HET-Discovery seminar: Claude Duhr

After reviewing the basic definitions and properties of elliptic polylogarithms, we introduce a class of elliptic generalisations of polylogarithms which can be seen as an elliptic generalisation of the notion of pure functions known from the non-elliptic case.

The definition is derived from the analysis of explicit results for two-loop elliptic Feynman integrals with up to 4 external legs. Once written in terms of pure functions, all these integrals have a remarkable simplicity, and in particular the results are of uniform transcendental weight. As a corollary of our construction, we find strong indications that the elliptic double-box that shows up in planar N=4 Super Yang-Mills at two loops is a pure function of uniform weight four, hinting towards the fact that the principle of maximal transcendentality extends to the elliptic sector of the theory.