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UID:7309@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180524T110000
DTEND;TZID=Europe/Paris:20180524T120000
DTSTAMP:20241120T203907Z
URL:https://www.i2m.univ-amu.fr/evenements/reseaux-ayant-beaucoup-de-vecte
 urs-minimaux/
SUMMARY:Serge Vladuts (I2M\, Aix-Marseille Université): Réseaux ayant bea
 ucoup de vecteurs minimaux
DESCRIPTION:Serge Vladuts: We construct a sequence of lattices $\\{L_{n_i}\
 \subset\\mathbb{R}^{n_i}\\}$ for $n_i\\longrightarrow \\infty$\, with expo
 nentially large kissing numbers\, namely\, $\\log_2 \\tau(L_{n_i})/n_i &gt
 \; 0.0338 - o(1)$. We also show that the maximum lattice kissing number $ 
 \\tau^l(n)$ in $n$ dimensions verifies $\\lim\\inf \\log_2\\tau^l(n)/n \\g
 e 0.0219$. Before our work the best known bound was quasipolynomial\, $\\t
 au^l(n) = \\Omega( n^{c\\log_2 n})$.\n\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Serge_Vladuts.jpg
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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DTSTART:20180325T030000
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