Research

As I mention on the home page, my main research interests are in geometry and ergodic theory. I am particularly interested in problems surrounding the dynamics of group actions and flows in geometric contexts. Some keywords surrounding my main interests and current work:

• Higher Teichmüller-Thurston theory

• Anosov representations

• Thermodynamic formalism

• Geometry and dynamics in higher rank Lie groups

• Discrete subgroups of Lie groups

In the past, some of my research projects have also dabbled with analytic number theory, convex analysis, differential topology, and more.

Publications/Preprints

1. Weakly Mixing Systems with Dense Prime Orbits (Colloquium Mathematicum 169 (2022), 11-23; arXiv:2010.09812)

2. Extremizers of the J functional with respect to the d_1 metric; joint with Sam Bachhuber, Benjamin Christophel, and Tamás Darvas (Analysis Mathematica 48 (2022), no. 2, 307-330; arXiv:2304.06323)

In preparation

None (...though I am currently studying the pressure metric on various spaces of Anosov representations)

Talks and Presentations

Please be warned that notes linked below are very rough in some cases and are really just designed to help me prepare for the corresponding talk.

Slides, on the other hand, will generally be much more polished.

Conferences/Workshops Attended

1. SL Math: Graduate School on Geometry and Dynamics in Higher Rank Lie Groups - July 2025

2. IHP: Workshop on Low Dimensional Phenomena in Geometry and Dynamics - June 2025

3. UT Austin: Mini-school in Analytic Group Theory - March 2025

4. UIC: Big Ideas in Dynamics and Geometry (attended virtually) - September 2024

5. UMD: Dynamics Workshop - April 2024

6. Texas A&M: Workshop on Groups and Dynamics - March 2024

7. UT Austin: Graduate Mini-school in Groups, Dynamics, and Probability - June 2023

8. UMD: Workshop on Partial Hyperbolicity - May 2023

9. UT Austin: Graduate Mini-school in Groups and Dynamics - July 2022

10. Rice University: Ergodic Theory and its Connections (in honor of Michael Boshernitzan) - May 2022

11. Penn State: Dynamics Workshop - September 2019