I will share a story of two polynomials, the Poincarè polynomial of Chow rings of toric varieties of matroids, and the h-polynomials of nested set complexes of matroids. The story is set in a rich network of positivity properties coming from geometry and combinatorics of matroids, with connections to moduli spaces of rational stable curves. The main theorems are matroidal analogues of Gal’s conjecture, and real-rootedness of some of these polynomials. (Joint works with Basile Coron, and Luis Ferroni)