Discrete Applied Math Seminar By Logan Crew:The Chromatic Symmetric Function: A Refinement of the Chromatic Polynomial

Speaker:

Logan Crew, University of Waterloo

Title:

The Chromatic Symmetric Function: A Refinement of the Chromatic Polynomial

Abstract:

The chromatic symmetric function X_G, introduced by Richard Stanley in 1995, refines the chromatic polynomial by distinguishing proper n-colorings by the number of times each color is used. By combining this enumerative refinement with techniques from algebraic combinatorics, many classical properties of the chromatic polynomial may be generalized and even given representation-theoretic meaning.

In this talk, we survey recent developments in chromatic symmetric function research, particularly surrounding its extension to vertex-weighted graphs in 2020 that allows the function to exhibit an edge deletion-contraction relation and thus gives more direct connections to enumerative combinatorics.  Connections to the chromatic polynomial and potential applications to generalizations of coloring (e.g. list-coloring) will be discussed.

This is based on joint work with Sophie Spirkl.

Bio:

Logan Crew received his PhD in mathematics from the University of Pennsylvania in 2020 studying algebraic combinatorics under Jim Haglund and Greta Panova, and is currently a Research Assistant Professor in the Department of Combinatorics and Optimization at the University of Waterloo.

His primary research area is the chromatic symmetric function and its generalizations, including connections to other graph polynomials and functions. He often collaborates with his wife and frequent coauthor Sophie Spirkl, an Assistant Professor in the same department specializing in structural graph theory, producing the unique interdisciplinary blend of algebraic and enumerative techniques that is central to many of his works.

The Discrete Applied Math seminar will be held most Fridays from 3:30 p.m. - 4:30 p.m. on Zoom during the Spring 2022 semester.

 

Discrete Applied Math seminar