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Graphs and Matroids Seminar- Ahmed AshrafExport this event to calendar

Wednesday, February 27, 2019 — 3:30 PM EST

Title: Cyclic flat approach to matroid base polytopes

Speaker: Ahmed Ashraf
Affiliation: Western University
Room: MC 5501

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. 

Location 
MC - Mathematics & Computer Building
5501
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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