Digital Commons Network^™

Arithmetical Structures On Paths With A Doubled Edge, Darren B. Glass, Joshua R. Wagner

Math Faculty Publications

An arithmetical structure on a graph is given by a labeling of the vertices that satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical structures for graphs in these families.

The Consent Of The Governed, Carter A. Hanson

Student Publications

The Consent of the Governed is a Kolbe Fellowship project investigating gerrymandering through the lens of mathematics, Supreme Court litigation, and the potential for redistricting reform. It was produced as a five-episode podcast during the summer of 2020; this paper is the transcription of the podcast script. The project begins with an analysis of the impact of gerrymandering on the composition of the current U.S. House of Representatives. It then investigates the arguments and stories of Supreme Court gerrymandering cases in the past twenty years within their political contexts, with a focus on the Court's reaction to different mathematical methods …

Multiparty Non-Interactive Key Exchange And More From Isogenies On Elliptic Curves, Dan Boneh, Darren B. Glass, Daniel Krashen, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi, Mark Zhandry

Math Faculty Publications

We describe a framework for constructing an efficient non-interactive key exchange (NIKE) protocol for n parties for any n ≥ 2. Our approach is based on the problem of computing isogenies between isogenous elliptic curves, which is believed to be difficult. We do not obtain a working protocol because of a missing step that is currently an open mathematical problem. What we need to complete our protocol is an efficient algorithm that takes as input an abelian variety presented as a product of isogenous elliptic curves, and outputs an isomorphism invariant of the abelian variety.

Our framework builds a cryptographic …

Analysis Of An Ode Model For Sea Turtle Populations With Temperature-Dependent Sex Determination, Lindsey A. Ukishima

Student Publications

The sex of green sea turtles is determined by the temperature at which the eggs are incubated. Recent studies have shown that the sex ratios of sea turtle populations have changed over recent years, likely due to climate change, which has produced a more female-biased population. This paper finds the nonzero equilibrium point of the novel system developed by Herrera et a. (2019) and attempts to determine the stability of the population at that point.