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DTSTAMP:20250813T200059Z
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	\n	Poonen and Stoll developed a beautiful model for the be
 haviours of $p$-Selmer groups of elliptic curves\, and gave heuristics for
  all moments 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 cur
 ves is bounded above by 15 (which is the constant predicted by Poonen--Sto
 ll).The Goldfeld and Katz--Sarnak conjectures predict that 50% of elliptic
  curves have rank 0\, that 50% have rank 1\, and that the average rank of 
 elliptic curves is 1/2 (the remaining 0% of elliptic curves not interferin
 g in the average). Successive works of Brumer\, Heath-Brown\, and Young\, 
 have approached this problem by studying the central values of the L funct
 ions of elliptic curves. In this talk\, we will take an algebraic approach
 \, in which we study the ranks of elliptic curves via studying their Selme
 r groups.\n	\n	Poonen and Stoll developed a beautiful model for the behaviou
 rs of $p$-Selmer groups of elliptic curves\, and gave heuristics for all m
 oments 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
  bounded 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:/mathstat/channels/event/arul-shankar-university-t
 oronto-345517
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