Research interests
My broad area of research interest is geometric group theory. Topics include:
Subgroup Distortion
Dehn Functions
CAT(0) Groups and Cube Complexes
Right Angled Artin Groups, Right Angled Coxeter Groups
Preprints
Superexponential Distortion of Free Groups in Virtually Special Groups (joint with Maya Verma) [arxiv]
Abstract: For all integers k, m > 0, we construct a virtually special group G containing a finite rank free subgroup F whose distortion function in G grows like exp^k(x^m). We also construct examples of virtually special groups containing finite rank free subgroups whose distortion functions grow bigger than any iterated exponential.
Isoperimetric Behavior of Generalized Stallings-Bieri Groups (joint with Noel Brady and Rob Merrell) [arxiv]
Abstract: We introduce the notion of n-split for an epimorphism from a group to a finite rank free abelian group. This is used to provide bounds for the Dehn functions of certain coabelian subgroups of direct products of finitely presented groups. Such subgroups include and significantly generalize the Stallings-Bieri groups.