Algebra Seminar: Chromatic polynomials and moduli of curves

Title: Chromatic polynomials and moduli of curves

Speaker: Rob Silversmith
Abstract: 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. 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. 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)