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. The Interaction between Geometry and Physics....Pages 1-15 Uhlenbeck Spaces via Affine Lie Algebras....Pages 17-135 New Questions Related to the Topological Degree....Pages 137-154 Quantum Cobordisms and Formal Group Laws....Pages 155-171 On the Foundations of Noncommutative Geometry....Pages 173-204 Stable Distributions Supported on the Nilpotent Cone for the Group G 2 ....Pages 205-262 Infinite-Dimensional Vector Bundles in Algebraic Geometry....Pages 263-304 Algebraic Lessons from the Theory of Quantum Integrable Models....Pages 305-320 Affine Structures and Non-Archimedean Analytic Spaces....Pages 321-385 Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II....Pages 387-420 Mirror Symmetry and Localizations....Pages 421-442 Character Sheaves and Generalizations....Pages 443-455 Symplectomorphism Groups and Quantum Cohomology....Pages 457-471 Algebraic Structure of Yang-Mills Theory....Pages 473-523 Seiberg-Witten Theory and Random Partitions....Pages 525-596 Quantum Calabi-Yau and Classical Crystals....Pages 597-618 Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis....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 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