Katie Bruegge: Counting Facets of Symmetric Edge Polytopes

Abstract: Lattice polytopes defined from graphs are a subject of extensive study in combinatorics. One such class of polytopes that have received much attention are symmetric edge polytopes (SEPs). Some recent work has been motivated by a deceptively simple question: In what ways does the structure of a graph affect the number of facets of its polytope? As is often the case, this question has surprisingly complex answers. In this talk, we will define symmetric edge polytopes, describe some theoretical and computational tools we have to count their facets, and discuss the findings of some recent work regarding SEPs arising from some families of sparse graphs and from random graphs generated by several models.

This talk will be given via Zoom.