My research focuses on the representations of Lie algebras and Lie groups.
My work so far has focused on G-harmonic polynomials and generalized exponents/graded multiplicities using Kirillov's recent and largely unexplored family algebra construction. My PhD dissertation topic was on the structure of family algebras corresponding to the adjoint representations of simple Lie groups, available here.
Here is a paper I wrote on the case of SL(n) on arXiv. Here is a rough script of the talk I gave on family algebras at the University of Colorado Boulder in October 2014, with slides.
I am also writing a set of lecture notes on family algebras with Alexandre Kirillov.
I am currently working on finding combinatorial relations between the representations of simple Lie algebras and representations of their Weyl groups, inspired by work from my thesis.