Supersingular curves in Hurwitz families

Abstract: Despite extensive research, it is not known whether Oort's conjecture about the existence of supersingular curves is true or false. In the first part of the talk, I will describe supersingular curves and discuss the status of Oort's conjecture (both evidence for and counter-indications). In the second part of the talk, I will explain: new existence results for supersingular curves of low genus (joint work with Booher); and mass formulas for the number of supersingular curves in families (joint work with Cavalieri and Mantovan). This latter project generalizes the Eichler--Deuring mass formula for supersingular elliptic curves. If time permits, I will talk about basic reductions of genus four curves having an automorphism of order 5 (joint work with Li, Mantovan, Tang).

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