I study geometric group theory, the study of groups through their actions on metric spaces. I am particularly interested in groups that act by isometries on hyperbolic metric spaces. My research focuses on the following main areas:

Here is my current research statement.

- acylindrically hyperbolic groups and their various acylindrical actions on hyperbolic spaces
- hierarchically hyperbolic groups and spaces, which include mapping class groups, fundamental groups of 3-manifolds, and CAT(0) cubical groups
- (not necessarily acylindrical) actions of groups on hyperbolic spaces, including solvable Baumslag-Solitar groups, fundamental groups of mapping tori and flip graph manifolds.
- big mapping class groups (these are mapping class groups of surfaces with infinitely generated fundamental group)

Here is my current research statement.

**Papers:**- Not all finitely generated groups have universal acylindrical actions.
*Proc. Amer. Math. Soc.*, 144(10):4151–4155, 2016, pdf. *(with F. Dahmani)*Acylindrically hyperbolic groups have property P_naive. arXiv:1610.04143.*Math. Z., 291(1-2):555-568, 2019.**(with S. Balasubramanya and D. Osin)*Hyperbolic structures on groups. arXiv:1710.05197.*Algebr. Geom. Topol., 19-4, 1747-1835, 2019.**(with D. Hume and D. Osin)*Extending group actions on metric spaces. arXiv:1703.03010. To appear in*J. Topol. Anal*.*(with D. Hume)*The geometry of generalized loxodromic elements. arXiv:1802.03089. To appear in*Ann. I. Fourier.**(with J. Behrstock and M. Durham)*Largest acylindrical actions and stability in hierarchically hyperbolic groups.

arXiv:1705.06219. To appear in*Trans. Amer. Math. Soc.**(with D. Hume)*Actions of small cancellation groups on hyperbolic spaces. arXiv:1807.10524. To appear in*Geom. Dedicata**(with J. Behrstock)*Conjugator lengths in hierarchically hyperbolic groups. arXiv:1808.09604.*(with A. Rasmussen)*Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces. arXiv:1906.04227*(with M. Hull)*Random walks and quasi-convexity in acylindrically hyperbolic groups. arXiv:1909.10876*(with T. Ng and D. Spriano)*Uniform exponential growth in hierarchically hyperbolic groups. arxiv.org/abs/1909.00439*(with J. Manning)*Boundaries of coned-off hyperbolic spaces, arXiv:1906.09319.*(with A. Rasmussen)*Largest hyperbolic actions and quasi-parabolic actions of groups. arXiv:1910.14157.*(with N. Miller and P. Patel)*Big mapping class groups and quasi-morphisms. In preparation.