My research interests are mainly in the representation theory of Lie algebras.
I am working with methods from combinatorics, discrete mathematics and algebraic geometry to answer question that rise in classical representation theory.
In recent times, I am focused on degenerate representations (of Lie algebra and Lie groups) and degenerate flag varieties . In this context mainly, appropriate monomial bases and the induced toric degenerations as well as degenerations of the corresponding quantum groups. PBW fitrations and degenerations might be the most appropriate name tag here.
I am also interested in positivity questions of Schur functions and their relations to fusion product of simple modules for classical Lie algebras (in the sense of current algebras) .
This is closely related to understanding indecomposable modules for generalized current algebras, especially truncated current algebras.