Report on the Current State of the French Dmls Thierry Bouche
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Distributions:The Evolutionof a Mathematicaltheory
Historia Mathematics 10 (1983) 149-183 DISTRIBUTIONS:THE EVOLUTIONOF A MATHEMATICALTHEORY BY JOHN SYNOWIEC INDIANA UNIVERSITY NORTHWEST, GARY, INDIANA 46408 SUMMARIES The theory of distributions, or generalized func- tions, evolved from various concepts of generalized solutions of partial differential equations and gener- alized differentiation. Some of the principal steps in this evolution are described in this paper. La thgorie des distributions, ou des fonctions g&&alis~es, s'est d&eloppeg 2 partir de divers con- cepts de solutions g&&alis6es d'gquations aux d&i- &es partielles et de diffgrentiation g&&alis6e. Quelques-unes des principales &apes de cette &olution sont d&rites dans cet article. Die Theorie der Distributionen oder verallgemein- erten Funktionen entwickelte sich aus verschiedenen Begriffen von verallgemeinerten Lasungen der partiellen Differentialgleichungen und der verallgemeinerten Ableitungen. In diesem Artikel werden einige der wesentlichen Schritte dieser Entwicklung beschrieben. 1. INTRODUCTION The founder of the theory of distributions is rightly con- sidered to be Laurent Schwartz. Not only did he write the first systematic paper on the subject [Schwartz 19451, which, along with another paper [1947-19481, already contained most of the basic ideas, but he also wrote expository papers on distributions for electrical engineers [19481. Furthermore, he lectured effec- tively on his work, for example, at the Canadian Mathematical Congress [1949]. He showed how to apply distributions to partial differential equations [19SObl and wrote the first general trea- tise on the subject [19SOa, 19511. Recognition of his contri- butions came in 1950 when he was awarded the Fields' Medal at the International Congress of Mathematicians, and in his accep- tance address to the congress Schwartz took the opportunity to announce his celebrated "kernel theorem" [195Oc]. -
A Short Survey of Cyclic Cohomology
Clay Mathematics Proceedings Volume 10, 2008 A Short Survey of Cyclic Cohomology Masoud Khalkhali Dedicated with admiration and affection to Alain Connes Abstract. This is a short survey of some aspects of Alain Connes’ contribu- tions to cyclic cohomology theory in the course of his work on noncommutative geometry over the past 30 years. Contents 1. Introduction 1 2. Cyclic cohomology 3 3. From K-homology to cyclic cohomology 10 4. Cyclic modules 13 5. Thelocalindexformulaandbeyond 16 6. Hopf cyclic cohomology 21 References 28 1. Introduction Cyclic cohomology was discovered by Alain Connes no later than 1981 and in fact it was announced in that year in a conference in Oberwolfach [5]. I have reproduced the text of his abstract below. As it appears in his report, one of arXiv:1008.1212v1 [math.OA] 6 Aug 2010 Connes’ main motivations to introduce cyclic cohomology theory came from index theory on foliated spaces. Let (V, ) be a compact foliated manifold and let V/ denote the space of leaves of (V, ).F This space, with its natural quotient topology,F is, in general, a highly singular spaceF and in noncommutative geometry one usually replaces the quotient space V/ with a noncommutative algebra A = C∗(V, ) called the foliation algebra of (V,F ). It is the convolution algebra of the holonomyF groupoid of the foliation and isF a C∗-algebra. It has a dense subalgebra = C∞(V, ) which plays the role of the algebra of smooth functions on V/ . LetA D be a transversallyF elliptic operator on (V, ). The analytic index of D, index(F D) F ∈ K0(A), is an element of the K-theory of A. -
Laurent Schwartz (1915–2002), Volume 50, Number 9
Laurent Schwartz (1915–2002) François Treves, Gilles Pisier, and Marc Yor classics scholar and that of a mathematician. He had won the Concours Général in Latin; the Con- Biographical cours Général was and still is the most prestigious nationwide competition in France for high school- Sketch ers. Meanwhile he had become fascinated by the beauty of geometry, and, in the end, with the en- François Treves couragement of one of his professors in classics and of his uncle, the pediatrician Robert Debré, and Laurent Schwartz died in Paris on the 4th of July despite the rather unhelpful attitude of Hadamard, 2002. He was born in Paris on March 5, 1915. His dismayed that the sixteen-year-old Laurent was father, Anselme Schwartz, had been born in 1872 not acquainted with the Riemann zeta function, he in a small Alsatian town soon after the annexation of Alsatia by Germany. A fervent patriot, Anselme tried for admission to the science classes of the Schwartz had emigrated to France at the age of four- École Normale Supérieure (ENS), the most selective teen (before speaking French). In Paris he man- and most scholarly oriented of the “Grandes aged to carry out successful studies in medicine and Écoles”. He underwent the rather grueling two-year was to become a prominent surgeon in France in training (“hypotaupe”, followed by “taupe”, the the years between the two world wars. In 1907, tunnelling “submole” and “mole” years, so to speak) having just become the first Jewish surgeon ever preparatory to entrance to the ENS, where he was officially employed in a Paris hospital, Anselme admitted in 1934. -
Annals of K-Theory Vol. 1 (2016)
ANNALSOF K-THEORY Paul Balmer Spencer Bloch vol. 1 no. 4 2016 Alain Connes Guillermo Cortiñas Eric Friedlander Max Karoubi Gennadi Kasparov Alexander Merkurjev Amnon Neeman Jonathan Rosenberg Marco Schlichting Andrei Suslin Vladimir Voevodsky Charles Weibel Guoliang Yu msp A JOURNAL OF THE K-THEORY FOUNDATION ANNALS OF K-THEORY msp.org/akt EDITORIAL BOARD Paul Balmer University of California, Los Angeles, USA [email protected] Spencer Bloch University of Chicago, USA [email protected] Alain Connes Collège de France; Institut des Hautes Études Scientifiques; Ohio State University [email protected] Guillermo Cortiñas Universidad de Buenos Aires and CONICET, Argentina [email protected] Eric Friedlander University of Southern California, USA [email protected] Max Karoubi Institut de Mathématiques de Jussieu – Paris Rive Gauche, France [email protected] Gennadi Kasparov Vanderbilt University, USA [email protected] Alexander Merkurjev University of California, Los Angeles, USA [email protected] Amnon Neeman amnon.Australian National University [email protected] Jonathan Rosenberg (Managing Editor) University of Maryland, USA [email protected] Marco Schlichting University of Warwick, UK [email protected] Andrei Suslin Northwestern University, USA [email protected] Vladimir Voevodsky Institute for Advanced Studies, USA [email protected] Charles Weibel (Managing Editor) Rutgers University, USA [email protected] Guoliang Yu Texas A&M University, USA [email protected] PRODUCTION Silvio Levy (Scientific Editor) [email protected] Annals of K-Theory is a journal of the K-Theory Foundation(ktheoryfoundation.org). The K-Theory Foundation acknowledges the precious support of Foundation Compositio Mathematica, whose help has been instrumental in the launch of the Annals of K-Theory. -
Combinatorics of Square-Tiled Surfaces and Geometry of Moduli Spaces
COMBINATORICS OF SQUARE-TILED SURFACES AND GEOMETRY OF MODULI SPACES VINCENT DELECROIX, QUENTIN GENDRON, AND CARLOS MATHEUS Abstract. This text corresponds to the lecture notes of a minicourse delivered from August 16 to 20, 2021 at the IMPA{ICTP online summer school \Aritm´etica,Grupos y An´alisis(AGRA) IV". In particular, we discuss the same topics from our minicourse, namely, the basic theory of origamis and its connections to the calculation of Masur{Veech volumes of moduli spaces of translation surfaces. Contents 1. Square-tiled surfaces, Veech groups and arithmetic Teichm¨ullercurves 2 1.1. Basic definitions and some examples 2 1.2. Action of SL(2; Z) and Veech groups 4 1.3. Arithmetic Teichm¨ullercurves 5 1.4. Exercises 5 2. Some properties of Veech groups 7 2.1. Characteristic origamis 7 2.2. Origamis with prescribed Veech groups 8 2.3. Non-congruence Veech groups within H(2) 8 2.4. Exercises 10 3. Translation surfaces, moduli spaces and Masur{Veech volumes 11 3.1. Translation surfaces and GL(2; R)-action 11 3.2. Strata of translation surfaces 11 3.3. Masur-Veech volume and enumeration of square-tiled surfaces 12 3.4. Reduced versus non-reduced origamis 12 3.5. The Masur-Veech volume of H(2) 13 3.6. Further readings 15 4. Enumeration of square-tiled surfaces via quasi-modular forms 17 4.1. Frobenius formula and the generating function of square-tiled surfaces 17 4.2. Bloch-Okounkov and Kerov-Olshanski theorems 17 4.3. Computations 17 5. Classification of SL(2; Z)-orbits of origamis 18 Date: August 17, 2021. -
Lie Groupoids, Pseudodifferential Calculus and Index Theory
Lie groupoids, pseudodifferential calculus and index theory by Claire Debord and Georges Skandalis Université Paris Diderot, Sorbonne Paris Cité Sorbonne Universités, UPMC Paris 06, CNRS, IMJ-PRG UFR de Mathématiques, CP 7012 - Bâtiment Sophie Germain 5 rue Thomas Mann, 75205 Paris CEDEX 13, France [email protected] [email protected] Abstract Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pio- neering work on the index theory of foliations. In the present paper, we recall the basic notion involved: groupoids, their C∗-algebras, their pseudodifferential calculus... We review several re- cent and older advances on the involvement of Lie groupoids in noncommutative geometry. We then propose some open questions and possible developments of the subject. Contents 1 Introduction 2 2 Lie groupoids and their operators algebras 3 2.1 Lie groupoids . .3 2.1.1 Generalities . .3 2.1.2 Morita equivalence of Lie groupoids . .7 2.2 C∗-algebra of a Lie groupoid . .7 2.2.1 Convolution ∗-algebra of smooth functions with compact support . .7 2.2.2 Norm and C∗-algebra . .8 2.3 Deformation to the normal cone and blowup groupoids . .9 2.3.1 Deformation to the normal cone groupoid . .9 2.3.2 Blowup groupoid . 10 3 Pseudodifferential calculus on Lie groupoids 11 3.1 Distributions on G conormal to G(0) ........................... 12 3.1.1 Symbols and conormal distributions . 12 3.1.2 Convolution . 15 3.1.3 Pseudodifferential operators of order ≤ 0 ..................... 16 3.1.4 Analytic index . 17 3.2 Classical examples . -
The Top Mathematics Award
Fields told me and which I later verified in Sweden, namely, that Nobel hated the mathematician Mittag- Leffler and that mathematics would not be one of the do- mains in which the Nobel prizes would The Top Mathematics be available." Award Whatever the reason, Nobel had lit- tle esteem for mathematics. He was Florin Diacuy a practical man who ignored basic re- search. He never understood its impor- tance and long term consequences. But Fields did, and he meant to do his best John Charles Fields to promote it. Fields was born in Hamilton, Ontario in 1863. At the age of 21, he graduated from the University of Toronto Fields Medal with a B.A. in mathematics. Three years later, he fin- ished his Ph.D. at Johns Hopkins University and was then There is no Nobel Prize for mathematics. Its top award, appointed professor at Allegheny College in Pennsylvania, the Fields Medal, bears the name of a Canadian. where he taught from 1889 to 1892. But soon his dream In 1896, the Swedish inventor Al- of pursuing research faded away. North America was not fred Nobel died rich and famous. His ready to fund novel ideas in science. Then, an opportunity will provided for the establishment of to leave for Europe arose. a prize fund. Starting in 1901 the For the next 10 years, Fields studied in Paris and Berlin annual interest was awarded yearly with some of the best mathematicians of his time. Af- for the most important contributions ter feeling accomplished, he returned home|his country to physics, chemistry, physiology or needed him. -
17 Oct 2019 Sir Michael Atiyah, a Knight Mathematician
Sir Michael Atiyah, a Knight Mathematician A tribute to Michael Atiyah, an inspiration and a friend∗ Alain Connes and Joseph Kouneiher Sir Michael Atiyah was considered one of the world’s foremost mathematicians. He is best known for his work in algebraic topology and the codevelopment of a branch of mathematics called topological K-theory together with the Atiyah-Singer index theorem for which he received Fields Medal (1966). He also received the Abel Prize (2004) along with Isadore M. Singer for their discovery and proof of the index the- orem, bringing together topology, geometry and analysis, and for their outstanding role in building new bridges between mathematics and theoretical physics. Indeed, his work has helped theoretical physicists to advance their understanding of quantum field theory and general relativity. Michael’s approach to mathematics was based primarily on the idea of finding new horizons and opening up new perspectives. Even if the idea was not validated by the mathematical criterion of proof at the beginning, “the idea would become rigorous in due course, as happened in the past when Riemann used analytic continuation to justify Euler’s brilliant theorems.” For him an idea was justified by the new links between different problems which it illuminated. Our experience with him is that, in the manner of an explorer, he adapted to the landscape he encountered on the way until he conceived a global vision of the setting of the problem. Atiyah describes here 1 his way of doing mathematics2 : arXiv:1910.07851v1 [math.HO] 17 Oct 2019 Some people may sit back and say, I want to solve this problem and they sit down and say, “How do I solve this problem?” I don’t. -
2003 Jean-Pierre Serre: an Overview of His Work
2003 Jean-Pierre Serre Jean-Pierre Serre: Mon premier demi-siècle au Collège de France Jean-Pierre Serre: My First Fifty Years at the Collège de France Marc Kirsch Ce chapitre est une interview par Marc Kirsch. Publié précédemment dans Lettre du Collège de France,no 18 (déc. 2006). Reproduit avec autorisation. This chapter is an interview by Marc Kirsch. Previously published in Lettre du Collège de France, no. 18 (déc. 2006). Reprinted with permission. M. Kirsch () Collège de France, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France e-mail: [email protected] H. Holden, R. Piene (eds.), The Abel Prize, 15 DOI 10.1007/978-3-642-01373-7_3, © Springer-Verlag Berlin Heidelberg 2010 16 Jean-Pierre Serre: Mon premier demi-siècle au Collège de France Jean-Pierre Serre, Professeur au Collège de France, titulaire de la chaire d’Algèbre et Géométrie de 1956 à 1994. Vous avez enseigné au Collège de France de 1956 à 1994, dans la chaire d’Algèbre et Géométrie. Quel souvenir en gardez-vous? J’ai occupé cette chaire pendant 38 ans. C’est une longue période, mais il y a des précédents: si l’on en croit l’Annuaire du Collège de France, au XIXe siècle, la chaire de physique n’a été occupée que par deux professeurs: l’un est resté 60 ans, l’autre 40. Il est vrai qu’il n’y avait pas de retraite à cette époque et que les pro- fesseurs avaient des suppléants (auxquels ils versaient une partie de leur salaire). Quant à mon enseignement, voici ce que j’en disais dans une interview de 19861: “Enseigner au Collège est un privilège merveilleux et redoutable. -
Presentation of the Austrian Mathematical Society - E-Mail: [email protected] La Rochelle University Lasie, Avenue Michel Crépeau B
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Features S E European A Problem for the 21st/22nd Century M M Mathematical Euler, Stirling and Wallis E S Society History Grothendieck: The Myth of a Break December 2019 Issue 114 Society ISSN 1027-488X The Austrian Mathematical Society Yerevan, venue of the EMS Executive Committee Meeting New 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. Todd Fisher (Brigham Young University, Provo, USA) and Boris Hasselblatt (Tufts University, Medford, USA) Hyperbolic Flows (Zürich Lectures in Advanced Mathematics) ISBN 978-3-03719-200-9. 2019. 737 pages. Softcover. 17 x 24 cm. 78.00 Euro The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consulta- tion with experts is often needed to find them. This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. -
A Brief Account on the Relationship Between SMF and VMS Lê Dung Tráng
Asia Pacific Mathematics Newsletter A Brief Account On the Relationship between SMF and VMS Lê Dung Tráng he history of the link between the French Mathematical Society (SMF) and the Vietnam Mathematical Society (VMS) goes back to Tthe time Professor Lê Van Thiêm studied at the Ecole Normale Supérieure in Paris. It was during the Second World War. He passed his thesis in Göttingen a few days before it fell in the hands of the American Army. During many years the northern part of Vietnam L Schwartz, his wife, and Ta Quang Buu in North Vietnam, 1968 was isolated from the World. Laurent Schwartz, Professor at Ecole Polytechnique, In spite of the danger of the war a man stood at the a Fields medalist (considered to be a Nobel Prize in side of Professor Lê Van Thiêm to develop Mathematics. mathematics), founded the organisation “Comités Minister Ta Quang Buu studied in France before the France–Vietnam” in 1966 and, then, joined the Tribune Second World War. He told me that he was supposed of Bertrand Russell for crimes against humanity of to study at the Sorbonne, but in order to make things the American War in Vietnam. But, only in 1967 did difficult to the French masters he decided to pass a a mathematician, Alexander Grothendieck, also a free Licence, studying some mathematics, physics, Fields medalist, visit Vietnam for the first time. Laurent literature, English. By this way he understood the Schwartz visited Vietnam in 1968. However, it was more value of science and the meaning of mathematics. At as member of the Russell’s Tribune than as a mathemati- some point he was private secretary of President Ho cian. -
Dear Friends of Mathematics, and Translations to Complement the Original Source Material
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 web. Part of this project, which will play out over time, is to provide online annotation, commentary, Dear Friends of Mathematics, and translations to complement the original source material. The same will be done with the results of an earlier project to digitize the 888 AD copy of For the past five years, the annual meeting of the Euclid’s Elements. See www.claymath.org/library/ Clay Mathematics Institute has been a one-after- historical. noon event, held each November in Cambridge, Massachusetts, devoted to presentation of the Mathematics has a millennia-long history during Clay Research Awards and to talks on the work which creative activity has waxed and waned. of the recipients.