The view above the Oregon caves

My research interests lie in geometric group theory and low dimensional topology, with an emphasis on the geometry of mapping class groups and Teichmuller space.  I have recently been also focusing on various generalizations of hyperbolicity, including subgroup stability, relative hyperbolicity, hierarchical hyperbolicity, acylindrical hyperbolicty, and the Morse boundary.  I am also interested in the geometry of hyperbolic 3-manifolds, cubical geometry, and Out(F_n), especially in its analogy to the mapping class group.

Publications:

  1. Convex cocompactness and stability in mapping class groups. (with Samuel Taylor) Algebraic & Geometric Topology 15-5 (2015), 2837--2857. (arXiv version)
  2. The augmented marking complex of a surface. Journal of the London Mathematical Society (2016) 94 (3): 933-969. (published version, arXiv version)
  3. Elliptic actions on Teichmuller space. To appear in Groups, Geometry, and Dynamics, 2014; 1-32. (arXiv version)
  4. Boundaries and automorphisms of hierarchically hyperbolic spaces. (with Mark Hagen and Alessandro Sisto) To appear in Geometry & Topology, 2016; 1-67. (arXiv version)
  5. Boundary convex cocompactness and stability of subgroups of finitely generated groups. (with Matthew Cordes) To appear in International Mathematics Research Notices, 2017; 1-15. (arXiv version)
  6. Middle recurrence and pulling back subgroup stability. (with Tarik Aougab and Samuel Taylor) To appear in the Journal of the London Mathematical Society, 2016; 1-18. (arXiv version)
Preprints:
  1. The asymptotic geometry of the Teichmuller metric: Dimension and rank. Submitted, 2014; 1-16. (arXiv version)
  2. Graphs of curves of infinite type surfaces with mapping class group actions. (with Federica Fanoni and Nicholas Vlamis) Submitted, 2016; 1-21. (arXiv version)
  3. Largest acylindrical actions and stability in hierarchically hyperbolic groups. (with Carolyn Abbott and Jason Behrstock) Preprint, 2017. (arXiv version)


Videos:

  1. A new boundary for the mapping class group.  Geometry of mapping class groups and Out(F_n) at MSRI, 10/28/2016.  Video.
  2. Boundaries and geometrically finite subgroups of hierarchically hyperbolic groups.  Beyond Hyperbolicity at Cambridge, 6/24/2016. Video 1, Video 2.
  3. Convex cocompactness in finitely generated groups. UIUC GEAR seminar, 5/2/1017. Video.

(The photo above was taken by Ric Wade.)