EMS Series of Congress Reports 2011; 740 pp; hardcover Volume: 5 ISBN10: 3037191015 ISBN13: 9783037191019 List Price: US$138 Member Price: US$110.40 Order Code: EMSSCR/5
 This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, CalabiYau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen selfcontained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and 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 researchers interested in algebra and algebraic geometry. Table of Contents  C. Amiot  On generalized cluster categories
 D. J. Benson, S. B. Iyengar, and H. Krause  Module categories for finite group algebras
 B. Keller<  On cluster theory and quantum dilogarithm identities
 B. Leclerc  Quantum loop algebras, quiver varieties, and cluster algebras
 H. Lenzing  Weighted projective lines and applications
 M. Linckelmann  Cohomology of block algebras of finite groups
 P. Malicki and A. Skowroński  Algebras with separating AuslanderReiten components
 I. Mori  Classification problems in noncommutative algebraic geometry and representation theory
 T. Nakanishi  Periodicities in cluster algebras and dilogarithm identities
 J. A. de la Peña and A. Skowroński  The Tits forms of tame algebras and their roots
 C. M. Ringel<  The minimal representationinfinite algebras which are special biserial
 D. Simson  Coalgebras of tame comodule type, comodule categories, and a tamewild dichotomy problem
 G. Zwara  Singularities of orbit closures in module varieties
