时 间：2014年11月10日 15:00-16:00
题 目：Congruent numbers and elliptic curves
A thousand years old problem is to determine which positive integers are congruent numbers, i.e. those numbers which could be the areas of right angled triangle with sides of rational lengths. This problem has some beautiful connections with elliptic curves and L-functions. In fact by the Birch and Swinnerton-Dyer conjecture, all n= 5, 6, 7 mod 8 should congruent numbers, and most of n=1, 2, 3 mod 8 should not not congruent numbers. In this lecture, I will explain these connections and then some recent progress.