This is a collection of papers on a variety of topics of current interest in mathematical physics: integrable systems, quantum groups, topological quantum theory, string theory. Some of the contributions are lengthy reviews of lasting value on subjects like symplectic geometry of the Chern-Simons theory or on mirror symmetry. The book addresses graduate students as well as researchers in mathematical physics.
The new results on lattice deformation of current algebra.- Baxterization, dynamical systems, and the symmetries of integrability.- A lecture on the Calogero-Sutherland models.- Quantum group and magnetic translations. Bethe-Ansatz solution for bloch electrons in a magnetic field.- Symplectic geometry of the Chern-Simons theory.- Quantization of field theories generalizing Gravity-Yang-Mills systems on the cylinder.- Wodzicki residue and anomalies of current algebras.- Spacetime locality of the antifield formalism: General theorems illustrated by means of examples.- On supersymmetric and topological quantum mechanical models.- Structures of K.Saito theory of primitive form in topological theories coupled to topological gravity.- String theory and classical integrable systems.- On background independence in string theory.- Lectures on mirror symmetry.