The Unity of Mathematics: In Honor of the Ninetieth Birthday of I.M. Gelfand (Progress in Mathematics Book 244)

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. 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.--publisher's Website. Talk Given At The Dinner At Royal East Restaurant On September 3, 2003 / Israel M. Gelfand -- Mathematics As An Adequate Language / Israel M. Gelfand -- Interaction Between Geometry And Physics / Michael Atiyah -- Unlenbeck Spaces Via Affine Lie Algebras / Alexander Braverman, Michael Finkelberg And Dennis Gaitsgory -- New Questions Related To The Topological Degree / Haim Brezis -- Quantum Cobordisms And Formal Group Laws / Tom Coates And Alexander Givental -- On The Foundations Of Noncommutative Geometry / A. Connes -- Stable Distributions Supported On The Nilpotent Cone For The Group G[subscript 2] / Stephen Debacker And David Kazhdan -- Infinite-dimensional Vector Bundles In Algebraic Geometry : An Introduction / Vladimir Drinfeld -- Algebraic Lessons From The Theory Of Quantum Integrable Models / L. D. Faddeev -- Affine Structures And Non-archimedean Analytic Spaces / Maxim Kontsevich And Yan Soibelman -- Gelfand-zeitlin Theory From The Perspective Of Classical Mechanics. Ii / Bertram Kostant And Nolan Wallach -- Mirror Symmetry And Localizations / Chien-hao Liu, Kefeng Liu And Shing-tung Yau -- Character Sheaves And Generalizations / G. Lusztig -- Symplectomorphism Groups And Quantum Cohomology / Dusa Mcduff -- Algebraic Structure Of Yang-mills Theory / M. Movshev And A. Schwarz -- Seiberg-witten Theory And Random Partitions / Nikita A. Nekrasov And Andrei Okounkov -- Quantum Calabi-yau And Classical Crystals / Andrei Okounkov, Nikolai Reshetikhin And Cumrun Vafa -- Gelfand-tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis / A. M. Vershik. Pavel Etingof, Vladimir Retakh, I.m. Singer, Editors. Includes Bibliographical References. Contents......Page 6 Preface......Page 8 Conference Program: An International Conference on "The Unity of Mathematics"......Page 10 Talk Given at the Dinner at Royal East Restaurant on September 3, 2003......Page 13 Mathematics as an Adequate Language......Page 15 The Interaction between Geometry and Physics......Page 23 Uhlenbeck Spaces via Affine Lie Algebras......Page 38 New Questions Related to the Topological Degree......Page 157 Quantum Cobordisms and Formal Group Laws......Page 175 On the Foundations of Noncommutative Geometry......Page 192 Stable Distributions Supported on the Nilpotent Cone for the Group G[sub(2)]......Page 224 Infinite-Dimensional Vector Bundles in Algebraic Geometry: An Introduction......Page 282 Algebraic Lessons from the Theory of Quantum Integrable Models......Page 324 Affine Structures and Non-Archimedean Analytic Spaces......Page 340 Gelfand–Zeitlin Theory from the Perspective of Classical Mechanics. II......Page 405 Mirror Symmetry and Localizations......Page 439 Character Sheaves and Generalizations......Page 461 Symplectomorphism Groups and Quantum Cohomology......Page 474 Algebraic Structure of Yang–Mills Theory......Page 489 Seiberg–Witten Theory and Random Partitions......Page 540 Quantum Calabi–Yau and Classical Crystals......Page 612 Gelfand–Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis......Page 634 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 between the fields of geometry, physics, and representation theory. Written by distinguished mathematicians, the text is divided as follows: several articles are devoted to developments at the intersection of geometry and physics, while others treat the interaction of representation theory, Poisson- and algebraic geometry. Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, Gelfand-Kirillov theory, 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. Tribute to the vision and legacy of Israel Moiseevich Gel'fand Written by leading mathematicians, these invited papers reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, physics, and representation theory Topics include conformal field theory, K-theory, noncommutative geometry, gauge theory, representations of infinite-dimensional Lie algebras, and various aspects of the Langlands program