© 2006

The Unity of Mathematics

In Honor of the Ninetieth Birthday of I.M. Gelfand

  • Pavel Etingof
  • Vladimir Retakh
  • I. M. Singer

Part of the Progress in Mathematics book series (PM, volume 244)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Alexander Braverman, Michael Finkelberg, Dennis Gaitsgory
    Pages 17-135
  3. Tom Coates, Alexander Givental
    Pages 155-171
  4. Stephen DeBacker, David Kazhdan
    Pages 205-262
  5. Maxim Kontsevich, Yan Soibelman
    Pages 321-385
  6. Bertram Kostant, Nolan Wallach
    Pages 387-420
  7. Chien-Hao Liu, Kefeng Liu, Shing-Tung Yau
    Pages 421-442
  8. G. Lusztig
    Pages 443-455
  9. M. Movshev, A. Schwarz
    Pages 473-523
  10. Nikita A. Nekrasov, Andrei Okounkov
    Pages 525-596
  11. Andrei Okounkov, Nikolai Reshetikhin, Cumrun Vafa
    Pages 597-618

About this book


A tribute to the vision and legacy of Israel Moiseevich Gelfand, the invited papers in this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory. Written by leading mathematicians, the text is broadly divided into two sections: the first is devoted to developments at the intersection of geometry and physics, and the second to representation theory and algebraic geometry. Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program.

Graduate students and researchers will benefit from and find inspiration in this broad and unique work, which brings together fundamental results in a number of disciplines and highlights the rewards of an interdisciplinary approach to mathematics and physics.

Contributors: M. Atiyah; A. Braverman; H. Brezis; T. Coates; A. Connes; S. Debacker; V. Drinfeld; L.D. Faddeev; M. Finkelberg; D. Gaitsgory; I.M. Gelfand; A. Givental; D. Kazhdan; M. Kontsevich; B. Kostant; C-H. Liu; K. Liu; G. Lusztig; D. McDuff; M. Movshev; N.A. Nekrasov; A. Okounkov; N. Reshetikhin; A. Schwarz; Y. Soibelman; C. Vafa; A.M. Vershik; N. Wallach; and S-T. Yau.


Algebraic structure Gauge theory K-theory Representation theory Volume cohomology homology vector bundle

Editors and affiliations

  • Pavel Etingof
    • 1
  • Vladimir Retakh
    • 2
  • I. M. Singer
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA

Bibliographic information


"This book is a unique and wonderful collection of papers presented at a conference honoring one of the most productive, influential and still young mathematicians of the 20th century, I. M. Gelfand. As the title suggests, the articles refer to the connections between several fields: geometry, physics, representation theory, algebraic geometry.... The authors of the papers are some of the best mathematicians of present day...[and] most of them emphasize the crucial contribution that Gelfand's work had in many different ways.... [T]he papers are unique, very deep and very well written. Mathematicians and graduate students will find lots of connections, ideas and inspiration in this wonderful collection of papers."   —MAA