Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Motivated by geometry, we introduced a purely combinatorial integration theory which takes a lattice polytope P and a piecewise linear function λ and outputs a power series \tilde{h}^*(P, λ) ∈ \mathbb{Z}[[t^1/N]], for some positive integer N. We prove a change of variables formula relating these 'integrals' on different lattice polytopes, and, in the case when λ is identically zero, we show how \tilde{h}^*(P, 0) reveals some hidden symmetry in the Ehrhart h^*-vector of P.