About Laboratory

The laboratory was founded in 2014. 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.

Case studies are conducted in several related to each other directions and involve 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.