EVENT DETAILS AND ABSTRACT

Title: The average 5-Selmer rank of elliptic curves
Speaker: Arul Shankar
Speaker Info: Harvard
Brief Description:
Special Note:
Abstract:

We use geometry-of-numbers techniques to show that the average size of the 5-Selmer group of elliptic curves is equal to 6. From this, we deduce an upper bound on the average rank of elliptic curves. Then, by constructing families of elliptic curves with equidistributed root number we show that the average rank is less than 1. This is joint work with Manjul Bhargava.