Algebra and Combinatorics Seminar

Date: October 20, 2017

Time: 3:00PM - 3:50PM

Location: BLOC 117

Speaker: Benjamin Schröter, TU-Berlin

Title: Multi-splits in hypersimplicies and split matroids

Abstract: Multi-splits are a class of coarsest regular subdivisions of convex polytopes. In this talk I will present a characterization of all multi-splits of two types of polytopes, namely products of simplices and hypersimplices. It turns out that the multi-splits of these polytopes are in correspondence with one another and matroid theory is the key in their analysis, as all cells in a multi-split of a hypersimplex are matroid polytopes. Conversely, the simplest case of multi-splits of hypersimplices give rise to a new class of matroids, which we call split matroids. The structural properties of split matroids can be exploited to obtain new results in tropical geometry.