My main fields of study are 3-dimensional topology, hyperbolic geometry, Riemann surface theory (Teichmüller theory) and mapping class groups. I've also dabbled in holomorphic dynamics and combinatorial group theory.

For a (somewhat out of date) collection of pictures of the kind of objects I am interested in, see these lecture slides.

Papers, roughly in reverse chronological order: 

Some of the work shown here was supported by grants from the National Science Foundation and a fellowship from the Alfred P. Sloan foundation. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.