PIMS/WMAX Postdoctoral Colloquium: Weighted Ehrhart theory and orbifold cohomology

Motivated by geometry, we consider a `less discrete' way of counting lattice points in polytopes, in which one assigns a certain `weight' to each lattice point. On the combinatorial side, this approach reveals some `hidden symmetry' which improves upon and makes transparent some classical results in Ehrhart theory. On the geometric side, the combinatorial invariants count orbifold Betti numbers of toric stacks. If time permits, we will discuss a generalization involving motivic integration.