Benjamin Nill: The mixed degree of lattice polytopes

The Ehrhart polynomial counts lattice points in multiples of a lattice polytope (a polytope whose vertices are lattice points). Its generating function is a rational function whose enumerator is a polynomial, whose degree is called the degree of the lattice polytope. This invariant encodes lots of the complexity of the lattice polytope and was studied quite intensively during the last seven years. In this talk I would like to introduce the mixed degree of a family of lattice polytopes. I will explain why I think that this is an interesting notion, its relation to the mixed volume, and what kind of results we might hope to get.