The Department of Mathematics & Statistics would like to welcome:
Steffan Marcus, on Friday, December 6th, at 11:30 am, in SCP 229.
Title: Moduli spaces and Hurwitz theory: counting covers of curves using ideas from mathematical physics
Abstract: A moduli space solves a classification problem for some collection of other mathematical objects, giving us the opportunity to study the “universe” of objects we care about as a geometric space. In this talk I will describe how moduli spaces can be constructed and how mathematicians might use them. We will discuss some moduli space constructions that are inspired by problems in string theory, but have found use in new approaches to classical questions in geometry and combinatorics. Finally, I will present such an application to counting certain finite covers of the sphere — generalizing a problem originally posed by Hurwitz in 1891. Along the way we may spend a good amount of time thinking about triangles.