My research is in algebraic combinatorics, which means I use algebraic tools to study problems like how many ways to color a map such that neighboring countries get different colors, or how many steps it takes to get back to where you started if you play a game similar to the 15-puzzle.

 

More specifically, I'm currently thinking a lot about the chromatic symmetric function, a power series encoding the proper colorings of a graph, and variations of it such as the Kromatic symmetric function, H-chromatic symmetric functions, and the chromatic symmetric homology.

 

I've also been thinking a lot lately about the orbit lengths for promotion on standard Young tableaux. In the past, I've also done projects related to permutation patterns, symmetric group representations, the Tutte polynomial of a matroid, and various polynomials arising from combinatorial K-theory.

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My Master's thesis was called On K-theoretic polynomials and the chromatic symmetric function, and won the Governor General's Gold Medal. These are my papers on arXiv, and they are also listed on  this page.