McNair Scholar 2020 Ethan R. Partida

Ethan R. Partida is a junior at the University of Minnesota, Twin Cities, double majoring in Mathematics and Computer Science. His research interests lie in combinatorics, algebra, and geometry. He plans to get his Ph.D in Mathematics.

Ethan R. Partida headshot
My dream is to obtain my Ph.D in Mathematics and continue doing research for the rest of my life. I hope to collaborate with people around the world and leverage my education to give back to my culture and community.

Research project

Symmetry of a Pastry: A Mathematical Investigation into the Braid Group

Abstract: We will introduce braid groups from two perspectives, physical and algebraic. While a physical interpretation provides good intuition for the braid group, it lacks the precision that is useful for proving properties of this group. By first giving an introduction to the algebraic structure of the symmetric group and then shifting this perspective to the more generalized braid group, we gain the precision our physical interpretation lacks. Finally, we use this understanding to explore applications of the braid group in cryptography and knot theory.

View the poster presentation

Faculty mentor

Prof. Vic Reiner is currently a Professor and Associate Head in the School of Mathematics at the University of Minnesota. Prof. Reiner received his Ph.D in Mathematics from Massachusetts Institute of Technology. His research interests are in combinatorial algebra, geometry, and topology. Prof. Reiner is published in numerous research journals and is also an editor for two research journals. Prof. Reiner is also an accomplished mentor. He has mentored many Ph.D and Masters students while helping run an annual combinatorics REU.