Research Group
Geometry on Surfaces
We are interested in many kinds of geometric structures on surfaces and 3-manifolds. We want to understand the geometry of individual geometric structures and how they deform. Certain deformations give rise to dynamical systems on the moduli spaces; the ergodic theory of such systems is often very rich, offering a new perspective on the geometric objects themselves.
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Research
Our research projects can be summarized as:
- Classifying horospherical orbit closures in cyclic covers of closed hyperbolic manifolds
- Bending convex real projective structures on closed surfaces in projective 3-space
- Ergodic theory and topological dynamics of the earthquake flow
- Symplectic geometry of character varieties and the action of the mapping class group
- Properties of typical affine measured laminations
