Research, Grants, and Projects

Research

I am interested in geometric group theory and hyperbolic geometry. My current work examines discrete and faithful actions on hyperbolic space by Coxeter groups.

An effective compactness theorem for Coxeter groups
(in preparation)

We find that if a Coxeter group does not split over a small subgroup, then there is a bound on the mininum distance that all generators move points in hyperbolic n-space. We assume that we have fixed a presentation and only consider discrete and faithful actions of the Coxeter group on hyperbolic n-space. The bound depends only on the dimension n and the number of generators in the presentation.


A sample small splitting.

Talks/Travel for 2008:

Grants

I co-authored a grant proposal to the U.C. Davis College of Letters and Sciences to fund the Explore Math Program for five years. An abbreviated version of our proposal was incorporated as Section 3.3 of the U.C. Davis Math Department's successful NSF-VIGRE 2007-2013 grant proposal (DMS-0636297).

Other Projects

This year, I am working with Jon Wagner and the U.C. Davis Teaching Resources Center (TRC) to coordinate reviews of all programs affiliated with the TRC. This comprehensive evaluation will include reviews of the Chancellor's Teaching Fellowship and the Freshman Seminar Program.

Miscellanea