Benjamin Nill: Ehrhart polynomials and discriminants

Given a convex set, counting the points with integer coordinates is a topic that is of interest in many areas of pure and applied mathematics such as the geometry of numbers or integer linear optimization. There is beautifully developed part of this research field, called Ehrhart theory, that is concerned with counting lattice points in dilates of polytopes. In this talk I will illustrate how to use Ehrhart theory to solve a problem on A-discriminants. I will introduce all the necessary notions such as Ehrhart polynomials, lattice polytopes and A-discriminants. As it turns out, the problem will be reduced to a question about binomial coefficients.