Anastasia Nathanson: Chow rings of matroids as permutations representations

ABSTRACT: This talk will discuss the induced group action on the Chow ring of the matroid when given a matroid and a group of its matroid automorphisms. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincar\'e duality and the Hard Lefschetz theorem. We lift these to statements about this permutation action, and suggest further conjectures in this vein.