Irrationality Proofs for Zeta Values, Moduli Spaces and Dinner Parties

A simple geometric construction on the moduli spaces M0,n of curves of genus 0 with n ordered marked points is described which gives a common framework for many irrationality proofs for zeta values. This construction yields Apéry’s approximations to (2) and (3), and for larger n, an infinite family of small linear forms in multiple zeta values with an interesting algebr..