Contains papers presented at the conference on Banach Algebras and Several Complex Variables held June 21-24, 1983, to honor Professor Charles E Rickart upon his retirement from Yale University. This work includes articles that present advances in topics related to Banach algebras, function algebras and infinite dimensional holomorphy.

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

This volume contains the proceedings of a conference in honor of Goro Azumaya's seventieth birthday, held at Indiana University of Bloomington in May 1990. Professor Azumaya, who has been on the faculty of Indiana University since 1968, has made many important contributions to modern abstract algebra. His introduction and investigation of what have come to be known as Azumaya algebras subsequently stimulated much research on such rings and algebras, as well as applications to geometry and number theory. In addition to honoring Professor Azumaya's contributions, the conference was intended to stimulate interaction among three areas of his research interests; Azumaya algebras, group and Hopf algebra actions, and module theory. Aimed at researchers in algebra, this volume contains contributions by some of the leaders in these areas.

High dimensional integration arises naturally in two major sub-fields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both. Recent advances in computational power have stimulated significant new advances in both Bayesian and classical multivariate statistics. In many statistical problems, however, multiple integration can be the major obstacle to solutions. This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Statistical Multiple Integration, held in June 1989 at Humboldt State University in Arcata, California. The conference represents an attempt to bring together mathematicians, statisticians, and computational scientists to focus on the many important problems in statistical multiple integration. The papers document the state of the art in this area with respect to problems in statistics, potential advances blocked by problems with multiple integration, and current work directed at expanding the capability to integrate over high dimensional surfaces.

Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.

Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.

This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S Muhly (which will be published in a CBMS Regional Conference Series volume), there were twenty-eight lectures delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, there are over one hundred problems and questions scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.

A three-volume series of proceedings of the Solomon Lefschetz Centennial Conference, held in 1984 in Mexico City to celebrate Lefschetz's 100th birthday. The conference focused on three main areas of Lefschetz's research: algebraic geometry, algebraic topology, and differential geometry.

During his lifetime, L. K. Hua played a leading role in and exerted a great influence upon the development in China of modern mathematics, both pure and applied. His mathematical career began in 1931 at Tsinghua University where he continued as a professor for many years. Hua made many significant contributions to number theory, algebra, geometry, complex analysis, numerical analysis, and operations research. In particular, he initiated the study of classical groups in China and developed new matrix methods which, as applied by him as well as his followers, were instrumental in the successful attack of many problems. To honor his memory, a joint China-U.S. conference on Classical Groups and Related Topics was held at Tsinghua University in Beijing in May 1987. This volume represents the proceedings of that conference and contains both survey articles and research papers focusing on classical groups and closely related topics.