My research is primarily concerned with geometric structures on surfaces and 3-manifolds. 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 3-manifolds
  • convex real projective structures; Hitchin representations
  • low-dimensional topology; mapping class groups
  • circle packings on complex projective structures
Currently, I am working on circle (and Delaunay) packings of projective stuctures with Jean-Marc Schlenker and random triangles on surfaces with Olivier Glorieux. In addition, I have been working on a large project on classifying families of one-cusped hyperbolic 3-manifolds of low volume with Rob MeyerhoffDavid 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
Notes and slides
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" 2-circle 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 3-manifold given by a box parameter and a variety word (see Hyperbolic 3-manifolds of low cusp volume)
    • Requires python 2 or 3
    • The GitHub repository for the full project can be found here.