The London Mathematical Society Spitalfields Days are an opportunity for recent developments in specialist topics to be made known to the general mathematical community. This Spitalfields Day concerns the Birch and Swinnerton-Dyer conjecture, which describes a deep connection between the rank of an elliptic curve and the order of vanishing of an L-function. Particular attention will be paid to recent work which uses random matrix theory to make precise predictions for the ranks of families of elliptic curves.

**10:30 – 11:00**
- Coffee
**11:00 – 11:45**
- Bryan Birch and Peter Swinnerton-Dyer (Oxford/Cambridge) The origins of the Birch/Swinnerton-Dyer conjecture: some personal reminiscences
**12:00 – 12:45**
- Alice Silverberg (Ohio State University) Ranks of elliptic curves more info
**13:00 – 14:00**
- Lunch
**14:30 – 15:15**
- Christophe Delaunay (École Polytechnique Fédérale de Lausanne) Heuristics on Class groups and on Tate-Shafarevich groups more info
**15:30 – 16:15**
- Michael Rubinstein (University of Waterloo) Moments, L-values, and Ranks more info
**16:15 – 16:45**
- Tea
**16:45 – 17:30**
- Chantal David (Concordia University ) Vanishing of L-functions of elliptic curves over number fields more info
**17:30 – 18:30**
- Wine Reception

These lectures are linked to the Isaac Newton Institute programme on Random Matrix Approaches in Number Theory (26 January - 16 July 2004). Anyone interested is welcome to attend; talks will be aimed at a general mathematical audience. Please let Tracey Andrew at the Institute know by 23 January 2004 if you intend to come, to help us plan for lunch: telephone (01223) 335984; fax: (01223) 330508; e-mail: t.andrew@newton.ac.uk

There are limited funds available to assist research students to attend, please apply by 23 January 2004 to Tracey Andrew by email or post at the Newton Institute, 20 Clarkson Road, Cambridge, CB3 0EH.

Scientific enquiries may be addressed to Nina Snaith (e-mail: n.c.snaith@bristol.ac.uk)

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