Research
My research focuses on the geometry, topology, and deformation theory of locally homogeneous geometric structures on manifolds, a subject with roots in Felix Klein’s 1872 Erlangen program that features a blend of differential geometry, Lie theory, representation theory, and dynamics. I study an array of lowdimensional geometric structures modeled on nonRiemannian geometries including semiRiemannian, affine, and projective geometries. Of particular interest to me is a phenomenon known as geometric transition, by which different moduli spaces of geometric manifolds interact with one another.
Here is a short Research Summary.
Recently JeanMarc Schlenker gave a Séminaire Bourbaki about my joint work with François Guéritaud and Fanny Kassel.
Recent papers

Proper affine actions of rightangled Coxeter groups
joint with F. Guéritaud and F. Kassel.

Convex cocompact actions in real projective geometry
joint with F. Guéritaud and F. Kassel.

Convex cocompactness in pseudoRiemannian symmetric spaces
joint with F. Guéritaud and F. Kassel, Geometriae Dedicata, special issue Geometries: A celebration of Bill Goldman's 60th birthday (to appear).

Higher signature Delaunay triangulations
joint with S. Maloni and J.M. Schlenker

Convex projective structures on nonhyperbolic threemanifolds
joint with S. Ballas and G.S. Lee, Geometry and Topology, 22 (2018), pp 15931646.

Fundamental domains for free groups acting on antide Sitter 3space
joint with F. Guéritaud and F. Kassel, Math. Res. Lett. 23 (2016), no. 3, pp. 735770.

Polyhedra inscribed in a quadric
joint with S. Maloni and J.M. Schlenker

Limits of geometries
joint with D. Cooper and A. Wienhard, Trans. Amer. Math. Soc., DOI: https://doi.org/10.1090/tran/7174, 2017.

Margulis spacetimes via the arc complex
joint with F. Guéritaud and F. Kassel, Invent. Math., 204 (2016), no. 1, pp. 133193.

Geometry and topology of complete Lorentz spacetimes of constant curvature
joint with F. Guéritaud and F. Kassel, Ann. Sci. Éc. Norm. Supér. 49 (2016), no. 1, pp/ 156.

Ideal triangulations and geometric transitions
J. Topol. 7 (2014), no. 4, pp. 11181154. 
A Geometric transition from hyperbolic to anti de Sitter geometry
Geom. Topol. 17 (2013), no. 5, pp. 30773134 
Some open questions on anti de Sitter geometry
joint with T. Barbot, F. Bonsante, W.M. Goldman, F. Guéritaud, F. Kassel, K. Krasnov, J.M. Schlenker, A. Zeghib
The following works are in preparation. Preliminary drafts may be available upon request.

Margulis spacetimes with parabolic elements
joint with F. Guéritaud and F. Kassel
(in preparation) 
Proper affine actions of right angled Coxeter groups
joint with F. Guéritaud and F. Kassel
(in preparation) 
Examples and counterexamples of convex cocompact groups
joint with F. Guéritaud and F. Kassel
(in preparation) 
Induced metrics on convex hulls of quasicircles
joint with Francesco Bonsante , S. Maloni, and J.M. Schlenker
(in preparation)
Thesis
Geometric transitions: from hyperbolic to AdS geometry
ph.d. thesis, Stanford University (2011).