PhD, University of Michigan
Geometric topology, geometric group theory.
My research interests grow out of hyperbolic geometry and low-dimensional topology, and center on mapping class groups and methods of geometric group theory.
The geometry of purely loxodromic subgroups of right-angled Artin groups, with Thomas Koberda and Samuel J. Taylor; (slides)
An algorithm to detect full irreducibility by bounding the volume of periodic free factors, with Matt Clay and Alexandra Pettet; to appear in Michigan Mathematical Journal.
An effective algebraic detection of the Nielsen-Thurston classification of mapping classes, with Thomas Koberda; Journal of Topology and Analysis (2014).
Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups, with Samuel J. Taylor; submitted. (slides)
The Geometry of Right-Angled Artin Subgroups of Mapping Class Groups, with Matt Clay and Chris Leininger; Groups, Geometry, and Dynamics 6 (2012), no. 2.
Uniform Uniform Exponential Growth of the Mapping Class Group; Geometric and Functional Analysis 19 (2010), no. 5. (slides)