Research

My research interests include:

• Kleinian surface groups

• (Higher) Teichmüller theory

• Dynamics of the earthquake flow

• Horospherical orbit closures in geometrically infinite hyperbolic manifolds.

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

Papers:

1. On Mirzakhani's twist torus conjecture, with  Aaron Calderon. (arXiv:2405.12106)

2. Affine laminations and coaffine representations, with M. D. Bobb. (arXiv:2404.14284)

3. Topological and geometric restrictions on hyperconvex representations, with Beatrice Pozzetti and Gabriele Viaggi. (arXiv:2403.13668)

4. Continuity of the orthogeodesic foliation and ergodic theory of the earthquake flow, with Aaron Calderon. (arXiv:2401.12299)

5. Minimizing laminations in regular covers, horospherical orbit closures, and circle-valued Lipschitz maps, with Or Landesberg and Yair Minsky. (arXiv:2306.14296.)

6. Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow, with Aaron Calderon. Geometry & Topology.  To appear. ( arXiv:2102.13124.)

7. Hamiltonian flows for pseudo-Anosov mapping classes.  Commentarii Mathematici Helvetici.  (2023). ( arXiv:2106.13510.)

8. Minimal area surfaces and fibered hyperbolic 3-manifolds, with Franco Vargas Pallete.  Proceedings of the American Mathematical Society.  (2022). (arXiv:2105.02631.)

9. Borel and volume classes for dense representations of discrete groups. International Mathematical Research Notices (2021). (arXiv:1811.12761.)

10. Relations in Bounded Cohomology.  Journal of Topology (2020). ( arXiv:1808.05711 )

11. Bounded Cohomology of Finitely Generated Kleinian Groups.  Geometric and Functional Analysis  (2018).  ( arXiv:1706:02001)

From Earlier:

12. 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).

13. 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).

In Preparation:

• Classification of horocycle orbit closures in Z-covers, with Or Landesberg and Yair Minsky. 

• Dynamics of the mapping class group on Euler number zero PSL(2,R) characters, with M. D.  Bobb and Peter Smillie.

• Geometry of hyperconvex representations of surface groups, with Beatrice Pozzetti and Gabriele Viaggi.