Prof. Dr. John Coates, Cambridge
The Conjecture of Birch and Swinnerton-Dyer
The conjecture of Birch and Swinnerton-Dyer is one of the principal open problems in number theory today. It can be viewed as the analogue for elliptic curves of Dirichlet's celebrated class number formular. In my lecture, I will give a brief account of the history related to the conjecture, and recall its precise statement. Then I will discuss some of the partial results proven in the direction of the conjecture, including some recent ones.