Alan Stapledon (University of Michigan)

Friday 20th June, 12.05-12.55pm, Carslaw 373

Weighted Ehrhart theory and orbifold cohomology

If P is a lattice polytope, then one can define a polynomial delta_P(t), which encodes the number of lattice points in any fixed dilation of P. The polynomial delta_P(t) is a classic combinatorial invariant, called the Ehrhart delta-polynomial of P. We will present a new geometric interpretation of the coefficients of delta_P(t). That is, they are sums of dimensions of orbifold cohomology groups of a toric stack. As a combinatorial application, we will prove a weighted version of Ehrhart Reciprocity.