The Unity of Mathematics

by Etingof, Pavel; Retakh, Vladimir S.; Singer, I. M.

• ISBN13: 9780817640767
• ISBN10: 0817640762
• Format: Hardcover
• Copyright: 2005-11-01
• Publisher: Birkhauser

Summary

A tribute to the vision and legacy of Israel Moisevich Gel'fand, 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; 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.

Table of Contents

Preface	vii
Conference Program: An International Conference on "The Unity of Mathematics"	ix
Talk Given at the Dinner at Royal East Restaurant on September 3, 2003
Israel M. Gelfand	xiii
Mathematics as an Adequate Language
Israel M. Gelfand	xv
The Interaction between Geometry and Physics
Michael Atiyah	1	(16)
Uhlenbeck Spaces via Affine Lie Algebras
Alexander Braverman, Michael Finkelberg, and Dennis Gaitsgory	17	(120)
New Questions Related to the Topological Degree
Haim Brezis	137	(18)
Quantum Cobordisms and Formal Group Laws
Tom Coates and Alexander Givental	155	(18)
On the Foundations of Noncommutative Geometry
A. Connes	173	(32)
Stable Distributions Supported on the Nilpotent Cone for the Group G2
Stephen DeBacker and David Kazhdan	205	(58)
Infinite-Dimensional Vector Bundles in Algebraic Geometry: An Introduction
Vladimir Drinfeld	263	(42)
Algebraic Lessons from the Theory of Quantum Integrable Models
L.D. Faddeev	305	(16)
Affine Structures and Non-Archimedean Analytic Spaces
Maxim Kontsevich and Yan Soibelman	321	(66)
Gelfand–Zeitlin Theory from the Perspective of Classical Mechanics. II
Bertram Kostant and Nolan Wallach	387	(34)
Mirror Symmetry and Localizations
Chien-Hao Liu, Kefeng Liu, and Shing-Tung Yau	421	(22)
Character Sheaves and Generalizations
G. Lusztig	443	(14)
Symplectomorphism Groups and Quantum Cohomology
Dusa McDuff	457	(16)
Algebraic Structure of Yang–Mills Theory
M. Movshev and A. Schwarz	473	(52)
Seiberg–Witten Theory and Random Partitions
Nikita A. Nekrasov and Andrei Okounkov	525	(72)
Quantum Calabi–Yau and Classical Crystals
Andrei Okounkov, Nikolai Reshetikhin, and Cumrun Vafa	597	(22)
Gelfand–Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis
A.M. Vershik	619