SFU Number Theory and Algebraic Geometry Seminar: Rachel Pries

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).