Speaker
Description
Multiple polylogarithms at genus zero are by themselves multi-valued functions but can be completed to single-valued polylogarithms by adding suitable combinations of their complex conjugates and multiple zeta values. As a generalization to genus one, this talk presents an explicit construction of single-valued elliptic polylogarithms depending on one point on the torus where the monodromies from the homology cycles and the singular point at the origin cancel. The construction is carried out at the level of Lie-algebra valued generating series where the combinations of elliptic polylogarithms, their complex conjugates and (elliptic) multiple zeta values are controlled by certain operations on the generators. The series in single-valued polylogarithms at genus zero and genus one exhibit striking parallels since the appearance of multiple zeta values is controlled by the action of so-called zeta generators on the Lie-algebra setup of both cases.