Australian Mathematical Society
Mathematics Department at Macquarie University

AMS Medal George Szekeres Medal B H Neumann Prize

Homepage Conference Detail and Conference Bag Enquiries
Welcome Party Opening Ceremony Timetable Conference Dinner
Academic Program Plenary Talks Special Sessions Abstracts
Organizing Committee Program Committee Book Launch Subject Review
Education Afternoon Book Display and Software Demonstration Important Deadlines
Local Information Social Program Registration Accommodation

 

50th Annual Meeting of the Australian Mathematical Society

Plenary Talk in Macquarie Theatre

Thursday 28 September 2006 at 10:00

 

Christopher Skinner (University of Michigan)

 

What Do We Know about the Birch-Swinnerton-Dyer (and Related) Conjectures?

 

The Birch-Swinnerton-Dyer conjecture (BSD) predicts that the order of vanishing at s=1 of the L-function L(E,s) of an elliptic curve E is equal to the rank of the group of rational points on E and that the first non-zero Taylor series coefficient around s=1 can be expressed in terms of various number-theoretic information about E. Today, this is just one conjecture in a vast array of conjectures about special values of L-functions (with the names Deligne, Beilinson, Bloch-Kato, ... attached). This talk will be a survey of some of the things we know about BSD and related conjectures for modular forms, focusing on recent results making use of Shimura varieties for groups other than GL2.