Research Interests: conformal and holomorphic dynamics; Teichmueller theory; hyperbolic geometry
I am intrigued by instances when combinatorial information determines geometric structure. Examples include Mostow Rigidity (e.g. a closed hyperbolic three-manifold is determined up to isometry by its fundamental group), Thurston Rigidity (e.g. a postcritically finite rational map with hyperbolic orbifold is determined up to Moebius conjugacy by its combinatorial class). Also intriguing is when combinatorial information quasi-, or almost, determines a geometric structure. For example, a Gromov hyperbolic group determines a preferred quasi-Moebius class of metrics on its boundary.
Research:
- Holomorphic dynamics, especially combinatorial aspects
- Conformal geometry
- Analysis on metric spaces
