Scholarship
My primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, one area of interest is the combinatorics of Coxeter groups. 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. My research also includes combinatorial game theory. More recently my scholarly interests have expanded into enumerative combinatorics with current research projects focused on the combinatorics of genome rearrangements, as well as pattern avoidance in combinatorical structures such Cayley permutations. The combinatorial nature of my research naturally lends itself to collaborations with undergraduate students, and my goal is to incorporate undergraduates in my research as much as possible. Check out my undergraduate research page for examples of recent projects.
My interests also include the scholarship of teaching and learning(SoTL) with a focus on inquiry-based learning (IBL) as an approach to teaching/exploring mathematics. I am currently Co-Director for the Academy of Inquiry-Based Learning and a mentor for several new IBL practitioners. Moreover, I actively give talks and organize workshops on the benefits of IBL as well as the nuts and bolts of how to implement this approach in the mathematics classroom.
Additional Information
- Academic Writing
- My Curriculum Vitae
- Undergraduate Research (a little outdated)
- My Talks
- Math Ed Matters
- Teaching Tidbits
The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.