VOLUME 41 ULLETI ( N E W S ERIES ) OF THE AMERICAN MATHEMATICAL SOCIETY EDITORS Donald G. Saari, Chief Editor Robert L. Devaney, Book Reviews ASSOCIATE EDITORS John C. Baez Barry Mazur William D. Blair Philip E. Protter Martin R. Bridson Paul H. Rabinowitz Lawrence C. Evans Panagiotis E. Souganidis Steven Krantz Audrey A. Terras Krystyna M. Kuperberg Michael Wolf John C. Mayer PROVIDENCE, RHODE ISLAND USA ISSN 0273-0979 Available electronically at www.ams.org/bull/ Bulletin (New Series) of the American Mathematical Society This journal is devoted to articles of the following types: Bulletin Articles Two types of articles will be included in this section: (1) papers that present a clear and insightful exposition of significant aspects of contemporary mathematical research, including Gibbs Lectures, Progress in Mathematics Lectures, and Retiring Presidential Addresses; and (2) brief, timely reports on important mathematical developments, which are normally solicited and often written by a disinterested expert. Book Reviews Book Reviews are accepted for publication by invitation only. Unsolicited manuscripts will not be considered. Submission information. See Information for Authors at the end of this issue Publisher Item Identifier. The Publisher Item Identifier (PII) appears at the top of the first page of each article published in this journal. 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Postmaster: Send address changes to Bulletin, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA ©) 2004 American Mathematical Society All rights reserved This journal is indexed in Mathemati Reviews. Science Citation Indez Science Citation Index Expanded, ISI Alerting Services=™, CompuMat} Citation Index and Current Contents Physical, Chermecal & Earth Sciences Printed in the United States of America ~) The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability 1098765432 1 09 O88 OTF O06 O58 O04 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY CONTENTS Vol. 41, No. 1 January 2004 Bulletin Articles Charles Pugh and Michael Shub, with an appendix by Alexander Starkov, Stable ergodicity Tauno Metsankyla, Catalan’s Conjecture: Another old Diophantine problem solved Stephen S. Gelbart and Stephen D. Miller, Riemann’s zeta function and beyond Book Reviews Earl Taft (Reviewer), The concise handbook of algebra, edited by Alexander V. Mikhalev and Giinter F. Pilz Stephen J. DeCanio (Reviewer), Computation and complexity in economic behavior and organization, by Kenneth R. Mount and Stanley Reiter Richard Moeckel (Reviewer), Classical and celestial mechanics, the Recife lectures, edited by Hildeberto Cabral and Florin Diacu David Goss (Reviewer), Number theory in function fields, by Michael Rosen Daniel S. Silver (Reviewer), Knots, by G. Burde and H. Zieschang; Algebraic invariants of links, by Jonathan Hillman Vol. 41, No. 2 April 2004 Bulletin Articles David Eisenbud, Current events sessions Edward Frenkel, Recent advances in the Langlands Program Daniel Tataru, The wave maps equation Benoit Perthame, Mathematical tools for kinetic equations Book Reviews Donald Dawson (Reviewer), Diffusions, superdiffusions and partial differential equations, by E. B. Dynkin Rostislav I. Grigorchuk (Reviewer), Subgroup growth, by Alexander Lubotzky and Dan Segal Michael Harris (Reviewer), Introduction to the Langlands program, edited by J. Bernstein and S. Gelbart, with contributions by D. Bump, J. W. Cogdell, D. Gaitsgory, E. de Shalit, E. Kowalski, and S. S. Kudla .... Robert F. Brown (Reviewer), Fixed point theory, by Andrzej Granas and James Dugundji Vol. 41, No. 3 July 2004 Bulletin Articles Jean-Pierre Bourguignon, René Thom: “Mathématicien et apprenti philosophe” David Ruelle, Application of hyperbolic dynamics to physics: Some problems and conjectures Steve Simale and Ding-Xuan Zhou, Shannon sampling and function reconstruction from point values B. Mazur, Perturbations. deformations. and variations (and “near-misses” ) in geometry, physics, and number theory Michael Atiyah, The impact of Thom’s cobordism theory Dennis Sullivan, René Thom’s work on geometric homology and bordism Book Reviews Juan J. Morales-Ruiz (Reviewer), Galois theory of linear differential equations, by Marius van der Put and Michael Singer Susan Landau (Reviewer), RSA and Public-Key Cryptography, by Richard Mollin: Introduction to Cryptography, by Hans Delfs and Helmut Knebl; Cryptography: Theory and Practice, by Douglas Stinson; Algebraic Aspects of Cryptography, by Neal Koblitz; Elliptic Curves: Number Theory and Cryptography, by Lawrence Washington; Elliptic Curves in Cryptography, by Ian Blake, Gadiel Seroussi, and Nigel Smart; Modern Cryptography, Probabilistic Proofs, and Pseudorandomness, by Oded Goldreich; Foundations of Cryptography: Basic Tools, by Oded Goldreich; The Design of Rijndael: AES the Advanced Encryption Standard, by Joan Daemen and Vincent Rijmen; Handbook of Applied Cryptography, by Alfred Menezes, Paul van Oorschot, and Scott Vanstone J. P. C. Greenlees (Reviewer), Homotopy theoretic methods in group cohomology, by W. G. Dwyer and H.-W. Henn Jean-Pierre Kahane (Reviewer). Trigonometric series, Vols. I, Il, by Antoni Zygmund John T. Baldwin (Reviewer), Finite structures with few types, by Gregory Cherlin and Ehud Hrushovski Alexander Barvinok (Reviewer), Discrete convex analysis, by Kazuo Murota Donald Sarason (Reviewer), Hankel operators and their applications, by Vladimir V. Peller Vol. 41, No. 4 October 2004 Bulletin Articles Lawrence C. Evans, A survey of entropy methods for partial differential equations Gunnar Aronsson, Michael G. Crandall, and Petri Juutinen, A tour of the theory of absolutely minimizing functions Henk W. Broer, KAM theory: The legacy of Kolmogorov’s 1954 paper Book Reviews Norbert Steinmetz (Reviewer), Painlevé differential equations in complex plane, by V. I. Gromak, I. Laine, and S. Shimomura Gabriele Nebe (Reviewer), Perfect lattices in Euclidean spaces, by Jacques Martinet Nik Weaver (Reviewer), State spaces of operator algebras: Basic theory, orientations, and C*-products, by Erik M. Alfsen and Frederic W. Shultz; Geometry of state spaces of operator algebras, by Erik M. Alfsen and Frederic W. Shultz Martin Schechter (Reviewer), Spectral theory of linear operators—and spectral systems in Banach algebras, by Vladimir Miiller Edward Nelson (Reviewer), Gnomes in the fog: The reception of Brouwer’s intuitionism in the 1920s, by Dennis E. Hesseling H. L. Smith (Reviewer), Spatial ecology via reaction-diffusion equations, by R. S. Cantrell and C. Cosner James Sneyd (Reviewer). Nonlinear dynamics in physiology and medicine, edited by A. Beuter, L. Glass, M. C. Mackey. and M.S. Titcombe ... 559