I am interested in Geometric Topology, Geometric Group Theory, Ergodic Theory and Dynamics. In particular;


  • Mapping class groups, Teichmüller spaces, Moduli spaces, Geodesic currents on surfaces

  • Out(FN), Culler-Vogtmann's Outer Space, Geometry of free factor and free splitting complexes, Geodesic currents on free groups

  • Veech Surfaces, Quadratic and Abelian Differentials, Dynamics on translation surfaces

  • Substitutions and symbolic dynamics

  • Random walks on groups and spaces, hyperbolic groups

  • Kleinian groups, representations of free and surface groups


Papers:


Collaborators / Mentors

Students

  • Yandi Wu (PhD student at UW Madison, co-advisor)

  • Catherine Lee (Senior thesis advisee at Yale, currently at UC Berkeley)

  • Jonah Berman (REU student at Yale)

  • Ananth Miller-Murthy (REU student at Yale)

  • Hamilton Wan (REU student at Yale)

I also supervise several other undergraduates through the Madison Experimental Mathematics Lab.