“The older I get, the more I believe that at the bottom of most deep mathematical problems there is a combinatorial problem.”
- Israel Gelfand -
My research is in the area of algebraic combinatorics. I like to use combinatorial arguments and techniques to enumerate, examine, and investigate the existence of discrete mathematical structures with certain properties. The areas of interest for these applications are in algebra, number theory, and graph theory. I am particularly interested in problems related to the representation theory of Lie algebras, whose study intersects number theory via vector partition functions.
I have enjoyed working on research with undergraduate students and during this time I have supervised over 60 undergraduate researchers. Their projects have been in enumerative and algebraic combinatorics, number theory, and graph theory. This work has culminated in many publications coauthored with students.