Speaker: Ben Braun, University of Kentucky
Title: Geometric properties of r-stable hypersimplices
Abstract: Hypersimplices are well-studied objects in combinatorics, optimization, and representation theory. For each hypersimplex, I'll define a new family of subpolytopes, called r-stable hypersimplices. I'll discuss how a standard unimodular triangulation of the hypersimplex restricts to a unimodular triangulation of each r-stable hypersimplex. For the case of the second hypersimplex defined by the two-element subsets of an n-set with n odd, I will describe a shelling of this triangulation that sequentially shells each r-stable sub-hypersimplex. In this case, there are also interesting connections between the Ehrhart h*-vector of the second hypersimplex and the r-stable sub-hypersimplices that I will talk about if time permits. This is joint work with Liam Solus.