Colloquium Publications 2004; 375 pp; hardcover Volume: 51 ISBN10: 0821835289 ISBN13: 9780821835289 List Price: US$80 Member Price: US$64 Order Code: COLL/51
 This longawaited publication contains the results of the research of two distinguished professors from the University of Chicago, Alexander Beilinson and Fields Medalist, Vladimir Drinfeld. Years in the making, this is a oneofakind book featuring previously unpublished material. Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as wellknown and widely used vertex algebras. The exposition of this book covers the following topics:  the "classical" counterpart of the theory, which is an algebraic theory of nonlinear differential equations and their symmetries;
 the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the chiral algebras of differential operators;
 the formalism of chiral homology treating "the space of conformal blocks" of the conformal field theory, which is a "quantum" counterpart of the space of the global solutions of a differential equation.
The book is intended for researchers working in algebraic geometry and its applications to mathematical physics and representation theory. Readership Graduate students and research mathematicians interested in algebraic geometry and its applications to field theory. Reviews "Without a doubt, it will become a standard reference on the subject."  Francisco J. Plaza Martin for Mathematical Reviews Table of Contents  Introduction
 Axiomatic patterns
 Geometry of \(\mathcal{D}\)schemes
 Local theory: Chiral basics
 Global theory: Chiral homology
 Bibliography
 Index and notation
