Volume and covolume polynomials of projective varieties

I will introduce the notion of volume and covolume polynomials over a fixed field and explain their relationship

with homology and cohomology classes of irreducible cycles in products of projective spaces. The support of volu-

me polynomials characterizes algebraic polymatroids. We will explain how the theory of volume and covolume poly-

nomials can be used to deduce new results about algebraic (poly)matroids. This is joint work with Lukas Grund, June

Huh, Mateusz Michalek and Hendrik Suss.