Deformation Theory and Symplectic Geometry

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This volume contains papers presented at the meeting on deformation theory, symplectic geometry and applications, held in June 17-21, 1996. The contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include major contributions by leading scientists. Developments in the fields of symplectic geometry, deformation quantization, noncommutative geometry (NCG) and Lie theory are presented. Among the subjects treated are: quantization of general Poisson manifolds; new deformations needed for the quantization of Nambu mechanics; quantization of intersection cardinalities; quantum shuffles; new types of quantum groups and applications; quantum cohomology; strong homotopy Lie algebras; finite- and infinite-dimensional Lie groups; and 2D field theories and applications of NCG to gravity coupled with the standard model. This book should be of interest to researchers and postgraduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, non-associative rings and algebras, and Lie algebras.