Luis Ferroni: The Chow polynomial of a poset

ABSTRACT: In this talk I will introduce a new family of polynomial invariants of posets exhibiting remarkable properties. Our motivation comes from the study of Chow rings of matroids, but as it turns out, our theory can also be motivated by Stanley--Reisner rings of barycentric subdivisions of face lattices of convex polytopes (in a sense, it interpolates between both matroids and convex polytopes). I will define the main tools and discuss the relation of Chow polynomials with the Kazhdan--Lusztig polynomials of matroids and the toric g-vectors of polytopes. Finally, I will mention a few open conjectures and problems. This is based on joint work with Jacob Matherne and Lorenzo Vecchi.