Toronto (Canada) 2000-03 Assistant Professor (tenure track) Department of Mathematics, University of Toronto (Canada) 1999-2000 Researcher (Member of the) School of Mathematics, Institute of Advanced Study, Princeton (USA) 1998 Researcher Department of Mathematics & Newton Institute, Cambridge University (UK) 1996-99 Assistant Professor (C.L.E. Moore Instructor) Department of Mathematics, M.I.T. (USA). -
Algebra & Number Theory Vol. 7 (2013)
Algebra & Number Theory Volume 7 2013 No. 3 msp Algebra & Number Theory msp.org/ant EDITORS MANAGING EDITOR EDITORIAL BOARD CHAIR Bjorn Poonen David Eisenbud Massachusetts Institute of Technology University of California Cambridge, USA Berkeley, USA BOARD OF EDITORS Georgia Benkart University of Wisconsin, Madison, USA Susan Montgomery University of Southern California, USA Dave Benson University of Aberdeen, Scotland Shigefumi Mori RIMS, Kyoto University, Japan Richard E. Borcherds University of California, Berkeley, USA Raman Parimala Emory University, USA John H. Coates University of Cambridge, UK Jonathan Pila University of Oxford, UK J-L. Colliot-Thélène CNRS, Université Paris-Sud, France Victor Reiner University of Minnesota, USA Brian D. Conrad University of Michigan, USA Karl Rubin University of California, Irvine, USA Hélène Esnault Freie Universität Berlin, Germany Peter Sarnak Princeton University, USA Hubert Flenner Ruhr-Universität, Germany Joseph H. Silverman Brown University, USA Edward Frenkel University of California, Berkeley, USA Michael Singer North Carolina State University, USA Andrew Granville Université de Montréal, Canada Vasudevan Srinivas Tata Inst. of Fund. Research, India Joseph Gubeladze San Francisco State University, USA J. Toby Stafford University of Michigan, USA Ehud Hrushovski Hebrew University, Israel Bernd Sturmfels University of California, Berkeley, USA Craig Huneke University of Virginia, USA Richard Taylor Harvard University, USA Mikhail Kapranov Yale University, USA Ravi Vakil Stanford University, -
IMU Secretary An: [email protected]; CC: Betreff: IMU EC CL 05/07: Vote on ICMI Terms of Reference Change Datum: Mittwoch, 24
Appendix 10.1.1 Von: IMU Secretary An: [email protected]; CC: Betreff: IMU EC CL 05/07: vote on ICMI terms of reference change Datum: Mittwoch, 24. Januar 2007 11:42:40 Anlagen: To the IMU 2007-2010 Executive Committee Dear colleagues, We are currently experimenting with a groupware system that may help us organize the files that every EC member should know and improve the voting processes. Wolfgang Dalitz has checked the open source groupware systems and selected one that we want to try. It is more complicated than we thought and does have some deficiencies, but we see no freeware that is better. Here is our test run with a vote on a change of the ICMI terms of reference. To get to our voting system click on http://www.mathunion.org/ec-only/ To log in, you have to type your last name in the following version: ball, baouendi, deleon, groetschel, lovasz, ma, piene, procesi, vassiliev, viana Right now, everybody has the same password: pw123 You will immediately get to the summary page which contains an item "New Polls". The question to vote on is: Vote-070124: Change of ICMI terms of reference, #3, see Files->Voting->Vote- 070124 for full information and you are supposed to agree, disagree or abstain by clicking on the corresponding button. Full information about the contents of the vote is documented in the directory Voting (click on the +) where you will find a file Vote-070124.txt (click on the "txt icon" to see the contents of the file). The file is also enclosed below for your information. -
DMV Congress 2013 18Th ÖMG Congress and Annual DMV Meeting University of Innsbruck, September 23 – 27, 2013
ÖMG - DMV Congress 2013 18th ÖMG Congress and Annual DMV Meeting University of Innsbruck, September 23 – 27, 2013 Contents Welcome 13 Sponsors 15 General Information 17 Conference Location . 17 Conference Office . 17 Registration . 18 Technical Equipment of the Lecture Halls . 18 Internet Access during Conference . 18 Lunch and Dinner . 18 Coffee Breaks . 18 Local Transportation . 19 Information about the Congress Venue Innsbruck . 19 Information about the University of Innsbruck . 19 Maps of Campus Technik . 20 Conference Organization and Committees 23 Program Committee . 23 Local Organizing Committee . 23 Coordinators of Sections . 24 Organizers of Minisymposia . 25 Teachers’ Day . 26 Universities of the Applied Sciences Day . 26 Satellite Conference: 2nd Austrian Stochastics Day . 26 Students’ Conference . 26 Conference Opening 27 1 2 Contents Meetings and Public Program 29 General Assembly, ÖMG . 29 General Assembly, DMV . 29 Award Ceremony, Reception by Springer-Verlag . 29 Reception with Cédric Villani by France Focus . 29 Film Presentation . 30 Public Lecture . 30 Expositions . 30 Additional Program 31 Students’ Conference . 31 Teachers’ Day . 31 Universities of the Applied Sciences Day . 31 Satellite Conference: 2nd Austrian Stochastics Day . 31 Social Program 33 Evening Reception . 33 Conference Dinner . 33 Conference Excursion . 34 Further Excursions . 34 Program Overview 35 Detailed Program of Sections and Minisymposia 39 Monday, September 23, Afternoon Session . 40 Tuesday, September 24, Morning Session . 43 Tuesday, September 24, Afternoon Session . 46 Wednesday, September 25, Morning Session . 49 Thursday, September 26, Morning Session . 52 Thursday, September 26, Afternoon Session . 55 ABSTRACTS 59 Plenary Speakers 61 M. Beiglböck: Optimal Transport, Martingales, and Model-Independence 62 E. Hairer: Long-term control of oscillations in differential equations .. -
The Weil Proof and the Geometry of the Adeles Class Space
THE WEIL PROOF AND THE GEOMETRY OF THE ADELES CLASS SPACE ALAIN CONNES, CATERINA CONSANI, AND MATILDE MARCOLLI Dedicated to Yuri Manin on the occasion of his 70th birthday O simili o dissimili che sieno questi mondi non con minor raggione sarebe bene a l'uno l'essere che a l'altro Giordano Bruno { De l’infinito, universo e mondi Contents 1. Introduction 2 2. A look at the Weil proof 4 2.1. Correspondences and divisors 6 2.2. The explicit formula 8 2.3. Riemann{Roch and positivity 9 2.4. A tentative dictionary 11 3. Quantum statistical mechanics and arithmetic 12 3.1. The Bost{Connes endomotive 14 3.2. Scaling as Frobenius in characteristic zero 15 4. The adeles class space 16 4.1. Cyclic module 17 4.2. The restriction map 17 4.3. The Morita equivalence and cokernel for K = Q 19 4.4. The cokernel of ρ for general global fields 20 4.5. Trace pairing and vanishing 24 5. Primitive cohomology 25 6. A cohomological Lefschetz trace formula 27 6.1. Weil's explicit formula as a trace formula 27 6.2. Weil Positivity and the Riemann Hypothesis 28 7. Correspondences 29 7.1. The scaling correspondence as Frobenius 29 7.2. Fubini's theorem and the trivial correspondences 31 8. Thermodynamics and geometry of the primes 33 8.1. The global Morita equivalence 34 8.2. The valuation systems 36 8.3. The curve inside the adeles class space 39 8.4. The valuation systems for K = Q 40 1 2 CONNES, CONSANI, AND MARCOLLI 8.5. -
Programme & Information Brochure
Programme & Information 6th European Congress of Mathematics Kraków 2012 6ECM Programme Coordinator Witold Majdak Editors Agnieszka Bojanowska Wojciech Słomczyński Anna Valette Typestetting Leszek Pieniążek Cover Design Podpunkt Contents Welcome to the 6ECM! 5 Scientific Programme 7 Plenary and Invited Lectures 7 Special Lectures and Session 10 Friedrich Hirzebruch Memorial Session 10 Mini-symposia 11 Satellite Thematic Sessions 12 Panel Discussions 13 Poster Sessions 14 Schedule 15 Social events 21 Exhibitions 23 Books and Software Exhibition 23 Old Mathematical Manuscripts and Books 23 Art inspired by mathematics 23 Films 25 6ECM Specials 27 Wiadomości Matematyczne and Delta 27 Maths busking – Mathematics in the streets of Kraków 27 6ECM Medal 27 Coins commemorating Stefan Banach 28 6ECM T-shirt 28 Where to eat 29 Practical Information 31 6ECM Tourist Programme 33 Tours in Kraków 33 Excursions in Kraków’s vicinity 39 More Tourist Attractions 43 Old City 43 Museums 43 Parks and Mounds 45 6ECM Organisers 47 Maps & Plans 51 Honorary Patron President of Poland Bronisław Komorowski Honorary Committee Minister of Science and Higher Education Barbara Kudrycka Voivode of Małopolska Voivodship Jerzy Miller Marshal of Małopolska Voivodship Marek Sowa Mayor of Kraków Jacek Majchrowski WELCOME to the 6ECM! We feel very proud to host you in Poland’s oldest medieval university, in Kraków. It was in this city that the Polish Mathematical Society was estab- lished ninety-three years ago. And it was in this country, Poland, that the European Mathematical Society was established in 1991. Thank you very much for coming to Kraków. The European Congresses of Mathematics are quite different from spe- cialized scientific conferences or workshops. -
EMS Newsletter September 2012 1 EMS Agenda EMS Executive Committee EMS Agenda
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. Matemática, Faculdade Facultad de Matematicas de Ciências, Edifício C6, Universidad Complutense Piso 2 Campo Grande Mathematical de Madrid 1749-006 Lisboa, Portugal e-mail: [email protected] Plaza de Ciencias 3, 28040 Madrid, Spain Eva-Maria Feichtner e-mail: [email protected] (2012–2015) Society Department of Mathematics Lucia Di Vizio (2012–2016) Université de Versailles- University of Bremen St Quentin 28359 Bremen, Germany e-mail: [email protected] Laboratoire de Mathématiques Newsletter No. 85, September 2012 45 avenue des États-Unis Eva Miranda (2010–2013) 78035 Versailles cedex, France Departament de Matemàtica e-mail: [email protected] Aplicada I EMS Agenda .......................................................................................................................................................... 2 EPSEB, Edifici P Editorial – S. Jackowski ........................................................................................................................... 3 Associate Editors Universitat Politècnica de Catalunya Opening Ceremony of the 6ECM – M. -
Yuri Ivanovich Manin
Yuri Ivanovich Manin Academic career 1960 PhD, Steklov Mathematical Institute, Moscow, Russia 1963 Habilitation, Steklov Mathematical Institute, Moscow, Russia 1960 - 1993 Principal Researcher, Steklov Mathematical In- stitute, Russian Academy of Sciences, Moscow, Russia 1965 - 1992 Professor (Algebra Chair), University of Mos- cow, Russia 1992 - 1993 Professor, Massachusetts Institute of Technolo- gy, Cambridge, MA, USA 1993 - 2005 Scientific Member, Max Planck Institute for Ma- thematics, Bonn 1995 - 2005 Director, Max Planck Institute for Mathematics, Bonn 2002 - 2011 Board of Trustees Professor, Northwestern Uni- versity, Evanston, IL, USA Since 2005 Professor Emeritus, Max Planck Institute for Mathematics, Bonn Since 2011 Professor Emeritus, Northwestern University, Evanston, IL, USA Honours 1963 Moscow Mathematical Society Award 1967 Highest USSR National Prize (Lenin Prize) 1987 Brouwer Gold Medal 1994 Frederic Esser Nemmers Prize 1999 Rolf Schock Prize 1999 Doctor honoris causa, University of Paris VI (Universite´ Pierre et Marie Curie), Sorbonne, France 2002 King Faisal Prize for Mathematics 2002 Georg Cantor Medal of the German Mathematical Society 2002 Abel Bicentennial Doctor Phil. honoris causa, University of Oslo, Norway 2006 Doctor honoris causa, University of Warwick, England, UK 2007 Order Pour le Merite,´ Germany 2008 Great Cross of Merit with Star, Germany 2010 Janos´ Bolyai International Mathematical Prize 2011 Honorary Member, London Mathematical Society Invited Lectures 1966 International Congress of Mathematicians, Moscow, Russia 1970 International Congress of Mathematicians, Nice, France 1978 International Congress of Mathematicians, Helsinki, Finland 1986 International Congress of Mathematicians, Berkeley, CA, USA 1990 International Congress of Mathematicians, Kyoto, Japan 2006 International Congress of Mathematicians, special activity, Madrid, Spain Research profile Currently I work on several projects, new or continuing former ones. -
Asher Auel Curriculum Vitae
Asher Auel Curriculum Vitae Department of Mathematics Office: Kemeny 339 Dartmouth College Phone: (603) 646-3559 6188 Kemeny Hall asher.auel @ dartmouth.edu Hanover, NH 03755-3551 math.dartmouth.edu/∼auel/ Education 2009 University of Pennsylvania, Philadelphia, Pennsylvania Ph.D. Mathematics (Advisor Ted Chinburg) 2004 Universite´ Paris-Sud XI Orsay, Paris, France D.E.A. (Dipl^omed'Etudes´ Approfondies) Math´ematiquesPures (Advisor Guy Henniart) 2003 Reed College, Portland, Oregon A.B. Mathematics (Advisor Joe P. Buhler) Appointments 2019{ Dartmouth College, Hanover, New Hampshire Assistant Professor 2013{2019 Yale University, New Haven, Connecticut Gibbs Assistant Professor and Postdoctoral Associate 2012{2013 Courant Institute of Mathematical Sciences, New York University, New York NSF Postdoctoral Research Fellow (Sponsor Yuri Tschinkel) 2010{2011 Max Planck Institute for Mathematics, Bonn, Germany Postdoctoral Fellow/Guest 2009{2012 Emory University, Atlanta, Georgia NSF Postdoctoral Research Fellow (Sponsor R. Parimala) Grants 2020{2025 Simons Foundation Collaboration Grant for Mathematicians (PI) $42,000, Sep 2020{Aug 2025 2016{2018 NSA Young Investigator Grant (PI) $39,338, H98230-16-1-0321, Nov 2016{Dec 2018 2013{2015 NSA Young Investigator Grant (PI) $39,755, H98230-13-1-0291, Aug 2013{Aug 2015 2011 NSA Conference Grant (co-PI) $14,800, May 2011 2010{2011 NSF Conference Grant (co-PI) $24,295, May 2011 2009{2013 NSF Mathematical Sciences Postdoctoral Research Fellowship (PI) $135,000, DMS-0903039 Awards and Fellowships 2019 Walter and Constance Burke Research Initiation Award, Dartmouth College 2009 Carlitz-Zippin Thesis Prize, Mathematics Department, University of Pennsylvania 2008 School of Arts and Sciences Dissertation Completion Fellowship, University of Pennsylvania 2004{2008 Calabi Fellow, Mathematics Department, University of Pennsylvania 2003{2004 U.S. -
Birds and Frogs Equation
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Quadratic Diophantine Multiscale Principles of Equations Finite Harmonic of the American Mathematical Society T. Andreescu, University of Texas at Element Analysis February 2009 Volume 56, Number 2 Dallas, Richardson, TX, USA; D. Andrica, Methods A. Deitmar, University Cluj-Napoca, Romania Theory and University of This text treats the classical theory of Applications Tübingen, quadratic diophantine equations and Germany; guides readers through the last two Y. Efendiev, Texas S. Echterhoff, decades of computational techniques A & M University, University of and progress in the area. The presenta- College Station, Texas, USA; T. Y. Hou, Münster, Germany California Institute of Technology, tion features two basic methods to This gently-paced book includes a full Pasadena, CA, USA investigate and motivate the study of proof of Pontryagin Duality and the quadratic diophantine equations: the This text on the main concepts and Plancherel Theorem. The authors theories of continued fractions and recent advances in multiscale finite emphasize Banach algebras as the quadratic fields. It also discusses Pell’s element methods is written for a broad cleanest way to get many fundamental Birds and Frogs equation. audience. Each chapter contains a results in harmonic analysis. simple introduction, a description of page 212 2009. Approx. 250 p. 20 illus. (Springer proposed methods, and numerical 2009. Approx. 345 p. (Universitext) Monographs in Mathematics) Softcover examples of those methods. Softcover ISBN 978-0-387-35156-8 ISBN 978-0-387-85468-7 $49.95 approx. $59.95 2009. X, 234 p. (Surveys and Tutorials in The Strong Free Will the Applied Mathematical Sciences) Solving Softcover Theorem Introduction to Siegel the Pell Modular Forms and ISBN: 978-0-387-09495-3 $44.95 Equation page 226 Dirichlet Series Intro- M.