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SUMMARY:Alex Smith (Stanford)
DTSTART:20220203T220000Z
DTEND:20220203T230000Z
DTSTAMP:20260423T022807Z
UID:UCSD_NTS/54
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/54/
 ">$2^k$-Selmer groups and Goldfeld's conjecture</a>\nby Alex Smith (Stanfo
 rd) as part of UCSD number theory seminar\n\nLecture held in APM 6402 and 
 online.\n\nAbstract\nTake $E$ to be an elliptic curve over a number field 
 whose four torsion obeys certain technical conditions. In this talk\, we w
 ill outline a proof that 100% of the quadratic twists of $E$ have rank at 
 most one. To do this\, we will find the distribution of $2^k$-Selmer ranks
  in this family for every positive $k$. We will also show how are techniqu
 es may be applied to find the distribution of $2^k$-class groups of quadra
 tic fields.\n\nThe pre-talk will focus on the definition of Selmer groups.
  We will also give some context for the study of the arithmetic statistics
  of these groups.\n\npre-talk at 1:20pm\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/54/
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