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Hardcover ISBN:  9780821820322 
Product Code:  TRANS2/194 
List Price:  $175.00 
MAA Member Price:  $157.50 
AMS Member Price:  $140.00 
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Product Code:  TRANS2/194.E 
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AMS Member Price:  $132.00 
Hardcover ISBN:  9780821820322 
eBook ISBN:  9781470434052 
Product Code:  TRANS2/194.B 
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Book DetailsAmerican Mathematical Society Translations  Series 2Advances in the Mathematical SciencesVolume: 194; 1999; 313 ppMSC: Primary 14; 17; 58
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.
ReadershipGraduate students, research mathematicians, and physicists interested in algebraic geometry; theoretical physicists.

Table of Contents

Chapters

V. I. Arnold — First steps of local symplectic algebra

Pavel Etingof — Whittaker functions on quantum groups and $q$deformed Toda operators

Boris Feigin and Edward Frenkel — Integrable hierarchies and Wakimoto modules

B. Feigin and S. Loktev — On generalized Kostka polynomials and the quantum Verlinde rule

Michael Finkelberg and Ivan Mirković — Semiinfinite flags. I. Case of global curve $\mathbb {P}^1 $

Boris Feigin, Michael Finkelberg, Alexander Kuznetsov and Ivan Mirković — Semiinfinite flags. II. Local and global intersection cohomology of quasimaps’ spaces

Fyodor Malikov and Vadim 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 $S^1$

Alexander Postnikov, Boris Shapiro and Mikhail Shapiro — Algebras of curvature forms on homogeneous manifolds

Vladimir Retakh, Christophe Reutenauer and Arkady Vaintrob — Noncommutative rational functions and Farber’s invariants of boundary links

Serge 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

Albert Schwarz, Alexei Sossinsky, Claude Roger, Boris Feigin, Sergei Tabachnikov and Alexander Astashkevich — Appendix. Personal notes


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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 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.
Graduate students, research mathematicians, and physicists interested in algebraic geometry; theoretical physicists.

Chapters

V. I. Arnold — First steps of local symplectic algebra

Pavel Etingof — Whittaker functions on quantum groups and $q$deformed Toda operators

Boris Feigin and Edward Frenkel — Integrable hierarchies and Wakimoto modules

B. Feigin and S. Loktev — On generalized Kostka polynomials and the quantum Verlinde rule

Michael Finkelberg and Ivan Mirković — Semiinfinite flags. I. Case of global curve $\mathbb {P}^1 $

Boris Feigin, Michael Finkelberg, Alexander Kuznetsov and Ivan Mirković — Semiinfinite flags. II. Local and global intersection cohomology of quasimaps’ spaces

Fyodor Malikov and Vadim 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 $S^1$

Alexander Postnikov, Boris Shapiro and Mikhail Shapiro — Algebras of curvature forms on homogeneous manifolds

Vladimir Retakh, Christophe Reutenauer and Arkady Vaintrob — Noncommutative rational functions and Farber’s invariants of boundary links

Serge 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

Albert Schwarz, Alexei Sossinsky, Claude Roger, Boris Feigin, Sergei Tabachnikov and Alexander Astashkevich — Appendix. Personal notes