ICTS

The Birch and Swinnerton-Dyer conjecture, one of the millenium problems, is a bridge between the algebra and the analysis of elliptic curves. (Here is an elliptic curve: y^2=x^3+1.) In one sentence, the conjecture says that L-function associated to an elliptic curve should know 'everything' about the rational points on it. Other than explaining what the L-function is, we will discuss what is known about the conjecture, and how we can attack it one prime at a time. This talk assumes no specialized background in number theory.