American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1999; 313 pp; hardcover Volume: 194 ISBN10: 082182032X ISBN13: 9780821820322 List Price: US$130 Member Price: US$104 Order Code: TRANS2/194
 This volume presents contributions by leading experts in the field. The articles are dedicated to D. B. Fuchs on the occasion of his 60th birthday. Contributors to the book were directly influenced by Professor Fuchs and include his students, friends, and professional colleagues. In addition to their research, they offer personal reminicences about Professor Fuchs, giving insight into the history of Russian mathematics. The main topics addressed in this unique work are infinitedimensional Lie algebras with applications (vertex operator algebras, conformal field theory, quantum integrable systems, etc.) and differential topology. The volume provides an excellent introduction to current research in the field. Readership Graduate students, research mathematicians, and physicists interested in algebraic geometry; theoretical physicists. Table of Contents  V. I. Arnold  First steps of local symplectic algebra
 P. Etingof  Whittaker functions on quantum groups and \(q\)deformed Toda operators
 B. Feigin and E. Frenkel  Integrable hierarchies and Wakimoto modules
 B. Feigin and S. Loktev  On generalized Kostka polynomials and the quantum Verlinde rule
 M. Finkelberg and I. Mirković  Semiinfinite flags. I. Case of global curve \(\mathbb P^1\)
 B. Feigin, M. Finkelberg, A. Kuznetsov, and I. Mirković  Semiinfinite Flags. II. Local and global intersection cohomology of quasimaps' spaces.
 F. Malikov and V. Schechtman  Chiral de Rham complex. II
 E. Mukhin and A. Varchenko  On algebraic equations satisfied by hypergeometric solutions of the qKZ equation.
 V. Ovsienko and C. Roger  Deforming the Lie algebra of vector fields on \({S}^1\) inside the Lie algebra of pseudodifferential symbols on \({S}^1\)
 A. Postnikov, B. Shapiro, and M. Shapiro  Algebras of curvature forms on homogeneous manifolds
 V. Retakh, C. Reutenauer, and A. Vaintrob  Noncommutative rational functions and Farber's invariants of boundary links
 S. Tabachnikov  Remarks on the geometry of exact transverse line fields
 B. Tsygan  Formality conjectures for chains
 V. A. Vassiliev  On finite order invariants of triple point free plane curves
 A. Schwarz, A. Sossinski, C. Roger, B. Feigin, S. Tabachnikov, and A. Astashkevich  Appendix. Personal notes
