Functions in Scattering Amplitudes: From QFT to Gravitational Waves

Multi-loop Feynman integrals for collider physics are known to contain intricate geometries and to evaluate to complicated transcendental numbers and functions. After an introduction to how those arise in Quantum Field Theory, I will investigate Feynman integrals contributing to the emission of gravitational waves in classical gravity. I will provide a full classification of the contributing Feynman integrals up to fifth order in the post-Minkowskian expansion, identifying new geometries that lead to new transcendental functions. Moreover, I will demonstrate how the corresponding differential equations can be solved by bringing them into canonical form.