The Les Houches theory wishlist contains many challenging multi-loop processes. An important technical difficulty in the calculation of the virtual amplitudes is the evaluation of the Feynman integrals that depend on various scales, such as scattering angles and particle masses.
A key insight is that important properties of these functions can be predicted by inspecting the singularity structure of the Feynman integrand. Combined with the differential equations technique, this gives a powerful method for computing the necessary Feynman integrals. I will review these ideas, based on Phys.Rev.Lett. 110 (2013) 25, and present recent new results relevant for QCD scattering amplitudes.
