Seminar: What is ... Hurwitz Theory?

Abstract: Hurwitz theory is about counting holomorphic maps from Riemann surfaces to a fixed target Riemann surface. The goal is to count all such maps that satisfy an appropriate list of conditions. In this talk I will explain what this means, and how it ties together complex analysis, representation theory, topology, and given time, even other exotic ideas like tropical geometry.


Topics/Background: Really just a bit of complex analysis and definition of the symmetric group. Some covering space theory from topology is useful.