03.07.2019 um 16:00 Uhr
Prof. Dr. Michael Gnewuch und Prof. Dr. Markus Spitzweck
25.06.2019 um 16:15 Uhr in 69/125:
Jose Alejandro Samper (MPI Leipzig)
Slicing matroid polytopes
We introduce the notion of a matroid threshold hypergraph: a set system obtained by slicing a matroid basis polytope and keeping the bases on one side. These hypergraphs can be then used to define a class of objects that slightly extends matroids and has a few new techincal advantages. For example, it is amenable to several inductive procedures that are out of reach to matroid theory. In this talk we will motivate the study of these families of hypergraphs, relate it to some old open questions and pose some new conjectures. To conclude we will show that the study of these objects helps us find a link between the geometry of the normal fan of the matroid polytope and shellability invariants/activities of independence complexes.