# Elliptic curves and the conjecture of Birch and Swinnerton-Dyer.

**Date**: Monday 23 April 2018, 16:00 – 17:00**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Pure Mathematics Colloquium, Seminars, Pure Mathematics, Colloquia**Cost**: Free

#### Professor Sarah Zerbes, University College London. Part of the pure mathematics colloquium.

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 special cases.

The talks will be followed by a reception in the common room