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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: Numerical evidence for the BSD Conjecture

Presented by John Cremona, Warwick University

5 March 2012 16:00 in CM221

The Birch Swinnerton-Dyer Conjectures assert a link between two
invariants of elliptic curves, one algebraic and one analytic.
Despite 50 years of effort, some partial results of breathtaking
ingenuity (and difficulty) and a prize of a million follars offered by
the Clay Mathenatics Institute, the conjectures remain wide open in
general. Even to verify the conjectures for individual curves is a
non-trivial task which relies on deep theoretical results: how do you
verify a formula predicting the order of a group when you can neither
prove that the group is finite, nor that the number giving the
conjectural order is even rational?

In the talk, which will assume no prior knowledge of the subject, I
will describe the conjectures, what is known, and report on some
large-scale numerical evidence for over 1.4 million curves.

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