Speaker:  Luis Ferroni (KTH)

Title:  Hilbert series of matroid Chow rings and intersection cohomology

Abstract:

Starting with a matroid M one can construct three important algebraic objects: the Chow ring, the augmented Chow ring and the intersection cohomology module. They play instrumental roles within the proofs of the log-concavity of the Whitney numbers of the first kind, and the top-heaviness of the Whitney numbers of the second kind. We will describe the combinatorics of their Hilbert series for matroids in general and uniform matroids in particular. Several aspects such as unimodality, gamma-positivity and real-rootedness will be discussed under different perspectives. Based on joint work with Jacob Matherne, Matthew Stevens and Lorenzo Vecchi.