Lilla Tóthmérész: h*-vectors of edge polytopes and symmetric edge polytopes

Abstract: Symmetric edge polytopes of graphs and edge polytopes of directed graphs are two classes of lattice polytopes whose \(h^*\)-polynomials have interesting properties and generalize important graph polynomials. I will talk about graph-theoretic formulas for these polynomials using activity statistics, and about the connection of the degree of the \(h^*\)-polynomial and the graph structure. We will also see that both results hold more generally in the case of regular oriented matroids. I will also mention some conjectures about the relationship of the \(h^*\)-polynomials for different orientations of a given graph. Joint work with Tamás Kálmán.