Michael Atiyah (auth.), Pavel Etingof, Vladimir Retakh, I. M. Singer (eds.)0817640762, 9780817640767
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.
Table of contents :
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
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