I work within two broad areas, arithmetic geometry and the study of representation and character varieties. Within the former, I am interested in varieties over finite fields, étale fundamental groups and étale covers of curves, local-global principles, profinite groups, and nearly anything with a Galois correspondence.
Together with Clément Guerin I am working on problems related to singularities of character varieties and the character varieties of braid groups. My thesis was on representation varieties of fundamental groups of abelian varieties in characteristic p. This is closely related to the study of varieties of commuting matrices. You can access a preprint (nearly identical to the published version) here.
I sometimes combine these two interests by counting points on character varieties over finite fields. Over the past decade this has been a particularly fruitful approach to understanding the cohomology of character varieties.
A copy of my research statement is available here.
A slightly less technical version, with more about possible undergraduate projects, is available here.
Here is a whimsical (and vague) description of my work for those outside the mathematics profession: I work within a broad area of mathematics known as algebra. Within algebra, my sub-area is sometimes called arithmetic. Some of the problems I am intersted in involve counting.
You can see a copy of my teaching portfolio here. The document contains a copy of my teaching statement and diversity statement, but I have omitted some samples of student work and an observational essay. I prefer not to post these items publicly on the web since I am not the author, but I have permission from the authors to distribute these materials and would be happy to send copies upon request.