Research Interests
Research Interests
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My research is largely centered around various number-theoretic and algebraic questions that arise in the context of low-dimensional topology, hyperbolic geometry and geometric group theory. More specifically, I'm interested in discrete subgroups of Lie groups, higher Teichmüller theory and Anosov representations (in particular, the arithmetic aspects of these objects), as well as thin subgroups of lattices.
Publications and Preprints
Publications and Preprints
Integral Zariski dense surface groups in SL(n,R). Math. Proc. Cambridge Philos. Soc. 179 (2025) no. 1, 63–78. (arXiv)
Rational approximation for Hitchin representations (with Jacques Audibert). To appear in Groups Geom. Dyn. (2023). (arXiv)
A family of accumulation points of non-free rational numbers (with Christopher (Bobby) Buyalos*, Jayden Thadani*, Xinbei Wang* and Bradley Zykoski), preprint, (2025). (arXiv)
(* indicates undergraduate author)
Conferences & travel
Conferences & travel
Computational problems about 3-manifolds, associated groups and varieties, Rutgers University-Newark (2025).
Higher rank geometric structures, IHP (2025).
Hyperbolic Manifolds, Their Submanifolds and Fundamental Groups, IMPA (2025).
20 years of Anosov representations, Max Planck Institute for Mathematics in the Sciences (2024).
Big Ideas in Dynamics and Geometry, University of Illinois Chicago (2024).
NU Trends in Ergodic Theory, Northwestern University (2024).
Moving to higher rank: from hyperbolic to Anosov, Cetraro (2024).
Computational Aspects of Thin Groups, IMS NUS (2024, lightning talk).
Group Actions and Rigidity: Around the Zimmer Program - Introductory School, CIRM (2024, lightning talk).
Young Geometric Group Theory XII, University of Bristol (2024).
Group Actions Seminar, UC San Diego (2024).
Group Actions and Dynamics Seminar, University of Wisconsin-Madison (2024).
Riverside Workshop on Geometric Group Theory follow-up, UC Riverside (2024).
Joint Math Meetings 2024, Special Session on Geometric Group Theory (2024, invited talk).
Texas Geometry and Topology Conference, Rice University (2023, lightning talk).
Wasatch Topology Conference, University of Utah (2023, lightning talk).
Higgs bundles, character varieties and higher Teichmüller spaces, ICMAT (2023).
Dynamics, Rigidity and Arithmetic in Hyperbolic Geometry, ICERM (2023).
Riverside Workshop on Geometric Group Theory, UC Riverside (2023).
Young Geometric Group Theory XI, WWU Münster (2023, lightning talk).
Geometry, Arithmetic, and Groups, UT Austin (2022).
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