____ i 1 Proceedings of ~------ the I nternationa I Congress of Mathematicians August 3-ll, 1994 ZUrich, Switzerland Birkhauser Verlag Basel · Boston · Berlin Editor: S. D. Chatterji EPFL Departement de Mathematiques I 015 Lausanne Switzerland The logo for ICM 94 was designed by Georg Staehelin, Bachweg 6, 8913 Ottenbach, Switzerland. A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA Deutsche Bibliothek Cataloging-in-Publication Data International Congress of Mathematicians <1994, Ziirich>: Proceedings of the International Congress of Mathematicians 1994: August 3- I I, 1994, Zurich, Switzerland I [Ed.: S.D. Chatterji]. - Basel ; Boston ; Berlin : Birkhauser. ISBN 978-3-0348-9897-3 ISBN 978-3-0348-9078-6 (eBook) DOI 10.1007/978-3-0348-9078-6 NE: S. D. Chauerji [Hrsg.] Vol. I ( 1995) 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. broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission from the copyright owner must be obtained. © 1995 B irkhauser Verlag Softcover reprint of the hardcover 1st edition 1995 P.O. Box 133 CH-4010 Basel Switzerland Printed on acid-free paper produced from chlorine-free pulp. TCF oo Layout, typesetting by mathScreen online, Allschwil 98765432 1 Table of Contents Volume I Preface vii Past Congresses viii Past Fields Medalists and Rolf Nevanlinna Prize Winners ix Organization of the Congress . xi The Organizing Committee of the Congress . xiii List of Donors . XV Opening Ceremonies xvii Closing Ceremonies xxxi Scientific Program xxxvii Invited One-Hour Addresses at the Plenary Sessions Invited Forty-Five Minute Addresses at the Section Meetings List of Participants (Ordinary Members) xlv Membership by Country . lxx The Work of the Fields Medalists and the Rolf Nevanlinna Prize Winner . 1 Invited One-Hour Plenary Addresses . 29 Invited Forty-Five Minute Addresses at the Section Meetings 267 Section 1. Logic .. 269 Section 2. Algebra 298 Section 3. Number theory 363 Section 4. Geometry 443 Section 5. Topology. 548 Section 6. Algebraic geometry 648 Author Index . 716 vi Table of Contents Volume II Table of Contents . v Scientific Program vii Invited Forty-Five Minute Addresses at the Section Meetings (cont.) 719 Section 7. Lie groups and representations 721 Section 8. Real and complex analysis . 817 Section 9. Operator algebras and functional analysis 922 Section 10. Probability and statistics . 980 Section 11. Partial differential equations 1055 Section 12. Ordinary differential equations and dynamical systems . 1159 Section 13. Mathematical physics 1238 Section 14. Combinatorics . 1333 Section 15. Mathematical aspects of computer science 1395 Section 16. Numerical analysis and scientific computing 1420 Section 17. Applications of mathematics in the sciences 1473 Section 18. Teaching and popularization of mathematics 1546 Section 19. History of mathematics 1568 Author Index . 1604 Preface The Proceedings of the International Congress of Mathematicians 1994, held in Zurich from August 3rd to 11th, 1994, are published in two volumes. Volume I con­ tains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1-6. Volume II contains the invited addresses for Section Meetings 7-19. A complete author index is included in both volumes. The five invited lectures organized by the ICMI (International Commission on Mathematical Instruction) and the five invited lectures organized by the ICHM (In­ ternational Commission on History of Mathematics) which were a part of the sci­ entific programme have not been included in these Proceedings. Also not included are the short communications presented in poster sessions during the Congress; summaries of those communications which were received in due time were printed in a separate volume Abstracts of Short Communications; another volume contain­ ing the available abstracts of the plenary addresses, the invited section lectures and the ICMI and ICHM lectures was also prepared. Both volumes of abstracts were given to all ordinary members at the time of their registration at the Congress. Lausanne, April 1995 The Editor Past Congresses 1897 Zurich 1900 Paris 1904 Heidelberg 1908 Roma 1912 Cambridge, UK 1920 Strasbourg 1924 Toronto 1928 Bologna 1932 Zurich 1936 Oslo 1950 Cambridge, USA 1954 Amsterdam 1958 Edinburgh 1962 Stockholm 1966 Moskva 1970 Nice 1974 Vancouver 1978 Helsinki 1982 Warszawa (held in 1983) 1986 Berkeley 1990 Kyoto Past Fields Medalists and Rolf N evanlinna Prize Winners Recipients of Fields Medals 1936 1974 Lars V. Ahlfors Enrico Bombieri Jesse Douglas David B. Mumford 1950 1978 Laurent Schwartz Pierre R. Deligne Atle Selberg Charles F. Fefferman Grigorii A. Margulis 1954 Daniel G. Quillen K unihiko Kodaira Jean-Pierre Serre 1982 Alain Connes 1958 William P. Thurston Klaus F. Roth Shing-Thng Yau Rene Thorn 1986 1962 Simon K. Donaldson Lars Hi:irmander Gerd Faltings John W. Milnor Michael H. Freedman 1966 1990 Michael F. Atiyah Vladimir G. Drinfeld Paul J. Cohen Vaughan F. R. Jones Alexander Grothendieck Shigefumi Mori Stephen Smale Edward Witten 1970 Alan Baker Heisuke Hironaka Sergei P. N ovikov John G. Thompson Rolf Nevanlinna Prize Winners 1982 Robert E. Tarjan 1986 Leslie G. Valiant 1990 Alexander A. Razborov The Kongresshaus in Zurich Organization of the Congress The 1994 International Congress of Mathematicians (ICM) was held in Zurich, Switzerland, at the invitation of the Swiss Mathematical Society (SMS), repre­ senting the Swiss mathematical community, and under the auspices of the Inter­ national Mathematical Union (IMU) whose official approval was announced at the 1990 ICM held in Kyoto. The SMS invitation was made possible by the support promised at the very outset by the appropriate authorities of the Federal Govern­ ment, the Government of the Canton of Zurich and the Municipality of the city of Zurich. Financial help given by these and other public and academic bodies as well as the donations of many private corporations and individuals were crucial for the realization of the Congress; a list of the donors is given in these Proceedings. Naturally, the registration fees paid by the participants of the Congress were an essential element in financing the organization. The members of the Organizing Committee are listed in the following pages; also listed are the members of the Honorary Committee, the Finance Committee, the Scientific Committee and the Administrative Staff. The scientific program of the Congress was in the hands of the Programme Committee appointed by the IMU. Its members were Louis Nirenberg (Chair­ man), Simon K. Donaldson, Vladimir Drinfeld, Pierre de laHarpe, Richard Karp, Hanspeter Kraft, Andrew J. Majda, Michel Raynaud andY. Sinai. Recipients of the Fields Medals and the Rolf Nevanlinna Prize were selected by the respective committees appointed by the IMU. The Fields Medal Commit­ tee consisted of David Mumford (Chairman), Masaki Kashiwara, Barry Mazur, Alexander Schrijver, Dennis Sullivan, Jacques Tits and S. R. S. Varadhan. The Rolf Nevanlinna Prize Committee consisted of Jacques-Louis Lions (Chairman), H. W. Lenstra, R. Tarjan, M. Yamaguti and J. Matiyasevic. The Organizing Committee was responsible for all the other activities of the Congress. MCI Travel (Zurich) handled accomodation and related arrangements as the official travel agency of the Organizing Committee. The opening and the closing ceremonies as well as all the one-hour Plenary Addresses were held in the Zurich KongreBhaus. The forty-five minute section lectures were organized in various parallel sessions in the auditoria of the ETH Zurich and the University of Zurich. There were 16 plenary lectures and 148 sec­ tion lectures on the program. In addition, there were five lectures organized by the International Commission on Mathematical Instruction and five lectures organized by the International Commission on the History of Mathematics which were sched­ uled along with the section lectures. Poster sessions arranged at the ETH Zurich permitted the presentation of numerous short communications; summaries of 782 of these, received before a fixed deadline, were printed in a separate abstracts volume and a further 100 additional contributions were actually presented at the xii Organization of the Congress poster sessions. There were also several informal seminars as well as a symposium organized on Thursday, August 4, by the Association for Women in Mathematics and the European Women in Mathematics. In the afternoon of August 3, lectures reporting on the works of the Fields Medalists and the N evanlinna Prize Winner were presented; an account will be found in these Proceedings. A total of 2476 participants from 92 countries along with 363 accompanying members attended the Congress; 77 exhibitors were present. The Organizing Committee was able to give financial support for the partic­ ipation of the prize winners, the officials of the IMU, 19 of the invited speakers and some 200 participants from Eastern Europe. The IMU, through its special Development Fund, paid the travel expenses of 79 young scholars from developing countries whose living expenses were covered by the Organizing Committee. All participants were invited to a number of social events. A reception was offered by the city of Zurich in the Kongrel3haus on the evening of the opening day of the Congress, on Wednesday, August 3. A Buffet-Banquet was given in the Irchel campus of the Universiy of Zurich, on the evening of Friday, August 5. Tuesday evening, August 9, a violin recital by Hansheinz Schneeberger, accompanied by Gerard Wyss, in the Tonhalle (Kongrel3haus) and a performance by the pantomime group Mummenschanz together with the folk music group Trio da Besto in the Kongrel3saal (Kongrel3haus) were proposed. Evening reception at Irchel Campus of the University of Zurich The Organizing Committee of the Congress Honorary Committee Mrs.