I had the chance to work under the mentorship of Dr. Koch again from halfway through my junior year until I graduated. For this project I worked alongside Laura Stordy to study braces, an algebraic structure used in Hopf-Galois theory.

Our most recent abstract from SPARC: Braces are a relatively new construction, created to find solutions to the Yang-Baxter equation. A left skew brace is a set B with two binary operations, · and ◦ such that (B, ·) and (B, ◦) are groups, and for all a, b, c ∈ B; a ◦ (bc) = (a ◦ b)a −1 (a ◦ c). The Truman opposite of a brace B, denoted B’, is defined by (B, ·, ◦’), where a ◦’ b = (a −1 ◦ b −1 ) −1. We gave instances where B is not isomorphic to B’.

I gave an oral presentation on this research at:
Nebraska Conference for Undergraduate Women in Mathematics, Lincoln, NE, January 2019
Agnes Scott College Spring Annual Research Conference, Atlanta, GA, April 2018 and April 2019