The main objective of the laboratory is to develop a common approach to a variety of issues at the interface between the theory of integrable systems and representation theory of quantum and infinite-dimensional groups and algebras.
Research are conducted in several inter-related directions and involves close cooperation between mathematicians and mathematical physicists.
These areas include:
- Quantum cohomology in the theory of integrable systems;
- Questions of mirror symmetry;
- Multidimensional hypergeometric functions and geometric representation theory;
- Elliptic conformal blocks and elliptic hypergeometric functions;
- Geometric Langlands correspondence;
- Combinatorial development, homology and geometric methods in the theory of moduli spaces of various geometric and analytic structures with applications to problems of mathematical physics.