Stable curves and chromatic polynomials

Speakers: Bernhard Reinke (Aix-Marseille Université)\n\nThe intersection numbers of moduli spaces of stable curves are well-studied and are known to have rich combinatorial structure. We introduce a natural class of these intersection numbers indexed by finite graphs. In genus zero, these numbers are closely related to several previously-studied quantities, including maximum likelihood degrees in algebraic statistics, counts of regions of certain hyperplane arrangements, and Kapranov degrees. For undirected graphs, we recover the chromatic polynomial of the graph evaluated at negative integers. This leads us to propose a new generalization of the chromatic polynomial of a directed graph.\nIn my talk, I will sketch a proof for the equality in the undirected case using the theory of hyperplane arrangements, and discuss various properties of the generalization to directed graphs.\nThis talk is based on joint work with Rob Silversmith.\n\nhttps://indico.math.cnrs.fr/event/17047/