An Invitation to Integer Point Enumeration in Polytopes

One problem in convex polytopes can be summed up with the question: "how many lattice points does this polytope contain?". One answer is the Ehrhart polynomial which enumerates the lattice points of a polytope P for positive integer dilates of P. In this talk we will begin with a discussion of integer polytopes and how one may find their Ehrhart polynomials in general. Then, we will discuss a specific class of polytope, zonotopes, and their Ehrhart polynomials.