Céline Maistret

Elliptic curves and the Birch and Swinnerton-Dyer conjecture

The Diophantine equations associated to elliptic curves are very particular and important objects in Number Theory. In this talk, I will present these equations, explain their importance and what stops us from systematically solving them. This will naturally lead me to discuss the Birch and Swinnerton-Dyer conjecture, one of the Clay Mathematics Institute’s Millenium problems, which is the key to their solutions and much more. I will explain the origin of the conjecture and present some related recent progress.