VOLUME 38 0{q17° 4 0 l NDED ysa > ULLETIN ( N E W SERIE S OF THE AMERICAN MATHEMATICAL SOCIETY EDITORS Donald G. Saari, Chief Editor Bhama Srinivasan, Book Reviews ASSOCIATE EDITORS John C. Baez Haynes R. Miller L. Craig Evans Philip E. Protter John M. Franks Hugo Rossi Eric M. Friedlander Daniel Ruberman Craig L. Huneke Panagiotis E. Souganidis Douglas A. Lind Audrey A. Terras Andy R. Magid David A. Vogan Barry Mazur Wolfgang Ziller PROVIDENCE, RHODE ISLAND USA ISSN 0273-0979 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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All rights reserved. his journal is indexed in Mathematical Reviews, Science Citation Inder®, Science Citation Index'™ -Expanded, ISI Alerting Services™ , CompuMath Citation Index®, and Current Contents® / Physical, Chemical & 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. 10987654321 06 05 04 03 02 O1 BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY CONTENTS Vol. 38, No. 1 January 2001 Research-Expository Surveys Urmie Ray, Generalized Kac-Moody algebras and some related topics .... Brian C. Hall, Harmonic analysis with respect to heat kernel measure .... Book Reviews Uta C. Merzbach (Reviewer), James Joseph Sylvester: Life and work in letters by Karen Hunger Parshall Melvin Hochster (Reviewer), Multiplicities and Chern classes in local algebra by Paul C. Roberts Wendell H. Fleming (Reviewer), Extending H,. control to nonlinear systems by J. W. Helton and M. R. James Jacques Thévenaz (Reviewer), On the local structure of Morita and Rickard equivalences between Brauer blocks by Lluis Puig Ezra Getzler (Reviewer), Frobenius manifolds, quantum cohomology, and moduli spaces by Yuri 1. Manin Miles Reid (Reviewer), Rational curves on algebraic varieties by Janos M. Ram Murty (Reviewer), Elementary methods in number theory by Melvyn B. Nathanson Vol. 38, No. 2 April 2001 Bulletin Articles I. M. James, Portrait of Alexander (1888-1971) Shreeram S. Abhyankar, Resolution of singularities and modular Galois theory J. T. Stafford and M. Van den Bergh, Noncommutative curves and I III 66x p.ac s cet inceenvisecsuscceveqtvavansdiustece Book Reviews Brayton Gray (Reviewer), Simplicial homotopy theory by Paul G. Goerss and John F. Jardine Margaret Robinson (Reviewer), An introduction to the theory of local zeta functions by Jun-ichi Igusa Dave Auckly (Reviewer), 4-manifolds and Kirby calculus by Robert Gompf SE EE INS 55 ecacincictonsaawdne wecmeuueby seuari eessewniaemenb s Helmut V6lklein (Reviewer), Inverse Galois theory by G. Malle and B. H. Matzat John McCleary (Reviewer), Rings, modules, and algebras in stable homotopy theory by A. D. Elmendorf, I. Kriz, M. A. Mandell, and J. P. May, with an appendix by M. Cole; Equivariant homotop., and cohomology theory by J. P. May, with contributions by M. Cole, G. Comezana, S$. Costenoble, A. D. Elmendorf, J. P. C. Greenlees, L. G. Lewis, Jr., R. J. Piacenza, G. Triantafillou, and S. Waner; A concise course in algebraic topology by J. P. May Josef Dorfmeister (Reviewer), Harmonic maps, loop groups, and integrable systems by M. A. Guest Irwin Kra (Reviewer), Quasiconformal Teichmiiller theory by F. P. Gardiner and N. Lakic Yujiro Kawamata (Reviewer), Birational geometry of algebraic varieties by Janos Kollar and Shigefumi Mori, with the collaboration of C. H. Clemens and A. Corti Vol. 38, No. 3 July 2001 Bulletin Articles Ole Christensen, Frames, Riesz bases, and discrete Gabor/wavelet expansions Eknath Ghate and Eriko Hironaka, The arithmetic and geometry of Salem numbers Ronald Solomon, A brief history of the classification of the finite simple groups Book Reviews Karsten Grove (Reviewer), Metric structures for Riemannian and non- Riemannian spaces by M. Gromov Ranjan Roy (Reviewer), Complex analysis, fundamentals of the classical theory of functions by John Stalker Vaughan F. R. Jones (Reviewer), Quantum symmetries on operator algebras by D. Evans and Y. Kawahigashi Robert Gross (Reviewer), Diophantine geometry: An introduction by Marc Hindry and Joseph H. Silverman Harm Derksen (Reviewer), Classical invariant theory by Peter Olver Vol. 38, No. 4 October 2001 Bulletin Articles Pierre Cartier, A mie day’s work: From Grothendieck to Connes and Kontsevich The evolution of concepts of space and symmetry Janos Kollar, Which are the simplest algebraic varieties? ................. Philippe Biane, Jim Pitman, and Marc Yor, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions Book Reviews Igor Dolgachev (Reviewer), The geometry of schemes by David Eisenbud and Joe Harris Alexander Lubotzky (Reviewer), Profinite groups by J. S. Wilson; Profinite groups by L. Ribes and P. Zalesskii; Analytic pro-p groups by J. D. Dixon, M. P. F. du Sautoy, A. Mann, and D. Segal; New horizons in pro-p groups by M. du Sautoy, D. Segal, and A. Shalen (eds.) Mikhail Kapranov (Reviewer), Grébner deformations of hypergeometric differential equations by M. Saito, B. Sturmfels, and N. Takayama Louis H. Kauffman (Reviewer), Quantum fields and strings: A course for mathematicians, Volumes 1 and 2 by Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison, and Edward Witten (eds.) John Hubbard (Reviewer), Dynamics in one complex variable, Introductory lectures by John Milnor Bhama Srinivasan, Note from the book reviews editor