This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.

Readership

Research mathematicians.

Table of Contents

• K. Aomoto and Y. Kato -- Connection coefficients for \(A\)-type Jackson integral and Yang-Baxter equation
• C. Dong -- Representations of the moonshine module vertex operator algebra
• C. Dong and G. Mason -- The construction of the moonshine module as a \(\mathbf Z_p\)-orbifold
• M. Flato and D. Sternheimer -- Star products, quantum groups, cyclic cohomology, and pseudodifferential calculus
• C. Fronsdal and A. Galindo -- The universal \(T\)-matrix
• G. Georgiev and O. Mathieu -- Fusion rings for modular representations of Chevalley groups
• V. Ginzburg, N. Reshetikhin, and E. Vasserot -- Quantum groups and flag varieties
• Y.-Z. Huang and J. Lepowsky -- Operadic formulation of the notion of vertex operator algebra
• L. C. Jeffrey and J. Weitsman -- Torus actions, moment maps, and the symplectic geometry of the moduli space of flat connections on a two-manifold
• V. Kac and W. Wang -- Vertex operator superalgebras and their representations
• T. Kohno -- Topological invariants for \(3\)-manifolds using representations of mapping class groups II: Estimating tunnel number of knots
• M. A. Semenov-Tian-Shansky -- Poisson Lie groups, quantum duality principle, and the quantum double
• Y. S. Stanev and I. T. Todorov -- Local \(4\)-point functions and the Knizhnik-Zamolodchikov equation