REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

Vasilisa Shramchenko

ABSTRACT:  Hurwitz spaces are moduli spaces of functions on Riemann surfaces, or moduli spaces of ramified coverings of the Riemann sphere. They can also be seen as spaces of certain deformations of complex structures. In this talk I will discuss in detail the structure of the Hurwitz spaces and show how various objects defined on Riemann surfaces depend on the variations of the underlying complex structure arising in the framework of Hurwitz spaces.