Title: Edge Ideals via Independence Polynomials of Graphs
Abstract: Given a graph G, one can build an algebraic object called its edge ideal I(G), which translates the combinatorial structure of the graph into the language of commutative algebra. A natural question in this area is: what can combinatorics tell us about algebra? In this talk, I will introduce two polynomials: the h-polynomial of I(G) and the independence polynomial of G, denoted P_G(x), and how P_G(x) encodes surprisingly rich information about the Hilbert series of I(G). In particular, I will discuss how P_G(x) determines both the degree and the top coefficient of the h-polynomial. No background in commutative algebra will be assumed; I'll introduce the relevant objects along the way. I'll work through familiar examples, and I'll also describe a simple construction that makes these invariants easy to track and compare.
Title: Mathdramatics: Math on Stage
Abstract: Math/Theater scholar, Dr. Emma LaPlace, will raise the curtain on plays that put mathematics in the spotlight. Join Dr. LaPlace as she explores how mathematics is portrayed and represented in theatrical productions. Part lecture, part performance, this presentation will bring the scripts to life, and move math from the page to the stage.
Topic: Babylonian Mathematics; Title: TBA
Abstract: TBA
Topic: Two-player games on knots and links; Title: TBA
Abstract: TBA