Contemporary Mathematics 2009; 227 pp; softcover Volume: 497 ISBN10: 0821848402 ISBN13: 9780821848401 List Price: US$83 Member Price: US$66.40 Order Code: CONM/497
 Vertex operator algebras were introduced to mathematics in the work of Richard Borcherds, Igor Frenkel, James Lepowsky and Arne Meurman as a mathematically rigorous formulation of chiral algebras of twodimensional conformal field theory. The aim was to use vertex operator algebras to explain and prove the remarkable Monstrous Moonshine conjectures in group theory. The theory of vertex operator algebras has now grown into a major research area in mathematics. These proceedings contain expository lectures and research papers presented during the international conference on Vertex Operator Algebras and Related Areas, held at Illinois State University in Normal, IL, from July 7 to July 11, 2008. The main aspects of this conference were connections and interactions of vertex operator algebras with the following areas: conformal field theories, quantum field theories, Hopf algebra, infinite dimensional Lie algebras, and modular forms. This book will be useful for researchers as well as for graduate students in mathematics and physics. Its purpose is not only to give an uptodate overview of the fields covered by the conference but also to stimulate new directions and discoveries by experts in the areas. Readership Graduate students and research mathematicians interested in vertex operator algebras and its relations to infinitedimensional Lie algebra, quantum field theory, and modular forms. Table of Contents  D. Adamović and A. Milas  An analogue of modular BPZequation in logarithmic (super)conformal field theory
 P. Bantay  Vectorvalued modular forms
 K. Barron  Alternate notions of N=1 superconformality and deformations of N=1 vertex superalgebras
 A. J. Feingold, A. Kleinschmidt, and H. Nicolai  Hyperbolic Weyl groups and the four normed division algebras
 M. R. Gaberdiel and T. Gannon  Zhu's algebra, the \(C_2\) algebra, and twisted modules
 C. Goff  Fusion algebras for vertex operator algebras and finite groups
 M. E. Hoffman  Rooted trees and symmetric functions: Zhao's homomorphism and the commutative hexagon
 Y.Z. Huang  Representations of vertex operator algebras and braided finite tensor categories
 M. Jerković  Recurrences and characters of FeiginStoyanovsky's type subspaces
 C. H. Lam and H. Yamauchi  The FLM conjecture and framed VOA
 H. Li  On quantum vertex algebras and their modules
 A. R. Linshaw  Introduction to invariant chiral differential operators
 F. Patras  Dynkin operators and renormalization group actions in pQFT
 T. J. Robinson  New perspectives on exponentiated derivations, the formal Taylor theorem, and Faà di Bruno's formula
 G. Trupčević  Combinatorial bases of FeiginStoyanovsky's type subspaces for \(\tilde{\mathfrak{sl}}_{\ell+1}(\mathbb C)\)
 M. P. Tuite  Exceptional vertex operator algebras and the Virasoro algebra
