Speaker: Johannes Broedel

Title:Higher-genus special functions for sophisticated Feynman calculations

Abstract: While polylogarithms — understood as iterated integrals on the compactified complex plane — are the backbone of modern amplitude calculations, it pays off to to consider polylogarithms defined on elliptic and higher manifolds: in this way, various parameters of the scattering amplitude can be related to the geometry of the underlying manifold. I will show, how the underlying geometry affects and implies available algebraic and analytic tools for classes of polylogarithmic functions defined on Riemann surfaces of various genera. In particular, I will discuss how to express higher-genus polylogarithms in terms of well-known elliptic polylogarithms. This language, which utilizes the so-called Kronecker function, can be employed to numerically evaluate higher-genus polylogarithms, thus allowing their use in sophisticated Feynman calculations.