Math Education - Embrace the Core!
The most contentious topic in U.S. education for this generation is the lack of a system of consistent standards for student achievement. For most states, the fix has been the Common Core. My research in Math Education focuses on developing teacher content knowledge and weaving it into my courses. Whether you embrace the core or not, content knowledge is at the forefront of this debate. Teachers need to have the ability to nurture a creative process and promote originality, which strengthens problem solving skills.

Topological Data Analysis
I'm interested in the applicatations of TDA. Specifically, using TDA to invesigate wildlife corridors in the Northern Great Plains. Much of the analysis is based on the Mapper algorithm, and a Python Mapper GUI. If you're interested check out my presentation at the JMM.

Tiling Spaces
My dissertation focused on studying asymptotic structure in substitution tiling spaces.  Here is the abstract.

Every sufficiently regular space of tilings of R^d has at least one pair of distinct tilings that are asymptotic under translation in all the directions of some open (d−1)-dimensional hemisphere. If the tiling space comes from a substitution, there is a way of defining a location on such tilings at which asymptoticity `starts'. This leads to the definition of the branch locus of the tiling space. We prove that if a d-dimensional self-similar substitution tiling space has a pair of distinct tilings that are asymptotic in a set of directions that contains a closed (d−1)-hemisphere in its interior, then the branch locus is a topological invariant of the tiling space. If the tiling space is a 2-dimensional self-similar Pisot substitution tiling space, the branch locus has a description as an inverse limit of an expanding Markov map on a 1-dimensional simplicial complex.

Recently my research in topological dynamical systems has focusing on the homology of asymptotic components formed from translations on tiling spaces. My work consists of two major  components:  establishment of techniques in visualizing the contribution from asymptotic behavior; and  identification of conditions under which torsion will appear.