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:
- Representation theory of vertex algebras and of their quantum analogs (in particular, double affine quantum groups and q-W-algebras);
- Developing methods of vertex algebras in low-dimensional Topology and in Quantum Field Theory;
- Quantum cohomology of moduli spaces of sheaves and related Geometric Representation Theory and Integrable Systems (in particular, Toda and Calogero systems and their generalizations);
- Geometric Langlands correspondence;
- Cluster structures on moduli spaces, their geometry and combinatorics;
- Combinatorics of Kashiwara crystals in quantum integrable systems.