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DTSTAMP:20260405T064838Z
DESCRIPTION:Title: The distribution of Selmer groups of elliptic curves\n\n
 Abstract: The Goldfeld and Katz--Sarnak conjectures predict that 50% of el
 liptic curves have rank 0\, that 50% have rank 1\, and that the average ra
 nk of elliptic curves is 1/2 (the remaining 0% of elliptic curves not inte
 rfering in the average). Successive works of Brumer\, Heath-Brown\, and Yo
 ung\, have approached this problem by studying the central values of the L
  functions of elliptic curves. In this talk\, we will take an algebraic ap
 proach\, in which we study the ranks of elliptic curves via studying their
  Selmer groups.\n	Poonen and Stoll developed a beautiful model for the beha
 viours of $p$-Selmer groups of elliptic curves\, and gave heuristics for a
 ll moments of the sizes of these groups. In this talk\, I will describe jo
 int work with Manjul Bhargava and Ashvin Swaminathan\, in which we prove t
 hat the second moment of the size of the 2-Selmer groups of elliptic curve
 s is bounded above by 15 (which is the constant predicted by Poonen--Stoll
 ).The Goldfeld and Katz--Sarnak conjectures predict that 50% of elliptic c
 urves have rank 0\, that 50% have rank 1\, and that the average rank of el
 liptic curves is 1/2 (the remaining 0% of elliptic curves not interfering 
 in the average). Successive works of Brumer\, Heath-Brown\, and Young\, ha
 ve approached this problem by studying the central values of the L functio
 ns of elliptic curves. In this talk\, we will take an algebraic approach\,
  in which we study the ranks of elliptic curves via studying their Selmer 
 groups.\n	Poonen and Stoll developed a beautiful model for the behaviours o
 f $p$-Selmer groups of elliptic curves\, and gave heuristics for all momen
 ts of the sizes of these groups. In this talk\, I will describe joint work
  with Manjul Bhargava and Ashvin Swaminathan\, in which we prove that the 
 second moment of the size of the 2-Selmer groups of elliptic curves is bou
 nded above by 15 (which is the constant predicted by Poonen--Stoll).\n
DTSTART:20230127T203000Z
DTEND:20230127T213000Z
LOCATION:Room 1205\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Arul Shankar (University of Toronto)
URL:https://www.mcgill.ca/channels/channels/event/arul-shankar-university-t
 oronto-345517
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