Samit Dasgupta – Professor of Mathematics
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Contemporary Mathematics 358
! CONTEMPORARY MATHEMATICS 358 Stark/ s Conjectures: Recent Work and New Directions An International Conference on Stark's Conjectures and Related Topics August 5-9, 2002 Johns Hopkins University David Burns Cristian Popescu Jonathan Sands David Solomon Editors http://dx.doi.org/10.1090/conm/358 CoNTEMPORARY MATHEMATICS 358 Stark's Conjectures: Recent Work and New Directions An International Conference on Stark's Conjectures and Related Topics August 5-9, 2002 Johns Hopkins University David Burns Cristian Popescu Jonathan Sands David Solomon Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor Andreas Blass Andy R. Magid Michael Vogelius This volume contains articles based on talks given at the International Conference on Stark's Conjectures and Related Topics, held August 5-9, 2002, at Johns Hopkins University, Baltimore, Maryland. 2000 Mathematics Subject Classification. Primary 11G40, 11R23, 11R27, 11R29, 11R33, 11R42, 11840, 11 Y 40. Library of Congress Cataloging-in-Publication Data International Conference on Stark's Conjectures and Related Topics (2002 : Johns Hopkins Uni- versity) Stark's conjectures : recent work and new directions : an international conference on Stark's conjectures and related topics, August 5-9, 2002, Johns Hopkins University / David Burns ... [et a!.], editors. p. em. -(Contemporary mathematics, ISSN 0271-4132; 358) Includes bibliographical references. ISBN 0-8218-3480-0 (soft : acid-free paper) 1. Stark's conjectures-Congresses. I. Burns, David, 1963- II. Title. III. Contemporary mathematics (American Mathematical Society) ; v. 358. QA246 .!58 2002 512.7'4-dc22 2004049692 Copying and reprinting. Material in this book may be reproduced by any means for edu- cational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledg- ment of the source is given. -
The Legacy of Leonhard Euler: a Tricentennial Tribute (419 Pages)
P698.TP.indd 1 9/8/09 5:23:37 PM This page intentionally left blank Lokenath Debnath The University of Texas-Pan American, USA Imperial College Press ICP P698.TP.indd 2 9/8/09 5:23:39 PM Published by Imperial College Press 57 Shelton Street Covent Garden London WC2H 9HE Distributed by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. THE LEGACY OF LEONHARD EULER A Tricentennial Tribute Copyright © 2010 by Imperial College Press All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-1-84816-525-0 ISBN-10 1-84816-525-0 Printed in Singapore. LaiFun - The Legacy of Leonhard.pmd 1 9/4/2009, 3:04 PM September 4, 2009 14:33 World Scientific Book - 9in x 6in LegacyLeonhard Leonhard Euler (1707–1783) ii September 4, 2009 14:33 World Scientific Book - 9in x 6in LegacyLeonhard To my wife Sadhana, grandson Kirin,and granddaughter Princess Maya, with love and affection. -
Benedict Gross Harvard University, Professor
THE ALBERT LEON WHITEMAN MEMORIAL MATHEMATICS LECTURES February 22 and 23, 2016 Benedict Gross Harvard University, Professor Benedict Gross is the George Vasmer Leverett Professor of Mathematics at Harvard University and the former Dean of Harvard College. He is very well known for his research in number theory. His many honors and awards include his election as a Fellow of the American Academy of Arts and Sciences, Membership of the National Academy of Sciences and a Fellow of the American Mathematical Society. He received a MacArthur Fellowship and the Cole Prize in number theory from the AMS. How large is n! = n(n-1)(n-2)…3.2.1 ? Monday, February 22, 2016 Andrus Gerontology Center Time: 4:00-4:30 pm: Reception in Gerontology Courtyard Time: 4:30 pm: LECTURE - Gerontology: Leonard Davis Auditorium located in 124 Short abstract: The number n! (pronounced "n factorial") occurs in many counting problems. For example, that 52! is the number of ways to shuffle a deck of cards. This number grows very rapidly with n, and mathematicians of the 17th century used the new methods of calculus to estimate it. After reviewing some of this work, I'll discuss Euler's Gamma function, which interpolates the function F(n) = (n-1)! to the real numbers, as well as a more recent analog. The rank of elliptic curves Tuesday, February 23, 2016 3:00-3:30 pm: Reception in Kaprielian Hall 410 3:30-4:30 pm: LECTURE in Kaprielian Hall 414 Abstract: Elliptic curves, which are given by cubic equations in two variables, have been a central object of study in number theory since the time of Fermat. -
OF the AMERICAN MATHEMATICAL SOCIETY 157 Notices February 2019 of the American Mathematical Society
ISSN 0002-9920 (print) ISSN 1088-9477 (online) Notices ofof the American MathematicalMathematical Society February 2019 Volume 66, Number 2 THE NEXT INTRODUCING GENERATION FUND Photo by Steve Schneider/JMM Steve Photo by The Next Generation Fund is a new endowment at the AMS that exclusively supports programs for doctoral and postdoctoral scholars. It will assist rising mathematicians each year at modest but impactful levels, with funding for travel grants, collaboration support, mentoring, and more. Want to learn more? Visit www.ams.org/nextgen THANK YOU AMS Development Offi ce 401.455.4111 [email protected] A WORD FROM... Robin Wilson, Notices Associate Editor In this issue of the Notices, we reflect on the sacrifices and accomplishments made by generations of African Americans to the mathematical sciences. This year marks the 100th birthday of David Blackwell, who was born in Illinois in 1919 and went on to become the first Black professor at the University of California at Berkeley and one of America’s greatest statisticians. Six years after Blackwell was born, in 1925, Frank Elbert Cox was to become the first Black mathematician when he earned his PhD from Cornell University, and eighteen years later, in 1943, Euphemia Lofton Haynes would become the first Black woman to earn a mathematics PhD. By the late 1960s, there were close to 70 Black men and women with PhDs in mathematics. However, this first generation of Black mathematicians was forced to overcome many obstacles. As a Black researcher in America, segregation in the South and de facto segregation elsewhere provided little access to research universities and made it difficult to even participate in professional societies. -
UNIVERSITY of CALIFORNIA, SAN DIEGO the Brauer-Siegel Theorem for Fields of Bounded Relative Degree a Dissertation Submitted In
UNIVERSITY OF CALIFORNIA, SAN DIEGO The Brauer-Siegel Theorem for Fields of Bounded Relative Degree A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Aaron Wong Committee in charge: Professor Harold Stark, Chair Professor Charles Elkan Professor Ronald Evans Professor Benjamin Grinstein Professor Audrey Terras 2007 Copyright Aaron Wong, 2007 All rights reserved. The dissertation of Aaron Wong is approved, and it is acceptable in quality and form for publication on microfilm: Chair University of California, San Diego 2007 iii To my family and my friends. He named it Ebenezer, saying, “Thus far has the LORD helped us.” – 1 Samuel 7:12 iv TABLE OF CONTENTS Signature Page . iii Dedication . iv Table of Contents . v List of Figures . vii List of Tables . viii Acknowledgements . ix Abstract of the Dissertation . xi 1 Preliminaries . 1 1.1 Algebraic Theory . 1 1.1.1 An Example . 1 1.1.2 Field Basics . 3 1.1.3 Algebraic Integers and Unique Factorization . 4 1.1.4 Field Invariants . 8 1.1.5 Extensions of Number Fields . 10 1.1.6 CM Fields . 10 1.2 Analytic Theory . 11 1.2.1 The Riemann Zeta Function . 11 1.2.2 Dedekind Zeta Functions . 13 1.2.3 Dirichlet L-Functions . 14 1.2.4 Artin L-Functions . 18 1.3 Brauer’s Theorem . 20 1.4 The Brauer-Siegel Theorem . 21 1.4.1 The Original Theorem . 21 1.4.2 Some Effective Cases of the Theorem . 21 1.4.3 Fields of Bounded Relative Degree . -
Henri Darmon
Henri Darmon Address: Dept of Math, McGill University, Burnside Hall, Montreal, PQ. E-mail: [email protected] Web Page: http://www.math.mcgill.ca/darmon Telephone: Work (514) 398-2263 Home: (514) 481-0174 Born: Oct. 22, 1965, in Paris, France. Citizenship: Canadian, French, and Swiss. Education: 1987. B.Sc. Mathematics and Computer Science, McGill University. 1991. Ph.D. Mathematics, Harvard University. Thesis: Refined class number formulas for derivatives of L-series. University Positions: 1991-1994. Princeton University, Instructor. 1994-1996. Princeton University, Assistant Professor. 1994-1997. McGill University, Assistant Professor. 1997-2000. McGill University, Associate Professor. 2000- . McGill University, Professor. 2005-2019. James McGill Professor, McGill University. Other positions: 1991-1994. Cercheur hors Qu´ebec, CICMA. 1994- . Chercheur Universitaire, CICMA. 1998- . Director, CICMA (Centre Interuniversitaire en Calcul Math´ematique Alg´ebrique). 1999- . Member, CRM (Centre de Recherches Math´ematiques). 2005-2014. External member, European network in Arithmetic Geometry. Visiting Positions: 1991. IHES, Paris. 1995. Universit´a di Pavia. 1996. Visiting member, MSRI, Berkeley. 1996. Visiting professor and guest lecturer, University of Barcelona. 1997. Visiting Professor, Universit´e Paris VI (Jussieu). 1997. Visitor, Institut Henri Poincar´e. 1998. Visiting Professor and NachDiplom lecturer, ETH, Zuric¨ h. 1999. Visiting professor, Universit`a di Pavia. 2001. Visiting professor, Universit`a di Padova. 2001. Korea Institute for Advanced Study. 2002. Visiting professor, RIMS and Saga University (Japan). 1 2003. Visiting Professor, Universit´e Paris VI, Paris. 2003. Visiting professor, Princeton University. 2004. Visiting Professor, Universit´e Paris VI, Paris. 2006. Visiting Professor, CRM, Barcelona, Spain. 2008. Visiting Professor, Universit´e Paris-Sud (Orsay). -
Introduction to the Tate Issue
BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 54, Number 4, October 2017, Pages 541–543 http://dx.doi.org/10.1090/bull/1585 Article electronically published on July 10, 2017 INTRODUCTION TO THE TATE ISSUE SUSAN FRIEDLANDER Last year the AMS published the Collected Works of John Tate1 whose bril- liant mathematics revolutionized areas of number theory, algebraic geometry, and algebra. His scientific accomplishments place him among the most significant math- ematicians of the 20th century. This issue of the Bulletin of the American Mathe- matical Society celebrates John Tate and the publication of his collected works. For over more than six decades, Tate’s work has been recognized by many awards and distinctions including the Abel prize in 2010 “for his vast and lasting impact on the theory of numbers and the wealth of essential mathematical ideas and constructions that he initiated”. The articles in this issue of the Bulletin illustrate some of these ideas and give a historical overview of Tate’s prolific collaboration with Jean Pierre Serre. The influence of Tate’s work was spread not only through his groundbreaking publications but also through his many PhD students, mainly during his professor- ship at Harvard from 1954 to 1990 after which he became the Sid W. Richardson Chair in Mathematics at the University of Texas in Austin. These mathematicians are listed in Table 1. Table 1. List of former students2 Edward Assmus, Jr. Harvard University 1958 Leonard Evens Harvard University 1960 James Cohn Harvard University 1961 Andrew Ogg Harvard University 1961 Stephen Shatz Harvard University 1962 Jonathan Lubin Harvard University 1963 Saul Lubkin Harvard University 1963 Judith Obermayer Harvard University 1963 Stephen Lichtenbaum Harvard University 1964 J. -
Vitae Ken Ono Citizenship
Vitae Ken Ono Citizenship: USA Date of Birth: March 20,1968 Place of Birth: Philadelphia, Pennsylvania Education: • Ph.D., Pure Mathematics, University of California at Los Angeles, March 1993 Thesis Title: Congruences on the Fourier coefficients of modular forms on Γ0(N) with number theoretic applications • M.A., Pure Mathematics, University of California at Los Angeles, March 1990 • B.A., Pure Mathematics, University of Chicago, June 1989 Research Interests: • Automorphic and Modular Forms • Algebraic Number Theory • Theory of Partitions with applications to Representation Theory • Elliptic curves • Combinatorics Publications: 1. Shimura sums related to quadratic imaginary fields Proceedings of the Japan Academy of Sciences, 70 (A), No. 5, 1994, pages 146-151. 2. Congruences on the Fourier coefficeints of modular forms on Γ0(N), Contemporary Mathematics 166, 1994, pages 93-105., The Rademacher Legacy to Mathe- matics. 3. On the positivity of the number of partitions that are t-cores, Acta Arithmetica 66, No. 3, 1994, pages 221-228. 4. Superlacunary cusp forms, (Co-author: Sinai Robins), Proceedings of the American Mathematical Society 123, No. 4, 1995, pages 1021-1029. 5. Parity of the partition function, 1 2 Electronic Research Annoucements of the American Mathematical Society, 1, No. 1, 1995, pages 35-42 6. On the representation of integers as sums of triangular numbers Aequationes Mathematica (Co-authors: Sinai Robins and Patrick Wahl) 50, 1995, pages 73-94. 7. A note on the number of t-core partitions The Rocky Mountain Journal of Mathematics 25, 3, 1995, pages 1165-1169. 8. A note on the Shimura correspondence and the Ramanujan τ(n)-function, Utilitas Mathematica 47, 1995, pages 153-160. -
Spring 2015 — Volume 21, No 1 — Le Centre De Recherches Mathématiques
C CENTRE R DE RECHERCHES Le Bulletin M MATHÉMATIQUES Printemps/Spring 2015 — Volume 21, No 1 — Le Centre de recherches mathématiques A conversation with Marco Bertola (Concordia), Robert Bran- type IIb string theory on AdS 5, and N = 4 Super Yang–Mills denberger (McGill), John Harnad (Concordia) and Johannes theory. Walcher (McGill) on December 8, 2014. Integrability, which is our third theme, has also been play- ing a role in mathematical investigations of string theory Bulletin: Can you elaborate on the theme of the semester? for a long time: its role in the AdS/CFT correspondence J. Walcher [JW]: Our semester has a 3-pronged theme: it’s emerged around 2004, and has been playing an increasing called AdS/CFT, holography and integrability, and I’ll start role in the quantitative development of the correspondence. trying to explain what AdS/CFT is. AdS/CFT stands for That is what our semester is about: it’s the intersection of the Anti–de Sitter/Conformal Field Theory correspondence. It AdS/CFT correspondence as a holographic duality, and inte- was the last of the major dualities discovered in the wake of grable methods as far as they are relevant to the AdS/CFT the second super string revolution of the mid-1990s, and it correspondence. plays a rather special role in the web of dualities. First of all it’s not a duality between two different string theories or two I will let Robert take it from here. different field theories, but rather it involves an equivalence RB: I will start from the physicist’s point of view, and in par- between, on the one side, a theory of quantum gravity, string ticular from the point of view of someone interested in gravity theory, and on the other side a more standard, although very and cosmology. -
Beckenbach Book Prize
MATHEMATICAL ASSOCIATION OF AMERICA MATHEMATICAL ASSOCIATION OF AMERICA BECKENBACH BOOK PRIZE HE BECKENBACH BOOK PRIZE, established in 1986, is the successor to the MAA Book Prize established in 1982. It is named for the late Edwin T Beckenbach, a long-time leader in the publications program of the Association and a well-known professor of mathematics at the University of California at Los Angeles. The prize is intended to recognize the author(s) of a distinguished, innovative book published by the MAA and to encourage the writing of such books. The award is not given on a regularly scheduled basis. To be considered for the Beckenbach Prize a book must have been published during the five years preceding the award. CITATION Nathan Carter Bentley University Introduction to the Mathematics of Computer Graphics, Mathematical Associa- tion of America (2016) The Oxford logician Charles Dodgson via his famed Alice character rhetorically asked, “Of what use is a book without pictures?” And most of us believe that a picture is worth a thousand words. In the same spirit, Nathan Carter in his Introduction to the Mathematics of Computer Graphics has given us a how-to book for creating stunning, informative, and insightful imagery. In an inviting and readable style, Carter leads us through a cornucopia of mathematical tricks and structure, illustrating them step-by-step with the freeware POV-Ray—an acronym for Persistence of Vision Raytracer. Each section of his book starts with a natural question: Why is this fun? Of course, the answer is a striking image or two—to which a reader’s impulsive response is, How might I do that? Whereupon, Carter proceeds to demonstrate. -
Report for the Academic Year 2016–2017
Institute for Advanced Study Re port for 2 0 1 6–2 0 1 7 INSTITUTE FOR ADVANCED STUDY EINSTEIN DRIVE Report for the Academic Year PRINCETON, NEW JERSEY 08540 (609) 734-8000 www.ias.edu 2016–2017 Cover: The School of Mathematics’s inaugural Summer Collaborators program invited to the Institute campus small groups of mathematicians to further their collaborative research projects. Opposite: A view of the allée leading from Fuld Hall to Olden Farm, the residence of the Institute’s Director since 1940 COVER PHOTO: ANDREA KANE OPPOSITE PHOTO: DAN KOMODA Table of Contents DAN KOMODA DAN Reports of the Chair and the Director 4 The Institute for Advanced Study 6 School of Historical Studies 10 School of Mathematics 22 School of Natural Sciences 32 School of Social Science 42 Special Programs and Outreach 50 Record of Events 60 83 Acknowledgments 91 Founders, Trustees, and Officers of the Board and of the Corporation 92 Administration 93 Present and Past Directors and Faculty 95 Independent Auditors’ Report DAN KOMODA REPORT OF THE CHAIR Basic research, driven by fundamental inquiry, freedom, and and institutions: Trustees, Friends, former Members, founda- curiosity, is crucial for all true understanding and the advance- tions, corporations, government agencies, and philanthropists, ment and integrity of knowledge. Given this, I was extremely who recognize basic research as a vital public good. pleased to see the publication of The Usefulness of Useless The Board was very pleased to welcome new Trustees Jeanette Knowledge by Princeton University Press in March. It features Lerman-Neubauer, trustee of the Neubauer Family Foundation founding Director Abraham Flexner’s classic essay of the same and owner of a boutique communications practice; Christopher title, first published in Harper’s magazine in 1939, and a new A. -
(Ecole Polytechnique, Palaiseau, France) Yves Andre
PARTICIPANTS Emiliano Ambrosi (Ecole Polytechnique, Palaiseau, France) Yves Andre (CNRS, Paris, France) Dario Antolini (University of Rome, Italy) Stanislav Atanasov (Columbia University, NY, USA) Gregorio Baldi (University College London, UK) Jennifer Balakrishnan (Boston University, USA) Raphael Beuzart-Plessis (Institut de Mathematiques de Marseille, France) Fabrizio Barroero (Universit degli Studi Roma Tre, Italy) Florian Breuer (University of Newcastle, Australia) Anna Cadoret (Jussieu, Paris) Laura Capuano (University of Oxford, UK) Bumkyu Cho (Dongguk University, Seoul, South Korea) Kevin Kwan Chung (Columbia University, NY, USA) Giovanni Coppola (University of Salerno, Italy) Pietro Corvaja (University of Udine, Italy) Henri Darmon (McGill University, Montreal, Canada) Christopher Daw (University of Reading, UK) Alexis (Suki) Dasher (University of Minnesota, USA) Julian Lawrence Demeio (Scuola Normale Superiore, Pisa, Italy) Daniel Disegni (Ben Gurion University, Israel) Ick Sun Eum ( Dongguk University, Gyeongju City, South Korea) Rita Eppler-Goss (Ohio, USA) Bernadette Faye (Universite Cheikh Anta Diop De Dakar, Senegal) Ziyang Gao (Princeton University, USA) Michel Giacomini (University College, London, UK) Dorian Goldfeld (Columbia University, NY, USA) Giada Grossi (University College London, UK) Akash Jena (Indiana University, Bloomington, USA) Boris Kadets (MIT, Cambridge MA, USA) Sudesh Kaur Khanduja (IISER, Punjab, India) Ilya Khayutin (Princeton University, USA) Seema Kushwaha (Harish-Chandra Research Institute, Prayagraj,