# Harrison Bray

Department of MathematicsUniversity of Michigan

E-mail: hbray [at] umich [dot] edu

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# Research

My research interests are in dynamics, geometry, and topology. I think about the interactions among:

- geodesic flows (Besson-Courtois-Gallot rigidity, Patterson-Sullivan theory and applications)
- ergodic theory (measure of maximal entropy, SRB measure, thermodynamic formalism)
- geometric structures (convex projective structures, Hilbert geometry, rank one geometry)

### Preprints and Papers

**The Shape of Thurston's Master Teapot**. Joint with D. Davis, K. Lindsey, and C. Wu

submitted [arXiv]-
**Ergodicity of Bowen-Margulis measure for the Benoist 3-manifolds**.

submitted [arXiv] [extended version] **Geodesic flow of nonstrictly convex Hilbert geometries**.

accepted [arXiv]**Entropy rigidity and Hilbert volume**. Joint with I. Adeboye and D. Constantine

Discrete Contin. Dyn. Syst. Ser. A (2019) no. 39(4): 1731-1744. doi: 10.3934\/dcds.2019075.

[journal] [arXiv]

### Exposition

Slides from my talk at the conference Dynamics of Group Actions, a conference in honor of Yves Benoist are available here.