HSE – Skoltech International Laboratory of Representation Theory and Mathematical Physics

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. The laboratory develops several inter-related research directions with close cooperation between mathematicians and mathematical physicists.

research areas

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

team