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Advances in the Mathematical Sciences
Differential Topology, Infinite-Dimensional Lie Algebras, and Applications: D. B. Fuchs' 60th Anniversary Collection
Edited by: Alexander Astashkevich, Renaissance Technologies, East Setauket, NY, and Serge Tabachnikov, University of Arkansas, Fayetteville, AR
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American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
1999; 313 pp; hardcover
Volume: 194
ISBN-10: 0-8218-2032-X
ISBN-13: 978-0-8218-2032-2
List Price: US$126
Member Price: US$100.80
Order Code: TRANS2/194
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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 infinite-dimensional 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 -- Semi-infinite flags. I. Case of global curve \(\mathbb P^1\)
  • B. Feigin, M. Finkelberg, A. Kuznetsov, and I. Mirković -- Semi-infinite 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
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