Back to Departmental Colloquium: Spring 2016
Departmental Colloquium
Date: Tuesday, Jan 12, 2016
Time: 4:00PM
Location: LCB 219
*Tuesday*
Arul Shankar
Harvard University
Title |
The average rank of elliptic curves |
Abstract |
It is a classical result of Mordell that the rational points on an elliptic curve form a finitely generated abelian group. The rank of an elliptic curve is the rank of the corresponding finitely generated abelian group. A conjecture, due to Goldfeld and Katz-Sarnak, asserts that the average rank of elliptic curves over Q is equal to 1/2. However, it was previously not known that the average rank was even finite. We will prove that the average rank is finite, and in fact less than 1. This is joint work with Manjul Bhargava. |
Mathematical Biology