My research is primarily concerned with geometric structures on surfaces and 3manifolds. My research statement can be found here. In particular, my interests include :
 hyperbolic geometry; identities on hyperbolic manifolds
 Teichmüller theory and Kleinian groups
 computational approaches to hyperbolic 3manifolds
 convex real projective structures; Hitchin representations
 lowdimensional topology; mapping class groups
 circle packings on complex projective structures
Currently, I am working on circle (and Delaunay) packings of projective stuctures with JeanMarc Schlenker and random triangles on surfaces with Olivier Glorieux. In addition, I have been working on a large project on classifying families of onecusped hyperbolic 3manifolds of low volume with Rob Meyerhoff, David Gabai, Nathaniel Thurston, and Robert Haraway. My recent publications include joint work with Nick Vlamis on hyperbolic identities in Higher Teichmüller Theory.
In preparation
Preprints
Publications
Software

Circle packing convex projective structures
 This little program lets you visualize the image of the developing map of projective tori that admit the specific "square" 2circle packing. The full parameter space is drawn on the right and the red point indicates your position. The coordinates are two shearing parameters for an associated punctured torus hyperbolic structure. On the right, you can see the holonomy traces and the underlying upper half plane parameter for the conformal structure of the torus.
 Requires python 3 and pyqt5

Horoball necklaces, variety words, and boxes
 This is a visualization program for the maximal horoball neighborhood of a hyperbolic 3manifold given by a box parameter and a variety word (see Hyperbolic 3manifolds of low cusp volume)
 Requires python 2 or 3
 The GitHub repository for the full project can be found here.

