How to stab a polytope

In this talk, I will present a method for constructing defining inequalities for the set of linear subspaces of fixed dimension that intersect a given polytope. This set can be described as a union of cells in the complement of a Schubert arrangement associated with the polytope, within the Grassmannian. In particular, I will provide a detailed description of the subspaces that intersect a cyclic polytope and explore its connections to the amplituhedron and positive geometries. Based on joint work with Sebastian Seemann.