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DTSTART;VALUE=DATE:20171107T171500
DTEND;VALUE=DATE:20171107T171500
UID:5769@agenda.unifr.ch
DESCRIPTION:What is the supremum density of a measurable set in $\mathbb R^n$ avoiding distance 1?\nIf the distance is the Euclidean distance, the answer is known only in  \nthe trivial case n = 1. This problem is closely related to that of the  \ndetermination of the chromatic number of the Euclidean space, a  \nsurprisingly difficult problem even in dimension 2, which is open  \nsince it was posed by Nelson and Hadwiger in 1950. We will discuss  \nrecent results obtained on this question and also on several variants  \nthat rely on a combination of methods from convex optimization and  \nFourier analysis.\nIn one of these variants, one replaces the Euclidean norm by a norm defined\nby a convex symmetric polytope. When the polytope tiles the space by  \ntranslations, we conjecture that the answer is $\mathbb 1/2^n$  and that the  \nproof should be much easier that in the Euclidean setting.\nWe will present a proof of this conjecture in dimension 2 and discuss  \na few other cases of Voronoi polytopes associated to lattices.
SUMMARY:Prof. Christine Bachoc (Bordeaux): sets avoiding the distance 1 in $\mathbb R^n$ 
CATEGORIES:Colloque / Congrès / Forum
LOCATION:PER 08\, Phys 2.52\, Chemin du Musée 3\, 1700 Fribourg
URL;VALUE=URI:https://agenda.unifr.ch/e/fr/5769
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