Proceedings of the International Congress of Mathematicians: August 3–11, 1994 Zürich, Switzerland

898 Pages·1995·24.42 MB·English

by  Jeffrey Adams (auth.)

_ _ _ i
Proceedings of
the Intern-a-t-i-o-n-a--l ~---------
Congress of
Mathema-t-ic~i-a-n--s- ----------
August 3-11,1994
Zurich, Switzerland
BirkhCiuser Verlag
Basel· Boston· Berlin
Editor:
S. D. Chatterji
EPFL
Departement de Mathematiques
1015 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 - II, 1994, ZUrich, Switzerland / [Ed.: S. D.
ChatterjiJ. -Basel; Boston; Berlin: Birkhiiuser.
ISBN-13: 978-3-0348-9897-3 e-ISBN-13: 978-3-0348-9078-6
DOl: 10.1007/978-3-0348-9078-6
NE: S. D. Chatterji [Hrsg.J
Vol. 2 (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
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or in other ways, and storage in data banks. For any kind
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must be obtained.
© 1995 Birkhiiuser Verlag
Softcover reprint of the hardcover I st edition 1995
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Printed on acid-free paper produced from chlorine-free pulp. TCF oc
Layout, typesetting by mathScreen online, Allschwil
987654321
Table of Contents
Volume I
Preface Vll
Past Congresses viii
Past Fields Medalists and Rolf Nevanlinna Prize Winners ix
Organization of the Congress. . . . . . . . . Xl
The Organizing Committee of the Congress . Xlll
List of Donors . . . . xv
Opening Ceremonies XVll
Closing Ceremonies XXXI
Scientific Program XXXVll
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 Addrf)sses 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 Vll
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
Scientific Program
The Work of the Fields Medalists and the Rolf Nevanlinna Prize Winner
Luis Caffarelli: The work of Jean Bourgain ....... . 3
s. R. S. Varadhan: The work of Pierre-Louis Lions ... . 6
Adrien Douady: Presentation de Jean-Christophe Yoecoz 11
Walter Feit: On the work of Efim Zelmanov ..... . 17
Yuri Matiyasevich: On some works of A vi Wigderson 25
Invited One-Hour Addresses at the Plenary Sessions
Lasz16 Babai: Transparent proofs and limits to approximation
( Manuscript not submitted) *
Jean Bourgain: Harmonic analysis and nonlinear partial differential
equations ............................ . 31
John H. Conway: Sphere packings, lattices, codes, and greed 45
Ingrid Daubechies: Wavelets and other phase space localization methods 57
Jurg Frohlich: The fractional quantum Hall effect, Chern-Simons theory,
and integral lattices . . . . . . . . . . . . . . . . . . . . 75
Joseph B. Keller: Wave propagation . . . . . . . . . . . . . . . . 106
Maxim Kontsevich: Homological algebra of mirror symmetry . . 120
Pierre-Louis Lions: On some recent methods for nonlinear partial
differential equations . . . . . . . . . . . . . . . . . . . . . 140
Marina Ratner: Interactions between ergodic theory, Lie groups and
number theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Paul Seymour: Progress on the four-colour theorem . . . . . . . . . 183
Clifford H. Taubes: Anti-self dual geometry (Manuscript not submitted)
S. R. S. Varadhan: Entropy methods in hydrodynamic scaling ..... 196
Victor A. Vassiliev: Topology of discriminants and their complements 209
Dan Voiculescu: Free probability theory: Random matrices and
von Neumann algebras ................ . 227
Andrew Wiles: Modular forms, elliptic curves and Fermat's
Last Theorem . . . . . . . . . . . . . . . . . . . . . . 243
Jean-Christophe Yoccoz: Recent developments in dynamics 246
*) The material presented is largely covered by a recent survey under this title by L. Babai
in: First European Congress of Mathematics, Paris 1992 (A. Joseph et aI., eds.), Vol. I,
Progress in Math. 119, Birkhiiuser Verlag, Basel und Boston 1994, pp. 31-91.
viii Scientific Program
Invited Forty-Five Minute Addresses at the Section Meetings
Section 1. Logic
James E. Baumgartner: New trends in partition calculus
(Manuscript not submitted)
Alain Louveau: On the size of quotients by definable equivalence
relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
Anand Pillay: Model theory, differential algebra, and number theory 277
Pavel Pudlak: Logic and complexity: Independence results and the
complexity of propositional calculus . . . . . . . . . . . . . . 288
Section 2. Algebra
Peter Littelmann: The path model for representations of symmetrizable
Kac-Moodyalgebras ........................ 298
Alexander Lubotzky: Subgroup growth . . . . . . . . . . . . . . . . . 309
Jean-Fran<;ois Mestre: Constructions polynomiales et tMorie de Galois 318
Raman Parimala: Study of quadratic forms - Some connections with
geometry . . . . . . . . . . . . . . . . . . . . . . . . . 324
Gerald W. Schwarz: Invariant differential operators 333
Andrei Suslin: Algebraic K-theory and motivic cohomology 342
Michel Van den Bergh: Modules of covariants. . . . . . . . 352
Section 3. Number theory
Noam Elkies: Linearized algebra (Manuscript not submitted)
John B. Friedlander: Bounds for L-functions ........ . 363
Alexander B. Goncharov: Polylogarithms in arithmetic and geometry . 374
Andrew Granville: Unexpected irregularities in the distribution of
prime numbers ......................... 388
Bernadette Perrin-Riou: Fonctions L p-adiques . . . . . . . . . . . 400
Carl Pomerance: The role of smooth numbers in number theoretic
algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 411
Michael Rapoport: Non-archimedean period domains. . . . . . 423
Richard Taylor: Representations of Galois groups associated to
modular forms. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 435
Section 4. Geometry
Michael T. Anderson: Einstein metrics and metrics with bounds on
Ricci curvature .. . . . . . . . . . . . . . . . . . . . 443
Victor Bangert: Minimal foliations and laminations 453
Kevin Corlette: Harmonic maps, rigidity and Hodge theory 465
Alexander B. Givental: Homological geometry and mirror symmetry 472
Nikolaos Kapouleas: Constant mean curvature surfaces in Euclidean
spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Frances Kirwan: Intersection pairings on quotients and moduli spaces,
and Witten's nonabelian localisation. . . . . . . . . . . . . . . . 491
Scientific Program ix
Claude LeBrun: Anti-self-dual metrics and Kahler geometry . . 498
Jun Li: The geometry of moduli spaces of vector bundles over
algebraic surfaces ..................... . 508
Tomasz S. Mrowka: Embedded surfaces and the structure of
Donaldson's polynomial invariants (Manuscript not submitted)
G. Perelman: Spaces with curvature bounded below ..... 517
Dietmar Salamon: Lagrangian intersections, 3-manifolds with
boundary, and the Atiyah-Floer conjecture ...... . 526
Claude Viterbo: Generating functions, symplectic geometry and
applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
Section 5. Topology
Robert E. Gompf: Smooth 4-manifolds and symplectic topology. 548
Michael J. Hopkins: Topological modular forms, the Witten genus,
and the theorem of the cube . . . . . . . . . . . . . . . . . . 554
Jean Lannes: Applications dont la source est un classifiant. . . . . 566
H. Blaine Lawson, Jr.: Spaces of algebraic cycles: Levels of holomorphic
approximation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
John Luecke: Dehn surgery on knots in the 3-sphere . . . . . . . . . . . 585
E. Rips: Cyclic splittings of finitely presented groups and the canonical
JSJ-decomposition ..................... 595
Joachim H. Rubinstein: An algorithm to recognize the 3-sphere . . . . . 601
Julius L. Shaneson: Characteristic classes, lattice points, and
Euler-MacLaurin formulae . . . . . . . . . . . . . . . .. ..... 612
Stephan Stolz: Positive scalar curvature metrics - Existence and
classification questions . . . . . . . . . . . . . . . . . . . 625
Shmuel Weinberger: Nonlocally linear manifolds and orbifolds . 637
Section 6. Algebraic geometry
Gerd Faltings: Mumford-Stabilitat in der algebraischen Geometrie 648
David Harbater: Fundamental groups of curves in characteristic p . 656
Uwe Jannsen: Mixed motives, motivic cohomology, and Ext-groups 667
Yoichi Miyaoka: Rational curves on algebraic varieties . . . . . . . 680
Madhav V. Nori: Some Eisenstein cohomology classes for the integral
unimodular group . . . . . . . . . . . . . . . . . . . . . . . . . . 690
Alexei N. Rudakov: Rigid and exceptional vector bundles and sheaves on
a Fano variety . . . . . . . . . . . . . . . . . . . . . . . . . 697
Claire Voisin: Variations of Hodge structure and algebraic cycles 706
Section 7. Lie groups and representations
Jeffrey Adams: Genuine representations of the metaplectic group and
epsilon factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721
Henning Haahr Anderson: The irreducible characters for semi-simple algebraic
groups and for quantum groups .................... 732
x Scientific Program
Richard E. Borcherds: Automorphic forms on Os+2,2(lR)+ and generalized
Kac-Moodyalgebras 744
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Michel Brion: Spherical varieties 753
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Marc Burger: Rigidity properties of group actions on CAT(O)-spaces 761
0 0
Colin Jo Bushnell: Smooth representations of p-adic groups: The role of
compact open subgroups 770
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
So Go Dani: Flows on homogeneous spaces and diophantine approximation 780
Jian-Shu Li: Singular automorphic forms 790
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wolfgang Soergcl: Gradings on representation categories 800
0 0 0 0 0 0 0
Jean-Loup Waldspurger: Comparaison d'integrales orbit ales pour des
groupes p-adiques 807
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Section 8. Real and complex analysis
Jean-Pierre Demailly: L2-methods and effective results in
algebraic geometry 817
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
David Drasin: Meromorphic functions: Progress and problems 828
0
Howard Masur: Teichmuller space, dynamics, probability 836
0 0 0
Ngaiming Mok: Fibering compact Kahler manifolds over projective
algebraic varieties of general type 850
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Duong Ho Phong: Regularity of Fourier integral operators 862
0 0 0 0 0
Stephen Wo Semmes: Finding structure in sets with little smoothness 875
0
Mitsuhiro Shishikura: Topological, geometric, and complex analytic
properties of Julia sets 886
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Christopher Do Sogge: Smoothing estimates for the wave equation and
applications 896
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Pekka Tukia: A survey of Mobius groups 907
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Sidney Mo Webster: Geometric and dynamical aspects of real submanifolds
of complex space 917
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Section 9. Operator algebras and functional analysis
George Ao Elliott: The classification problem for amenable C*-algebras 922
Wo To Gowers: Recent results in the theory of infinite-dimensional
Banach spaces 933
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Eberhard Kirchberg: Exact C*-algebras, tensor products, and the
classification of purely infinite algebras 943
0 0 0 0 0 0 0 0 0
E. Odell (with Tho Schlumprecht): Distortion and stabilized
structure in Banach spaces; New geometric phenomena
for Banach and Hilbert spaces 955
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Antony Jo Wassermann: Operator algebras and conformal field theory 966
Mariusz Wodzicki: The algebra of functional analysis
(Manuscript not submitted)
Section 10. Probability and statistics
Richard Fo Bass: Brownian motion, heat kernels, and
harmonic functions 980
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Scientific Program xi
Donald Dawson: Interaction and hierarchy in measure-valued processes. 986
David L. Donoho: Abstract statistical estimation and modern harmonic
analysis ................................ 997
Hans Follmer: Probabilistic methods in finance (Manuscript not submitted)
Jurgen Gartner: Parabolic systems in random media and aspects of
intermittency ( Manuscript not submitted)
Zhi-Ming Ma: Quasi-regular Dirichlet forms and applications . . 1006
Charles M. Newman: A surface view of first-passage percolation 1017
K. R. Parthasarathy: Quantum stochastic calculus . . . . . . . . 1024
Edwin A. Perkins: Measure-valued branching diffusions and interactions 1036
Hiroshi Tanaka: Diffusion processes in random environments ...... 1047
Section 11. Partial differential equations
J. Thomas Beale: Analytical and numerical aspects of fluid interfaces. 1055
Kung-ching Chang: Morse theory in differential equations ..... . 1065
Jean-Yves Chemin: Analyse microlocale et mecanique des flu ides en
dimension deux . . . . . . . . . . . . . . . . . . . . . . . . . 1077
Peter Constantin: Some mathematical problems of fluid mechanics . 1086
Constantine M. Dafermos: Hyperbolic systems of conservation laws . 1096
David Jerison: Eigenfunctions and harmonic functions in convex and
concave domains. . . . . . . . . . . . . . . . . . . . . . . . . . 1108
Hiroshi Matano: Singularities of solutions of nonlinear parabolic and
elliptic equations (Manuscript not submitted)
Benoit Perthame: Kinetic equations and hyperbolic systems of
conservation laws . . . . . . . . . . . . . . . . . . . 1118
Jalal Shatah: The Cauchy problem for harmonic maps on
Minkowski space. . . . . . . . . . . . . . . . . . . . 1126
Panagiotis E. Souganidis: Interface dynamics in phase transitions 1133
Joel Spruck: Fully nonlinear elliptic equations and applications
to geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 1145
Vladimir Sverak: Lower-semicontinuity of variational integrals and
compensated compactness .................. . 1153
Section 12. Ordinary differential equations and dynamical systems
A. A. Bolibruch: The Riemann-Hilbert problem and Fuchsian differential
equations on the Riemann sphere .................. 1159
Sergey V. Bolotin: Invariant sets of hamiltonian systems and variational
methods . . . . . . . . . . . . . . . . . . . . . . . . . . 1169
John Franks: Rotation vectors for surface diffeomorphisms. . 1179
Manoussos G. Grillakis: A priori estimates and regularity of
nonlinear waves . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1187
Fran<;ois Ledrappier: Applications of dynamics to compact manifolds of
negative curvature. . . . . . . . . . . . . . . . . . . . . . . . 1195
Mikhail Lyubich: On the borderline of real and complex dynamics . .. 1203