Log-concavity of matroid h-vectors and mixed Eulerian numbers

Abstract: (Joint with Andrew Berget and Dennis Tseng) For any matroid $M$, we compute the Tutte polynomial using the mixed intersection numbers of certain tautological classes in the combinatorial Chow ring arising from Grassmannians. Using mixed Hodge-Riemann relations, we deduce a strengthening of the log-concavity of the h-vector of a matroid complex, improving on an old conjecture of Dawson that was resolved contemporaneously by Ardila, Denham, and Huh.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html