Elliptic curves and the conjecture of Birch and Swinnerton-Dyer
Vortrag von Prof. Dr. Sarah Zerbes Datum: 08.02.17 Zeit: 14.30 - 15.10 Raum: Y27H28
Abstract: An important problem in number theory is to understand the rational solutions to algebraic equations. One of the first non-trivial examples, cubics in two variables, leads to the theory of so-called elliptic curves. The famous Birch—Swinnerton-Dyer conjecture, one of the Clay Millenium Problems, predicts a relation between the rational points on an elliptic curve and a certain complex-analytic function, the L-function on an elliptic curve. In my talk, I will give an overview of the conjecture and of some new results establishing the conjecture in certain cases.