Undergraduate Research
I attended Davidson College for undergrad, where I majored in math and minored in educational studies.
I'm pictured here with my two undergraduate thesis advisors, Donna Molinek (left) and Heather Smith (right)
My first research project was with Axel Brandt, studying the additive choice numbers of graphs.
For my senior thesis, I studied zero forcing with the guidance of my advisors, Donna Molinek and Heather Smith. See below for more specifics!
I also worked on a project with Mindy Adnot on school choice and segregation in North Carolina. Here's a map of NC I made with all of the 2018 charter and magnet school data.
Zero forcing polynomials: mapping spiders to paths
Abstract
This paper explores zero forcing sets and zero forcing polynomials on simple graphs. We begin with a graph with all white vertices, and we choose a set of vertices of size i to color blue. We then iteratively apply a color change rule to our graph. If we can force the remaining vertices blue with this color change rule, then our initial set was a zero forcing set. The zero forcing polynomial of a graph G is a generating function, defined such that the coefficient on x^i is the number of zero forcing sets of G of size i. In "The zero forcing polynomial of a graph," where this polynomial was introduced, the authors conjecture that a path of length n has at least as many zero forcing sets of size i as any other graph on n vertices. In this paper, in addition to constructing new zero forcing polynomials, we prove that this conjecture holds for certain families of graphs, namely spiders.
