## Columbia Mathematics Department Colloquium

On the average rank of elliptic curves over function fields

by

# Ngô Bảo Châu

# (U. Chicago)

Abstract:

Some years ago, Bhargava and Shankar
proved a stunning result on the average rank of elliptic curves defined
over Q. With Ho Phu Quoc and Le Hung Viet Bao, we studied similar
questions over function fields. The geometric setup happens to be very
similar to that of the fundamental lemma.