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SUMMARY:From the order of vanishing of $L$-function of elliptic curves to 
 the universal main conjecture for eigencuspforms and back - Olivier Fouque
 t (Université de Franche-Comté)
DTSTART:20220629T150000Z
DTEND:20220629T160000Z
UID:TALK174467@talks.cam.ac.uk
DESCRIPTION:In the early 1960s\, B. Birch and P. Swinnerton-Dyer formulate
 d a bold conjecture stating that the order of vanishing of the $L$-functio
 n of a rational elliptic curve at $s=1$ is equal to the rank of its group 
 of rational points. In this talk\, we explain how to prove that one of the
 se number is equal to zero if and only if the other is and why the proof r
 equires (at present\, at least) a very long detour through Iwasawa theory 
 of universal deformation spaces. This is joint work with X. Wan.
LOCATION:Seminar Room 2\, Newton Institute
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