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TZID:Europe/Paris
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UID:6497@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210318T170000
DTEND;TZID=Europe/Paris:20210318T180000
DTSTAMP:20241120T201723Z
URL:https://www.i2m.univ-amu.fr/evenements/codes-from-families-of-varietie
 s-over-a-fixed-finite-field/
SUMMARY:Nathan Kaplan (University of California\, Irvine): Codes from famil
 ies of varieties over a fixed finite field
DESCRIPTION:Nathan Kaplan: How many of the $q^{10}$ homogeneous cubic polyn
 omials in $x\,y\,z$ with coefficients in $\\mathbb{F}_q$ define a cubic cu
 rve with a given number of points?  How many of the $q^{20}$ pairs of the
 se polynomials have exactly $k$ common zeros?  We will show how to phrase
  these kinds of questions in terms of the weight enumerators of projective
  Reed-Muller codes.  We will then see how ideas from the theory of error-
 correcting codes\, in particular the MacWilliams identity and its variatio
 ns\, can help answer them.\n\nResults from number theory and algebraic geo
 metry play an important role in modern coding theory\, but it is less comm
 on to see examples where ideas from coding theory are used to solve proble
 ms in number theory.  This talk will not assume any previous background i
 n coding theory.  We will start with the basics of coding theory and emph
 asize concrete examples.\n \n \nLien Zoom : https://univ-amu-fr.zoom.u
 s/j/92195848065?pwd=dEVoUmx1b1JUYTdERVZ1c1NPazN0QT09 \nMeeting ID : 921 9
 584 8065\nPasscode : voir mail\n\n \nSite : https://sites.google.com/vi
 ew/samuele-anni/home/s%C3%A9minaire-ati  \n \nDossier avec les vidéos
  et les présentations des exposés précédents : https://amubox.univ-am
 u.fr/s/dew3ycyHKDDcotZ  \n\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/02/Nathan_Kaplan.jpg
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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DTSTART:20201025T020000
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