Papers and preprints
Brief expository stuff :
Rigidity of mapping class group actions on S^1. With Maxime Wolff.
We show that every action of the group of automorphisms of a surface group on the circle is either
conjugate to the standard action on the (Gromov) boundary of the group, or factors through a finite group.
Realization problems for diffeomorphism groups With B. Tshishiku.
A survey/problems list on Nielsen realization problems and their friends.
Part 4 subsumes a previous short note on braid groups whose draft was available
- A characterization of Fuchsian actions by topological rigidity.
With Maxime Wolff.
We prove a converse to a rigidity theorem of Matsumoto.
This work can be read as an introduction to some of the ideas in the paper Rigidity and geometricity below.
- Rigidity and geometricity for surface group actions on the circle.
With Maxime Wolff.
We show that the only source of strong topological rigidity for surface group actions on the circle is an underlying geometric structure.
This is the converse to the main result in my paper "Spaces of surface group representations."
- Unboundedness of some higher Euler classes.
The Milnor-Wood inequality is the statement that the Euler class for flat, topological circle bundles is bounded;
this paper shows that analogous classes for flat Seifert fibered 3-manifold bundles are not.
- Ping-pong configurations and circular orders on free groups.
With Dominique Malicet, Cristobal Rivas, and Michele Triestino.
This paper describes isolated circular orders on free groups, answering a question from previous work with Rivas.
- On the number of circular orders on a group.
With Adam Clay and Cristobal Rivas.
Journal of Algebra 504 (2018) 336-363.
- Strong distortion in transformation groups.
With Frederic Le Roux.
Bulletin of the London Math. Soc. 50.1 (2018) 46-62.
- Group orderings, dynamics, and rigidty. With Cristobal Rivas
To appear in Annales de l'Institut Fourier.
- The large-scale geometry of homeomorphism groups. With Christian Rosendal.
To appear in Ergodic Theory and Dynamical Systems.
- PL(M) has no Polish group topology.
Fundamenta Mathematicae 238 (2017), 285-296.
- Rigidity and flexibility of group actions on S^1.
To appear in the Handbook of group actions. L. Ji, A. Papadopoulos, and S.-T. Yau, eds
- Automatic continuity for homeomorphism groups and applications.
With an appendix on the structure of groups of germs of homeomorphism, written with Frederic Le Roux.
Geometry & Topology 20-5 (2016), 3033-3056.
- A short proof that the group of compactly supported diffeomorphisms on a manifold is perfect
following a strategy of Haller, Rybicki and Teichmann. In New York J. Math 22 (2016), 49-55.
- Left-orderable groups that don't act on the line.
Math. Zeit. 280 no 3 (2015) 905-918
- Spaces of surface group representations.
Inventiones Mathematicae. 201, Issue 2 (2015), 669-710. (link to published version)
- Diffeomorphism groups of balls and spheres.
New York J. Math. 19 (2013) 583-596.
- The simple loop conjecture is false for PSL(2,R).
Pacific Journal of Mathematics 269-2 (2014), 425-432.
- Homomorphisms between diffeomorphism groups.
Ergodic Theory and Dynamical Systems, 35 no. 01 (2015) 192-214.
- Bounded orbits and global fixed points for groups acting on the plane.
Algebraic and Geometric Topology 12 (2012) 421-433
- My dissertation, Components of representation spaces (2014)
mostly overlaps with the content of the paper "Spaces of surface group representations" above, although I also very briefly discussed rigidity of universal circle actions of 3-manifold groups, and the thurston norm, at the end.
Some advertisement of my recent work in the AMS sectional sampler
for the 2018 fall meeting.
Illumination and Security with Alex Wright.
An exposition of some problems involving translation surfaces, from MSRI's dynamics on moduli spaces program.
Lectures on homeomorphism and diffeomorphism groups (in progress, notes from 2015 summer school, ~40 pages)
Related: many lecture notes from a seminar on Cohomology of diffeomorphism groups here .
Do-it-yourself Hyperbolic Geometry. A course I taught at Mathcamp.
Notes are a work in progress, feedback welcome!
- The mini-course I taught at "Beyond Uniform Hyperbolicity 2015" turned into
the survey paper Rigidity and flexibility of group actions on S^1.
Slides and videos from recent talks:
- Geometry implies rigidity (No Boundaries conference for Benson Farb, 2017)
video and notes
- Boundedness and Distortion in transformation groups at MSRI (December 2016) video
- Orderability and groups of homeomorphisms of the circle (Luminy, fall 2016)
Large scale geometry of homeomorphism groups (Young Geometric Group Theory, feb. 2016)
Groups acting on the circle (MSRI, January 2015) slides and video
(warning: the "notes" from the talk on the video page seem to contain some errors!)
Three proofs of rigidity of surface group actions at MSRI "Dynamics on moduli spaces" conference (2015) video
Many notes from my lectures in the 2014-15 "cohomology of diffeomorphism groups" seminar can be found here