Zurich Lectures in Advanced Mathematics 2007; 102 pp; softcover Volume: 4 ISBN10: 3037190345 ISBN13: 9783037190340 List Price: US$34 Member Price: US$27.20 Order Code: EMSZLEC/4
 CalogeroMoser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of CalogeroMoser systems, highlighting their interplay with these fields. Since these lectures are designed for nonexperts, the author gives short introductions to each of the subjects involved and provides a number of exercises. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in representation theory, noncommutative algebra, algebraic geometry, and related areas. Table of Contents  Introduction
 Poisson manifolds and Hamiltonian reduction
 Classical mechanics and integrable systems
 Deformation theory
 Moment maps, Hamiltonian reduction and the LevasseurStafford theorem
 Quantum mechanics, quantum integrable systems and the CalogeroMoser system
 CalogeroMoser systems associated to finite Coxeter groups
 The rational Cherednik algebra
 Symplectic reflection algebras
 Deformationtheoretic interpretation of symplectic reflection algebras
 The center of the symplectic reflection algebra
 Representation theory of rational Cherednik algebras
 Bibliography
 Index
