April 9, 2021

About the speaker

Ms. Kristen Hallas is a first-generation, first-year graduate student pursuing a PhD in Mathematics and Statistics with Interdisciplinary Applications at the University of Texas Rio Grande Valley (UTRGV). She earned her B.S. in Applied Mathematics with Computer Science minor at UTRGV in Spring 2022, graduating Summa Cum Laude. She is a 2021 Gilman scholar/alumni and funded independent research on STEM identity formation through UTRG's Engaged Scholar; Artist Awards, successfully defending this work as her undergraduate honors thesis. A strong believer of community advocacy, Kristen is an officer for two student organizations, serves as Graduate Senator for Student Government Association, and represents UTRGV on UT System's Student Advisory Council. Kristen interned with the High-Performance Computing (HPC) Security Analytics & Monitoring Group at Oak Ridge National Lab in Summer 2022, designing a full-stack, interactive visualization of an HPC system. In Fall 2022, she became a graduate research assistant for UTRGV's Center of Advanced Manufacturing Innovation and Cyber Systems (CAMICS). She is interested in developing smart manufacturing technologies, creating reliable/long-lasting HPC systems, and furthering inclusive/accessible STEM education. After graduating, Kristen envisions herself building systems towards positive aims, such as expanding environmental sustainability or protecting digital connectivity, on a team dedicated to advancing scientific progress. The project presented in this work was one of several projects completed for Kristen's honors curriculum as an undergraduate at UTRGV.

Distinguishable Paintings For Odd and Even n -sided Regular Polygons in x Colors

We illustrate how group theory can answer questions in a wide array of disciplines by presenting the distinguishable paintings problem for an n - sided regular polygon. We provide the notation necessary to understand Lagrange’s theorem and Burnside’s lemma and show a couple of examples of solving these problems when n is defined. After proving the formula to count the number of distinguishable paintings for odd and even n-sided regular polygons, we discuss other interesting results and additional applications of the tools presented in this work for solving problems in art and science.