My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, I study the combinatorics of Coxeter groups and their associated Hecke algebras, Kazhdan-Lusztig theory, generalized Temperley–Lieb algebras, diagram algebras, and heaps of pieces. By employing combinatorial tools such as diagram algebras and heaps of pieces, one can gain insight into algebraic structures associated to Coxeter groups, and, conversely, the corresponding structure theory can often lead to surprising combinatorial results. The combinatorial nature of my research naturally lends itself to collaboration with advanced undergraduate students, and I strive to incorporate undergraduates in my research whenever possible.
I am also passionate about undergraduate mathematics education and recently my research interests have included topics in this area. In particular, I am studying the effectiveness of a collaborative approach to inquiry-based learning (IBL) in proof-based courses. Furthermore, I am interested in the use of technology, such as Sage, screencasts, and other Web2.0 technology, to aid in the learning of mathematics.
