Speaker
Description
This goal of this talk is to review two equivalent constructions of polylogarithms on Riemann surfaces of arbitrary genus. In both cases, iterated integrals of explicitly known flat connections are combined into function spaces that close under integration over marked points. A first, string-theory inspired flat connection is built from single-valued but non-holomorphic one-forms on a genus-h surface that transform as tensors under the modular group Sp(2h, Z). An alternative flat connection comprising meromorphic but multivalued differentials was introduced in mathematical work of Enriquez through its functional properties and recently found explicit realizations. These two types of differentials exhibit striking parallels not only in their construction from convolution integrals but also in their algebraic relations and moduli variations.
