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The rank of elliptic curves

Speaker: Benedict Gross

Date: Fri, Oct 10, 2014

Location: PIMS, University of British Columbia

Conference: PIMS/UBC Distinguished Colloquium

Subject: Mathematics, Number Theory

Class: Scientific

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)