The Interaction between Geometry and Physics -- Uhlenbeck Spaces via Affine Lie Algebras -- New Questions Related to the Topological Degree -- Quantum Cobordisms and Formal Group Laws -- On the Foundations of Noncommutative Geometry -- Stable Distributions Supported on the Nilpotent Cone for the Group G 2 -- Infinite-Dimensional Vector Bundles in Algebraic Geometry -- Algebraic Lessons from the Theory of Quantum Integrable Models -- Affine Structures and Non-Archimedean Analytic Spaces -- Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II -- Mirror Symmetry and Localizations -- Character Sheaves and Generalizations -- Symplectomorphism Groups and Quantum Cohomology -- Algebraic Structure of Yang-Mills Theory -- Seiberg-Witten Theory and Random Partitions -- Quantum Calabi-Yau and Classical Crystals -- Gelfand-Tsetlin Algebras, Expectations, Inverse Limits, Fourier Analysis.

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.