Infinite Dimensional Lie Algebras, Quantum Groups, and their Applications

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Principal Investigator: Nicolai ReshetikhinProposal Number: 0307599Institution: University of California-BerkeleyABSTRACT: Infinite Dimensional Lie Algebras, Quantum Groups, and their ApplicationsThe main theme of this proposal is representation theory and its applications. The proposal is focused on the representation theory of quantum groups at roots of 1, on invariants of 3-manifolds with flat connections and related topological quantum field theories, on classical and quantum integrable systems, and on some solvable models of statistical mechanics.The last several decades have been characterized by an intense and productive interaction between mathematics and physics. A large part of this process was initiated in the study of classical and quantum integrable systems. This interaction has led to revolutionary progress in both quantum field theory and string theory on the physical side, and geometry, algebra and topology on the mathematical side. The research of this proposal is focused mostly on the study of algebraic structures resulting from this interaction and on applications of these structures.