This talk will focus on some recent results concerning the low energy expansion of superstring scattering amplitudes. Whereas tree-level amplitudes generate a series of multiple zeta values (MZV) the genus-one amplitudes generate a series of elliptic generalisations (“modular graph functions”) that satisfy fascinating polynomial relations analogous to those satisfied by MZV’s. The latter part of the talk will briefly review how these features fit in with the non-perturbative structure of superstring amplitudes, studied some time ago.

This talk will review perturbative and non-perturbative properties of string theory scattering amplitudes with particular emphasis on the constraints imposed by duality with M-theory on their low energy action.

Graeme Segal FRS (Oxford) 'Noncommutative geometry and quantum field theory' and Michael Green FRS (Cambridge) '2007 Naylor Lecture: Some dualities of string theory and quantum gravity'. Ends at 18:00. See www.mth.kcl.ac.uk/'tilde'anderl/LMSpremeeting/

This talk will survey recently deduced features of the ten-dimensional effective action for four gravitons in type II string theories. Duality with M-theory together with supersymmetry leads to a number of nontrivial higher derivative four-graviton interactions whose non-perturbative structure is completely determined by a collection of Poisson equations on moduli space and is consistent with data provided by string perturbation theory.