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:
  • 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:
  1. Not all finitely generated groups have universal acylindrical actions. Proc. Amer. Math. Soc., 144(10):4151–4155, 2016, pdf.
  2. (with F. Dahmani) Acylindrically hyperbolic groups have property P_naive. arXiv:1610.04143.  Math. Z., 291(1-2):555-568, 2019.
  3. (with S. Balasubramanya and D. Osin) Hyperbolic structures on groups.  arXiv:1710.05197. Algebr. Geom. Topol., 19-4, 1747-1835, 2019.
  4. (with D. Hume and D. Osin) Extending group actions on metric spaces.   arXiv:1703.03010. To appear in J. Topol. Anal.
  5. (with D. Hume) The geometry of generalized loxodromic elements.  arXiv:1802.03089. To appear in Ann. I. Fourier.
  6. (with J. Behrstock and M. Durham) Largest acylindrical actions and stability in hierarchically hyperbolic groups.
     arXiv:1705.06219.
  7. (with D. Hume) Actions of small cancellation groups on hyperbolic spaces.  arXiv:1807.10524.
  8. (with J. Behrstock) Conjugator lengths in hierarchically hyperbolic groups.  arXiv:1808.09604.
  9. (with A. Rasmussen) Actions of solvable Baumslag-Solitar groups on hyperbolic metric spaces.  arXiv:1906.04227​
  10. (with M. Hull) Random walks and quasi-convexity in acylindrically hyperbolic groups.  arXiv:1909.10876
  11. (with T. Ng and D. Spriano) Uniform exponential growth in hierarchically hyperbolic groups. arxiv.org/abs/1909.00439
  12. (with J. Manning) Boundaries of coned-off hyperbolic spaces, arXiv:1906.09319.
  13. (with A. Rasmussen) Largest hyperbolic actions and quasi-parabolic actions of groups.  arXiv:1910.14157.
  14. (with N. Miller and P. Patel) Big mapping class groups and quasi-morphisms.  In preparation.