ICM 1998 Contents of Volumes I, II, and III

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  11
Past Congresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  12
Past Fields Medalists and Rolf Nevanlinna Prize Winners . . . . . . . . . . . . I  13
Martin Grötschel: Organization of the Congress . . . . . . . . . . . . . . . . . I  15
The Committees of the Congress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  19
List of Donors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  21
Opening Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  23

Yuri I. Manin: Presentation of the Fields Medals and a Special

Tribute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 45

David Mumford: Presentation of the Rolf Nevanlinna Prize . . . . . . . . I  49
Fax to the Federal President and to the Governing Mayor . . . . . . . . . . . . I  50
Closing Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  53
List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  61
Participants by Country . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  96

The Work of the Fields Medalists and of the Rolf Nevanlinna Prize Winner

Peter Goddard: The Work of Richard Ewen Borcherds . . . . . . . . . . . . I  99
Béla Bollobás: The Work of William Timothy Gowers . . . . . . . . . . . . I  109
Clifford Henry Taubes: The Work of Maxim Kontsevich . . . . . . . . . I  119
Steve Smale: The Work of Curtis T. McMullen . . . . . . . . . . . . . . . . . . . . I  127
Ronald Graham: The Work of Peter W. Shor . . . . . . . . . . . . . . . . . . . . . . I  133

Invited One-Hour Plenary Lectures

Jean-Michel Bismut: Local Index Theory and Higher Analytic

Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 143 Christopher Deninger: Some Analogies Between Number Theory

and Dynamical Systems on Foliated Spaces . . . . . . . . . . . . . . . . . . . . . . . . I 163 Persi Diaconis: From Shuffling Cards to Walking Around the

Building: An Introduction to Modern Markov Chain Theory . . . . . . . I 187 Giovanni Gallavotti: Chaotic Hypothesis and Universal Large

Deviations Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 205 Wolfgang Hackbusch: From Classical Numerical Mathematics to

Scientific Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 235 Helmut H. W. Hofer: Dynamics, Topology, and Holomorphic

Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 255

Ehud Hrushovski: Geometric Model Theory . . . . . . . . . . . . . . . . . . . . . . . I  281

I. G. Macdonald: Constant Term Identities, Orthogonal

Polynomials, and Affine Hecke Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 303

Stéphane Mallat: Applied Mathematics Meets Signal Processing . . I  319
Dusa McDuff: Fibrations in Symplectic Topology . . . . . . . . . . . . . . . . . . I  339

Tetsuji Miwa: Solvable Lattice Models and Representation Theory of

Quantum Affine Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 359

Jürgen Moser: Dynamical Systems – Past and Present . . . . . . . . . . . . . I  381

George Papanicolaou: Mathematical Problems in Geophysical

Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 403

Gilles Pisier: Operator Spaces and Similarity Problems . . . . . . . . . . . . I  429
Peter Sarnak: L-Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  453
Peter W. Shor: Quantum Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  467

Karl Sigmund: The Population Dynamics of Conflict and

Cooperation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 487 Michel Talagrand: Huge Random Structures and Mean Field

Models for Spin Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 507

Cumrun Vafa: Geometric Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I  537

Marcelo Viana: Dynamics: A Probabilistic and Geometric

Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 557

Vladimir Voevodsky: A^{1}-Homotopy Theory . . . . . . . . . . . . . . . . . . . . . . I  579

Lectures by the Fields Medalists and by the Rolf Nevanlinna Prize Winner

Richard E. Borcherds: What is Moonshine? . . . . . . . . . . . . . . . . . . . . . I 607
W. T. Gowers: Fourier Analysis and Szemerédi’s Theorem . . . . . . . . . I 617

Curtis T. McMullen: Rigidity and Inflexibility in Conformal Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 841

see also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 630
Peter W. Shor: Quantum Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 467

Appendix: Invited Forty-Five Minute Lectures at the Section Meetings

This appendix contains three manuscripts of Invited Speakers which are not included in Volume II or III

Section 1. Logic:

A. J. Wilkie: O-Minimality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 633 Section 10. Partial Differential Equations:

Mikhail Safonov: Estimates Near the Boundary for Solutions of Second Order Parabolic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 637

Section 12. Probability and Statistics:

F. Götze: Errata: Lattice Point Problems . . . . . . . . . . . . . . . . . . . . . . . . I 648 Section 16. Applications:

Serafim Batzoglou, Bonnie Berger, Daniel J. Kleitman,

Eric S. Lander, and Lior Pachter: Recent Developments in

Computational Gene Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I 649

Author Index for Volumes I, II, and III . . . . . . . . . . . . . . .  I  659

Invited Forty-Five Minute Lectures at the Section Meetings

Contents of Volumes II and III

In case of several authors, Invited Speakers are marked with a ^{∗}. The author index is at the end of each of these two volumes.

Section 1. Logic

Matthew Foreman: Generic Large Cardinals: New Axioms for

Mathematics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 11

Greg Hjorth: When is an Equivalence Relation Classifiable? . . . . . . . II 23
Ludomir Newelski: Meager Forking and m-Independence . . . . . . . . . . II 33
Stevo Todorcevic: Basis Problems in Combinatorial Set Theory . . II 43

Section 2. Algebra

Eric M. Friedlander: Geometry of Infinitesimal Group Schemes . . II 55

Sergei V. Ivanov: On the Burnside Problem for Groups of Even

Exponent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 67 William M. Kantor: Simple Groups in Computational Group

Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 77

Gunter Malle: Spetses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 87

Aleksandr V. Pukhlikov: Birational Automorphisms of

Higher-Dimensional Algebraic Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 97

Idun Reiten: Tilting Theory and Quasitilted Algebras . . . . . . . . . . . . . . II 109
Jeremy Rickard: The Abelian Defect Group Conjecture . . . . . . . . . . . II 121
Aner Shalev: Simple Groups, Permutation Groups, and Probability II 129

Section 3. Number Theory and Arithmetic Algebraic Geometry

Vladimir G. Berkovich: p-Adic Analytic Spaces . . . . . . . . . . . . . . . . . . II 141
Pierre Colmez: Représentations p-Adiques d’un Corps Local . . . . . . . II 153
W. Duke: Bounds for Arithmetic Multiplicities . . . . . . . . . . . . . . . . . . . . . . II 163
François Gramain: Quelques Résultats d’Indépendance Algébrique II 173
Loïc Merel: Points Rationnels et Séries de Dirichlet . . . . . . . . . . . . . . . . II 183

Shinichi Mochizuki: The Intrinsic Hodge Theory of p-Adic

Hyperbolic Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 187

Hans Peter Schlickewei: The Subspace Theorem and Applications II 197

Takeshi Tsuji: p-Adic Hodge Theory in the Semi-Stable Reduction

Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 207

Shou-Wu Zhang: Small Points and Arakelov Theory . . . . . . . . . . . . . . . II 217

Section 4. Algebraic Geometry

Paul S. Aspinwall: String Theory and Duality . . . . . . . . . . . . . . . . . . . . II 229
Victor V. Batyrev: Mirror Symmetry and Toric Geometry . . . . . . . . II 239
Maurizio Cornalba: Cohomology of Moduli Spaces of Stable Curves II 249

A. J. de Jong: Barsotti-Tate Groups and Crystals . . . . . . . . . . . . . . . . . . II 259
Mark L. Green: Higher Abel-Jacobi Maps . . . . . . . . . . . . . . . . . . . . . . . . . II 267
M. Kapranov: Operads and Algebraic Geometry . . . . . . . . . . . . . . . . . . . II 277

Section 5. Differential Geometry and Global Analysis

Dmitri Burago: Hard Balls Gas and Alexandrov Spaces of

Curvature Bounded Above . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 289

Tobias H. Colding: Spaces with Ricci Curvature Bounds . . . . . . . . . . II 299
S. K. Donaldson: Lefschetz Fibrations in Symplectic Geometry …. II 309

Boris Dubrovin: Geometry and Analytic Theory of Frobenius

Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 315

Yakov Eliashberg: Invariants in Contact Topology . . . . . . . . . . . . . . . . II 327
S. Gallot: Curvature-Decreasing Maps are Volume-Decreasing . . . . . . II 339

Gerhard Huisken: Evolution of Hypersurfaces by Their Curvature

in Riemannian Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 349

Dominic Joyce: Compact Manifolds with Exceptional Holonomy …. II 361
François Labourie: Large Groups Actions on Manifolds . . . . . . . . . . . II 371
Joachim Lohkamp: Curvature Contents of Geometric Spaces . . . . . . . II 381

Franz Pedit and Ulrich Pinkall^{∗}: Quaternionic Analysis on

Riemann Surfaces and Differential Geometry . . . . . . . . . . . . . . . . . . . . . . . II 389 Leonid Polterovich: Geometry on the Group of Hamiltonian

Diffeomorphisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 401

Yongbin Ruan: Quantum Cohomology and its Application . . . . . . . . . II 411

Section 6. Topology

A. N. Dranishnikov: Dimension Theory and Large Riemannian

Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 423

W. G. Dwyer: Lie Groups and p-Compact Groups . . . . . . . . . . . . . . . . . II 433

Ronald Fintushel^{∗} and Ronald J. Stern^{∗}: Constructions of

Smooth 4-Manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 443 Michael H. Freedman: Topological Views on Computational

Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 453

Mark Mahowald: Toward a Global Understanding of π_{∗}(S^{n}) . . . . . . II 465

Tomotada Ohtsuki: A Filtration of the Set of Integral Homology

3-Spheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 473

Bob Oliver: Vector Bundles over Classifying Spaces . . . . . . . . . . . . . . . . II 483

Clifford Henry Taubes: The Geometry of the Seiberg-Witten Invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 493

Section 7. Lie Groups and Lie Algebras

James Arthur: Towards a Stable Trace Formula . . . . . . . . . . . . . . . . . . . . II 507

Joseph Bernstein: Analytic Structures on Representation Spaces of

Reductive Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 519

Ivan Cherednik: From Double Hecke Algebra to Analysis . . . . . . . . . . II 527
Alex Eskin: Counting Problems and Semisimple Groups . . . . . . . . . . . . II 539

Robert E. Kottwitz: Harmonic Analysis on Semisimple p-Adic Lie

Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 553

L. Lafforgue: Chtoucas de Drinfeld et Applications . . . . . . . . . . . . . . . . II 563
Shahar Mozes: Products of Trees, Lattices and Simple Groups . . . . . II 571

Vera Serganova: Characters of Irreducible Representations of

Simple Lie Superalgebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 583

Kari Vilonen: Topological Methods in Representation Theory . . . . . . II 595

Minoru Wakimoto: Representation Theory of Affine Superalgebras at the Critical Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 605

Section 8. Analysis

Kari Astala: Analytic Aspects of Quasiconformality . . . . . . . . . . . . . . . II 617
Michael Christ: Singularity and Regularity — Local and Global … II 627
Nigel Higson: The Baum-Connes Conjecture . . . . . . . . . . . . . . . . . . . . . . . II 637
Michael T. Lacey: On the Bilinear Hilbert Transform . . . . . . . . . . . . . II 647

Pertti Mattila: Rectifiability, Analytic Capacity, and Singular

Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 657 Vitali Milman: Randomness and Pattern in Convex Geometric

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 665 Detlef Müller: Functional Calculus on Lie Groups and Wave

Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 679 Stefan Müller^{∗} and Vladimir Šverák: Unexpected Solutions of

First and Second Order Partial Differential Equations . . . . . . . . . . . . . . II 691 Klas Diederich and Sergey Pinchuk^{∗}: Reflection Principle in

Higher Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 703

Kristian Seip: Developments from Nonharmonic Fourier Series . . . . . II 713
Hart F. Smith: Wave Equations with Low Regularity Coefficients . . II 723

Nicole Tomczak-Jaegermann: From Finite- to Infinite-Dimensional Phenomena in Geometric Functional Analysis on Local and Asymptotic Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 731

Stephen Wainger: Discrete Analogues of Singular and Maximal

Radon Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 743 Thomas Wolff: Maximal Averages and Packing of One Dimensional

Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 755

Section 9. Ordinary Differential Equations and Dynamical Systems

W. de Melo: Rigidity and Renormalization in One Dimensional

Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 765 L. H. Eliasson: Reducibility and Point Spectrum for Linear

Quasi-Periodic Skew-Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 779 Shuhei Hayashi: Hyperbolicity, Stability, and the Creation of

Homoclinic Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 789

Michael Herman: Some Open Problems in Dynamical Systems …. II 797
Yuri Kifer: Random Dynamics and its Applications . . . . . . . . . . . . . . . . II 809

Sergei B. Kuksin: Elements of a Qualitative Theory of Hamiltonian

PDEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 819

Krystyna Kuperberg: Counterexamples to the Seifert Conjecture . II 831

Curtis T. McMullen: Rigidity and Inflexibility in Conformal

Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 841 Grzegorz Świa̧tek: Induced Hyperbolicity for One-Dimensional

Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II 857

Zhihong Xia: Arnold Diffusion: A Variational Construction . . . . . . . . . II 867

Section 10. Partial Differential Equations

Fabrice Bethuel: Vortices in Ginzburg-Landau Equations . . . . . . . . . III 11

Frédéric Hélein: Phenomena of Compensation and Estimates for

Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 21 Robert R. Jensen: Viscosity Solutions of Elliptic Partial Differential

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 31 Hans Lindblad: Minimal Regularity Solutions of Nonlinear Wave

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 39 M. Machedon: Fourier Analysis of Null Forms and Non-linear Wave

Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 49 Frank Merle: Blow-up Phenomena for Critical Nonlinear

Schrödinger and Zakharov Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 57

Gustavo Ponce: On Nonlinear Dispersive Equations . . . . . . . . . . . . . . . III 67

Gunther Uhlmann: Inverse Boundary Value Problems for Partial

Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 77

D. Yafaev: Scattering Theory: Some Old and New Problems . . . . . . . . III 87

Section 11. Mathematical Physics

Eugene Bogomolny: Spectral Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . III 99

Detlev Buchholz: Scaling Algebras in Local Relativistic Quantum

Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 109

J. T. Chayes: Finite-Size Scaling in Percolation . . . . . . . . . . . . . . . . . . . . . III 113
P. Collet: Extended Dynamical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . III 123
Robbert Dijkgraaf: The Mathematics of Fivebranes . . . . . . . . . . . . . . III 133

Antonio Giorgilli: On the Problem of Stability for Near to

Integrable Hamiltonian Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 143 Gian Michele Graf: Stability of Matter in Classical and Quantized

Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 153 Alexander Berkovich and Barry M. McCoy^{∗}:

Rogers-Ramanujan Identities: A Century of Progress from

Mathematics to Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 163

Roberto H. Schonmann: Metastability and the Ising Model . . . . . . . III 173

Feodor A. Smirnov: Space of Local Fields in Integrable Field

Theory and Deformed Abelian Differentials . . . . . . . . . . . . . . . . . . . . . . . . III 183 Horng-Tzer Yau: Scaling Limit of Particle Systems, Incompressible

Navier-Stokes Equation and Boltzmann Equation . . . . . . . . . . . . . . . . . . III 193 Section 12. Probability and Statistics

David J. Aldous: Stochastic Coalescence . . . . . . . . . . . . . . . . . . . . . . . . . . . III 205
Maury Bramson: State Space Collapse for Queueing Networks . . . . . III 213

Mark I. Freidlin: Random and Deterministic Perturbations of

Nonlinear Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 223

Jayanta K. Ghosh: Bayesian Density Estimation . . . . . . . . . . . . . . . . . . . III 237

F. Götze: Lattice Point Problems and the Central Limit Theorem in

Euclidean Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 245 Peter Hall^{∗} and Brett Presnell: Applications of Intentionally

Biased Bootstrap Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 257 Iain M. Johnstone: Oracle Inequalities and Nonparametric Function

Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 267 Jean-François Le Gall: Branching Processes, Random Trees and

Superprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 279 David Siegmund: Genetic Linkage Analysis: an Irregular Statistical

Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 291

Alain-Sol Sznitman: Brownian Motion and Random Obstacles …. III 301

Boris Tsirelson: Within and Beyond the Reach of Brownian

Innovation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 311

R. J. Williams: Reflecting Diffusions and Queueing Networks . . . . . . . III 321

Section 13. Combinatorics

Béla Bollobás: Hereditary Properties of Graphs: Asymptotic

Enumeration, Global Structure, and Colouring . . . . . . . . . . . . . . . . . . . . . III 333

András Frank: Applications of Relaxed Submodularity . . . . . . . . . . . . III 343

Alain Lascoux: Ordonner le Groupe Symétrique: Pourquoi Utiliser

l’Algèbre de Iwahori-Hecke ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 355 Jiří Matoušek: Mathematical Snapshots from the Computational

Geometry Landscape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 365 Harald Niederreiter: Nets, (t, s)-Sequences, and Algebraic Curves

over Finite Fields with Many Rational Points . . . . . . . . . . . . . . . . . . . . . . III 377

N. J. A. Sloane: The Sphere Packing Problem . . . . . . . . . . . . . . . . . . . . . III 387
Joseph A. Thas: Finite Geometries, Varieties and Codes . . . . . . . . . . . III 397

Andrei Zelevinsky: Multisegment Duality, Canonical Bases and Total Positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 409

Section 14. Mathematical Aspects of Computer Science

Miklós Ajtai: Worst-Case Complexity, Average-Case Complexity

and Lattice Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 421 Joan Feigenbaum: Games, Complexity Classes, and Approximation

Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 429

Johan Håstad: On Approximating NP-Hard Optimization Problems III 441

Toniann Pitassi: Unsolvable Systems of Equations and Proof

Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 451

Madhu Sudan: Probabilistic Verification of Proofs . . . . . . . . . . . . . . . . . . III 461

Artur Andrzejak and Emo Welzl^{∗}: Halving Point Sets . . . . . . . . . III 471

Section 15. Numerical Analysis and Scientific Computing

Gregory Beylkin: On Multiresolution Methods in Numerical

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 481 P. Deift^{∗}, T. Kriecherbauer, K. T-R McLaughlin, S.

Venakides and X. Zhou: Uniform Asymptotics for Orthogonal

Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 491

Bjorn Engquist: Wavelet Based Numerical Homogenization . . . . . . . . III 503

Hisashi Okamoto: A Study of Bifurcation of Kolmogorov Flows with

an Emphasis on the Singular Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 513 Jan-Olov Strömberg: Computation with Wavelets in Higher

Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 523 Lloyd N. Trefethen^{∗} and Tobin A. Driscoll:

Schwarz–Christoffel Mapping in the Computer Era . . . . . . . . . . . . . . . . . III 533

Section 16. Applications

Marco Avellaneda: The Minimum-Entropy Algorithm and Related

Methods for Calibrating Asset-Pricing Models . . . . . . . . . . . . . . . . . . . . . III 545 Andreas Dress^{∗}, Werner Terhalle: The Tree of Life and Other

Affine Buildings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 565 Leslie Greengard^{∗} and Xiaobai Sun: A New Version of the Fast

Gauss Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 575

Ulf Grenander: Strategies for Seeing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 585

Frank Hoppensteadt^{∗} and Eugene Izhikevich: Canonical

Models in Mathematical Neuroscience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 593 Thomas Yizhao Hou: Numerical Study of Free Interface Problems

Using Boundary Integral Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 601 Gérard Iooss: Travelling Water-Waves, as a Paradigm for

Bifurcations in Reversible Infinite Dimensional “Dynamical” Systems

III 611

Yury Grabovsky and Graeme W. Milton^{∗}: Exact Relations for

Composites: Towards a Complete Solution . . . . . . . . . . . . . . . . . . . . . . . . . III 623

Charles S. Peskin: Optimal Dynamic Instability of Microtubules . . III 633

Section 17. Control Theory and Optimization

David Applegate, Robert Bixby, Vašek Chv’atal and

William Cook^{∗}: On the Solution of Traveling Salesman Problems III 645 Michel X. Goemans: Semidefinite Programming and Combinatorial

Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 657 Richard H. Byrd and Jorge Nocedal^{∗}: Active Set and Interior

Methods for Nonlinear Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 667 Ranga Anbil, John J. Forrest and William R. Pulleyblank^{∗}:

Column Generation and the Airline Crew Pairing Problem . . . . . . . . . III 677 Alexander Schrijver: Routing and Timetabling by Topological

Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 687

Jan C. Willems: Open Dynamical Systems and their Control . . . . . . . III 697
Michal Kočvara and Jochem Zowe^{∗}: Free Material Optimization III 707

Section 18. Teaching and Popularization of Mathematics

George E. Andrews: Mathematics Education: Reform or Renewal? III 719

Michèle Artigue: De la Comprehension des Processus

d’Apprentissage a la Conception de Processus d’Enseignement . . . . . . III 723 Maria G. Bartolini Bussi: Drawing Instruments: Theories and

Practices from History to Didactics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 735 Miguel de Guzmán^{∗}, Bernard R. Hodgson^{∗}, Aline Robert^{∗}

and Vinicio Villani^{∗}: Difficulties in the Passage from Secondary to Tertiary Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 747

D. J. Lewis: Mathematics Instruction in the Twenty-first Century . . III 763

Mogens Niss: Aspects of the Nature and State of Research in

Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 767

David A. Smith: Renewal in Collegiate Mathematics Education . . . . . III 777

Section 19. History of Mathematics

Karine Chemla: History of Mathematics in China: A Factor in

World History and a Source for New Questions . . . . . . . . . . . . . . . . . . . . III 789 Joseph W. Dauben: Marx, Mao and Mathematics: The Politics of

Infinitesimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 799 Jeremy J Gray: The Riemann-Roch Theorem and Geometry,

1854-1914 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III 811 10

Documenta Mathematica · Extra Volume ICM 1998 · I