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SUMMARY:Congruent numbers - John Coates (Cambridge)
DTSTART:20130219T161500Z
DTEND:20130219T171500Z
UID:TALK42679@talks.cam.ac.uk
CONTACT:Teruyoshi Yoshida
DESCRIPTION:The congruent number problem is the oldest unsolved major prob
 lem in number\ntheory\, and\, in retrospect\, the simplest and most down t
 o earth example of the conjecture of Birch and Swinnerton-Dyer. After a br
 ief description of the history\nof the problem\, I shall discuss Y. Tian
 ’s beautiful recent extension to composite\nnumbers\, with arbitrarily m
 any prime factors\, of Heegner’s original proof of the\nexistence of in
 finitely many congruent numbers. I hope also to say a little at the\nend 
 about possible generalizations of Tian’s work to other elliptic curves.
LOCATION:MR14
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