URA Seminar - Logan Crew

Monday, May 29, 2023 2:30 pm - 2:30 pm EDT (GMT -04:00)

Title: Chromatic Symmetric Functions: Combining Algebra and Graph Theory

Speaker: Logan Crew
Affiliation: University of Waterloo
Room: MC 5479

Abstract: The chromatic polynomial, enumerating the proper colorings of a graph by number of colors used, was created by Birkhoff in the early 1900s to study the then Four-Color Conjecture.  In the 1990s, Stanley generalized this to a chromatic symmetric function, which further counts for each proper n-coloring how many times each of the n colors is used.  This talk will give a general overview of the chromatic polynomial, symmetric function theory, and the chromatic symmetric function.  Recent research will be highlighted demonstrating new properties of the chromatic symmetric function, and conversely how considering intuition from graph theory has led to the discovery of new bases and results in general symmetric function theory.   This seminar is intended for general audiences and assumes no knowledge of graph theory beyond elementary concepts from MATH239, and no knowledge of algebra beyond knowing what a vector space is.