Graduate:
My current research interest is graph theory, although I enjoy most all forms of discrete math. My dissertation research under Dr. Felix Lazebnik deals with a subset of algebraically defined graphs; specifically, the adjacency in our graphs is governed by solutions to polynomial systems over certain fields. These graphs arise naturally in the context of extremal graph theory and some finite geometries, most notably the generalized quadrangles. We have been examining how changing the polynomials that define adjacency affect the question of whether we can construct a generalized quadrangle. A large portion of this work has been carried out using Mathematica. I have presented on this research at various places, as detailed in my CV.
Undergraduate:
At Muhlenberg College, I studied Apollonian circle packings and their number theoretic properties with Dr. Byungchul Cha, Dr. Daniel File, and Sharif Moustafa. We discovered new absent admissible curvatures for several primitive integral packings, and presented on said research multiple times.
