My research interests lie generally in the area of algebraic topology. Topology, which as been nicely described as “rubber sheet geometry”, is the branch of mathematics that studies which properties of shapes are preserved under continuous deformations. For example, deformations that involve stretching or bending, but no tearing or gluing. Algebraic topology brings the tools of abstract algebra (groups and homomorphisms, vector spaces and linear transformations, etc.) to the study of topological spaces.
I have recently become interested in applied and computational topology.
Below are scholarly articles, expository papers, and a few presentations that I’ve given.
- Unstable Analogues of the Lichtenbaum-Quillen-Conjecture, with Marion Anton, to appear in the Proceedings of the Romanian Science Academy
- An Algorithm for Low Dimensional Group Homology, Homology, Homotopy, and Applications, Vol. 12 (2010)
- Algorithms for Upper Bounds of Low Dimensional Group Homology, University of Kentucky Doctoral Dissertations (2010)
- Transgressive Elements and a Vanishing Conjecture in Group Homology, with Marion Anton (in progress)
- A Topological Interpretation of Milnor's $K_2$ (in progress)
- Algorithms for Upper Bounds of Low Dimensional Group Homology (pdf slides) Dissertation Defense
- An Algorithm for Low Dimensional Group Homology (pdf slides)
- Topological Data Analysis (pdf slides) (to view the movie file on slide 8, you’ll need to save this file in the same directory as the pdf file)
- An Introduction to Applied Algebraic Topology: Persistent Homology (pdf slides)
- Mathematics of a Zombie Attack (Prezi) presented at Piedmont's math/science seminar for undergraduates