Curriculum Vitae List of Publications
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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 .. -
Noncommutative Geometry Models for Particle Physics and Cosmology, Lecture I
Noncommutative Geometry models for Particle Physics and Cosmology, Lecture I Matilde Marcolli Villa de Leyva school, July 2011 Matilde Marcolli NCG models for particles and cosmology, I Plan of lectures 1 Noncommutative geometry approach to elementary particle physics; Noncommutative Riemannian geometry; finite noncommutative geometries; moduli spaces; the finite geometry of the Standard Model 2 The product geometry; the spectral action functional and its asymptotic expansion; bosons and fermions; the Standard Model Lagrangian; renormalization group flow, geometric constraints and low energy limits 3 Parameters: relations at unification and running; running of the gravitational terms; the RGE flow with right handed neutrinos; cosmological timeline and the inflation epoch; effective gravitational and cosmological constants and models of inflation 4 The spectral action and the problem of cosmic topology; cosmic topology and the CMB; slow-roll inflation; Poisson summation formula and the nonperturbative spectral action; spherical and flat space forms Matilde Marcolli NCG models for particles and cosmology, I Geometrization of physics Kaluza-Klein theory: electromagnetism described by circle bundle over spacetime manifold, connection = EM potential; Yang{Mills gauge theories: bundle geometry over spacetime, connections = gauge potentials, sections = fermions; String theory: 6 extra dimensions (Calabi-Yau) over spacetime, strings vibrations = types of particles NCG models: extra dimensions are NC spaces, pure gravity on product space becomes gravity -
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. -
Lectures on Factorization Homology, ∞-Categories, and Topological
SPRINGER BRIEFS IN MATHEMATICAL PHYSICS 39 Hiro Lee Tanaka Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories Contributed by Araminta Amabel · Artem Kalmykov · Lukas Müller SpringerBriefs in Mathematical Physics Volume 39 Series Editors Nathanaël Berestycki, University of Vienna, Vienna, Austria Mihalis Dafermos, Mathematics Department, Princeton University, Princeton, NJ, USA Atsuo Kuniba, Institute of Physics, The University of Tokyo, Tokyo, Japan Matilde Marcolli, Department of Mathematics, University of Toronto, Toronto, Canada Bruno Nachtergaele, Department of Mathematics, Davis, CA, USA Hirosi Ooguri, Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA, USA SpringerBriefs are characterized in general by their size (50–125 pages) and fast production time (2–3 months compared to 6 months for a monograph). Briefs are available in print but are intended as a primarily electronic publication to be included in Springer’s e-book package. Typical works might include: • An extended survey of a field • A link between new research papers published in journal articles • A presentation of core concepts that doctoral students must understand in order to make independent contributions • Lecture notes making a specialist topic accessible for non-specialist readers. SpringerBriefs in Mathematical Physics showcase, in a compact format, topics of current relevance in the field of mathematical physics. Published titles will encompass all areas of theoretical and mathematical physics. -
LECTURE Series
University LECTURE Series Volume 52 Koszul Cohomology and Algebraic Geometry Marian Aprodu Jan Nagel American Mathematical Society http://dx.doi.org/10.1090/ulect/052 Koszul Cohomology and Algebraic Geometry University LECTURE Series Volume 52 Koszul Cohomology and Algebraic Geometry Marian Aprodu Jan Nagel M THE ATI A CA M L ΤΡΗΤΟΣ ΜΗ N ΕΙΣΙΤΩ S A O C C I I R E E T ΑΓΕΩΜΕ Y M A F O 8 U 88 NDED 1 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Jerry L. Bona NigelD.Higson Eric M. Friedlander (Chair) J. T. Stafford 2000 Mathematics Subject Classification. Primary 14H51, 14C20, 14H60, 14J28, 13D02, 16E05. For additional information and updates on this book, visit www.ams.org/bookpages/ulect-52 Library of Congress Cataloging-in-Publication Data Aprodu, Marian. Koszul cohomology and algebraic geometry / Marian Aprodu, Jan Nagel. p. cm. — (University lecture series ; v. 52) Includes bibliographical references and index. ISBN 978-0-8218-4964-4 (alk. paper) 1. Koszul algebras. 2. Geometry, Algebraic. 3. Homology theory. I. Nagel, Jan. II. Title. QA564.A63 2010 512.46—dc22 2009042378 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. -
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. -
Lectures on Arithmetic Noncommutative Geometry Matilde Marcolli
Lectures on Arithmetic Noncommutative Geometry Matilde Marcolli And indeed there will be time To wonder \Do I dare?" and, \Do I dare?" Time to turn back and descend the stair. ... Do I dare Disturb the Universe? ... For I have known them all already, known them all; Have known the evenings, mornings, afternoons, I have measured out my life with coffee spoons. ... I should have been a pair of ragged claws Scuttling across the floors of silent seas. ... No! I am not Prince Hamlet, nor was meant to be; Am an attendant lord, one that will do To swell a progress, start a scene or two ... At times, indeed, almost ridiculous{ Almost, at times, the Fool. ... We have lingered in the chambers of the sea By sea-girls wreathed with seaweed red and brown Till human voices wake us, and we drown. (T.S. Eliot, \The Love Song of J. Alfred Prufrock") Contents Chapter 1. Ouverture 5 1. The NCG dictionary 7 2. Noncommutative spaces 8 3. Spectral triples 9 Chapter 2. Noncommutative modular curves 17 1. Modular curves 17 2. The noncommutative boundary of modular curves 24 3. Modular interpretation: noncommutative elliptic curves 24 4. Limiting modular symbols 29 5. Hecke eigenforms 40 6. Selberg zeta function 43 7. The modular complex and K-theory of C∗-algebras 44 8. Intermezzo: Chaotic Cosmology 45 Chapter 3. Quantum statistical mechanics and Galois theory 53 1. Quantum Statistical Mechanics 54 2. The Bost{Connes system 58 3. Noncommutative Geometry and Hilbert's 12th problem 63 4. The GL2 system 65 5. Quadratic fields 72 Chapter 4.