- Series
- Athens-Atlanta Number Theory Seminar
- Time
- Tuesday, October 28, 2025 - 5:15pm for 1 hour (actually 50 minutes)
- Location
- Emory, Mathematics and Science Center, W303
- Speaker
- David Zywina – Cornell University – zywina@math.cornell.edu – https://pi.math.cornell.edu/~zywina/
- Organizer
- Raman Parimala
Consider an elliptic curve $E$ defined over a number field $K$. The set of $K$-points of $E$ is a finitely generated abelian group $E(K)$ whose rank is an important invariant. It is an open and difficult problem to determine which ranks occur for elliptic curves over a fixed number field $K$. We will discuss recent work which shows that there are infinitely many elliptic curves over $K$ of rank $r$ for each integer $0\leq r \leq 4$. Our curves will be found in some explicit families. We will use a result of Kai, which generalizes work of Green, Tao and Ziegler to number fields, to carefully choose our curves in the families.