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.

Readership

Graduate students and research mathematicians and mathematical physicists interested in integrable systems, quantum groups and string theory; theoretical physicists.

Table of Contents

• M. Semenov-Tian-Shansky -- Some personal historic notes on our seminar
• E. Meinrenken and A. Alekseev -- An elementary derivation of certain classical dynamical \(r\)-matrices
• I. Ya. Aref'eva and O. A. Rytchkov -- Incidence matrix description of intersection \(p\)-brane solutions
• A. I. Bobenko and Yu. B. Suris -- A discrete time Lagrange top and discrete elastic curves
• A. M. Budylin and V. S. Buslaev -- The Gelfand-Levitan-Marchenko equation and the long-time asymptotics of the solutions of the nonlinear Schrödinger equation
• R. M. Kashaev and A. Yu. Volkov -- From the tetrahedron equation to universal \(R\)-matrices
• A. N. Kirillov -- On some quadratic algebras
• V. Korepin and N. Slavnov -- Quantum inverse scattering method and correlation functions
• A. Losev, N. Nekrasov, and S. Shatashvili -- Testing Seiberg-Witten solution
• J. M. Maillet and J. S. de Santos -- Drinfeld twists and algebraic Bethe Ansatz
• V. B. Matveev -- Darboux transformations, covariance theorems and integrable systems
• A. L. Pirozerski and M. A. Semenov-Tian-Shansky -- Generalized \(q\)-deformed Gelfand-Dickey structures on the group of \(q\)-pseudodifference operators
• A. K. Pogrebkov -- On time evolutions associated with the nonstationary Schrödinger equation
• N. Reshetikhin and L. A. Takhtajan -- Deformation quantization of Kähler manifolds
• E. K. Sklyanin -- Canonicity of Bäcklund transformation: \(r\)-matrix approach. I
• F. A. Smirnov -- Quasi-classical study of form factors in finite volume
• V. Tarasov -- Completeness of the hypergeometric solutions of the \(qKZ\) equation at level zero