Research

My research interests lie in geometric group theory, low-dimensional topology, and hyperbolic geometry.  Common topics in my work include:

• Metric versions of non-positive curvature, especially hierarchically hyperbolic, relatively hyperbolic, and CAT(0) spaces.

• Notions of convex subsets in metric spaces such as Morse geodesics, quasiconvexity,  and stable subgroups.

• Quasi-isometric classification of groups and metric spaces.

• The mapping class group and its subgroups.

 A detailed summary of my research is available in this research statement.

Preprints

1. Hierarchical hyperbolicity of admissible curve graphs and the boundary of marked strata, with Aaron Calderon.

2. Quasi-isometries of HHGs with one-ended maximal hyperbolic spaces.  Appendix to "Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity" by Antoine Goldsborough, Mark Hagen, Harry Petyt, Alessandro Sisto.

3. Extensions of multicurve stabilizers are hierarchically hyperbolic.

Publications

1. Relative hyperbolicity, thickness, and the hierarchically hyperbolic boundary, with Carolyn Abbott and Jason Behrstock. To appear in  the Michigan Mathematical Journal.

2. Equivariant hierarchically hyperbolic structures for 3-manifold groups via quasimorphisms, with Mark Hagen, Alessandro Sisto, and Davide Spriano. To appear in Annales de l’Institut Fourier.

3. Pseudo-Anosov subgroups of general fibered 3-manifold groups, with Chris Leininger. Transactions of the American Mathematical Society, series B. vol 10, 1141–1172, 2023

4. Structure invariant properties of the hierarchically hyperbolic boundary, with Carolyn Abbott and Jason Behrstock. To appear in Journal of Topology and Analysis.

5. Thickness and relative hyperbolicity for graphs of multicurves, with Kate Vokes.   Journal of Topology, vol 15(4), 2317–2351, 2022. Online Published Version.

6. Regularity of Morse geodesics and growth of stable subgroups, with Matthew Cordes, Davide Spriano, and Abdul Zalloum.  Journal  of Topology, vol 15(3), 1217–1247, 2022 . Online Published Version.

7. Hierarchical hyperbolicity of graph products, with Daniel Berlyne.  Groups, Geometry, and Dynamics, vol 16(2),  523–580, 2022.  Online Published Version.

8. Almost HHSs are HHSs, with Daniel Berlyne. Appendix to "Largest acylindrical actions and stability in hierarchically hyperbolic groups" by Carolyn Abbott, Jason Behrstock, and Matthew G. Durham. Transactions of the American Mathematical Society, series B. vol 8,  66–104, 2021.

9. The (non)-relative hyperbolicity of the separating curve graph, with Kate Vokes.  To appear in Geometric methods in group theory: papers dedicated to Ruth Charney.  Séminaires et Congrès (SMF).

10. The local-to-global property for Morse quasi-geodesics, with  Davide  Spriano and Hung  C. Tran.  Mathematische Zeitschrift, vol 300,  1557–1602, 2022. Online Published Version.

11. From hierarchical to relative hyperbolicity. International Mathematics Research Notices. vol 2022, 575–624, 2022.  Online Published Version.

12. Convexity in hierarchically hyperbolic spaces, with  Davide  Spriano and Hung  C. Tran.  Algebraic & Geometric Topology, vol 23(3), 1167–1248,2023 . Online Published Version.

13. Hierarchically hyperbolic groups are determined by their Morse boundaries, with Sarah Mousley.   Geometriae Dedicata, vol 202,  45–67, 2019. Online Published Version.

14. A lower bound for the number of finitely maximal C_p actions on a compact oriented surface, with Aaron Wootton. Contemporary Mathematics, vol 703,  1–11, 2018.

15. Maximal group actions on a compact oriented surface,  with Valerie Peterson and Aaron Wootton. Journal of Algebra, vol 472, 1–4, 2017.