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 nearly complete intersection ideal) and build on the well-established theory of 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 and in Springer’s Association for Women in Mathematics Series, vol 29.