SFU Number Theory and Algebraic Geometry Seminar: Jen Paulhus

A well-known result on compact Riemann surfaces says that the automorphism group of any such surface is a finite group of bounded size (based on the genus of the surface). Additionally, the Riemann-Hurwitz formula gives us an expectation for when a particular group should be the automorphism group of a Riemann surface of a particular genus. There has been a lot of work over the last 20 years to classify which groups show up for a given genus. This talk will introduce the core ideas in the field, explain the connection with curves over number fields, and talk about recent results to classify groups which are indeed automorphisms in just about every genus they should be. We’ll also make a surprising connection to simple groups.