## Algebra Seminar

Title: Birch and Swinterton-Dyer Conjecture

Speaker: Saikat Biswas

Abstract:
According to the Mordell-Weil theorem, the rational points on an elliptic curve form a finitely generated abelian group. Determining the rank of this group is one of the oldest outstanding problems in mathematics. The Birch and Swinnerton-Dyer (BSD) Conjecture (as yet, unproven!) relates the rank of an elliptic curve to the order of vanishing of a certain L-function associated to the curve at a certain fixed point. In this talk, I shall present a brief overview of the BSD conjecture including the origins of the conjecture as well as progress made towards proving it.

PS: In 2000, the Clay Mathematics Institute chose the BSD conjecture as one of seven 'Millenium Problems' with the solution of each problem worth a million dollars!