Matthias Lenz: Zonotopal algebra and Mason's conjecture

Zonotopal algebra is the study of a family of pairs of dual vector spaces of multivariate polynomials that can be associated with a list of vectors. It connects objects from combinatorics (e.g. matroids), discrete geometry (hyperplane arrangements, zonotopes), approximation theory (box splines), and algebraic geometry (Cox rings, fat point ideals).

Mason's conjecture states that the f-vector of a matroid complex is log-concave.

In this talk, I will give an introduction to zonotopal algebra, explain its connections to matroid theory and prove Mason's conjecture for realizable matroids.