Three Muhlenberg students shared their research at the Joint Mathematics Meeting’s Student Research Poster Session in Denver, Colorado, this January.

Brittany Gelb, ’21, a mathematics major from Schnecksville; Olivia Schwager ’20, a mathematics major and chemistry minor; and Jordan Segrave, ’20, a mathematics and business administration double major, presented their work at the session, which is designed for undergraduate and first-year graduate students to present posters on their work as undergraduate researchers.

Gelb conducted research at the Lafayette College Research Experience for Undergraduates funded by the National Science Foundation.

She worked with fellow students Kathryn Beck of Dickinson College and Lisa Cenek of Amherst College; the group was mentored by Megan Cream, professor of practice at Lehigh University.

Their work focused on graph theory, which is the mathematical study of connections.

One aim of graph theory is to analyze when a graph will contain particular structures, such as paths or cycles.

Gelb and her collaborators examined a newly defined cycle property called doubly chorded pancyclicity and determined conditions for when graphs have this property.

Their work supports extending a famous metaconjecture in the field about conditions for hamiltonicity (the existence of a largest possible cycle) and pancyclicity (the existence of a cycle of every possible length).

Their research also strengthens a new research direction in graph theory, which is to not only prove that certain cycles exist, but also to discover more about their structure.

Schwager performed computational arithmetic dynamics research during the summer of 2019 through an NSF-funded REU at the Institute for Computational and Experimental Research in Mathematics through Brown University.

Arithmetic dynamics is a field of mathematics in which dynamical systems are studied with a number-theoretic approach.

Dynamical systems refer to the study of functions under self-iteration, and arithmetic dynamics, specifically, integer and rational points with a focus on their behavior in polynomial and rational functions.

Her research group included three other students, who were mentored by professors from universities around the country.

Their project culminated in a set of conjectures mimicking the Uniform Boundedness Conjecture of Morton and Silverman, a conjecture proposed in 1994 that has yet to have been formally proven.

Segrave completed her mathematics culminating undergraduate experience with a research project involving the connection of integral calculus to Gothic architecture.

She worked with Professor of Mathematics Michael Huber to develop a technique that incorporates trigonometry to calculate areas of Gothic windows, after converting a 13th-century architecture process known as the “quinto acuto.”

Segrave wrote code using the Python programming language to calculate the area using window dimensions, such as rise-to-span ratios.

The technique was applied to several windows from the famous Milan Cathedral after Huber obtained exact dimensions from the Duomo’s Direttore dei Cantieri della Fabbrica.

Posters were viewed during the session, and feedback was provided by professionals and mathematicians.

The Joint Mathematics Meeting is the largest annual mathematics meeting in the world and offers a variety of sessions that are designed to appeal to undergraduates.