The Unity of Mathematics

1. Front Matter

   Pages i-xxii

   PDF

2. The Interaction between Geometry and Physics

   • Michael Atiyah

   Pages 1-15

3. Uhlenbeck Spaces via Affine Lie Algebras

   • Alexander Braverman, Michael Finkelberg, Dennis Gaitsgory

   Pages 17-135

4. New Questions Related to the Topological Degree

   • Haïm Brezis

   Pages 137-154

5. Quantum Cobordisms and Formal Group Laws

   • Tom Coates, Alexander Givental

   Pages 155-171

6. On the Foundations of Noncommutative Geometry

   • A. Connes

   Pages 173-204

7. Stable Distributions Supported on the Nilpotent Cone for the Group G ₂

   • Stephen DeBacker, David Kazhdan

   Pages 205-262

8. Infinite-Dimensional Vector Bundles in Algebraic Geometry

   • Vladimir Drinfeld

   Pages 263-304

9. Algebraic Lessons from the Theory of Quantum Integrable Models

   • L. D. Faddeev

   Pages 305-320

10. Affine Structures and Non-Archimedean Analytic Spaces

    • Maxim Kontsevich, Yan Soibelman

    Pages 321-385

11. Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II

    • Bertram Kostant, Nolan Wallach

    Pages 387-420

12. Mirror Symmetry and Localizations

    • Chien-Hao Liu, Kefeng Liu, Shing-Tung Yau

    Pages 421-442

13. Character Sheaves and Generalizations

    • G. Lusztig

    Pages 443-455

14. Symplectomorphism Groups and Quantum Cohomology

    • Dusa McDuff

    Pages 457-471

15. Algebraic Structure of Yang-Mills Theory

    • M. Movshev, A. Schwarz

    Pages 473-523

16. Seiberg-Witten Theory and Random Partitions

    • Nikita A. Nekrasov, Andrei Okounkov

    Pages 525-596

17. Quantum Calabi-Yau and Classical Crystals

    • Andrei Okounkov, Nikolai Reshetikhin, Cumrun Vafa

    Pages 597-618

18. Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis

    • A. M. Vershik

    Pages 619-631

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

"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

• Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

  Pavel Etingof, I. M. Singer

• Department of Mathematics, Rutgers University, Piscataway, USA

  Vladimir Retakh

Policies and ethics