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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

Documenta Mathematica · Extra Volume ICM 1998 · I