Title: Ehrhart from Hilbert

Abstract: Many discrete problems in various mathematical areas arise from linear systems, thus they ask about integer points of polytopes in disguise. Ehrhart theory tries to develop tools to encode information about integer points of polytopes. One of the most important objects in Ehrhart theory is the so-called Ehrhart function. We will show that Ehrhart theory is closely related to commutative algebra. In particular, we will show how graded modules and the Hilbert function can be used to prove interesting results about the Ehrhart function of a lattice polytope.