Graphs and Matroids Seminar- Ahmed Ashraf

Title: Cyclic flat approach to matroid base polytopes

Abstract: Ardila, Benedetti and Doker realised matroid polytopes as generalized permutohedra, and using the work of Postnikov, gave an expression of volume of a matroid polytope, in terms of a sum of products of Crapo's beta invariants of certain matroid minors. On the other hand, Derksen and Fink in their joint paper have proved universality of a valuative invariant for matroids, defined previously by Derksen. Recently, motivated by tropical geometry, Hampe defined the notion of matroid intersection ring and showed that it is generated additively by loopless Schubert matroids. Using these ideas, we describe another approach to finding volume of a base polytope from lattice of cyclic flats of its respective matroid. As an application, we give a closed formula for the volumes of connected (sparse) paving matroid polytopes.