Hodge Theory for Polymatroids

In the first part, we present classical results about hyperplane arrangements and matroids: starting from the definitions, we present the construction by De Concini and Procesi of wonderful models. We discuss the cohomology of the wonderful model and of the complement of the arrangement. We also sketch the proof by Huh, Adiprasito, Katz of log-concavity of coefficients of the characteristic polynomial. In the second part we introduce subspace arrangements and polymatroids. We provide a generalization of the Goresky, MacPherson formula and we discuss the Hodge package (i.e. Poincaré duality, Hard Lefschetz and Hodge Riemann bilinear relations) for the Chow ring of a polymatroid. This is a joint work with Gian Marco Pezzoli.