Recently Calabi-Yau (CY) periods and their special geometry have been used to solve the Post-Minkowskian (PM) approximation to black hole scattering in the fifth PM order, i.e. with very high precision. This approximation uses Quantum Field Theory methods and in particular a Feynman graph expansion and Feynman integrals.
In this talk we will outline the idea of the PM approximation and the general principles that explain why the period geometry of CY manifolds and their iterated periods integrals appear naturally in higher loop Feynman graph approximations to scattering amplitudes in any perturbative QFT and related physical problems. We will make a connection to the formalism of topological string theory on families of CY varieties.