My research interests lie in the area of combinatorics. With Brendon Rhoades I am working on generalized coinvariant
algebras, a collection of \(S_n\)-modules defined by Haglund, Rhoades and Shimozono as quotients of the polynomial
ring in \(n\) variables. I recently found isomorphic modules obtained as quotients of the Stanley-Reisner ring of the Boolean
algebra. Together with Jia Huang I am currently
trying to understand the \(S_n\)-module and \(H_n(0)\)-module structure of these and analagous quotients.
With Fan Chung Graham I will most likely be working on various problems in structural combinatorics, and structural and spectral graph theory. Currently we are trying to understand the spectral gap of the burnt pancake graph.