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.
- Applied Math and Analysis ( 90 Views )