The Gelfand Mathematical Seminars, 1990–1992

1. Front Matter

   Pages i-xii

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2. The Degeneracy of Two Spectral Sequences

   • Jean-Luc Brylinski

   Pages 1-10

3. Hopf Algebra Structures for the Heisenberg Algebra: I

   • L. Corwin, I. M. Gelfand

   Pages 11-17

4. Avalanches, Sandpiles and Tutte Decomposition

   • Andrei Gabrielov

   Pages 19-26

5. On the Dimension and Degree of the Projective Dual Variety: A q-Analog of the Katz-Kleiman Formula

   • I. M. Gelfand, M. M. Kapranov

   Pages 27-33

6. Crofton Densities and Nonlocal Differentials

   • I. M. Gelfand, M. M. Smirnov

   Pages 35-50

7. On the Local Geometry of a Bihamiltonian Structure

   • Israel M. Gelfand, Ilya Zakharevich

   Pages 51-112

8. The Classical Polylogarithms, Algebraic K-Theory And ζ _F (n)

   • A. B. Goncharov

   Pages 113-135

9. A Brief History of the Sporadic Simple Groups

   • Daniel Gorenstein

   Pages 137-143

10. Vertex operator algebras and operads

    • Yi-Zhi Huang, James Lepowsky

    Pages 145-161

11. Representations of the Quantized Function Algebras, 2-Categories and Zamolodchikov Tetrahedra Equation

    • D. Kazhdan, Y. Soibelman

    Pages 163-171

12. Formal (Non)-Commutative Symplectic Geometry

    • Maxim Kontsevich

    Pages 173-187

13. Constructible functions, Lagrangian cycles and computational geometry

    • Pierre Schapira

    Pages 189-202

14. Quantum Groups and Perverse Sheaves: An Example

    • Vadim Schechtman

    Pages 203-216

15. Linearly Recursive Sequences, Witt Algebras and Quantum Groups

    • Earl J. Taft

    Pages 217-222

16. Complexes of Connected Graphs

    • V. A. Vassiliev

    Pages 223-235

This Seminar began in Moscow in November 1943 and has continued without interruption up to the present. We are happy that with this vol­ ume, Birkhiiuser has begun to publish papers of talks from the Seminar. It was, unfortunately, difficult to organize their publication before 1990. Since 1990, most of the talks have taken place at Rutgers University in New Brunswick, New Jersey. Parallel seminars were also held in Moscow, and during July, 1992, at IRES in Bures-sur-Yvette, France. Speakers were invited to submit papers in their own style, and to elaborate on what they discussed in the Seminar. We hope that readers will find the diversity of styles appealing, and recognize that to some extent this reflects the diversity of styles in a mathematical society. The principal aim was to have interesting talks, even if the topic was not especially popular at the time. The papers listed in the Table of Contents reflect some of the rich variety of ideas presented in the Seminar. Not all the speakers submit­ ted papers. Among the interesting talks that influenced the seminar in an important way, let us mention, for example, that of R. Langlands on per­ colation theory and those of J. Conway and J. McKay on sporadic groups. In addition, there were many extemporaneous talks as well as short discus­ sions.

• algebra
• computational geometry
• equation
• function
• geometry

• Department of Mathematics, Rutgers University, New Brunswick, USA

  Israel M. Gelfand, Lawrence Corwin, James Lepowsky

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