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.

- Math 202, Finite Math
- Math 220, Differential Calculus
- Math 368, Optimization
- Math 518, Graduate Topics in Number Theory

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.

Together with Rachael Norton, I founded and direct the Northwestern Emerging Scholars Program. (Thanks to Miguel Lerma for maintaining the program website)