Georgia Institute of Technology College of Sciences

The chromatic polynomial of a graph, which counts colorings of the graph, has a habit of showing up in unexpected places in geometry, e.g. in the theory of hyperplane arrangements. This sometimes has interesting purely combinatorial consequences, such as Huh's proof of Hoggar/Read's conjecture on coefficients of chromatic polynomials. 

I'll discuss a new incarnation of chromatic polynomials. To a graph G, we can naturally associate a sequence of intersection numbers on moduli spaces of stable curves. Surprisingly, we prove that these recover values of the chromatic polynomial of G at negative integers. 

I'll also discuss how this leads to new algebraic invariants of directed graphs.

(Joint with Bernhard Reinke)