Research

My research interests include:

• Hyperbolic geometry

• Teichmüller theory

• Dynamics of the earthquake flow

• Anosov representations of surface groups and convex projective geometry

• Horospheres in (geometrically infinite) hyperbolic manifolds.

• Symplectic geometry of character varieties and dynamics of the mapping class group

Papers (which can be downloaded here):

1. Invariant multi-functions and Hamiltonian flows for surface group representaitons, with Fernando Camacho Cadena and Anna Wienhard. (arXiv)

2. Classification of horocycle orbit closures in Z-covers, with Or Landesberg and Yair Minsky. (arXiv)

3. Geometry of hyperconvex representations of surface groups, with Beatrice Pozzetti and Gabriele Viaggi. (arXiv)

4. On Mirzakhani's twist torus conjecture, with  Aaron Calderon. (arXiv)

5. Affine laminations and coaffine representations, with M. D. Bobb. (arXiv)

6. Topological and geometric restrictions on hyperconvex representations, with Beatrice Pozzetti and Gabriele Viaggi. Accepted for publication in Crelle's Journal (arXiv)

7. Continuity of the orthogeodesic foliation and ergodic theory of the earthquake flow, with Aaron Calderon. Accepted for publication in Forum of Mathematics, Sigma (arXiv)

8. Minimizing laminations in regular covers, horospherical orbit closures, and circle-valued Lipschitz maps, with Or Landesberg and Yair Minsky. (arXiv)

9. Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow, with Aaron Calderon.  Geometry & Topology.  (2024). (journal, arXiv)

10. Hamiltonian flows for pseudo-Anosov mapping classes.  Commentarii Mathematici Helvetici.  (2023). (journal, arXiv)

11. Minimal area surfaces and fibered hyperbolic 3-manifolds. with Franco Vargas Pallete.  Proceedings of the American Mathematical Society.  (2022). (journal, arXiv)

12. Borel and volume classes for dense representations of discrete groups. International Mathematical Research Notices (2021).  (journal, arXiv)

13. Relations in Bounded Cohomology. Journal of Topology (2020).  (journal, arXiv)

14. Bounded Cohomology of Finitely Generated Kleinian Groups. Geometric and Functional Analysis  (2018). (jounal, arXiv)

From Earlier:

15. Algorithms for detecting dependencies and rigid subsystems for CAD, with Helena Kleinschmidt, Jessia Sidman, Audrey Lee-St. John, Stephanie Stark, Louis Theran, and Xilin Yu, Computer  Aided Geometric Design (2016). (journal)

16. The Freshman Research Initiative as a model for addressing shortages and disparities in STEM engagement, with  Josh Beckham, Sarah Simmons, and Gwendolyn Stovall.  Directions for mathematics research experience for undergraduates (2015). (book chapter)