Richard P. Stanley Seminar in Combinatorics: Christopher Manon (University of Kentucky)

Harvard Science Center, Room 232

Speaker: Christopher Manon (University of Kentucky)Where: Harvard Science Center Room 232Title: Toric matroid bundlesAbstract: Toric matroid bundles are combinatorial objects which serve as a tropical analogue to vector bundles over toric varieties. I'll explain how to construct toric matroid bundles, how to check if a toric matroid bundle is globally generated or ample, and how to compute the characteristic classes of a toric matroid bundle in the T-equivariant chow cohomology of the base. Finally, I'll show that each matroid determines a tautological toric matroid bundle over the permutahedral toric variety. I'll discuss some properties of these bundles, and I'll show that the characteristic classes of the tautological toric matroid bundle recover the tautological classes of matroids used by Berget, Eur, Spink, and Tseng to prove log-concavity properties of the Tutte polynomial.