I am interested in geometric group theory, CAT(0) and hyperbolic geometry, and low-dimensional topology. In my thesis I study outer automorphisms of free products of finite groups. They have natural connections to outer automorphisms of free groups, free-by-cyclic groups, right-angled Coxeter groups and braid groups. I am interested in exploring all of these connections, as well as studying the deformation theory of geometric group actions of the above groups on CAT(0) metric spaces.
Publications and Preprints
Train Tracks, Orbigraphs and CAT(0) Free-By-Cyclic Groups
Submitted. Available at: arXiv:1909.03097
Doubly-Uniform Exponential Growth for Free-By-Cyclic Groups
(with Robert Kropholler and Thomas Ng)
Out and Big Mapping Class Groups
(with Santana Afton)
Here are slides from a recent talk titled Train Tracks, Orbigraphs and CAT(0) Free-by-cyclic Groups.
This fall I have spoken at the Temple Geometry and Topology Seminar, the SUNY Albany Algebra/Topology Seminar, and at an AMS Special Session on Effective and Quantitative Advances in Low Dimensional Topology and Geometric Group Theory.
I will be attending Junior Geometry and Topology in the Midwest and Algorithms in Complex Dynamics and Mapping Class Groups.
In the spring I will speak at an AMS Special Session on Combinatorial Methods in Geometric Group Theory.