The papers in this volume are based on lectures given during the meeting of the Seminaire Sud Rhodanien de Geometrie which we organized at MSRI from May 22 to June 2, 1989, as part of a year-long program on Symplectic Geometry and Mechanics. The Seminaire Sud Rhodanien de Geometrie (SSRG) was established in 1982 by geometers and mathematical physicists at the Universities of Avignon, Lyon, Marseille, and Montpellier, with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. It has been designated by the Centre N...

The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "The Geometry of Hamiltonian Systems" which was held at MSRl from June 5 to 16, 1989. It was, in some sense, the last major event of the year-long program on Symplectic Geometry and Mechanics. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, and dynamical systems in general. The organizers of the conference were R. Devaney (co-chairman), H. Flaschka (co-chairman), K. Meyer,...

In January 1989 a Workshop on Algorithms, Word Problems and Classi fication in Combinatorial Group Theory was held at MSRl. This was part of a year-long program on Geometry and Combinatorial Group Theory or ganised by Adyan, Brown, Gersten and Stallings. The organisers of the workshop were G. Baumslag, F.B. Cannonito and C.F. Miller III. The pa pers in this volume are an outgrowth of lectures at this conference. The first three papers are concerned with decision problems and the next two with finitely presented simple groups. These are followed by two papers dealing with combinatorial...

This volume collects some of the survey lectures delivered at the Micro program on Noncommutative Rings held at MSRI, July 10-21, 1989. While the program was concerned with recent advances in ring theory, it also had as an important component lectures on related areas of mathematics where ring theory might be expected to have an impact. Thus, there are lectures of S. P. Smith on quantum groups and Marc Ri effel on algebraic aspects of quantum field theory. Martin Lorenz and Don ald Passman consider in their lectures various aspects of crossed products: homological and K-theoretic to group...

In the Fall of 1975 we started a joint project with the ultimate goal of topo logically classifying real algebraic sets. This has been a long happy collaboration (c.f., K2)). In 1985 while visiting M.S.R.1. we organized and presented our classification results up to that point in the M.S.R.1. preprint series AK14] - AK17]. Since these results are interdependent and require some prerequisites as well as familiarity with real algebraic geometry, we decided to make them self contained by presenting them as a part of a book in real algebraic geometry. Even though we have not arrived to our...

Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S....

This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my...

When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations." A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of...

James Lepowsky t The search for symmetry in nature has for a long time provided representation theory with perhaps its chief motivation. According to the standard approach of Lie theory, one looks for infinitesimal symmetry -- Lie algebras of operators or concrete realizations of abstract Lie algebras. A central theme in this volume is the construction of affine Lie algebras using formal differential operators called vertex operators, which originally appeared in the dual-string theory. Since the precise description of vertex operators, in both mathematical and physical settings, requires a...

This book provides an introduction to (1) various zeta functions (for example, Riemann, Hurwitz, Barnes, Epstein, Selberg, and Ruelle), including graph zeta functions; (2) modular forms (Eisenstein series, Hecke and Dirichlet L-functions, Ramanujan's tau function, and cusp forms); and (3) vertex operator algebras (correlation functions, quasimodular forms, modular invariance, rationality, and some current research topics including higher genus conformal field theory). Various concrete applications of the material to physics are presented. These include Kaluza-Klein extra dimensional gravity,...