Research Interests

My research has been focused on boundaries and how they can be used to study the geometric and algebraic properties of a group. In particular, I have been working with the contracting boundary of CAT(0) groups. This boundary is an analogue of the Gromov boundary of a hyperbolic group and shares some of the same properties.

More broadly I am interested in questions about quasi-isometric rigidity as well as splittings and the geometry of subgroups.

Here is my CV (pdf)

Papers and Preprints

  1. Quasi-Möbius maps on the morse boundary of finitely generated groups, Preprint.

  2. A rank-one CAT(0) group is determined by its Morse boundary, Preprint available at arXiv:1707.07028

  3. Topology and Dynamics of the Contracting Boundary of Cocompact CAT(0) Spaces, submited. Preprint available at arXiv:1509.09314

Invited Talks

Seminars and Contributing Talks

  1. Topology and Geometry Seminar, Buffalo University, "The morse boundary, groups, and quasi-isometric rigidity", Fall 2017

  2. Topology Seminar, Ohio State, "CAT(0) groups, rigidity, and the morse boundary", Fall 2016

  3. Topology Seminar, Wesleyan University, "CAT(0) groups, rigidity, and the morse boundary", Fall 2016

  4. Geometry and Topology Seminar, Brown University, "CAT(0) groups, rigidity, and the morse boundary", Fall 2016

  5. Topology Student Workshop, Georgia Institute of Technology, "The contracting boundary of CAT(0) groups", Summer 2016

  6. Geometric and Probabilistic Methods in Group Theory and Dynamical Systems, Texas A&M University "The contracting boundary of CAT(0) groups", Fall 2015

  7. Brandeis Topology Seminar, "The contracting boundary of CAT(0) groups", Fall 2015

  8. Graduate Student Seminar at Brandeis, "Non-standard analysis, asymptotic Cones, and rigidity", Fall 2015

  9. Graduate Student Seminar at Brandeis, "Surprising theorems which are independent of ZFC", Spring 2015

  10. Graduate Student Seminar at Brandeis, "Hyperbolic geometry, group theory and rigidity", Fall 2014

  11. Brandeis Topology Seminar, "The Gromov Boundary of δ-hyperbolic spaces", Fall 2013

  12. Graduate Student Seminar at Brandeis, "The fundamental group of the Hawaiian Earrings", Fall 2013