Combinatorics and Algebra Seminar- Characterizations of certain matroids by maximizing valuative invariants

Title:   Characterizations of certain matroids by maximizing valuative invariants

Speaker: Joe Bonin, GWU
Date and time: Wednesday 11/19, 4–5pm
Place: Phillips 108

 

Abstract:  Luis Ferroni and Alex Fink recently introduced a polytope of all unlabeled matroids of rank r on n elements, and they showed that the vertices of this polytope come from matroids that can be characterized by maximizing a sequence of valuative invariants.  In this talk, we will first sketch the background that is needed to understand their polytope and valuative invariants.  We will then provide the needed characterizations of many of the matroids that Ferroni and Fink conjectured to yield vertices, we will give additional examples of such matroids, and we will mention some open problems.