DOCSLIB.ORG

André Weil (1906–1998)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
André Weil (1906–1998) mem-weil.qxp 2/12/99 10:46 AM Page 440 André Weil (1906–1998) Armand Borel, Pierre Cartier, Komaravolu Chandrasekharan, Shiing-Shen Chern, and Shokichi Iyanaga Shiing-Shen Chern a book where all the theorems had complete and rigorous proofs. It is difficult to make success of I believe Weil and I first met in Paris in the fall such a plan if it is to include all mathematics. For of 1936 at the Julia seminar “Sur les travaux sci- instance, there is no generally agreeable Stokes entifiques de M. Élie Cartan”. He soon went to theorem in differential geometry. But in any case, Princeton, and I must have left no impression on the Bourbaki volumes contain a large collection of him. rigorously proven fundamental mathematical the- Our first scientific encounter came when he orems. It is a great asset in mathematical literature. wrote in the newly started Mathematical Reviews a lengthy review of a short article of mine on in- Komaravolu Chandrasekharan tegral geometry. Although he was somewhat crit- ical, he generally liked my paper. André Weil’s passing brings back to memory We first really met in the fall of 1943 when I Samuel Johnson’s remark on the death of a close came to the Institute for Advanced Study and he friend: “Howmuchsoever I valued him, I now wish was teaching at Lehigh University and we became I had valued him more.” Weil was the first to in- good friends. At that time he had just published troduce me (1947) to Georges de Rham’s work on his proof of the high-dimensional Gauss-Bonnet differential forms and multiple integrals and to the formula. But our common mathematical interest work of Laurent Schwartz on distributions. He per- goes over the whole of mathematics, and I was al- sonally introduced me to the glories of Greek ways impressed by his vast knowledge and judg- sculpture at the Louvre in Paris on my first visit ment. there (May 1949). After his lecture at the Amster- We soon became colleagues at the University of dam Congress (ICM 1954), to which he was fetched Chicago in 1949–59 during the Stone period. Under by Kloosterman direct from the airport, we spent Stone’s leadership Chicago became an active math- the afternoon among the treasures of the Rijksmu- ematical center with excellent students. We had seum. He was supportive in concrete ways at the constant contact and took long walks along the turning points of my career, when I moved to Bom- south coast of Lake Michigan when it was still safe. bay (1949), and when I moved out of there (1965)— Weil was known as a leader of the Bourbaki always kindly, hospitable, and encouraging. Un- group. This started when a group of young French forgettable are the days we spent together at Pon- mathematicians planned to introduce modern tresina, in the high Swiss Alps (1967), admiring the mathematics to France. It was an extremely talented snow-clad peaks as well as Hecke’s mathematical group. Among their plans was the compilation of achievements. Shiing-shen Chern is professor emeritus of mathematics Komaravolu Chandrasekharan is an emeritus professor at the University of California, Berkeley, and director of mathematics at Eidgenössische Technische Hochschule emeritus of the Mathematical Sciences Research Institute. (ETH) in Zürich. 440 NOTICES OF THE AMS VOLUME 46, NUMBER 4 mem-weil.qxp 2/12/99 10:46 AM Page 441 He left what he wanted his fellow human beings nothing else did either be- to know about him in his corpus of published fore or since. He acquired work. All his work, however, was governed and uni- sufficient Sanskrit to be fied by his remarkable personality. His French was able to read the Gı¯ta in the pellucid. He was endowed with poetic sensibility original with the help of a and metaphysical insight. His creative élan and Sanskrit-French dictionary intellectual power will long be missed. He had that and an English translation. kind of charisma which demanded respect through He was taken in as much admiration. When someone characterized him as by the beauty of the poem cantankerous, someone else rejoined that his long as by the thought that in- and happy marriage showed that he could not be spired it. The Gı¯ta is per- all that cantankerous. Eveline and he were as close haps the most systematic as candlewick to candle flame. The distinctive hard spiritual statement of the shell of his personality was established at an as- “perennial philosophy”, tonishingly early age; he was confident, articulate, embodying those univer- and independent. He had a tireless curiosity about sal truths to which no one the world, which was “so various, so beautiful, so people or age can make ex- new,” in Matthew Arnold’s words, and he had the clusive claim. Eminent In- dologists like A. K. capacity to assimilate ideas, attitudes, and quali- Photograph by Lucien Gillet, provided courtesy of Sylvie Weil. Coomaraswamy have ex- ties, combined with the sharply defined sense of André Weil in the family apartment pressed the opinion that his own wants. Mathematics and poetry (Greek in Paris, 1952. and Sanskrit) afforded him a way into the sublime; it is “probably the most travel lent enchantment to the enterprise. important single work pro- He was a radical in the true sense who always duced in India.” The Gı¯ta remained Weil’s close com- tried to get to the root of things, though there panion all his life, through thick and thin, as it did were strains of traditionalism in him. This was so with Gandhi. whether he was considering departmental bud- Ka¯lida¯sa’s lyric poem Meghadu¯ta (the Cloud-mes- gets or diophantine equations, functional analysis senger) enraptured him—as it has at least fifty gen- on groups or zeta-functions, abelian varieties or erations of Indians—with its delicacy and grace, its the theory of correspondences on an algebraic mellifluous diction, its lyrical concision, and its sug- curve. It has been said that the only success which gestive power. Ka¯lida¯sa’s deceptively simple San- is man’s to command is to bring to his work a skrit is the despair of translators. Weil was struck by mighty heart. This he certainly did with his Foun- Ka¯lida¯sa’s mastery of the Sanskrit language, of its dations of Algebraic Geometry (1946), with “the pre- grammar and rhetoric and dramatic theory, “subjects cision of its language and the completeness of its which Hindu savants have treated with great, if some- proofs” in Harish-Chandra’s words. His famous times hair-splitting, ingenuity,” in the words of Arthur theorem (1940, 1948) on the Riemann hypothesis Ryder (Berkeley, 1912). He came upon the fact that for curves over finite fields was built on those in India, Pa¯n. ini’s invention of grammar (ca. fourth foundations and will remain a standing witness to century B.C.) had preceded that of the decimal no- his triumph as a mathematician, a triumph which tation and negative numbers. Pa¯n. ini’s As.t.a¯dhya¯yi stemmed from uncompromising self-reliance. “He (eight chapters) consists of nearly four thousand lighted himself up with the fuel of himself.” His aphorisms, the su¯tras, enumerating the technical radicalist approach to questions of administra- terms used in grammar and the rules for their in- tion did not always endear him to the authorities, terpretation and application. The Sanskrit term for some of whom resented his success and found grammar is Vya¯karan.a, which literally means “un- his chirpy personality and dry humour not exactly doing”, implying linguistic analysis. Weil could very ingratiating. He never courted popularity but was well say that “nothing he later came across in the writ- grateful when it came, as it did with the publica- ings of Chomsky and his disciples seemed unfamil- tion of his book on topological groups, with its ded- iar to him.” ication to Élie Cartan written in the confines of Having delved that deep into Sanskrit studies, he prison, or his last one on the years of his appren- was ready to jump at any offer of a chair in India, ticeship. He carried an air of quiet satisfaction which eventually turned out to be mathematics whenever his audience in a lecture overflowed the (1930–32). It was in Helsinki on the opening day of auditorium, as it did at the Helsinki Congress (ICM the Congress (ICM 1978), as we emerged from a re- 1978). ception given by our Finnish hosts, and the evening His precocious fascination for epic poetry began was spread against the sky, that he suddenly asked with Homer’s Iliad, in Greek, which in turn quick- me to recite the first line of the first stanza of ened his interest in Sanskrit, and led inevitably to Meghadu¯ta, which he so dearly loved. I had not then the great epic Maha¯bha¯rata. Its core, the Bha- known, as I did later, the intensity of the impact of gavad-Gı¯ta (the Song of God) stirred his blood as India on his personality. Joseph Brodsky has said: “A APRIL 1999 NOTICES OF THE AMS 441 mem-weil.qxp 2/12/99 10:46 AM Page 442 man is what he agreed with someone’s opinion, this would usually loves. That is why translate into an oral or written comment which he loves it; be- could be biting, sometimes even hurting, or sim- cause he is a part ply amusing, with little or no venom. I would like of it.” His col- to describe two examples in the latter vein, per- leagues at Prince- taining to incidents which occurred while he was ton, Gödel and on the faculty at the Institute for Advanced Study.
Load more

Recommended publications
  • Arxiv:1006.1489V2 [Math.GT] 8 Aug 2010 Ril.Ias Rfie Rmraigtesre Rils[14 Articles Survey the Reading from Profited Also I Article
    Pure and Applied Mathematics Quarterly Volume 8, Number 1 (Special Issue: In honor of F. Thomas Farrell and Lowell E. Jones, Part 1 of 2 ) 1—14, 2012 The Work of Tom Farrell and Lowell Jones in Topology and Geometry James F. Davis∗ Tom Farrell and Lowell Jones caused a paradigm shift in high-dimensional topology, away from the view that high-dimensional topology was, at its core, an algebraic subject, to the current view that geometry, dynamics, and analysis, as well as algebra, are key for classifying manifolds whose fundamental group is infinite. Their collaboration produced about fifty papers over a twenty-five year period. In this tribute for the special issue of Pure and Applied Mathematics Quarterly in their honor, I will survey some of the impact of their joint work and mention briefly their individual contributions – they have written about one hundred non-joint papers. 1 Setting the stage arXiv:1006.1489v2 [math.GT] 8 Aug 2010 In order to indicate the Farrell–Jones shift, it is necessary to describe the situation before the onset of their collaboration. This is intimidating – during the period of twenty-five years starting in the early fifties, manifold theory was perhaps the most active and dynamic area of mathematics. Any narrative will have omissions and be non-linear. Manifold theory deals with the classification of ∗I thank Shmuel Weinberger and Tom Farrell for their helpful comments on a draft of this article. I also profited from reading the survey articles [14] and [4]. 2 James F. Davis manifolds. There is an existence question – when is there a closed manifold within a particular homotopy type, and a uniqueness question, what is the classification of manifolds within a homotopy type? The fifties were the foundational decade of manifold theory.
    [Show full text]
  • Stable Real Cohomology of Arithmetic Groups
    ANNALES SCIENTIFIQUES DE L’É.N.S. ARMAND BOREL Stable real cohomology of arithmetic groups Annales scientifiques de l’É.N.S. 4e série, tome 7, no 2 (1974), p. 235-272 <http://www.numdam.org/item?id=ASENS_1974_4_7_2_235_0> © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1974, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systé- matique est constitutive d’une infraction pénale. Toute copie ou impression de ce fi- chier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Ann. sclent. EC. Norm. Sup., 46 serie, t. 7, 1974, p. 235 a 272. STABLE REAL COHOMOLOGY OF ARITHMETIC GROUPS BY ARMAND BOREL A Henri Cartan, a Poccasion de son 70® anniversaire Let r be an arithmetic subgroup of a semi-simple group G defined over the field of rational numbers Q. The real cohomology H* (T) of F may be identified with the coho- mology of the complex Q^ of r-invariant smooth differential forms on the symmetric space X of maximal compact subgroups of the group G (R) of real points of G. Let 1^ be the space of differential forms on X which are invariant under the identity component G (R)° of G (R). It is well-known to consist of closed (in fact harmonic) forms, whence a natural homomorphism^* : 1^ —> H* (T).
    [Show full text]
  • Algebraic D-Modules and Representation Theory Of
    Contemporary Mathematics Volume 154, 1993 Algebraic -modules and Representation TheoryDof Semisimple Lie Groups Dragan Miliˇci´c Abstract. This expository paper represents an introduction to some aspects of the current research in representation theory of semisimple Lie groups. In particular, we discuss the theory of “localization” of modules over the envelop- ing algebra of a semisimple Lie algebra due to Alexander Beilinson and Joseph Bernstein [1], [2], and the work of Henryk Hecht, Wilfried Schmid, Joseph A. Wolf and the author on the localization of Harish-Chandra modules [7], [8], [13], [17], [18]. These results can be viewed as a vast generalization of the classical theorem of Armand Borel and Andr´e Weil on geometric realiza- tion of irreducible finite-dimensional representations of compact semisimple Lie groups [3]. 1. Introduction Let G0 be a connected semisimple Lie group with finite center. Fix a maximal compact subgroup K0 of G0. Let g be the complexified Lie algebra of G0 and k its subalgebra which is the complexified Lie algebra of K0. Denote by σ the corresponding Cartan involution, i.e., σ is the involution of g such that k is the set of its fixed points. Let K be the complexification of K0. The group K has a natural structure of a complex reductive algebraic group. Let π be an admissible representation of G0 of finite length. Then, the submod- ule V of all K0-finite vectors in this representation is a finitely generated module over the enveloping algebra (g) of g, and also a direct sum of finite-dimensional U irreducible representations of K0.
    [Show full text]
  • An Incomplete Bibliography of Publications in Historia Scientiarum (International Journal of the History of Science Society of Japan)
    An Incomplete Bibliography of Publications in Historia Scientiarum (International Journal of the History of Science Society of Japan) Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: beebe@math.utah.edu, beebe@acm.org, beebe@computer.org (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 27 December 2018 Version 1.03 Title word cross-reference $124.00 [Hij90]. $29.00 [Bur93a]. 3[+]1=8 [Hol03]. $49.95 [Yaj07]. 7 × 7 e `eme ieme th [Yam10]. 9 [Mur94]. [Gui86, Pen04, Yos81a]. [DP88].P [Ano94b]. ≈ n 2 2 [Pen04]. π [HKY89, Nak94a, Vol94]. π 3(1=8) [Mur92b]. i=1 xi = x [Ras94a]. × [Har87b]. 0 [Hig01a, Izu05, Miu03, Mor04b, Sat05, She06a, She06b]. 0-19-860665-6 [Sat05]. 0-19-927016-3 [Izu05]. 0-520-24607-1 [Yaj07]. 0-691-11445-5 [She06b]. 0-8018-8235-4 [She06a]. 0-86078-668-4 [Hig01a]. 000 [Sas81b]. 00FF [Yos82]. 02/06/2000 [Has01]. 1 [Kaw93a, Oka98, Yos98]. 10 [Høy03, Yos81c]. 10th [Suz81]. 11 [Hay94]. 12/02/1906 [Has01]. 1475/76 [Hig01b]. 1500 [Ito83]. 15073 [Mur05b]. 1 2 16th [Maa91]. 17 [Sat86, Sat87]. 1700 [Nak83]. 17th [Maa91, Oh14, Yin13]. 18.5cm [Har87b]. 1843 [Ito16]. 1847 [Nak00a]. 1847/48 [Nak00a]. 1880s [Kim08a]. 18th [Ano94b, Kaw11, Kob02, Lor86, Nag80, Oh14, Nak98, THI17]. 18th-century [Kob02]. 19 [Nis92]. 190F [Yos98]. 1920s [Bro07, Kan13, Kim08b]. 1930 [Yaj07]. 1930s [Bro89, Kan13]. 1940 [Fur97]. 1940s [Mat98, YW05]. 1950s [HR15, Yam09]. 1955 [Nis92]. 1960s [FH12].
    [Show full text]
  • Issue 118 ISSN 1027-488X
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY S E European M M Mathematical E S Society December 2020 Issue 118 ISSN 1027-488X Obituary Sir Vaughan Jones Interviews Hillel Furstenberg Gregory Margulis Discussion Women in Editorial Boards Books published by the Individual members of the EMS, member S societies or societies with a reciprocity agree- E European ment (such as the American, Australian and M M Mathematical Canadian Mathematical Societies) are entitled to a discount of 20% on any book purchases, if E S Society ordered directly at the EMS Publishing House. Recent books in the EMS Monographs in Mathematics series Massimiliano Berti (SISSA, Trieste, Italy) and Philippe Bolle (Avignon Université, France) Quasi-Periodic Solutions of Nonlinear Wave Equations on the d-Dimensional Torus 978-3-03719-211-5. 2020. 374 pages. Hardcover. 16.5 x 23.5 cm. 69.00 Euro Many partial differential equations (PDEs) arising in physics, such as the nonlinear wave equation and the Schrödinger equation, can be viewed as infinite-dimensional Hamiltonian systems. In the last thirty years, several existence results of time quasi-periodic solutions have been proved adopting a “dynamical systems” point of view. Most of them deal with equations in one space dimension, whereas for multidimensional PDEs a satisfactory picture is still under construction. An updated introduction to the now rich subject of KAM theory for PDEs is provided in the first part of this research monograph. We then focus on the nonlinear wave equation, endowed with periodic boundary conditions. The main result of the monograph proves the bifurcation of small amplitude finite-dimensional invariant tori for this equation, in any space dimension.
    [Show full text]
  • People, Events, and Documents of Icmi's First
    ACTES HIST 3-2.qxp:- 11/4/11 11:25 Pgina 11 ACTES D’HISTÒRIA DE LA CIÈNCIA I DE LA TÈCNICA NOVA ÈPOCA / VOLUM 3 (2) / 2010, p. 11-50 PEOPLE, EVENTS, AND DOCUMENTS OF ICMI’S FIRST CENTURY FULVIA FURINGHETTI;1 LIVIA GIACARDI2 1DIPARTIMENTO DI MATEMATICA DELL’UNIVERSITÀ, GENOVA, ITALY. furinghe@dima.unige.it 2DIPARTIMENTO DI MATEMATICA DELL’UNIVERSITÀ, TORINO, ITALY. livia.giacardi@unito.it Summary: On the occasion of the ICMI centenary, the authors of the present paper built the website “The First Century of the International Commission on Mathematical Instruction (1908-2008). History of ICMI,” which contains information and documents about people, events, and bodies intervening in the first century of this Commission. This website provides an effective instrument for revisiting the history of ICMI and for reflecting on some key moments. In particular, it makes it possible to identify how the key ideas (internationalization, communication, solidarity) that inspired the founding of ICMI were realized, as well as the how the relationship with the community of mathe- maticians changed. In the present paper we walk through the Portrait gallery section of the website, fo- cusing on the presidents of ICMI and their contributions to the evolution of both the Commission’s policies and its methodological approaches to problems, looking at the history of ICMI from the perspective of the people who built it. Moreover, we present some statistical data concerning the life of ICMI (people, countries, meetings, etc.) and also offer flashes of lesser-known aspects that came to light after a reading of the doc- uments housed in ICMI Archives in Helsinki.
    [Show full text]
  • Armand Borel (1923–2003), Volume 51, Number 5
    Armand Borel (1923–2003) James Arthur, Enrico Bombieri, Komaravolu Chandrasekharan, Friedrich Hirzebruch, Gopal Prasad, Jean-Pierre Serre, Tonny A. Springer, and Jacques Tits Citations within this article. Borel’s Collected Papers are [Œ], and his 17 books are referred to as [1] through [17]. These are all listed in a sidebar on page 501. An item like [Œ 23] is Borel paper number 23 in [Œ]. Ci- tations of work by people other than Borel are by letter combinations such as [Che], and the de- tails appear at the end of the article. their root systems. He spent the year 1949–50 in 1 Institute for Advanced Study, 1999. Paris, with a grant from the CNRS . A good choice Armand Borel (for us, as well as for him), Paris being the very spot where what Americans have called “French Topol- Jean-Pierre Serre ogy” was being created, with the courses from The Swiss mathematician Armand Borel died Leray at the Collège de France and the Cartan sem- August 11, 2003, in Princeton from a rapidly evolv- inar at the École Normale Supérieure. Borel was an ing cancer. Few foreign mathematicians had as active participant in the Cartan seminar while many connections with France. He was a student closely following Leray’s courses. He managed to of Leray, he took part in the Cartan seminar, and understand the famous “spectral sequence”, not an he published more than twenty papers in collabo- easy task, and he explained it to me so well that I ration with our colleagues Lichnerowicz and Tits, have not stopped using it since.
    [Show full text]
  • Lie Groups and Linear Algebraic Groups I. Complex and Real Groups Armand Borel
    Lie Groups and Linear Algebraic Groups I. Complex and Real Groups Armand Borel 1. Root systems x 1.1. Let V be a finite dimensional vector space over Q. A finite subset of V is a root system if it satisfies: RS 1. Φ is finite, consists of non-zero elements and spans V . RS 2. Given a Φ, there exists an automorphism ra of V preserving Φ 2 ra such that ra(a) = a and its fixed point set V has codimension 1. [Such a − transformation is unique, of order 2.] The Weyl group W (Φ) or W of Φ is the subgroup of GL(V ) generated by the ra (a Φ). It is finite. Fix a positive definite scalar product ( , ) on V invariant 2 under W . Then ra is the reflection to the hyperplane a. ? 1 RS 3. Given u; v V , let nu;v = 2(u; v) (v; v)− . We have na;b Z for all 2 · 2 a; b Φ. 2 1.2. Some properties. (a) If a and c a (c > 0) belong to Φ, then c = 1; 2. · The system Φ is reduced if only c = 1 occurs. (b) The reflection to the hyperplane a = 0 (for any a = 0) is given by 6 (1) ra(v) = v nv;aa − therefore if a; b Φ are linearly independent, and (a; b) > 0 (resp. (a; b) < 0), 2 then a b (resp. a + b) is a root. On the other hand, if (a; b) = 0, then either − a + b and a b are roots, or none of them is (in which case a and b are said to be − strongly orthogonal).
    [Show full text]
  • Kneser, Martin an Alan Baker Pronfelden, 2.8.1969
    Niedersächsische Staats- und Universitätsbibliothek Göttingen Nachlass Martin Kneser Professor der Mathematik 21.1.1928 – 16.2.2004 Provenienz: als Geschenk aus Familienbesitz erhalten Acc. Mss. 2007.3 Acc. Mss. 2010.4/2 Göttingen 2012 Inhaltsverzeichnis Seite Allgemeine Korrespondenz 3 Signatur: Ms. M. Kneser A 1 - A 437 Berufungsangelegenheiten 85 Signatur: Cod. Ms. M. Kneser B 1 - B 153 Habilitationsverfahren 116 Signatur: Cod. Ms. M. Kneser C 1 - C 9 Vorlesungsmanuskripte 118 Signatur: Cod. Ms. M. Kneser D 1 - D 74 Vorlesungs- und Seminarausarbeitungen, überwiegend von Schülern angefertigt 129 Signatur: Cod. Ms. M. Kneser E 1 - E 23 Übungen 136 Signatur: Cod. Ms. M. Kneser F 1 - F 44 Seminare und Arbeitsgemeinschaften 143 Signatur: Cod. Ms. M. Kneser G 1 - G 8 Manuskripte 145 Signatur: Cod. Ms. M. Kneser H 1 - H 23 Sonderdrucke eigener Veröffentlichungen 153 Signatur: Cod. Ms. M. Kneser I 1 Mathematikgeschichte : Materialien zu einzelnen Personen 154 Signatur: Cod. Ms. M. Kneser J 1 - J 9 Tagungen und Vortragsreisen 158 Signatur: Cod. Ms. M . Kneser K 1 - K 8 Arbeitsgemeinschaft Oberwolfach 165 Signatur: Cod. Ms. M. Kneser L 1 - L 4 Arbeiten von Doktoranden 166 Signatur: Cod. Ms. M. Kneser M 1 - M 16 Akten und Sachkorrespondenz zu wissenschaftlichen Einrichtungen 169 Signatur: Cod. Ms. M. Kneser N 1 - N 5 Urkunden 172 Signatur: Cod. Ms. M . Kneser O 1 - O 10 Varia 174 Signatur: Cod. Ms. M. Kneser P 1 - P 5 2 Allgemeine Korrespondenz Signatur: Cod. Ms. M. Kneser A 1 - A 437 COD. MS. M. KNESER A 1 Aleksandrov, Pavel S. Briefwechsel mit Martin Kneser / Pavel S.
    [Show full text]
  • Jean Delsarte
    JEAN DELSARTE Jean Delsarte naquit `aFourmies (Nord) le 19 octobre 1903, ann´eemˆeme o`ule math´ematicien Elie Cartan arriva `aNancy o`uil ´etait nomm´etitulaire de la chaire de calcul diff´erentiel et int´egralel’ann´eesuivante. En 1953, Del- sarte cr´ea l’Institut Elie Cartan dont nous c´el´ebrons cette ann´ee(2003) le cinquanti`emeanniversaire en mˆeme temps que le centenaire de la naissance de Delsarte qui joua un rˆoleprimordial dans le d´eveloppement des math´ema- tiques `aNancy. Apr`es une brillante scolarit´eprimaire et secondaire, Delsarte fut re¸cu en 1922 `al’Ecole Normale Sup´erieurede la rue d’Ulm. Il y partagea les conversations de salle d’´etude du math´ematicien Andr´eWeil et du phy- sicien Yves Rocard, tous de la mˆeme promotion. Se retrouv`erent aussi `a l’ENS les math´ematiciens Henri Cartan, fils d’Elie Cartan, Jean Coulomb (math´ematicien physicien), Paul Dubreil, Ren´ede Possel et le futur phi- losophe des math´ematiques Jean Cavaill`es (de la promotion 1923). Puis Marcel Brelot, Jean Dieudonn´eet Charles Ehresmann entr`erent `al’ENS en 1924, une promotion qui accueillit plusieurs futures c´el´ebrit´esdes sciences et des lettres tels le physicien Louis N´eel, les philosophes Raymond Aron, Georges Canguilhem, Paul Nizan et Jean-Paul Sartre. Delsarte avait quitt´e la rue d’Ulm quand les math´ematiciens Claude Chevalley et Jean Leray travers`erent l’illustre portail en 1926. Plusieurs de ces math´ematiciens nor- maliens form`erent plus tard le noyau originel du groupe Bourbaki.
    [Show full text]
  • On Conjugacy Classes of the Pro-$Ell$ Braid Group of Degree $2$
    九州大学学術情報リポジトリ Kyushu University Institutional Repository On conjugacy classes of the Pro-$ell$ braid group of degree $2$ Kaneko, Masanobu Department of Mathematics, Faculty of Science, University of Tokyo http://hdl.handle.net/2324/20418 出版情報：Proceedings of the Japan Academy. Ser. A, Mathematical sciences. 62 (7), pp.274-277, 1986. The Japan Academy バージョン： 権利関係： 274 Proc. Japan Acad., 62, Ser. A (1986) [Vol. 62 (A), On Conjugacy Classes of the Pro.l braid Group of Degree 2" By Masanobu KANEKO Department of Mathematics, Faculty of Science, University of Tokyo (Communicated by Shokichi IYANAGA, M. ft. A., Sept. 12, 1986) 0. Introduction. In [2], Y. Ihara studied the "pro-/braid group" of degree 2 which is a certain big subgroup #Out of the outer auto- morphism group of the free pro-/group of rank 2. There is a canonical representation 9: G-*# of the absolute Galois group G=Gal (/Q) which is unramified outside l, and for each prime p=/=l, the Frobenius of p deter- mines a conjugacy class C of which is contained in the subset formed of all elements of "norm" p (loc. cit. Ch. I). In this note, we shall prove that P contains infinitely many #-conjugacy classes, at least if p generates Z topologically. It is an open question whether one can dis- tinguish the Frobenius conjugacy class from other norm-p-conjugacy classes. The 1. result. Let be a rational prime. We denote by Zl, Z and Q, respectively, the ring of /-adic integers, the group of /-adic units and the field of/-adic numbers.
    [Show full text]
  • Armand Borel 1923–2003
    Armand Borel 1923–2003 A Biographical Memoir by Mark Goresky ©2019 National Academy of Sciences. Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. ARMAND BOREL May 21, 1923–August 11, 2003 Elected to the NAS, 1987 Armand Borel was a leading mathematician of the twen- tieth century. A native of Switzerland, he spent most of his professional life in Princeton, New Jersey, where he passed away after a short illness in 2003. Although he is primarily known as one of the chief archi- tects of the modern theory of linear algebraic groups and of arithmetic groups, Borel had an extraordinarily wide range of mathematical interests and influence. Perhaps more than any other mathematician in modern times, Borel elucidated and disseminated the work of others. family the Borel of Photo courtesy His books, conference proceedings, and journal publica- tions provide the document of record for many important mathematical developments during his lifetime. By Mark Goresky Mathematical objects and results bearing Borel’s name include Borel subgroups, Borel regulator, Borel construction, Borel equivariant cohomology, Borel-Serre compactification, Bailey- Borel compactification, Borel fixed point theorem, Borel-Moore homology, Borel-Weil theorem, Borel-de Siebenthal theorem, and Borel conjecture.1 Borel was awarded the Brouwer Medal (Dutch Mathematical Society), the Steele Prize (American Mathematical Society) and the Balzan Prize (Italian-Swiss International Balzan Foundation). He was a member of the National Academy of Sciences (USA), the American Academy of Arts and Sciences, the American Philosophical Society, the Finnish Academy of Sciences and Letters, the Academia Europa, and the French Academy of Sciences.1 1 Borel enjoyed pointing out, with some amusement, that he was not related to the famous Borel of “Borel sets." 2 ARMAND BOREL Switzerland and France Armand Borel was born in 1923 in the French-speaking city of La Chaux-de-Fonds in Switzerland.
    [Show full text]