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

1. Superexponential Distortion of Free Groups in Virtually Special Groups (joint with Maya Verma) [arxiv] (submitted)

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. 

2. Isoperimetric Behavior of Generalized Stallings-Bieri Groups (joint with Noel Brady and Rob Merrell) [arxiv] (submitted)

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.

In preparation

3. Sub-exponential Distortion of Free Groups in CAT(0) Groups

Abstract: We contsruct 2-dimensional CAT(0) groups containing free subgroups with distortion functions growing as x^s, for a dense set of real numbers s. 

4. Fractional Dehn Functions inside CAT(0) Groups (joint with Maya Verma) 

Abstract: We contsruct CAT(0) groups containing finitely presented subgroups whose Dehn functions grow as x^r for a dense set of rational numbers r. This expands the known isoperimetric behavior of subgroups of CAT(0) groups.