Research Interests

My primary research interests lie in representation theory, and its connections with algebraic combinatorics, topology, geometry, and categorification. Specifically, I am most interested in the representation theory of quantum algebras, such as the quantized enveloping Lie (super)algebras, q-Schur (super)algebras, (quiver) Hecke algebras. These algebras are related to a variety of topics including knot invariants and topological quantum field theories, the combinatorics of Young tableaux and crystals, and higher representation theory. My current research program involves the construction of canonical bases for quantum Lie superalgebras, and connecting these bases to categorifications appearing in higher representation theory.