My research interests lie primarily in the branch of Functional Analysis known as operator algebras.  In particular, I study the C*-algebras associated to topological groups, directed graphs, and their generalizations. In my PhD thesis, I studied what happens to the K-theory of the C*-algebra as I perturb the multiplication in the group(oid) C*-algebra via a 2-cocycle. Since finishing my PhD, I have also investigated other aspects of the structure of these C*-algebras, such as their representation theory, cohomology, KMS states, and Cartan subalgebras.  There's often a lot of interplay between the structure of the C*-algebra and the structure of the group (or directed graph) you started from; this opens the door to research questions about graphs and groups that can often be tackled by undergraduate students.  Come talk to me if you'd like to learn more!