McNair Scholar 2019 Yaren E. Euceda Mejia
Yaren E. Euceda Mejia is a student at UMN. She is majoring in mathematics and computer engineering. Her research interests include number theory and STEM education. Euceda plans to earn a Ph.D. in mathematics and use her degree to teach higher mathematics, solve mathematical problems emerging from computer science/computer engineering, and develop STEM outreach programs. Outside of mathematics she enjoys time with family, books, and the outdoors.
As a mathematician, my dream is to help make progress on and be alive to see Goldbach’s Conjecture proof [ecstatic emoji here]!
Research project
Counting Metaplectic Ice and Modified Alternating Sign Matrices
Abstract: Mills, Robbins, and Rumsey conjectured that for a given n, there exists (1!7!...(3n-2)!)/(n!(n+1)!...(2n-1)!) alternating sign matrices (ASM). Zeilberger proved the conjecture by establishing a bijection between ASMs and totally symmetric self-plane partitions. Kuperberg provided a second proof using the bijection between ASMs and ice models with domain wall boundary conditions. We introduce modified alternating sign matrices, and we prove a bijection with modified boundary conditions for the ice models. Furthermore, we modify Kuperberg's proof to provide a count for certain sizes of modified alternating sign matrices.
Faculty mentor
Dr. Ben Brubaker is currently a mathematics professor at the University of Minnesota (UMN). Dr. Brubaker attended Brown University where he received his Ph. D. in mathematics. His research interest includes analytic number theory and representation theory, specifically problems pertaining to automorphic forms and algebraic group representations and their generalization on arithmetic covering groups.