I am interested in the interplay between geometry, topology and group theory, which puts me somewhere in the nexus of geometric group theory, geometric topology, and low-dimensional topology. I am particularly interested in the relationship between mapping class groups, Teichmüller geometry, and flat surfaces.

### papers and preprints:

Framed mapping class groups and the monodromy of strata of Abelian differentials

(with Nick Salter)*Preprint *(2020). (pdf)(arXiv)

Relative homological representations of framed mapping class groups

(with Nick Salter)*Preprint *(2020). (pdf)(arXiv)

Higher spin mapping class groups and strata of Abelian differentials over Teichmüller space

(with Nick Salter)*Submitted* (2019). (pdf) (arXiv)

Connected components of strata of Abelian differentials over Teichmüller space*Comment. Math. Helv.* (Accepted) (2019)*.* (pdf) (arXiv)

How to hear the shape of a billiard table.

(with Solly Coles, Diana Davis, Justin Lanier, and Andre Oliveira)*Submitted* (2018)*.* (arXiv)

Generalized bipyramids and hyperbolic volume of alternating tiling links.

(with Colin Adams and Nat Mayer)*Topology Appl. *271:1–28, 2020. (pdf) (arXiv) (journal)

Volume and determinant densities of hyperbolic rational links.

(with Colin Adams, Xinyi Jiang, Alex Kastner, Greg Kehne, Nat Mayer, and Mia Smith)*J. Knot Theory Ramifications* 26 (1), 2017. (arXiv) (journal)

Conjugacy geodesics in Coxeter groups

(with S. Hermiller and T. Susse)*Senior Thesis.*

### selected talks:

- USC seminar for early career mathematicians working in (higher) Teichmüller theory and quantum topology. November 2019.
- Michigan Topology Seminar. October 2019.
- Flat Surfaces and Dynamics on Moduli Space, II, Oaxaca, Mexico. May 2019. (Video)
- Utah Max Dehn Seminar. April 2019.
- AMS Special Session on Mapping Class Groups. March 2019.
- Columbia Geometric Topology Seminar. February 2019.
- Tufts Geometric Group Theory and Topology Seminar. February 2017