Professor L. D. Faddeev's seminar at Steklov Mathematical Institute (St. Petersburg, Russia) has a record of more than 30 years of intensive work which has helped to shape modern mathematical physics. This collection, honoring Professor Faddeev's 65th anniversary, has been prepared by his students and colleagues. Topics covered in the volume include classical and quantum integrable systems (both analytic and algebraic aspects), quantum groups and generalizations, quantum field theory, and deformation quantization. Included is a history of the seminar highlighting important developments, such as the invention of the quantum inverse scattering method and of quantum groups. The book will serve nicely as a comprehensive, up-to-date resource on the topic.
Some personal historic notes on our seminar by M. Semenov-Tian-Shansky An elementary derivation of certain classical dynamical $r$-matrices by E. Meinrenken and A. Alekseev Incidence matrix description of intersection $p$-brane solutions by I. Ya. Aref'eva and O. A. Rytchkov A discrete time Lagrange top and discrete elastic curves by A. I. Bobenko and Yu. B. Suris The Gelfand-Levitan-Marchenko equation and the long-time asymptotics of the solutions of the nonlinear Schrodinger equation by A. M. Budylin and V. S. Buslaev From the tetrahedron equation to universal $R$-matrices by R. M. Kashaev and A. Yu. Volkov On some quadratic algebras by A. N. Kirillov Quantum inverse scattering method and correlation functions by V. Korepin and N. Slavnov Testing Seiberg-Witten solution by A. Losev, N. Nekrasov, and S. Shatashvili Drinfeld twists and algebraic Bethe Ansatz by J. M. Maillet and J. S. de Santos Darboux transformations, covariance theorems and integrable systems by V. B. Matveev Generalized $q$-deformed Gelfand-Dickey structures on the group of $q$-pseudodifference operators by A. L. Pirozerski and M. A. Semenov-Tian-Shansky On time evolutions associated with the nonstationary Schrodinger equation by A. K. Pogrebkov Deformation quantization of Kahler manifolds by N. Reshetikhin and L. A. Takhtajan Canonicity of Backlund transformation: $r$-matrix approach. I by E. K. Sklyanin Quasi-classical study of form factors in finite volume by F. A. Smirnov Completeness of the hypergeometric solutions of the $qKZ$ equation at level zero by V. Tarasov.