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.

Summer 2017 I took part in a research cluster on polygonal billiards led by Moon Duchin. Results from the summer are in preparation.

Previous research has concerned the geometry of decision problems, geodesic languages, and polyhedral decompositions of knot complements.

MaximalOctahedron_exploded

Papers and Preprints:
  1. (with S. Hermiller, T. Susse)
     Conjugacy geodesics of Coxeter groups. In preparation.
  2. (with C. Adams and N. Mayer)

    Generalized bipyramids and hyperbolic volume of alternating tiling links.
    Submitted. arXiv:1709.00432

  3. (with C. Adams, X. Jiang, A. Kastner, G. Kehne, N. Mayer and M. Smith)

    Volume and determinant densities of hyperbolic rational links.
    J. Knot Theory and its Ramifications 26 (2017), No. 1 1750002. arXiv:1510.06050

Selected Talks:
  1. Tufts Geometric Group Theory and Topology Seminar. February 2017
  2. Topology Students Workshop, Georgia Inst. of Tech. June 2016
  3. AMS Sectional Meeting Special Session: “Topological and Smooth Dynamics”, N. Dakota St. Univ. April 2016
  4. Univ. of Nebraska Groups, Semigroups and Topology Seminar. October 2015
  5. Univ. of Nebraska Groups, Semigroups and Topology Seminar. December 2014
  6. William Jewell College KME Invited Address. November 2014

All talks