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SUMMARY:Aaron Landesman (Harvard)
DTSTART:20211102T203000Z
DTEND:20211102T213000Z
DTSTAMP:20260423T125735Z
UID:MITNT/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/37/">T
 he geometric distribution of Selmer groups of Elliptic curves over functio
 n fields</a>\nby Aaron Landesman (Harvard) as part of MIT number theory se
 minar\n\nLecture held in Room 2-143 in the Simons building.\n\nAbstract\nB
 hargava\, Kane\, Lenstra\, Poonen\, and Rains proposed heuristics for the 
 distribution of arithmetic data relating to elliptic curves\, such as thei
 r ranks\, Selmer groups\, and Tate-Shafarevich groups.\nAs a special case 
 of their heuristics\, they obtain the minimalist conjecture\, which predic
 ts that $50\\%$ of elliptic curves have rank $0$ and $50\\%$ of elliptic c
 urves have rank $1$. \nAfter surveying these conjectures\, we will explain
  joint work with Tony Feng and Eric Rains\, \nverifying a variant of these
  conjectures over function fields of the form $\\mathbb F_q(t)$\, after ta
 king a certain large $q$ limit.\n
LOCATION:https://researchseminars.org/talk/MITNT/37/
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