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 deltaP(t), which encodes the number of lattice points in any fixed dilation of P. The polynomial deltaP(t) is a classic combinatorial invariant, called the Ehrhart delta-polynomial of P. We will present a new geometric interpretation of the coefficients of deltaP(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.