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Abstract:
The Birch and Swinnerton-Dyer conjecture, one of the millenium problems,
is a bridge between algebraic invariants of an elliptic curve and its
(complex analytic) L-function. In the case of low ranks, we prove this
conjecture up to the finitely many bad primes and the prime 2, by proving
the Iwasawa main conjecture in full generality. The ideas in the proof and
formulation also lead us to new and mysterious phenomena. This talk
assumes no specialized background in number theory.
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