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 Ap´ery’s approximations to ζ(2) and ζ(3), and for larger n, an infinite family of small linear forms in multiple zeta values with an interesting algebraic structure. It also contains a generalisation of the linear forms used by Ball and Rivoal to prove that infinitely many odd zeta values are irrational.