This atypical time for Slow Pitch is part of Welcome Weekend! Come learn some neat stuff and meet some prospective students.
We will explore some connections between simple graphs and polynomial rings. Generally speaking, finding monomial prime decompositions of ideals or minimal generating sets of ideals in polynomial rings can be rather unpleasant. If you start with a simple graph, we can construct some interesting ideals using vertices (called the cover ideal) or edges (called the edge ideal). Using properties of the graph, finding minimal generating sets of cover ideals or minimal monomial prime decompositions of the edge ideal is not so bad!
The short version: We're going to build some ideals, find some nice generating sets, and draw some pictures (as always)!
Simple Graphs and Monomial Ideals: How I Spent Summer 2014
Simple Graphs and Monomial Ideals: How I Spent Summer 2014