Areas of Research
- Development of representation theory of semisimple Lie algebras, their quantum and elliptic deformations and other modern generalizations. Elaboration of new methods and concepts in this theory based on ideas of the theory of integrable systems, symplectic geometry and the theory of equivariant quantum cohomologies of quiver varieties.
- Development of combinatorial, homological and geometric methods in the theory of moduli spaces of algebraic curves and their mappings, with applications to problems of mathematical physics.
- Algebraic analysis of integrable models of classical and quantum field theories, statistical physics and random processes, investigation of integrable structures which control dynamics of quiver gauge theories, analysis of their correspondence with two-dimensional conformal theories.
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