Construction of elliptic curves of large rank

Abstract: In this talk, I will first prove Néron's theorem and explain how we can use it as a basis to construct elliptic curves of large rank. Then, I will discuss two methods for constructing elliptic curves of rank at least 9 and one method for constructing elliptic curves of rank at least 10. If there is more time, I will discuss approaches for generating elliptic curves of rank at least $ 11$.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.