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Sir Andrew J. Wiles
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM. -
President's Report
AWM ASSOCIATION FOR WOMEN IN MATHE MATICS Volume 36, Number l NEWSLETTER March-April 2006 President's Report Hidden Help TheAWM election results are in, and it is a pleasure to welcome Cathy Kessel, who became President-Elect on February 1, and Dawn Lott, Alice Silverberg, Abigail Thompson, and Betsy Yanik, the new Members-at-Large of the Executive Committee. Also elected for a second term as Clerk is Maura Mast.AWM is also pleased to announce that appointed members BettyeAnne Case (Meetings Coordi nator), Holly Gaff (Web Editor) andAnne Leggett (Newsletter Editor) have agreed to be re-appointed, while Fern Hunt and Helen Moore have accepted an extension of their terms as Member-at-Large, to join continuing members Krystyna Kuperberg andAnn Tr enk in completing the enlarged Executive Committee. I look IN THIS ISSUE forward to working with this wonderful group of people during the coming year. 5 AWM ar the San Antonio In SanAntonio in January 2006, theAssociation for Women in Mathematics Joint Mathematics Meetings was, as usual, very much in evidence at the Joint Mathematics Meetings: from 22 Girls Just Want to Have Sums the outstanding mathematical presentations by women senior and junior, in the Noerher Lecture and the Workshop; through the Special Session on Learning Theory 24 Education Column thatAWM co-sponsored withAMS and MAA in conjunction with the Noether Lecture; to the two panel discussions thatAWM sponsored/co-sponsored.AWM 26 Book Review also ran two social events that were open to the whole community: a reception following the Gibbs lecture, with refreshments and music that was just right for 28 In Memoriam a networking event, and a lunch for Noether lecturer Ingrid Daubechies. -
Torification and Factorization of Birational Maps 3
TORIFICATION AND FACTORIZATION OF BIRATIONAL MAPS DAN ABRAMOVICH, KALLE KARU, KENJI MATSUKI, AND JAROSLAW WLODARCZYK Abstract. Building on work of the fourth author in [69], we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blowings up and blowings down with smooth centers. Contents 0. Introduction 1 1. Preliminaries 5 2. Birational Cobordisms 10 3. Torification 16 4. A proof of the weak factorization theorem 22 5. Generalizations 24 6. Problems related to weak factorization 27 References 28 0. Introduction We work over an algebraically closed field K of characteristic 0. We denote the multiplicative group of K by K∗. 0.1. Statement of the main result. The purpose of this paper is to give a proof for the following weak factorization conjecture of birational maps. We note that another proof of this theorem was given by the fourth author in [70]. See section 0.12 for a brief comparison of the two approaches. Theorem 0.1.1 (Weak Factorization). Let φ : X1 99K X2 be a birational map between complete nonsingular algebraic varieties X1 and X2 over an algebraically closed field K of characteristic zero, and let U ⊂ X1 be an open set where φ is an isomorphism. Then φ can be factored into a sequence of blowings up and blowings arXiv:math/9904135v4 [math.AG] 31 May 2000 down with smooth irreducible centers disjoint from U, namely, there exists a sequence of birational maps between complete nonsingular algebraic varieties ϕ1 ϕ2 ϕi ϕi+1 ϕi+2 ϕl−1 ϕl X1 = V0 99K V1 99K · · · 99K Vi 99K Vi+1 99K · · · 99K Vl−1 99K Vl = X2 where 1. -
President's Report
Volume 38, Number 4 NEWSLETTER July–August 2008 President’s Report Dear Colleagues: I am delighted to announce that our new executive director is Maeve Lewis McCarthy. I am very excited about what AWM will be able to accomplish now that she is in place. (For more about Maeve, see the press release on page 7.) Welcome, Maeve! Thanks are due to the search committee for its thought and energy. These were definitely required because we had some fabulous candidates. Thanks also to Murray State University, Professor McCarthy’s home institution, for its coopera- tion as we worked out the details of her employment with AWM. The AWM Executive Committee has voted to give honorary lifetime mem- IN THIS ISSUE berships to our founding presidents, Mary Gray and Alice T. Schafer. In my role as president, I am continually discovering just how extraordinary AWM is 7 McCarthy Named as an organization. Looking back at its early history, I find it hard to imagine AWM Executive Director how AWM could have come into existence without the vision, work, and persist- ence of these two women. 10 AWM Essay Contest Among newly elected members of the National Academy of Sciences in the physical and mathematical sciences are: 12 AWM Teacher Partnerships 16 MIT woMen In maTH Emily Ann Carter Department of Mechanical and Aerospace Engineering and the Program in 19 Girls’ Angle Applied and Computational Mathematics, Princeton University Lisa Randal Professor of theoretical physics, Department of Physics, Harvard University Elizabeth Thompson Department of Statistics, University of Washington, Seattle A W M The American Academy of Arts and Sciences has also announced its new members. -
New York Journal of Mathematics Lang's Conjectures, Fibered
New York Journal of Mathematics New York J. Math. 2 (1996) 20–34. Lang’s Conjectures, Fibered Powers, and Uniformity Dan Abramovich and Jos´e Felipe Voloch Abstract. We prove that the fibered power conjecture of Caporaso et al. (Con- jecture H, [CHM], §6) together with Lang’s conjecture implies the uniformity of rational points on varieties of general type, as predicted in [CHM]; a few applications on the arithmetic and geometry of curves are stated. In an opposite direction, we give counterexamples to some analogous results in positive characteristic. We show that curves that change genus can have arbitrarily many rational points; and that curves over Fp(t) can have arbitrarily many Frobenius orbits of non-constant points. Contents 1. Introduction 21 1.1. A Few Conjectures of Lang 21 1.2. The Fibered Power Conjecture 22 1.3. Summary of Results on the Implication Side 22 1.4. Summary of Results: Examples in Positive Characteristic 24 1.5. Acknowledgments 25 2. Proof of Theorem 1.5 25 2.1. Preliminaries 25 2.2. Prolongable Points 25 2.3. Proof of Theorem 1.5 26 3. A Few Refinements and Applications in Arithmetic and Geometry 26 3.1. Proof of Theorem 1.6 26 3.2. Uniformity in Terms of the Degree of an Extension 27 3.3. The Geometric Case 28 4. Examples in Positive Characteristic 30 4.1. Curves that Change Genus 30 Received December 20, 1995. Mathematics Subject Classification. 14G; 11G. Key words and phrases. arithmetic geometry, Lang’s conjecture, rational points. Abramovich partially supported by NSF grant DMS-9503276. -
RM Calendar 2019
Rudi Mathematici x3 – 6’141 x2 + 12’569’843 x – 8’575’752’975 = 0 www.rudimathematici.com 1 T (1803) Guglielmo Libri Carucci dalla Sommaja RM132 (1878) Agner Krarup Erlang Rudi Mathematici (1894) Satyendranath Bose RM168 (1912) Boris Gnedenko 2 W (1822) Rudolf Julius Emmanuel Clausius (1905) Lev Genrichovich Shnirelman (1938) Anatoly Samoilenko 3 T (1917) Yuri Alexeievich Mitropolsky January 4 F (1643) Isaac Newton RM071 5 S (1723) Nicole-Reine Étable de Labrière Lepaute (1838) Marie Ennemond Camille Jordan Putnam 2004, A1 (1871) Federigo Enriques RM084 Basketball star Shanille O’Keal’s team statistician (1871) Gino Fano keeps track of the number, S( N), of successful free 6 S (1807) Jozeph Mitza Petzval throws she has made in her first N attempts of the (1841) Rudolf Sturm season. Early in the season, S( N) was less than 80% of 2 7 M (1871) Felix Edouard Justin Émile Borel N, but by the end of the season, S( N) was more than (1907) Raymond Edward Alan Christopher Paley 80% of N. Was there necessarily a moment in between 8 T (1888) Richard Courant RM156 when S( N) was exactly 80% of N? (1924) Paul Moritz Cohn (1942) Stephen William Hawking Vintage computer definitions 9 W (1864) Vladimir Adreievich Steklov Advanced User : A person who has managed to remove a (1915) Mollie Orshansky computer from its packing materials. 10 T (1875) Issai Schur (1905) Ruth Moufang Mathematical Jokes 11 F (1545) Guidobaldo del Monte RM120 In modern mathematics, algebra has become so (1707) Vincenzo Riccati important that numbers will soon only have symbolic (1734) Achille Pierre Dionis du Sejour meaning. -
2020-2021 Annual Report
Institute for Computational and Experimental Research in Mathematics Annual Report May 1, 2020 – April 30, 2021 Brendan Hassett, Director, PI Mathew Borton, IT Director Ruth Crane, Assistant Director and Chief of Staff Juliet Duyster, Assistant Director Finance and Administration Sigal Gottlieb, Deputy Director Jeffrey Hoffstein, Consulting Associate Director Caroline Klivans, Deputy Director Benoit Pausader, co-PI Jill Pipher, Consulting Director Emerita, co-PI Kavita Ramanan, Associate Director, co-PI Bjorn Sandstede, Associate Director, co-PI Ulrica Wilson, Associate Director for Diversity and Outreach Table of Contents Mission ........................................................................................................................................... 5 Annual Report for 2020-2021 ........................................................................................................ 5 Core Programs and Events ............................................................................................................ 5 Participant Summaries by Program Type ..................................................................................... 7 ICERM Funded Participants ................................................................................................................. 7 ICERM Funded Speakers ...................................................................................................................... 9 All Speakers (ICERM funded and Non-ICERM funded) ................................................................ -
Arxiv:Math/9809023V1 [Math.AG] 5 Sep 1998 .W a That Say We 0
UNIFORMITY OF STABLY INTEGRAL POINTS ON PRINCIPALLY POLARIZED ABELIAN VARIETIES OF DIMENSION ≤ 2 DAN ABRAMOVICH AND KENJI MATSUKI Abstract. The purpose of this paper is to prove, assuming that the conjecture of Lang and Vojta holds true, that there is a uniform bound on the number of stably integral points in the complement of the theta divisor on a principally polarized abelian surface defined over a number field. Most of our argument works in arbitrary dimension and the restriction on the dimension ≤ 2 is used only at the last step, where we apply Pacelli’s stronger uniformity results for elliptic curves. Preliminary version, July 13, 2021. 0. Introduction 0.1. The conjecture of Lang and Vojta. Let X be a variety over a field of characteristic 0. We say that X is a variety of logarithmic general type, if there exists a desingularization X˜ → X, and a projective embedding X˜ ⊂ Y where D = Y X˜ is a divisor of normal crossings, such that the invertible sheaf ωY (D) is big. We note first that this peoperty is independent of the choices of X˜ and Y , and that it is a proper birational invariant, namely, if X′ → X is a proper birational morphism (or an inverse of such) then X is of logarithmic general type if and only if X′ is. Now let X be a variety of logarithmic general type defined over a number field K. Let S be a finite set of places in K and let OK,S ⊂ K be the ring of S-integers. Fix a model X of X over OK,S. -
Advanced Lectures in Mathematics (ALM)
Advanced Lectures in Mathematics (ALM) ALM 1: Superstring Theory ALM 2: Asymptotic Theory in Probability and Statistics with Applications ALM 3: Computational Conformal Geometry ALM 4: Variational Principles for Discrete Surfaces ALM 6: Geometry, Analysis and Topology of Discrete Groups ALM 7: Handbook of Geometric Analysis, No. 1 ALM 8: Recent Developments in Algebra and Related Areas ALM 9: Automorphic Forms and the Langlands Program ALM 10: Trends in Partial Differential Equations ALM 11: Recent Advances in Geometric Analysis ALM 12: Cohomology of Groups and Algebraic K-theory ALM 13: Handbook of Geometric Analysis, No. 2 ALM 14: Handbook of Geometric Analysis, No. 3 ALM 15: An Introduction to Groups and Lattices: Finite Groups and Positive Definite Rational Lattices ALM 16: Transformation Groups and Moduli Spaces of Curves ALM 17: Geometry and Analysis, No. 1 ALM 18: Geometry and Analysis, No. 2 ALM 19: Arithmetic Geometry and Automorphic Forms ALM 20: Surveys in Geometric Analysis and Relativity ALM 21: Advances in Geometric Analysis ALM 22: Differential Geometry: Under the Influence of S.-S. Chern ALM 23: Recent Developments in Geometry and Analysis ALM 24: Handbook of Moduli, Volume I ALM 25: Handbook of Moduli, Volume II ALM 26: Handbook of Moduli, Volume III Advanced Lectures in Mathematics Volume XXV Handbook of Moduli Volume II edited by Gavril Farkas · Ian Morrison International Press 浧䷘㟨十⒉䓗䯍 www.intlpress.com HIGHER EDUCATION PRESS Advanced Lectures in Mathematics, Volume XXV Handbook of Moduli, Volume II Volume Editors: Gavril Farkas (Humboldt-Universität, Berlin) Ian Morrison (Fordham University, New York) 2010 Mathematics Subject Classification. Primary: 14D20. -
1875–2012 Dr. Jan E. Wynn
HISTORY OF THE DEPARTMENT OF MATHEMATICS BRIGHAM YOUNG UNIVERSITY 1875–2012 DR. LYNN E. GARNER DR. GURCHARAN S. GILL DR. JAN E. WYNN Copyright © 2013, Department of Mathematics, Brigham Young University All rights reserved 2 Foreword In August 2012, the leadership of the Department of Mathematics of Brigham Young University requested the authors to compose a history of the department. The history that we had all heard was that the department had come into being in 1954, formed from the Physics Department, and with a physicist as the first chairman. This turned out to be partially true, in that the Department of Mathematics had been chaired by physicists until 1958, but it was referred to in the University Catalog as a department as early as 1904 and the first chairman was appointed in 1906. The authors were also part of the history of the department as professors of mathematics: Gurcharan S. Gill 1960–1999 Lynn E. Garner 1963–2007 Jan E. Wynn 1966–2000 Dr. Gill (1956–1958) and Dr. Garner (1960–1962) were also students in the department and hold B. S. degrees in Mathematics from BYU. We decided to address the history of the department by dividing it into three eras of quite different characteristics. The first era (1875–1978): Early development of the department as an entity, focusing on rapid growth during the administration of Kenneth L. Hillam as chairman. The second era (1978–1990): Efforts to bring the department in line with national standards in the mathematics community and to establish research capabilities, during the administration of Peter L. -
Curriculum Vitae: Brendan Hassett
Curriculum Vitae: Brendan Hassett Brown University brendan [email protected] Institute for Computational and Experimental Research in Mathematics 121 South Main Street, 11th Floor, Box E Providence, RI 02903 USA 401 863 7010 Department of Mathematics Box 1917 151 Thayer Street Providence, Rhode Island 02912 USA 401 863 7961 Positions Director, Institute for Computational and Experimental Research in Mathemat- ics, Brown University, from July 2016 Professor of Mathematics, from July 2015 Milton Brockett Porter Professor, Rice University, July 2013 to June 2015 Chair, Department of Mathematics, July 2009 to June 2014 Professor of Mathematics, July 2006 to June 2015 Associate Professor of Mathematics, July 2003 to June 2006 Assistant Professor of Mathematics, July 2000 to June 2003 Professeur Invit´e,Universit´eParis-Sud, Orsay, March to April 2005 Visiting Scholar, Institute of Mathematical Sciences, Chinese University of Hong Kong, August 2000 to July 2001 Dickson Instructor of Mathematics, University of Chicago, October 1996 to September 2000 Visitor at the Institut Mittag-Leffler, Stockholm, January to March 1997 Education Harvard University, M.A., 1994, and Ph.D., 1996 (supervised by Joe Harris) Yale College, B.A. in mathematics, summa cum laude, 1992 Awards Fellow of the American Mathematical Society, 2014 Charles W. Duncan Jr. Achievement Award for Outstanding Faculty, Rice Uni- versity, 2009 Grants and Fellowships Simons Foundation Award 815891: September 1, 2021{August 31, 2023; Simons Bridge for Postdoctoral Fellowships at ICERM -
2005 Satter Prize, Volume 52, Number 4
2005 Satter Prize The 2005 Ruth Lyttle Satter Prize in Mathematics sketch, and the awardee’s re- was awarded at the 111th Annual Meeting of the sponse upon receiving the prize. AMS in Atlanta in January 2005. The Satter Prize is awarded every two years to Citation recognize an outstanding contribution to mathe- The Ruth Lyttle Satter Prize in Math- matics research by a woman in the previous five ematics is awarded to Svetlana Jit- years. Established in 1990 with funds donated by omirskaya for her pioneering work Joan S. Birman, the prize honors the memory of Bir- on non-perturbative quasiperiodic man’s sister, Ruth Lyttle Satter. Satter earned a localization, in particular for re- bachelor’s degree in mathematics and then joined sults in her papers (1) “Metal-in- the research staff at AT&T Bell Laboratories dur- sulator transition for the almost ing World War II. After raising a family, she received Mathieu operator”, Ann. of Math. a Ph.D. in botany at the age of forty-three from the (2) 150 (1999), no. 3, 1159–1175, Svetlana Jitomirskaya University of Connecticut at Storrs, where she later and (2) with J. Bourgain, “Ab- became a faculty member. Her research on the bi- solutely continuous spectrum for 1D quasiperiodic ological clocks in plants earned her recognition in operators”, Invent. Math. 148 (2002), no. 3, 453–463. the U.S. and abroad. Birman requested that the In her Annals paper, she developed a non-perturba- prize be established to honor her sister’s commit- tive approach to quasiperiodic localization and solved ment to research and to encourage women in sci- the long-standing Aubry-Andre conjecture on the al- ence.