department of mathematics
Ph.D. Princeton University
My main areas of research are Hyperbolic geometry, Kleinian groups and Teichmüller theory. One interest is the relation between the convex hull of a Kleinian group and its conformal structure at infinity. Another is the interplay between the conformal dynamics and Kleinian groups via Patteron-Sullivan theory and geodesic currents, in order to develop structures and invariants for hyperbolic spaces and their moduli spaces. One such structure of interest is to extend the classical Weil-Petersson metric on Teichmüller space to other moduli spaces such as Quasifuchsian space and Schottky space.
- An extension of the Weil-Petersson metric to quasi-fuchsian space, (with Edward Taylor), Mathematische Annalen 341, No. 4 (2008).
- Distribution of intersection lengths of a random geodesic with a geodesic lamination, (with David Dumas), Ergodic Theory and Dynamical Systems 27, No. 4 (2007).
- Patterson-Sullivan measures and quasi-conformal deformations, (with Edward Taylor), Communications in Analysis and Geometry 13, No. 3 (2005).
- Bounding the bending of a hyperbolic three-manifold, (with Richard Canary), Pacific Journal of Mathematics 218, No. 2 (2005).
- From the boundary of the convex core to the conformal boundary, (with Richard Canary), Geometrica Dedicata 96, No. 1 (2003).
- Length distortion and the Hausdorff dimension of limit sets, (with Edward Taylor), American Journal of Mathematics 122 (2000).