Anders Lundman: Computing the volume of polytopes

A convex lattice polytope is the convex hull of a finite set of points with integer coordinates in R^n. One surprising fact is that the function that counts the number of lattice points in such a polytope when scaled by a natural number is in fact a polynomial. I will sketch a proof of this fact and explain why the leading coefficient of this so called Ehrhart polynomial gives the d-dimensional volume of the polytope.