The Unity of Mathematics: In Honor of the Ninetieth Birthday of I.M. Gelfand

ISBN-13: 9780817640767 / Angielski / Twarda / 2005 / 632 str.

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

Opis

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

Recenzje

"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

Spis treści

P. Etingof, V. Retakh, and I.M. Singer (eds.): Preface Conference Program: An International Conference on 'The Unity of Mathematics' I.M. Gelfand: Talk Given at the Dinner at Royal East Restaurant on September 3, 2003 I.M. Gelfand: Mathematics as an Adequate Language ----- M. Atiyah: The Interaction between Geometry and Physics A. Braverman, M. Finkelberg, and D. Gaitsgory: Uhlenbeck Spaces via Affine Lie Algebras H. Brezis: New Questions Related to the Topological Degree T. Coates and A. Givental: Quantum Cobordisms and Formal Group Laws A. Connes: On the Foundations of Noncommutative Geometry S. Debacker and D. Kazhdan: Stable Distributions Supported on the Nilpotent Cone for the Group G2 V. Drinfeld: Infinite-Dimensional Vector Bundles in Algebraic Geometry: An Introduction L.D. Faddeev: Algebraic Lessons from the Theory of Quantum Integrable Models M. Kontsevich and Y. Soibelman: Affine Structures and Non-Archimedean Analytic Spaces B. Kostant and N. Wallach: Gelfand–Zeitlin Theory from the Perspective of Classical Mechanics II C-H. Liu, K. Liu, and S-T. Yau: Mirror Symmetry and Localizations G. Lusztig: Character Sheaves and Generalizations D. McDuff: Symplectomorphism Groups and Quantum Cohomology M. Movshev and A. Schwarz: Algebraic Structure of Yang–Mills Theory N.A. Nekrasov and A. Okounkov: Seiberg–Witten Theory and Random Partitions A.Okounkov, N. Reshetikhin, and C. Vafa: Quantum Calabi–Yau and Classical Crystals A.M. Vershik: Gelfand–Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis

Blurb

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.