Simplicial generation of Chow rings of matroids
We present a new set of generators for the Chow ring of a matroid. We show that these generators behave like base-point-free divisors by establishing that (i) they correspond to matroid operations that combinatorially mirror hyperplane pullbacks, and (ii) the volume polynomial with respect to these generators satisfies Hodge-type inequalities. We thereby generalize Postnikov's results on generalized permutohedra, and also give a simplified proof of the combinatorially relevant portion of the Hodge theory of matroids developed by Adiprasito-Huh-Katz. No knowledge of matroids will be assumed. This is joint work with Spencer Backman and Connor Simpson.
The discussion for Christopher Eur’s talk is taking place not in zoom-chat, but at tinyurl.com/2020-09-04-ce (and will be deleted after 3-7 days).