Function Theory for Multiloop Feynman Integrals

Precise predictions for collider observables require the computation of higher orders in perturbation theory. This usually involves the evaluation of complicated multiloop integrals, which typically give rise to complicated special functions. In this contribution we discuss recent progress in understanding the mathematics underlying multiloop Feynman integrals. We review a class of functions that generalises the logarithms and that often appears in multiloop computations. The same class of functions is an active area of research in modern mathematics. This has led to the development of new powerful tools to compute Feynman integrals, and these tools are at the heart of some of the most complicated computations ever performed for a hadron collider.