Research
Research Interests
Broadly speaking, I am interested in combinatorial number theory and mathematical biology. This has lead me to do research in a variety of adjacent areas, such as graph theory, differential geometry, and arithmetic group theory. I have past and ongoing projects in all of these areas (see below). For the past several years, I have focused my attention on DNA self-assembly, a topic that lies at the intersection of mathematical biology, algebra, and combinatorics. My (Master's) thesis advisor was Cory Johnson, who is an Associate Professor of Mathematics at CSU San Bernardino.
Recently, I have become interested in difference necklaces, which are combinatorial objects arising from number theory. I anticipate this topic becoming a rich area of study for undergraduate students. If you're interested in getting involved, feel free to reach out.
Ongoing Projects
DNA Self-Assembly of Pots with 1 Bond-Edge Type, with Corrine Johnson
Difference Necklaces
Past Projects
Analysis and Algorithmic Construction of Self-Assembled DNA Complexes, with Corrine Johnson (Submitted)
A preprint of this paper can be found on arxiv: https://arxiv.org/abs/2310.04398
Analyzing Systoles of Arithmetic Genus 2 Surfaces, with Jeffrey S. Meyer
Determining the Metric of a Jordan-Normal Form Operator, with Corey M. Dunn
A Complete Description of Constant Vector Curvature in the 3-Dimensional Setting
A manuscript of this paper can be found at: https://www.math.csusb.edu/reu/studentwork.html