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DTSTART:20230312T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20231205T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-108
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:ARUL SHANKAR\, UNIVERSITY OF TORONTO\n\n\"SECONDARY TERMS IN TH
 E FIRST MOMENT OF THE 2-SELMER GROUPS OF\nELLIPTIC CURVES\"\n\nRanks of el
 liptic curves are often studied via their 2-Selmer groups.\nIt is known th
 at the average size of the 2-Selmer group of elliptic\ncurves is 3\, when 
 the family of all elliptic curves is ordered by\n(naive) height. On the co
 mputational side\, Balakrishnan\, Ho\, Kaplan\,\nSpicer\, Stein\, and Wei
 gand collect and analyze data on ranks\, 2-Selmer\ngroups\, and other arit
 hmetic invariants of elliptic curves\, when\nordered by height. Interestin
 gly\, they find a persistently smaller\naverage size of the 2-Selmer group
  in the data. Thus it is natural to\nask whether there exists a second ord
 er main term in the counting\nfunction of the 2-Selmer groups of elliptic 
 curves. In this talk\, I\nwill discuss joint work with Takashi Taniguchi\,
  in which we prove the\nexistence of such a secondary term.\n\nMC 5501
DTSTAMP:20260505T133123Z
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