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:

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)

Submitted. (pdf) (arXiv)


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 and its Ramifications 26 (2017), No. 1 1750002. (arXiv)


Conjugacy geodesics in Coxeter groups

(with S. Hermiller and T. Susse)

Senior Thesis.

selected talks:

  • 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
  • Topology Students Workshop, Georgia Inst. of Tech. June 2016
  • AMS Sectional Meeting Special Session: “Topological and Smooth Dynamics”, N. Dakota St. Univ. April 2016
  • Nebraska Groups, Semigroups and Topology Seminar. October 2015
  • Nebraska Groups, Semigroups and Topology Seminar. December 2014
  • William Jewell College KME Invited Address. November 2014

All talks