Title: p-torsion of curves in characteristic p

Rachel Pries, Colorado State University

Abstract: Understanding the p-torsion of Jacobians of curves in characteristic p is a fascinating problem in number theory that also has applications to cryptography. There are many open problems about the existence of curves whose p-torsion has given invariants such as p-rank, a-number, group scheme, or Newton polygon. In this talk, I will introduce these problems, explain some recent results of myself and others, and end with some questions of a computational nature.