Click here to see the poster in more detail.

Four-Color Theorem

Graph Coloring is a relatively recent area of mathematics that emerged in the 19th century. Its central concept revolves around the Four-Color Theorem, which asserts that any planar graph can be colored using no more than four colors. This presentation will provide an overview of the principles of Graph Coloring, explore real-world applications related to the Four-Color Theorem, and discuss the advancements made in proving this theorem.

Auron Moore is a senior majoring in business administration with an accounting emphasis and a mathematics minor. He is a member of the Beta Gamma Sigma Honor Society, Rotaract Club, Lander eSports, and Lander’s Honors College. He plans to pursue an MBA and a CPA after graduation through Lander’s Business Graduate Program.

Julia Sets and their Particular Laminations 

This poster shows a process of finding the corresponding Julia set from a particular lamination. The pullback lamination is used to create a Fatou Gap diagram which models where Fatou Gaps in our lamination map under iteration. Given a Fatou Gap diagram and its characteristics, we want to parameterize the corresponding complex polynomial. From this parameterization, we have a system of equations to solve for the set of possible polynomial coefficients. Using Bezout’s Theorem on the intersection of hypersurfaces, we expect the number of solutions to be the product of the degrees of each of the equations which can get large quite quickly. We use Mathematica to solve for these coefficients and to generate the possible Julia sets.

Robert Risdon is a current Math and Engineering student at Lander University with a minor in Business Administration. His achievements include being an active member of both Beta Gamma Sigma and the National Society of Leadership and Success, and participating in the 2025 Francis Marion Undergraduate Mathematics Conference. 

Kent McCathern, a sophomore Math and Engineering student at Lander University. Currently an active member in Alpha Lambda Delta and is Participating in the 2025 Francis Marion Undergraduate Mathematics Conference. 

Click here to see the poster in more detail.

Synthesis, Characterization, and Polymerization of a Bio-Based Epoxy Resin for Use in Epoxy Telescope Mirrors

Current methods of producing epoxy telescope mirrors include using environmentally unfriendly bisphenol A (BPA) derivatives.  These BPA derivatives are also known to be toxic to humans.  With a push to more sustainable reagents, eugenol, also known as clove oil, has shown promise with similar physical and chemical properties as the BPA derivatives.  A eugenol-based epoxy has been synthesized and characterized using 1H NMR and 13CNMR spectroscopy.  In addition, the eugenol-based epoxy has been polymerized with an amine curing agent to produce samples with varying amounts of the bio-based epoxy.  The coefficient of thermal expansion, glass transition temperatures and moduli will be given and compared to the original BPA-based epoxy system. 

Brayden Mack is a senior chemistry major with an emphasis in health sciences from Swansea, SC. After graduation, he will attend the Kentucky College of Osteopathic Medicine at the University of Pikeville, where he plans to earn a Doctor of Osteopathic Medicine degree and pursue his goal of becoming a physician.