The rank of elliptic curves

Speaker: 
Benedict Gross
Date: 
Fri, Oct 10, 2014
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 

After quadratic equations in two variables come cubic equations, or elliptic curves. The set of rational points on an elliptic curve has the structure of a finitely generated abelian group. I will recall the basic theory of elliptic curves, then discuss the conjecture of Birch and Swinnerton-Dyer, which attempts to predict the rank of the group of rational points from the number of solutions (mod p) for all primes p. I will also discuss some recent results on the average rank, due to Manjul Bhargava and his collaborators. (PIMS-UBC Distinguished Colloquium)