String Loop Amplitudes and 1/N Corrections

I will review work on string loop amplitudes with minimal supersymmetry in flat space, and discuss work in progress on generalization to RR flux backgrounds like AdS and its BMN plane-wave limit. Some of this work in progress is with mathematicians (e.g. on automorphic forms) and is somewhat analogous to recent work on the Langlands program. I will attempt to give a brief overview how string amplitudes of this kind control 1/N corrections in AdS/CFT duality.

References: 1603.05262, 1611.03459, work in progress