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