I study actions of infinite groups on manifolds, using techniques from geometric topology, geometric group theory, and low-dimensional dynamics.
A guiding principle in my work is that rigidity of group actions (a dynamical concept) is often the result of an underlying geometric or topological structure. I'm interested both in specific examples of actions, and also in understanding big "moduli spaces" of group actions, including character varieties, spaces of flat bundles or foliations, or spaces of left-invariant orders on groups. I'm also fascinated by the structure of homeomorphism groups of manifolds and the rich interplay between their topology, their algebraic structure, and the topology of the underlying manifold.
- Spaces of surface group representations. Inventiones Mathematicae. 201, Issue 2 (2015), 669-710
- Automatic continuity for homeomorphism groups and applications. (with an appendix joint with F. Le Roux) Geometry & Topology 20-5 (2016), 3033-3056.
- On the number of circular orders on a group. With Adam Clay and Cristobal Rivas. Journal of Algebra 504 (2018) 336-363.
- Group orderings, dynamics, and rigidity. With Cristobal Rivas. Annales de l'Institut Fourier Volume 68.4 (2018), 1399-1445,
- Structure theorems for actions of homeomorphism groups. With Lei Chen. Preprint, arXiv:1902.05117
- Rigidity and geometricity for surface group actions on the circle. With Maxime Wolff. Preprint, arXiv:1710.04902