The Theory Department of the Institute of Theoretical and Experimental Physics (ITEP) is internationally recognized for achievements in various branches of theoretical physics. The seminars at ITEP for many years have been among the main centers of scientific life in Moscow. This volume presents results from the seminar on mathematical physics that has been held at ITEP since 1983. It reflects the style and direction of some of the work done at the Institute. The majority of the papers in the volume describe the Knizhnik-Zamolodchikov-Bernard connection and its far-reaching generalizations. The remaining papers are related to other aspects of the theory and integrable models. Included are discussions on quantum Lax operators analyzed by methods of algebraic geometry, current algebras associated with complex curves, and the relationship between matrix models and integrable systems.
Quantum dynamical $R$-matrices by G. E. Arutyunov, L. O. Chekhov, and S. A. Frolov Some examples of quantum groups in higher genus by B. Enriquez and V. Rubtsov Poisson structure on moduli of flat connections on Riemann surfaces and the $r$-matrix by V. V. Fock and A. A. Rosly KZB equations as a flat connection with spectral parameter by D. A. Ivanov and A. S. Losev Kadomtsev-Petviashvili hierarchy and generalized Kontsevich model by S. Kharchev Yangian algebras and classical Riemann problems by S. Khoroshkin, D. Lebedev, and S. Pakuliak Vacuum curves of elliptic $L$-operators and representations of the Sklyanin algebra by I. Krichever and A. Zabrodin Hierarchies of isomonodromic deformations and Hitchin systems by A. M. Levin and M. A. Olshanetsky Infinite-dimensional algebras, many-body systems and gauge theories by N. Nekrasov.