Average Ranks of Elliptic Curves after $p$-Extension

Abstract: As $E$ varies among elliptic curves defined over the rational numbers, a theorem of Bhargava and Shankar shows that the average rank of the Mordell--Weil group $E(\mathbb{Q})$ is bounded. If we fix a number field $K$, it is natural to then ask: is the average rank of $E(K)$ also bounded in this family? Moreover, how does the average rank of $E(K)$ depend on $K$? This talk will discuss recent progress on these questions for a restricted set of $K$.

number theory

Audience: researchers in the discipline

POINT: New Developments in Number Theory

Series comments: There will be two 20-minute contributed talks during each meeting aimed at a general number theory audience, including graduate students.

Participants are welcome to stay following the talks to have further discussions with the speakers or meet other audience members.

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