research

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)
Submitted (2020). (pdf)(arXiv)

Higher spin mapping class groups and strata of Abelian differentials over Teichmüller space
(with Nick Salter)
Submitted (2019). (pdf) (arXiv)

Relative homological representations of framed mapping class groups
(with Nick Salter)
B. Lond. Math. Soc. (accepted) (2020). (pdf)(arXiv)(journal)

Connected components of strata of Abelian differentials over Teichmüller space
Comment. Math. Helv. 95 (2): 361–420 (2020). (pdf) (arXiv)(journal)


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.