Automorphism groups of Riemann surfaces

Abstract: 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.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca