My work is supported by NSF Topology Grant DMS-1812021.
CVHyperbolic quotients of projection complexes, with Matt Clay. To appear, Groups, Geometry, and Dynamics.
Right-angled Artin groups as normal subgroups of mapping class groups, with Matt Clay and Dan Margalit. To appear, Compositio Mathematica.
The geometry of purely loxodromic subgroups of right-angled Artin groups, with Thomas Koberda and Samuel J. Taylor. Transactions of the American Mathematical Society 369 (2017), no 11. (slides)
An algorithm to detect full irreducibility by bounding the volume of periodic free factors, with Matt Clay and Alexandra Pettet. Michigan Mathematical Journal. 64 (2015), no. 1
An effective algebraic detection of the Nielsen-Thurston classification of mapping classes, with Thomas Koberda; Journal of Topology and Analysis 7 (2015), no. 1.
Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups, with Samuel J. Taylor. Proceedings of the London Mathematical Society (3) 112 (2016), no 5. (slides)
A Recipe for Short-Word Pseudo-Anosovs, American Journal of Mathematics 135 (2013), no. 4. (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)
The Cartoon Story of Why the Mapping Class Group is Finitely Generated by Dehn Twists; slides from a talk given at the Graduate Student Topology Conference at U. Chicago, April 2007. The proof follows the one in Benson Farb and Dan Margalit's Primer on Mapping Class Groups.