Synopses & Reviews
These two volumes contain eighteen invited papers by distinguished mathematicians in honor of the eightieth birthday of Israel M. Gelfand, one of the most remarkable mathematicians of our time. Gelfand has played a crucial role in the development of functional analysis during the last half-century. His work and his philosophy have in fact helped shape our understanding of the term 'functional analysis'. The papers in these volumes largely concern areas in which Gelfand has a very strong interest today, including geometric quantum field theory, representation theory, combinatorial structures underlying various 'continuous' constructions, quantum groups and geometry. The second of the two volumes contains the somewhat more 'geometric' papers, although such a designation is to a certain extent arbitrary, because of the breadth of the papers.
Synopsis
A four-day conference, "Functional Analysis on the Eve of the Twenty First Century," was held at Rutgers University, New Brunswick, New Jersey, from October 24 to 27, 1993, in honor of the eightieth birthday of Professor Israel Moiseyevich Gelfand. He was born in Krasnye Okna, near Odessa, on September 2, 1913. Israel Gelfand has played a crucial role in the development of functional analysis during the last half-century. His work and his philosophy have in fact helped to shape our understanding of the term "functional analysis" itself, as has the celebrated journal Functional Analysis and Its Applications, which he edited for many years. Functional analysis appeared at the beginning of the century in the classic papers of Hilbert on integral operators. Its crucial aspect was the geometric interpretation of families of functions as infinite-dimensional spaces, and of op erators (particularly differential and integral operators) as infinite-dimensional analogues of matrices, directly leading to the geometrization of spectral theory. This view of functional analysis as infinite-dimensional geometry organically included many facets of nineteenth-century classical analysis, such as power series, Fourier series and integrals, and other integral transforms."
Table of Contents
Preface.-Speakers at Conference in Honor of I. M. Gelfand.-Curriculum Vitae of I. M. Gelfand.-List of Publications: 1987-1995.-A Tribute of I. M. Gelfand.-Connection Formulas in the q-analog de Rham Cohomolgy.-Lagrangian Models of Minimal Representations of E6, E7, and E8.-Trigonometric Solutions of the Yang-Baxter Equation, Nets, and Hypergeometric Functions.-Analogies between the Langlands Correspondence and Topological Quantum Field Theory.-"Forms" of the Principal Series for GLn.-Geometry of Determinants of Elliptic Operators.-Quantum Groups at v=infinity.-The Symplectic Operad.-Quadratic Unipotent Representations of p-adic Groups.-On the Master Field in Two Dimensions.-Physical Methods Applied to Donaldson Theory.