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UID:6292@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20211021T110000
DTEND;TZID=Europe/Paris:20211021T120000
DTSTAMP:20241120T201356Z
URL:https://www.i2m.univ-amu.fr/evenements/recognizing-the-sato-tate-group
 -ug_2/
SUMMARY:David KOHEL (I2M\, Aix-Marseille Université): Recognizing the Sato
 -Tate group UG_2
DESCRIPTION:David KOHEL: The character method\, developed by Yih-Dar Shieh 
 in his thesis\, recognizes a Sato-Tate from an associated Frobenius distri
 bution. Previous algorithms used moments of coefficients of a characterist
 ic polynomial of Frobenius. The higher moments are degrees of the tensor p
 roduct characters\, which are direct sums with high multiplicities\, hence
  the moment sequences converge (slowly\, with sufficient precision) to lar
 ge integers. The character method replaces the moments with a precomputed 
 list of irreducible characters. From the orthogonality relations of charac
 ters\, a Sato-Tate group G is recognized by inner products yielding 0 or 1
  (for which only one bit of precision is required to determine its value).
 \nThe exceptional Lie group G_2\, or rather its unitary subgroup UG_2\, em
 beds as a subgroup of SO(7). We describe the character theory of orthogona
 l groups SO(2n+1)\, specialize the character theory method to UG_2\, and t
 o demonstrate its effectiveness with certain character sums associated to 
 abelian factors of families of Jacboaisn known to give rise to the Sato-Ta
 te group UG_2.\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/David_Kohel.jpg
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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