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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.

Functional Analysis on the Eve of the 21st Century. Vol.1: In Honor of the Eightieth Birthday of I.M. Gelfand

Connection Formulas in the q-analog de Rham Cohomology.- 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 = ?.- The Symplectic Operad.- Quadratic Unipotent Representations of p-adic Groups.- On the Master Field in Two Dimensions.- Physical Methods Applied to Donaldson Theory.