Mathematicians I Have Known
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A Tribute to Henri Cartan
A Tribute to Henri Cartan This collection of articles paying tribute to the mathematician Henri Cartan was assembled and edited by Pierre Cartier, IHÉS, and Luc Illusie, Université Paris-Sud 11, in consultation with Jean-Pierre Serre, Collège de France. The collection begins with the present introductory article, which provides an overview of Cartan's work and a short contribution by Michael Atiyah. This overview is followed by three additional articles, each of which focuses on a particular aspect of Cartan's rich life. —Steven G. Krantz This happy marriage, which lasted until his death Jean-Pierre Serre (followed, a few months later, by that of his wife), Henri Cartan produced five children: Jean, Françoise, Étienne, 8 July 1904–13 August 2008 Mireille, and Suzanne. In September 1939, at the beginning of the Henri Cartan was, for many of the younger gen- war, he moved to Clermont-Ferrand, where the eration, the symbol of the resurgence of French University of Strasbourg had been evacuated. A mathematics after World War II. He died in 2008 year later he got a chair at the Sorbonne, where he at the age of 104 years. was given the task of teaching the students of the Personal Life ENS. This was a providential choice that allowed the “normaliens” (and many others) to benefit for Henri was the eldest son of the mathematician more than twenty-five years (1940–1965) from Élie Cartan (1869–1951), born in Dolomieu (Isère), his courses and seminars. In fact there was a two- and of his wife Marie-Louise Bianconi, of Corsican year interruption when he returned to Strasbourg origin. -
The Adams-Novikov Spectral Sequence for the Spheres
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY Volume 77, Number 1, January 1971 THE ADAMS-NOVIKOV SPECTRAL SEQUENCE FOR THE SPHERES BY RAPHAEL ZAHLER1 Communicated by P. E. Thomas, June 17, 1970 The Adams spectral sequence has been an important tool in re search on the stable homotopy of the spheres. In this note we outline new information about a variant of the Adams sequence which was introduced by Novikov [7]. We develop simplified techniques of computation which allow us to discover vanishing lines and periodic ity near the edge of the E2-term, interesting elements in E^'*, and a counterexample to one of Novikov's conjectures. In this way we obtain independently the values of many low-dimensional stems up to group extension. The new methods stem from a deeper under standing of the Brown-Peterson cohomology theory, due largely to Quillen [8]; see also [4]. Details will appear elsewhere; or see [ll]. When p is odd, the p-primary part of the Novikov sequence be haves nicely in comparison with the ordinary Adams sequence. Com puting the £2-term seems to be as easy, and the Novikov sequence has many fewer nonzero differentials (in stems ^45, at least, if p = 3), and periodicity near the edge. The case p = 2 is sharply different. Computing E2 is more difficult. There are also hordes of nonzero dif ferentials dz, but they form a regular pattern, and no nonzero differ entials outside the pattern have been found. Thus the diagram of £4 ( =£oo in dimensions ^17) suggests a vanishing line for Ew much lower than that of £2 of the classical Adams spectral sequence [3]. -
Symmetric Products of Surfaces; a Unifying Theme for Topology
Symmetric products of surfaces; a unifying theme for topology and physics Pavle Blagojevi´c Mathematics Institute SANU, Belgrade Vladimir Gruji´c Faculty of Mathematics, Belgrade Rade Zivaljevi´cˇ Mathematics Institute SANU, Belgrade Abstract This is a review paper about symmetric products of spaces SP n(X) := n X /Sn. We focus our attention on the case of 2-manifolds X and make a journey through selected topics of algebraic topology, algebraic geometry, mathematical physics, theoretical mechanics etc. where these objects play an important role, demonstrating along the way the fundamental unity of diverse fields of physics and mathematics. 1 Introduction In recent years we have all witnessed a remarkable and extremely stimulating exchange of deep and sophisticated ideas between Geometry and Physics and in particular between quantum physics and topology. The student or a young scientist in one of these fields is often urged to master elements of the other field as quickly as possible, and to develop basic skills and intuition necessary for understanding the contemporary research in both disciplines. The topology and geometry of manifolds plays a central role in mathematics and likewise in physics. The understanding of duality phenomena for manifolds, mastering the calculus of characteristic classes, as well as understanding the role of fundamental invariants like the signature or Euler characteristic are just examples of what is on the beginning of the growing list of prerequisites for a student in these areas. arXiv:math/0408417v1 [math.AT] 30 Aug 2004 A graduate student of mathematics alone is often in position to take many spe- cialized courses covering different aspects of manifold theory and related areas before an unified picture emerges and she or he reaches the necessary level of maturity. -
Bfm:978-1-4612-2582-9/1.Pdf
Progress in Mathematics Volume 131 Series Editors Hyman Bass Joseph Oesterle Alan Weinstein Functional Analysis on the Eve of the 21st Century Volume I In Honor of the Eightieth Birthday of I. M. Gelfand Simon Gindikin James Lepowsky Robert L. Wilson Editors Birkhauser Boston • Basel • Berlin Simon Gindikin James Lepowsky Department of Mathematics Department of Mathematics Rutgers University Rutgers University New Brunswick, NJ 08903 New Brunswick, NJ 08903 Robert L. Wilson Department of Mathematics Rutgers University New Brunswick, NJ 08903 Library of Congress Cataloging-in-Publication Data Functional analysis on the eve of the 21 st century in honor of the 80th birthday 0fI. M. Gelfand I [edited) by S. Gindikin, 1. Lepowsky, R. Wilson. p. cm. -- (Progress in mathematics ; vol. 131) Includes bibliographical references. ISBN-13:978-1-4612-7590-9 e-ISBN-13:978-1-4612-2582-9 DOl: 10.1007/978-1-4612-2582-9 1. Functional analysis. I. Gel'fand, I. M. (lzraU' Moiseevich) II. Gindikin, S. G. (Semen Grigor'evich) III. Lepowsky, J. (James) IV. Wilson, R. (Robert), 1946- . V. Series: Progress in mathematics (Boston, Mass.) ; vol. 131. QA321.F856 1995 95-20760 515'.7--dc20 CIP Printed on acid-free paper d»® Birkhiiuser ltGD © 1995 Birkhliuser Boston Softcover reprint of the hardcover 1st edition 1995 Copyright is not claimed for works of u.s. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the copyright owner. -
Bart, Hempfling, Kaashoek. (Eds.) Israel Gohberg and Friends.. on The
Israel Gohberg and Friends On the Occasion of his 80th Birthday Harm Bart Thomas Hempfling Marinus A. Kaashoek Editors Birkhäuser Basel · Boston · Berlin Editors: Harm Bart Marinus A. Kaashoek Econometrisch Instituut Department of Mathematics, FEW Erasmus Universiteit Rotterdam Vrije Universiteit Postbus 1738 De Boelelaan 1081A 3000 DR Rotterdam 1081 HV Amsterdam The Netherlands The Netherlands e-mail: [email protected] e-mail: [email protected] Thomas Hempfling Editorial Department Mathematics Birkhäuser Publishing Ltd. P.O. Box 133 4010 Basel Switzerland e-mail: thomas.hempfl[email protected] Library of Congress Control Number: 2008927170 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. ISBN 978-3-7643-8733-4 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced of chlorine-free pulp. TCF ∞ Printed in Germany ISBN 978-3-7643-8733-4 e-ISBN 978-3-7643-8734-1 9 8 7 6 5 4 3 2 1 www.birkhauser.ch Contents Preface.......................................................................ix CongratulationsfromthePublisher...........................................xii PartI.MathematicalandPhilosophical-MathematicalTales...................1 I. -
Discurso De Investidura Como Doctor “Honoris Causa” Del Excmo. Sr
Discurso de investidura como Doctor “Honoris Causa” del Excmo. Sr. Simon Kirwan Donaldson 20 de enero de 2017 Your Excellency Rector Andradas, Ladies and Gentlemen: It is great honour for me to receive the degree of Doctor Honoris Causa from Complutense University and I thank the University most sincerely for this and for the splendid ceremony that we are enjoying today. This University is an ancient institution and it is wonderful privilege to feel linked, through this honorary degree, to a long line of scholars reaching back seven and a half centuries. I would like to mention four names, all from comparatively recent times. First, Eduardo Caballe, a mathematician born in 1847 who was awarded a doctorate of Science by Complutense in 1873. Later, he was a professor in the University and, through his work and his students, had a profound influence in the development of mathematics in Spain, and worldwide. Second, a name that is familiar to all of us: Albert Einstein, who was awarded a doctorate Honoris Causa in 1923. Last, two great mathematicians from our era: Vladimir Arnold (Doctor Honoris Causa 1994) and Jean- Pierre Serre (2006). These are giants of the generation before my own from whom, at whose feet---metaphorically—I have learnt. Besides the huge honour of joining such a group, it is interesting to trace one grand theme running the work of all these four people named. The theme I have in mind is the interplay between notions of Geometry, Algebra and Space. Of course Geometry begins with the exploration of the space we live in—the space of everyday experience. -
Arxiv:1402.0409V1 [Math.HO]
THE PICARD SCHEME STEVEN L. KLEIMAN Abstract. This article introduces, informally, the substance and the spirit of Grothendieck’s theory of the Picard scheme, highlighting its elegant simplicity, natural generality, and ingenious originality against the larger historical record. 1. Introduction A scientific biography should be written in which we indicate the “flow” of mathematics ... discussing a certain aspect of Grothendieck’s work, indicating possible roots, then describing the leap Grothendieck made from those roots to general ideas, and finally setting forth the impact of those ideas. Frans Oort [60, p. 2] Alexander Grothendieck sketched his proof of the existence of the Picard scheme in his February 1962 Bourbaki talk. Then, in his May 1962 Bourbaki talk, he sketched his proofs of various general properties of the scheme. Shortly afterwards, these two talks were reprinted in [31], commonly known as FGA, along with his commentaries, which included statements of nine finiteness theorems that refine the single finiteness theorem in his May talk and answer several related questions. However, Grothendieck had already defined the Picard scheme, via the functor it represents, on pp.195-15,16 of his February 1960 Bourbaki talk. Furthermore, on p.212-01 of his February 1961 Bourbaki talk, he had announced that the scheme can be constructed by combining results on quotients sketched in that talk along with results on the Hilbert scheme to be sketched in his forthcoming May 1961 Bourbaki talk. Those three talks plus three earlier talks, which prepare the way, were also reprinted in [31]. arXiv:1402.0409v1 [math.HO] 3 Feb 2014 Moreover, Grothendieck noted in [31, p. -
Fall 2017 MATH 70330 “Intermediate Geometry and Topology” Pavel Mnev Detailed Plan. I. Characteristic Classes. (A) Fiber/Vec
Fall 2017 MATH 70330 \Intermediate Geometry and Topology" Pavel Mnev Detailed plan. I. Characteristic classes. (a) Fiber/vector/principal bundles. Examples. Connections, curvature. Rie- mannian case. Ref: [MT97]. (b) (2 classes.) Stiefel-Whitney, Chern and Pontryagin classes { properties, axiomatic definition. Classifying map and classifying bundle. RP 1; CP 1, infinite Grassmanians Gr(n; 1), CW structure, cohomology ring (univer- sal characteristic classes). Characteristic classes as obstructions (e.g. for embeddability of projective spaces). Euler class. Also: Chern character, splitting principle, Chern roots. Also: BG for a finite group/Lie group, group cohomology. Ref: [MS74]; also: [BT82, Hat98, LM98, May99]. (c) Chern-Weil homomorphism. Example: Chern-Gauss-Bonnet formula. Chern- Simons forms. Ref: Appendix C in [MS74]; [AM05, Dup78, MT97]. (d) Equivariant cohomology. Borel model (homotopy quotient), algebraic ver- sion { Cartan and Weil models. Ref: [GS99, Mei06, Tu13]. II. Bits of symplectic geometry. (a) Symplectic linear algebra, Lagrangian Grassmanian, Maslov class. Ref: [BW97, Ran, MS17]. (b) Symplectic manifolds, Darboux theorem (proof via Moser's trick). Dis- tinguished submanifolds (isotropic, coisotropic, Lagrangian). Examples. Constructions of Lagrangians in T ∗M (graph, conormal bundle). Ref: [DS00]. (c) Hamiltonian group actions, moment maps, symplectic reduction. Ref: [Jef] (lectures 2{4,7), [DS00]. (d) (Optional) Convexity theorem (Atyiah-Guillemin-Sternberg) for the mo- ment map of a Hamiltonian torus action. Toric varieties as symplectic re- ductions, their moment polytopes, Delzant's theorem. Ref: [Pra99, Sch], Part XI in [DS00], lectures 5,6 in [Jef]. (e) Localization theorems: Duistermaat-Heckman and Atiyah-Bott. Ref: [Mei06, Tu13], [Jef] (lecture 10). (f) (Optional) Classical field theory via Lagrangian correspondences. -
All That Math Portraits of Mathematicians As Young Researchers
Downloaded from orbit.dtu.dk on: Oct 06, 2021 All that Math Portraits of mathematicians as young researchers Hansen, Vagn Lundsgaard Published in: EMS Newsletter Publication date: 2012 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Hansen, V. L. (2012). All that Math: Portraits of mathematicians as young researchers. EMS Newsletter, (85), 61-62. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. -
Analysis in Complex Geometry
1946-4 School and Conference on Differential Geometry 2 - 20 June 2008 Analysis in Complex Geometry Shing-Tung Yau Harvard University, Dept. of Mathematics Cambridge, MA 02138 United States of America Analysis in Complex Geometry Shing-Tung Yau Harvard University ICTP, June 18, 2008 1 An important question in complex geometry is to char- acterize those topological manifolds that admit a com- plex structure. Once a complex structure is found, one wants to search for the existence of algebraic or geo- metric structures that are compatible with the complex structure. 2 Most geometric structures are given by Hermitian met- rics or connections that are compatible with the com- plex structure. In most cases, we look for connections with special holonomy group. A connection may have torsion. The torsion tensor is not well-understood. Much more research need to be done especially for those Hermitian connections with special holonomy group. 3 Karen Uhlenbeck Simon Donaldson By using the theorem of Donaldson-Uhlenbeck-Yau, it is possible to construct special holonomy connections with torsion. Their significance in relation to complex or algebraic structure need to be explored. 4 K¨ahler metrics have no torsion and their geometry is very close to that of algebraic geometry. Yet, as was demonstrated by Voisin, there are K¨ahler manifolds that are not homotopy equivalent to any algebraic manifolds. The distinction between K¨ahler and algebraic geometry is therefore rather delicate. Erich K¨ahler 5 Algebraic geometry is a classical subject and there are several natural equivalences of algebraic manifolds: bi- rational equivalence, biregular equivalence, and arith- metic equivalence. -
Arxiv:1003.6025V1 [Math.HO] 31 Mar 2010 Karl Stein (1913-2000)
Karl Stein (1913-2000) Alan Huckleberry Karl Stein was born on the first of January 1913 in Hamm in Westfalen, grew up there, received his Abitur in 1932 and immediately thereafter be- gan his studies in M¨unster. Just four years later, under the guidance of Heinrich Behnke, he passed his Staatsexam, received his promotion and became Behnke’s assistant. Throughout his life, complex analysis, primarily in higher dimensions (“mehrere Ver¨anderliche”), was the leitmotif of Stein’s mathematics. As a fresh Ph.D. in M¨unster in 1936, under the leadership of the master Behnke, he had already been exposed to the fascinating developments in this area. The brilliant young Peter Thullen was proving fundamental theorems, Henri Cartan had visited M¨unster, and Behnke and Thullen had just writ- ten the book on the subject. It must have been clear to Stein that this was the way to go. Indeed it was! The amazing phenomenon of analytic continuation in higher dimensions had already been exemplified more than 20 years be- fore in the works of Hartogs and E. E. Levi. Thullen’s recent work had gone much further. In the opposite direction, Cartan and Thullen had arXiv:1003.6025v1 [math.HO] 31 Mar 2010 proved their characterization of domains in Cn which admit a holomor- phic function which can not be continued any further. Behnke himself was also an active participant in mathematics research, always bringing new ideas to M¨unster. This was indeed an exciting time for the young researcher, Karl Stein. Even though the pest of the Third Reich was already invading academia, Behnke kept things going for as long as possible. -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes ....................................................................................................................