Fields Institute Communications 2004; 479 pp; hardcover Volume: 40 ISBN10: 0821834169 ISBN13: 9780821834169 List Price: US$131 Member Price: US$104.80 Order Code: FIC/40
 These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional "instructional" workshop preceding the conference, there were also workshops on "Commutative Algebra, Algebraic Geometry and Representation Theory", "Finite Dimensional Algebras, Algebraic Groups and Lie Theory", and "Quantum Groups and Hall Algebras". These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or CohenMacaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry. Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in representations of finitedimensional algebras and applications. Table of Contents Instructional Workshop  K. S. Brown  Semigroup and ring theoretical methods in probability
 T. Bruestle  Typical examples of tame algebras
 O. Iyama  Representation dimension and Solomon zeta function
 S. Koenig  Filtrations, stratifications and applications
 M. S. Putcha  BruhatRenner decomposition and Hecke algebras of reductive monoids
 L. E. Renner  Representations and blocks of algebraic monoids
 M. Schocker  The descent algebra of the symmetric group
Specialized Workshop Commutative Algebra, Algebraic Geometry and Representation Theory  Y. Berest  A remark on LetzterMakarLimanov invariants
 I. Burban  Derived categories of coherent sheaves on rational singular curves
 Y. A. Drozd  Vector bundles and CohenMacaulay modules
Specialized Workshop Finite Dimensional Algebras, Algebraic Groups and Lie Theory  J. Du  Finite dimensional algebras, quantum groups and finite groups of Lie type
 V. Mazorchuk  Stratified algebras arising in Lie theory
 T. Tanisaki  Character formulas of KazhdanLusztig type
 P. Webb  Weight theory in the context of arbitrary finite groups
Specialized Workshop Quantum Groups and Hall Algebras  G. Benkart and S. Witherspoon  Restricted twoparameter quantum groups
 B. Deng and J. Xiao  On RingelHall algebras
 Z. Lin  Lusztig's geometric approach to Hall algebras
 M. Reineke  The use of geometric and quantum group techniques for wild quivers
 K. Rietsch  An introduction to perverse sheaves
 Y. Saito  An introduction to canonical bases
 O. Schiffmann  Quivers of type \(A\), flag varieties and representation theory
