This volume contains papers presented at the meeting DeformationTheory, Symplectic Geometry and Applications, held in Ascona, June 17-21, 1996. The contents touch upon many frontier domains of modern mathematics, mathematical physics and theoretical physics and include authoritative, state-of-the-art contributions by leading scientists. New and important 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. Audience: This book will be of interest to researchers and post-graduate students of mathematical physics, global analysis, analysis on manifolds, topological groups, nonassociative rings and algebras, and Lie algebras.
Preface. Noncommutative Differential Geometry and the Structure of Space Time; A. Connes. Shift Operator for the Discrete sl(2) Current Algebra; L. Faddeev, A. Volkov. Nambu Mechanics, n-ary Operations and their Quantization; M. Flato, et al. The Geometrization Principle; J.Fröhlich. Generalization and Deformations of Quantum Groups; C.Fronsdal. Quantized Intersection Cardinalities; M. Gerstenhaber. Deformation Quantization and Mp^{c} Structures; S. Gutt, J.Rawnsley. Massless XXZ Model and Degeneration of the Elliptic Algebra A_{q,p}(sANDl_{2}); M. Jimbo, et al. Formality Conjecture; M. Kontsevich. Quantum Cohomology of the Flag Manifold as an Algebra of Rational Functions on a Unipotent Algebraic Group; B. Kostant. Homologies Associated with Poisson Structures; O. Mathieu. Maximal Tori of Some Symplectomorphism Groups and Applications to Convexity; A. Bloch, et al. On 2D Yang-Mills Theory and Invariants of Links; M. Polyak, N. Reshetikhin. Some Applications of Quantum Shuffles; M. Rosso. Character Formulas and Localization of Integrals; W. Schmid. Deformation Theory and the Batalin-Vilkovisky Master Equation; J. Stasheff. The Fukaya Type Categories for Associative Algebras; R. Nest, B. Tsygan. Tangential Deformation Quantization and Polarized Symplectic Groupoids; A. Weinstein. Formal GNS Construction and WKB Expansion in Deformation Quantization; M. Bordemann, S.Waldmann. On the Deformation of Time Harmonic Flows; J. Hoppe. Distinguished Essential Extensions of Infinite Dimensional Classical Lie Algebras; A. Lichnerowicz. Noncommutative Contact Algebras; H.Omori, et al. Braided Geometry and the Inductive Construction of Lie Algebras and Quantum Groups; S. Majid. Star Products in the Triangular Case; C. Moreno, L. Valero. Aspetti fisici della teoria delle deformazioni; G. Dito. Scientific Programme. List of Participants.