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# Shahed Sharif : Who wants to be a millionaire?

The Mordell-Weil theorem shows that the rational points on an elliptic curve defined over the field of rational numbers is a finitely generated abelian group. The Birch and Swinnerton-Dyer conjecture relates the rank of this group to a number of analytic and algebraic invariants of the curve. (More generally it considers an elliptic curve defined over a number field.) The conjecture is one of the Millennium Prize problems and the Clay Institute is offering a reward of 1 million dollars for a solution. This talk will be an introduction to the conjecture. In following weeks we will have lectures explaining each of the terms in the formula.

**Category**: Applied Math and Analysis**Duration**: 01:34:53**Date**: November 23, 2009 at 4:25 PM**Views**: 93-
**Tags:**seminar, Elliptic Curves Working Seminar

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