EMS Series of Congress Reports 2008; 722 pp; hardcover Volume: 1 ISBN10: 3037190620 ISBN13: 9783037190623 List Price: US$138 Member Price: US$110.40 Order Code: EMSSCR/1
 This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasihereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semiinvariants of quivers, CohenMacaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, AuslanderReiten theory, CalabiYau triangulated categories, Poincaré duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen selfcontained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field. 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. Table of Contents  S. Ariki  Finite dimensional Hecke algebras
 G. Bobiński, C. Riedtmann, and A. Skowroński  Semiinvariants of quivers and their zero sets
 I. Burban and Y. Drozd  Maximal CohenMacaulay modules over surface singularities
 J. F. Carlson  Rank varieties
 K. Erdmann and A. Skowroński  Periodic algebras
 C. Geiss, B. Leclerc, and J. Schröer  Preprojective algebras and cluster algebras
 I. G. Gordon  Symplectic reflection algebras
 O. Iyama  AuslanderReiten theory revisited
 P. Jørgensen  CalabiYau categories and Poincaré duality spaces
 S. Kasjan  Representation types of algebras from the model theory point of view
 B. Keller  CalabiYau triangulated categories
 S. Koenig  A panorama of diagram algebras
 H. Lenzing and J. A. de la Peńa  Spectral analysis of finite dimensional algebras and singularities
 M. Reineke  Moduli of representations of quivers
 A. Skowroński and K. Yamagata  Selfinjective algebras of quasitilted type
 List of contributors
