Prof. Mukhin studies symmetries and structures arising in the context of conformal field theory, quantum field theory and exactly solvable models of statistical physics. He is often working on the border of several areas of mathematics, employing a combination of tools from representation theory, combinatorics, and analysis.
He has made a number of important contributions to the theory of algebraic Bethe ansatz, to the theory of finite-dimensional representations of affine quantum groups, to the combinatorics of representations of affine Lie algebras and W-algebras, to the theory of Jack and Macdonald polynomials, to the representation theory of quantum toroidal algebras, to the theory of quantum and classical Knizhnik-Zamolodchikov equations.
