NEWSLETTER No
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
NEWSLETTER No
NEWSLETTER No. 455 February 2016 LMS INAUGURAL HIRST LECTURE: PROFESSOR EDMUND F. ROBERTSON he Society is pleased to announce that MacTutor History of Mathematics website has TProfessor Edmund F. Robertson (St Andrews) now become an important resource for those in- will give the inaugural Hirst Lecture at St terested in the history of mathematics. It contains Andrews on Wednesday 20 April 2016. Mark over 2,800 biographies of mathematicians and is McCartney (University of Ulster) will give an ac- used across the world by schoolchildren, under- companying lecture. graduates, graduates and their teachers. The Hirst Lecture celebrates the joint award of The Hirst Prize and Lectureship are named after the Hirst Prize & Lectureship, in the 150th Anni- Thomas A. Hirst, 5th President of the London versary year of the London Mathematical Society, Mathematical Society from 1872-1874. The prize to Professor Edmund Robertson (St Andrews) and is awarded in recognition of original and inno- Dr John O’Connor (St Andrews) for their creation, vative work in the history of mathematics, which development and maintenance of the MacTutor may be in any medium. History of Mathematics website (www-history. In 2015, the Council of the Society agreed to mcs.st-and.ac.uk). continue the Hirst Prize and Lectureship on a Originally developed in the early 1990s to enrich biennial basis with the next award to be made the Mathematical MacTutor System that supports in 2018 and the lecture to be given at a Society teaching mathematics to undergraduates, the Meeting in 2019. -
Manjul Bhargava
The Work of Manjul Bhargava Manjul Bhargava's work in number theory has had a profound influence on the field. A mathematician of extraordinary creativity, he has a taste for simple problems of timeless beauty, which he has solved by developing elegant and powerful new methods that offer deep insights. When he was a graduate student, Bhargava read the monumental Disqui- sitiones Arithmeticae, a book about number theory by Carl Friedrich Gauss (1777-1855). All mathematicians know of the Disquisitiones, but few have actually read it, as its notation and computational nature make it difficult for modern readers to follow. Bhargava nevertheless found the book to be a wellspring of inspiration. Gauss was interested in binary quadratic forms, which are polynomials ax2 +bxy +cy2, where a, b, and c are integers. In the Disquisitiones, Gauss developed his ingenious composition law, which gives a method for composing two binary quadratic forms to obtain a third one. This law became, and remains, a central tool in algebraic number theory. After wading through the 20 pages of Gauss's calculations culminating in the composition law, Bhargava knew there had to be a better way. Then one day, while playing with a Rubik's cube, he found it. Bhargava thought about labeling each corner of a cube with a number and then slic- ing the cube to obtain 2 sets of 4 numbers. Each 4-number set naturally forms a matrix. A simple calculation with these matrices resulted in a bi- nary quadratic form. From the three ways of slicing the cube, three binary quadratic forms emerged. -
AFFINE HECKE ALGEBRAS and THEIR GRADED VERSION 0.1. Let
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 2, Number 3, July 1989 AFFINE HECKE ALGEBRAS AND THEIR GRADED VERSION GEORGE LUSZTIG Dedicated to Sir Michael Atiyah on his sixtieth birthday INTRODUCTION 0.1. Let Hvo be an affine Hecke algebra with parameter Vo E C* assumed to be of infinite order. (The basis elements ~ E Hvo corresponding to simple reflections s satisfy (~+ 1)(Ts - v~C(s») = 0, where c(s) EN depend on s and are subject only to c(s) = c(s') whenever s, Sf are conjugate in the affine Weyl group.) Such Hecke algebras appear naturally in the representation theory of semisimple p-adic groups, and understanding their representation theory is a question of considerable interest. Consider the "special case" where c(s) is independent of s and the coroots generate a direct summand. In this "special case," the question above has been studied in [I] and a classification of the simple modules was obtained. The approach of [1] was based on equivariant K-theory. This approach can be attempted in the general case (some indications are given in [5, 0.3]), but there appear to be some serious difficulties in carrying it out. 0.2. On the other hand, in [5] we introduced some algebras H,o' depending on a parameter roE C , which are graded analogues of Hvo . The graded algebras H '0 are in many respects simpler than Hvo' and in [5] the representation theory of H,o is studied using equivariant homology. Moreover, we can make the machinery of intersection cohomology work for us in the study of H '0 ' while in the K-theory context of Hvo it is not clear how to do this. -
Editor's Note
ANNALES DE LA FACULTÉ DES SCIENCES DE TOULOUSE M. LEDOUX Editor’s note Annales de la faculté des sciences de Toulouse 6e série, tome 13, no 1 (2004), p. 1 <http://www.numdam.org/item?id=AFST_2004_6_13_1_1_0> © Université Paul Sabatier, 2004, tous droits réservés. L’accès aux archives de la revue « Annales de la faculté des sciences de Toulouse » (http://picard.ups-tlse.fr/~annales/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitu- tive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ This Special Issue of the Annales de la Faculté des Sciences de Toulouse collects papers from the laureates of the Fermât Prizes 1999 and 2001. The Fermat Prize for Mathematics Research is delivered by the Paul- Sabatier University of Toulouse under the patronage of ASTRIUM SAS. It rewards research work in fields where the contributions of Pierre de Fermat have been decisive: Variational Principles, Probability Theory and Analyti- cal Geometry, Number Theory. Former winners are A. Bahri, K. A. Ribbet, J.-L. Colliot-Thélène, J.-M. Coron, A. J. Wiles, M. Talagrand. The Fermat Prize for Mathematics Research 1999 was awarded jointly to F. Bethuel and F. Hélein for several important contributions to the theory of variational calculus, which have consequences in Physics and Geometry. The Fermat Prize for Mathematics Research 2001 was awarded jointly to R. L. -
Motivic Chern Classes and Iwahori Invariants of Principal Series
MOTIVIC CHERN CLASSES AND IWAHORI INVARIANTS OF PRINCIPAL SERIES CHANGJIAN SU Abstract. In this expository note, we review the proof [AMSS19] of conjectures of Bump, Nakasuji and Naruse about principal series representations of p-adic groups. The ingre- dients of the proof involve Maulik{Okounkov K-theoretic stable basis for the Springer resolution, and motivic Chern classes of Schubert cells for the Langlands dual group Contents 1. Introduction 1 Notations 3 2. p-adic side 3 2.1. Iwahori invariants of the principal series representations 3 2.2. Two bases in the Iwahori invariants of the principal series representations 4 2.3. Conjectures of Bump, Nakasuji and Naruse 5 3. Complex dual side 7 3.1. Definition of Motivic Chern classes 7 3.2. Two bases in the localized equivariant K theory of the flag variety 8 3.3. Hecke algebra action 8 3.4. Smoothness criterion 10 4. The proof 10 References 11 1. Introduction The Iwahori{Hecke algebra of a p-adic reductive group is the convolution algebra on the compactly supported functions on the rational points of the group, which are let and right invariant under the Iwahori subgroup. It contains the finite Hecke algebra and the group algebra of the character lattice of the complex dual maximal torus, which is called the lattice part of the Iwahori{Hecke algebra. The Iwahori invariant subspace of any unramfied principal series representation is a module over the Iwahori{Hecke algebra via convolution. In the invariant subspace, there is a natural basis induced from the cell decomposition of the group. -
Report for the Academic Year 1999
l'gEgasag^a3;•*a^oggMaBgaBK>ry^vg^.g^._--r^J3^JBgig^^gqt«a»J^:^^^^^ Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1998-99 PRINCETON • NEW JERSEY HISTORICAL STUDIES^SOCIAl SC^JCE LIBRARY INSTITUTE FOR ADVANCED STUDY PRINCETON, NEW JERSEY 08540 Institute /or ADVANCED STUDY REPORT FOR THE ACADEMIC YEAR 1 998 - 99 OLDEN LANE PRINCETON • NEW JERSEY • 08540-0631 609-734-8000 609-924-8399 (Fax) http://www.ias.edu Extract from the letter addressed by the Institute's Founders, Louis Bamberger and Mrs. FeUx Fuld, to the Board of Trustees, dated June 4, 1930. Newark, New Jersey. It is fundamental m our purpose, and our express desire, that in the appointments to the staff and faculty, as well as in the admission of workers and students, no account shall be taken, directly or indirectly, of race, religion, or sex. We feel strongly that the spirit characteristic of America at its noblest, above all the pursuit of higher learning, cannot admit of any conditions as to personnel other than those designed to promote the objects for which this institution is established, and particularly with no regard whatever to accidents of race, creed, or sex. ni' TABLE OF CONTENTS 4 • BACKGROUND AND PURPOSE 7 • FOUNDERS, TRUSTEES AND OFFICERS OF THE BOARD AND OF THE CORPORATION 10 • ADMINISTRATION 12 • PRESENT AND PAST DIRECTORS AND FACULTY 15 REPORT OF THE CHAIRMAN 18 • REPORT OF THE DIRECTOR 22 • OFFICE OF THE DIRECTOR - RECORD OF EVENTS 27 ACKNOWLEDGMENTS 41 • REPORT OF THE SCHOOL OF HISTORICAL STUDIES FACULTY ACADEMIC ACTIVITIES MEMBERS, VISITORS, -
Public Recognition and Media Coverage of Mathematical Achievements
Journal of Humanistic Mathematics Volume 9 | Issue 2 July 2019 Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre University of Alicante Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, and the Mathematics Commons Recommended Citation Sepulcre, J. "Public Recognition and Media Coverage of Mathematical Achievements," Journal of Humanistic Mathematics, Volume 9 Issue 2 (July 2019), pages 93-129. DOI: 10.5642/ jhummath.201902.08 . Available at: https://scholarship.claremont.edu/jhm/vol9/iss2/8 ©2019 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Public Recognition and Media Coverage of Mathematical Achievements Juan Matías Sepulcre Department of Mathematics, University of Alicante, Alicante, SPAIN [email protected] Synopsis This report aims to convince readers that there are clear indications that society is increasingly taking a greater interest in science and particularly in mathemat- ics, and thus society in general has come to recognise, through different awards, privileges, and distinctions, the work of many mathematicians. -
Mathematics People
Mathematics People 2001 Fermat Prize Awarded NRC-Ford Foundation Minority The 2001 Fermat Prize in Mathematics has been awarded Fellowships Awarded to RICHARD TAYLOR of Harvard University and WENDELIN The names of the recipients of Ford Foundation Minority WERNER of the Université de Paris-Sud. Taylor was hon- Fellowships for 2001 have been announced. The fellowship ored for his many contributions to the study of connec- programs are administered by the National Research Coun- tions between Galois representations and automorphic cil for the purpose of increasing the presence of under- forms. Werner was honored for his work on intersection represented groups among faculty members in colleges and exponents of Brownian motion and their impact on theo- universities. The recipients were selected based on merit retical physics. and promise of future achievement. The Fermat Prize is presented every two years and car- DANIEL A. WILEY of Cornell University was awarded a ries a monetary award of 100,000 FF (approximately Predoctoral Fellowship. He is a student in the field of ap- $15,500). The prize recognizes the work of one or more plications of mathematics. PAUL A. LOYA of the Massachu- mathematicians in the areas in which Pierre de Fermat setts Institute of Technology received a Postdoctoral Fel- worked, specifically, principles of variational theory, foun- lowship. He is a student of geometry. dations of the calculus and probability, analytic geometry, and number theory. The award is administered by the —From an NRC announcement Université Paul Sabatier and sponsored by Astrium Sas. Previous recipients of the Fermat Prize are: Abbas Bahri AAAS Fellows Elected and Kenneth A. -
The I Nstitute L E T T E R
THE I NSTITUTE L E T T E R INSTITUTE FOR ADVANCED STUDY PRINCETON, NEW JERSEY · FALL 2004 ARNOLD LEVINE APPOINTED FACULTY MEMBER IN THE SCHOOL OF NATURAL SCIENCES he Institute for Advanced Study has announced the appointment of Arnold J. Professor in the Life Sciences until 1998. TLevine as professor of molecular biology in the School of Natural Sciences. Profes- He was on the faculty of the Biochemistry sor Levine was formerly a visiting professor in the School of Natural Sciences where he Department at Princeton University from established the Center for Systems Biology (see page 4). “We are delighted to welcome 1968 to 1979, when he became chair and to the Faculty of the Institute a scientist who has made such notable contributions to professor in the Department of Microbi- both basic and applied biological research. Under Professor Levine’s leadership, the ology at the State University of New York Center for Systems Biology will continue working in close collaboration with the Can- at Stony Brook, School of Medicine. cer Institute of New Jersey, Robert Wood Johnson Medical School, Lewis-Sigler Center The recipient of many honors, among for Integrative Genomics at Princeton University, and BioMaPS Institute at Rutgers, his most recent are: the Medal for Out- The State University of New Jersey, as well as such industrial partners as IBM, Siemens standing Contributions to Biomedical Corporate Research, Inc., Bristol-Myers Squibb, and Merck & Co.,” commented Peter Research from Memorial Sloan-Kettering Goddard, Director of the Institute. Cancer Center (2000); the Keio Medical Arnold J. Levine’s research has centered on the causes of cancer in humans and ani- Science Prize of the Keio University mals. -
The Development of Intersection Homology Theory
The Development of Intersection Homology Theory The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Thomsen, A C. “Mycoplasmas in Human Pyelonephritis: Demonstration of Antibodies in Serum and Urine.” Journal of Clinical Microbiology 8.2 (1978): 197–202. Print. As Published http://arxiv.org/abs/math/0701462 Publisher American Society for Microbiology Version Final published version Citable link http://hdl.handle.net/1721.1/69980 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Pure and Applied Mathematics Quarterly Volume 3, Number 1 (Special Issue: In honor of Robert MacPherson, Part 3 of 3 ) 225–282, 2007 The Development of Intersection Homology Theory Steven L. Kleiman Contents Foreword 225 1. Preface 226 2. Discovery 227 3. A fortuitous encounter 231 4. The Kazhdan–Lusztig conjecture 235 5. D-modules 238 6. Perverse sheaves 244 7. Purity and decomposition 248 8. Other work and open problems 254 References 260 9. Endnotes 265 References 279 Foreword This historical introduction is in two parts. The first is reprinted with per- mission from “A century of mathematics in America, Part II,” Hist. Math., 2, Amer. Math. Soc., 1989, pp. 543–585. Virtually no change has been made to the original text. In particular, Section 8 is followed by the original list of references. However, the text has been supplemented by a series of endnotes, collected in the new Section 9 and followed by a second list of references. -
Kollár and Voisin Awarded Shaw Prize
COMMUNICATION Kollár and Voisin Awarded Shaw Prize The Shaw Foundation has for showing that a variety is not rational, a breakthrough announced the awarding of that has led to results that would previously have been the 2017 Shaw Prize in Math- unthinkable. A third remarkable result is a counterexam- ematical Sciences to János ple to an extension of the Hodge conjecture, one of the Kollár, professor of mathe- hardest problems in mathematics (it is one of the Clay matics, Princeton University, Mathematical Institute’s seven Millennium Problems); and Claire Voisin, professor the counterexample rules out several approaches to the and chair in algebraic geom- conjecture.” etry, Collège de France, “for their remarkable results in Biographical Sketch: János Kóllar János Kollár many central areas of algebraic János Kollár was born in 1956 in Budapest, Hungary. He geometry, which have trans- received his PhD (1984) from Brandeis University. He was formed the field and led to the a research assistant at the Hungarian Academy of Sciences solution of long-standing prob- in 1980–81 and a junior fellow at Harvard University from lems that had appeared out of 1984 to 1987. He was a member of the faculty of the Uni- reach.” They will split the cash versity of Utah from 1987 to 1999. In 1999 he joined the award of US$1,200,000. faculty of Princeton University, where he was appointed The Shaw Foundation char- Donner Professor of Science in 2009. He was a Simons acterizes Kollár’s recent work Fellow in Mathematics in 2012. He received the AMS Cole as standing out “in a direction Prize in Algebra in 2006 and the Nemmers Prize in Math- that will influence algebraic ematics in 2016. -
Lectures on Springer Theories and Orbital Integrals
IAS/Park City Mathematics Series Volume 00, Pages 000–000 S 1079-5634(XX)0000-0 Lectures on Springer theories and orbital integrals Zhiwei Yun Abstract. These are the expanded lecture notes from the author’s mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry of Springer fibers, affine Springer fibers and Hitchin fibers; representations of (affine) Weyl groups arising from these objects; relation between affine Springer fibers and orbital integrals. Contents 0 Introduction2 0.1 Topics of these notes2 0.2 What we assume from the readers3 1 Lecture I: Springer fibers3 1.1 The setup3 1.2 Springer fibers4 1.3 Examples of Springer fibers5 1.4 Geometric Properties of Springer fibers8 1.5 The Springer correspondence9 1.6 Comments and generalizations 13 1.7 Exercises 14 2 Lecture II: Affine Springer fibers 16 2.1 Loop group, parahoric subgroups and the affine flag variety 16 2.2 Affine Springer fibers 20 2.3 Symmetry on affine Springer fibers 22 2.4 Further examples of affine Springer fibers 24 2.5 Geometric Properties of affine Springer fibers 28 2.6 Affine Springer representations 32 2.7 Comments and generalizations 34 2.8 Exercises 35 3 Lecture III: Orbital integrals 36 3.1 Integration on a p-adic group 36 3.2 Orbital integrals 37 3.3 Relation with affine Springer fibers 40 Research supported by the NSF grant DMS-1302071, the Packard Foundation and the PCMI.. ©0000 (copyright holder) 1 2 Lectures on Springer theories and orbital integrals 3.4 Stable orbital integrals 41 3.5 Examples in SL2 45 3.6 Remarks on the Fundamental Lemma 47 3.7 Exercises 48 4 Lecture IV: Hitchin fibration 50 4.1 The Hitchin moduli stack 50 4.2 Hitchin fibration 52 4.3 Hitchin fibers 54 4.4 Relation with affine Springer fibers 57 4.5 A global version of the Springer action 58 4.6 Exercises 59 0.