Unity of Mathematics

"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

• 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.