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UID:20250813T003102EDT-4104UwPna0@132.216.98.100
DTSTAMP:20250813T043102Z
DESCRIPTION:Title: Sums of two cubes.\n\nAbstract: I'll give an overview of
  recent work with Alpoge-Bhargava showing that at least 10/21 (resp. 1/6) 
 of integers are (resp. are not) a sum of two rational cubes. To prove this
 \, we first show that the average size of the 2-Selmer group in any cubic 
 twist family of elliptic curves is 3\, by reducing to a certain counting p
 roblem: count integral G-orbits in a G-invariant quadric inside V\, where 
 G = SL_2^2 and V is the space of pairs of binary cubic forms. To perform t
 he lattice point count\, we combine tools from geometry of numbers and the
  circle method.  My talk will focus on the more algebraic aspects of the p
 roblem\, e.g.: how one reduces to the counting problem\, and how one deduc
 es the results about sums of two cubes from the Selmer average result. If 
 I have time\, I'll explain a result for cubic twist families of higher dim
 ensional abelian varieties as well.\n
DTSTART:20221027T143000Z
DTEND:20221027T160000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Ari Shnidman (Hebrew University of Jerusalem)
URL:/mathstat/channels/event/ari-shnidman-hebrew-unive
 rsity-jerusalem-342993
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