Research
My research interests are in geometry, topology, and dynamical
systems. More specifically, I am interested in geodesic flows,
geometric structures on manifolds, Hilbert geometries,
convex projective structures,
Patterson-Sullivan theory, ergodic theory, thermodynamic formalism,
symbolic dynamics, (nonuniformly) hyperbolic dynamical systems, and
(rel) hyperbolic spaces and groups.
I have also studied the Thurston set and Thurston Master Teapot.
Check out my collaborator Giulio Tiozzo's
visualizations of the Master Teapot.
Here is a Quanta
article on the Thurston set and related topics.
Here are pictures of objects I've studied, made by my
students: [Thurston's master teapot] [the Thurston set] [deformations of convex projective
triangle groups] [Benoist
3-manifold]
Preprints and Papers
-
On the almost sure spiraling of geodesics in CAT(0) spaces
With Andrew Zimmer
[arxiv]
- Constructing reducibly geometrically finite subgroups of the mapping class group.
With
Tarik Aougab, Spencer Dowdall, Hannah Hoganson,
Sara Maloni, and Brandis Whitfield
Accepted at Groups, Geometry and Dynamics
[arXiv]
- A global shadow lemma and logarithm law for geometrically
finite Hilbert geometries.
With
Giulio Tiozzo
Journal of Modern Dynamics (2025) Volume 21, 443-496
[arXiv]
[lecture
notes]
[older lecture notes
]
-
Pressure metrics for cusped Hitchin components.
With Dick
Canary, Nyima Kao,
and Giuseppe Martone.
Advances in Mathematics (2023) Volume 435, 109352
[arXiv]
-
Counting, equidistribution and entropy gaps at infinity with
applications to cusped Hitchin representations.
With Dick
Canary, Nyima Kao,
and Giuseppe Martone.
Journal für die reine und angewandte Mathematik (Crelles
Journal), vol. 2022, no. 791, 2022, pp. 1-51.
[journal][arXiv]
- Entropy rigidity for finite volume strictly convex projective manifolds.
With Dave Constantine
Geometrie Dedicata (2021) Volume 214, 543-557
[journal]
[arXiv]
- Pressure metrics for deformation spaces of quasifuchsian groups with parabolics.
With Dick
Canary and Nyima Kao
accepted at Algebraic & Geometric Topology
[arXiv]
- The Shape of Thurston's Master Teapot.
With Diana
Davis, Kathryn
Lindsey, and Chenxi Wu
Advances in Mathematics (2021) Volume 377, 107481
[journal]
[arXiv]
- Ergodicity of Bowen-Margulis measure for the Benoist 3-manifolds.
Journal of Modern Dynamics (2020) Volume 16, 305–329
[journal][arXiv]
- Geodesic flow of nonstrictly convex Hilbert geometries.
Annales de l’Institut Fourier (2020) Volume 70: 4 1563-1593
[journal][arXiv]
- Entropy rigidity and Hilbert volume.
With Ilesanmi
Adeboye and Dave Constantine
Discrete Contin. Dyn. Syst. Ser. A (2019) no. 39(4): 1731-1744. doi: 10.3934\/dcds.2019075.
[journal] [arXiv]
