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 am working on various problems in structural combinatorics, and structural and spectral graph theory. Currently Sam Spiro and I are working on understanding a model that generates random paperclip graphs, a type of graph that is introduced in a soon to appear paper and was brought to our attention via personal communication.