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.
Title: Material Culture of Babylonian Mathematics
Abstract: This talk introduces Babylonian maths and numerals, with particular focus on how Babylonian scribes used tablets to encode this information (e.g., how they created and used reference tablets, intermediary calculations, and even the 3-D space of the clay tablet itself). This talk includes hands-on clay activities so students can leave with their own "tablet."
Title: Two-Player Games on Knot and Link Diagrams
Abstract: Over the past decade, numerous two-player games on knot and link diagrams have been created and explored. For these turn-based games, each player has a goal to achieve in order to win the game. In this talk, we will introduce two examples of such games - the Linking-Unlinking Game and the Single Smoothing Per Twist Game - and will share results about winning strategies for these games. Work on these games came out of two separate undergraduate research projects, the former with Jake Murphy at the University of Connecticut and the latter with James Blair at Elmira College. The main goal of this talk is to promote the study of two-player combinatorial games as a rich source of undergraduate research projects.