Research
My research is about the interaction between geometric structures on manifolds, geometric group theory, and dynamics of discrete subgroups of Lie groups. The relationship between these three areas is quite strong in the classical context of convex cocompact and geometrically finite representations. These are representations of wordhyperbolic (or relatively hyperbolic) groups into rankone Lie groups (such as PSL(2, R) and PSL(2, C)) which behave well with respect to both the coarse geometry of the represented group and the smooth geometry of the target group.
I am particularly interested in the geometry and dynamics of higherrank generalizations of convex cocompactness and geometrical finiteness, including (but not limited to) Anosov representations. Many of the examples I work with come from convex projective structures on manifolds, and are often inspired by hyperbolic geometry.
Recent publications and preprints

(with K. Mann and J.F. Manning) Topological stability of relatively hyperbolic groups acting on their boundaries. arXiv:2402.06144, 2024.

Examples of extended geometrically finite representations. arXiv:2311.18653, 2023.

(with S. Douba, B. Fléchelles, and F. Zhu) Cubulated hyperbolic groups admit Anosov representations. arXiv:2309.03695, 2023. Submitted.

(with A. Traaseth) Combination theorems for geometrically finite convergence groups. arXiv:2305.08011, 2023. Submitted.

(with K. Mann and J.F. Manning) Stability of hyperbolic groups acting on their boundaries. arXiv:2206.14914, 2022. Submitted.

An extended definition of Anosov representation for relatively hyperbolic groups. arXiv:2205.07183, 2022. Submitted.

Dynamical properties of convex cocompact actions in projective space. J. Topol., 16(3):9901047, 2023.
PhD thesis: Higherrank generalizations of convex cocompact and geometrically finite dynamics.
Talk slides and videos
Combination theorems for geometrically finite convergence groups (NCNGT, June 2023)
video (part 1)  video (part 2)
Topological stability for (relatively) hyperbolic boundary actions (GTiNY, June 2023)
slides
Extended geometrically finite representations (STDC, March 2022)
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Extended convergence dynamics and relative Anosov representations (December 2021)
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Expansion/contraction dynamics for nonstrictly convex projective manifolds (GTA Philadelphia, June 2021)
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Group actions on boundaries of convex divisible domains (November 2019)
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