The boundedness of the average rank of elliptic curves
Princeton University, U.S.A.
The purpose of this talk is to prove that the average rank of elliptic curves when ordered by their heights is bounded. This is accomplished by bounding the mean size of the 2- and 3-Selmer groups of elliptic curves. As a consequence we deduce that a positive proportion of elliptic curves, when ordered by height, have rank 0. This is joint work with Professor Manjul Bhargava.