Mathematics Colloquium: Hypergraphs Applied to Commutative Algebra, or, why prove theorems when you can draw pictures?

Speaker:  Courtney Gibbons, Hamilton College

Title:  Hypergraphs Applied to Commutative Algebra, or, why prove theorems when you can draw pictures?

Abstract:  In this talk, we take a problem in commutative algebra (identifying an object called a \textit{nearly complete intersection ideal}) and build on the well-established theory of \textit{edge ideals} to come up with a graph theoretic condition to solve the problem. This sounds dry, but the talk will be full of pictures and intuition (and maybe even a short proof!) to introduce the audience to the big new idea and how it works. Please bring scratch paper, a sense of mathematical adventure, and a willingness to ask lots of questions. These results were obtained by my team of then-undergraduates (Chiara Bondi, Yuye Ke, Spencer Martin, Shrunal Pothagoni, and Ada Stelzer) during Clemson's COURAGE REU in the summer of 2020. Interested parties can find the paper on the arXiv: https://arxiv.org/abs/2101.08401 and in Springer's Association for Women in Mathematics Series, vol 29. 

Time:  Friday, April 7, 3:30pm – 4:20pm

Place:  Exploratory Hall, room 4106

Zoom and In-person