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SUMMARY:David Zywina
DTSTART:20260317T203000Z
DTEND:20260317T213000Z
DTSTAMP:20260419T151332Z
UID:BC-MIT/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/32/">
 Elliptic curves of low rank</a>\nby David Zywina as part of BC-MIT number 
 theory seminar\n\nLecture held in Maloney 560 at Boston College.\n\nAbstra
 ct\nFor an elliptic curve $E$ over a number field $K$\, the set $E(K)$ of 
 $K$-points is a finitely generated abelian group whose rank is an importan
 t/mysterious invariant.  It is an open and difficult problem to determine 
 which ranks occur for elliptic curves over a fixed number field $K$. We wi
 ll discuss recent work which shows that there are infinitely many elliptic
  curves over $K$ of rank $r$ for each integer $0 \\leq r \\leq 4$.   We wi
 ll construct our curves by specializing well-chosen nonisotrivial families
 .  We will use a result of Kai\, which generalizes work of Green\, Tao and
  Ziegler to number fields\, to carefully choose our curves in the families
 .\n
LOCATION:https://researchseminars.org/talk/BC-MIT/32/
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