EVENT DETAILS AND ABSTRACT

Title: Hurwitz spaces
Speaker: Chitrabhanu Chaudhuri
Speaker Info: Northwestern University
Brief Description:
Special Note:
Abstract:

I shall explore spaces that parametrize branched covers of the Riemann sphere of fixed degree d, by riemann surfaces of a fixed genus g. The spaces (schemes) are called Hurwitz spaces (schemes) after Hurwitz who first studied them. We shall see how these spaces get a natural complex structure and are covering spaces of suitable configuration spaces of the sphere. We shall also explore the monodromy action of the fundamental group of the configuration space on the Hurwitz space to deduce they are connected which gives a simple proof that M_g is irreducible for every g. I shall only assume basic complex analysis and covering space theory so it should appeal to a wide audience.