Tim Dokchitser, University of Cambridge
The Birch and Swinnerton-Dyer and Parity Conjectures for Elliptic Curves

The purpose of this series of lectures is to give a self-contained introduction to the various Parity Conjectures for elliptic curves over number fields and the proofs of the ones that are known to be true. The structure of the course is roughly as follows:

1. Review of the Birch-Swinnerton-Dyer and the Parity Conjectures for elliptic curves over number fields; rank growth predictions forced by the root numbers.
2. Root numbers of elliptic curves, their classification and related recent results.
3. Local formulae for Selmer ranks.
4. Proof of the Parity Conjecture for Selmer ranks of elliptic curves over Q and over totally real fields; other results.

Everybody is welcome: no registration for participation is needed. The lectures will take place at the Centre de Recerca Matemātica. For more information about the schedule, contact with the organizers.  

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