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)

Relative homological representations of framed mapping class groups
(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)

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

All talks