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
- Quasi-Möbius maps on the morse boundary of finitely generated groups, Preprint.
- A rank-one CAT(0) group is determined by its Morse boundary, Preprint available at arXiv:1707.07028
- Topology and Dynamics of the Contracting Boundary of Cocompact CAT(0) Spaces, submited. Preprint available at arXiv:1509.09314
Invited Talks
- Special Session Joint Mathematics Meetings, "Quasi-möobius maps on the morse boundary", January 2018
- Summer Conference on Topology and its Applications, "CAT(0) groups, rigidity, and the morse boundary", Summer 2017
- AMS Special Session on Geometric Group Theory, "The contracting boundary of CAT(0) groups". Fall 2016
Seminars and Contributing Talks
- Topology and Geometry Seminar, Buffalo University, "The morse boundary, groups, and quasi-isometric rigidity", Fall 2017
- Topology Seminar, Ohio State, "CAT(0) groups, rigidity, and the morse boundary", Fall 2016
- Topology Seminar, Wesleyan University, "CAT(0) groups, rigidity, and the morse boundary", Fall 2016
- Geometry and Topology Seminar, Brown University, "CAT(0) groups, rigidity, and the morse boundary", Fall 2016
- Topology Student Workshop, Georgia Institute of Technology, "The contracting boundary of CAT(0) groups", Summer 2016
- Geometric and Probabilistic Methods in Group Theory and Dynamical Systems, Texas A&M University "The contracting boundary of CAT(0) groups", Fall 2015
- Brandeis Topology Seminar, "The contracting boundary of CAT(0) groups", Fall 2015
- Graduate Student Seminar at Brandeis, "Non-standard analysis, asymptotic Cones, and rigidity", Fall 2015
- Graduate Student Seminar at Brandeis, "Surprising theorems which are independent of ZFC", Spring 2015
- Graduate Student Seminar at Brandeis, "Hyperbolic geometry, group theory and rigidity", Fall 2014
- Brandeis Topology Seminar, "The Gromov Boundary of δ-hyperbolic spaces", Fall 2013
- Graduate Student Seminar at Brandeis, "The fundamental group of the Hawaiian Earrings", Fall 2013