## Colloquium: “Coloring: the Algebraic Way”

Marshall University Math Colloquium

November 4, 2015

**Martha Yip**

*University of Kentucky*

Abstract:

Suppose we want to color the countries on a map so that if two countries share a border, then they must be assigned different colors. What is the smallest number of colors that will do the job? The answer is the famous Four Color Theorem, which states that any map can be colored by at most four colors.

Inspired by this problem, Birkhoff introduced the chromatic polynomial to study colorings of a graph. In this talk, we discuss some recent developments in the study of the chromatic polynomial; from a multivariable generalization known as the chromatic symmetric function, to a homology theory whose Euler characteristic recovers the chromatic symmetric function.

No prior knowledge of any of the above terminology is assumed.