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SUMMARY:Gabor Somlai (Eotvos Lorand University and   Alfred Renyi Institut
 e of Mathematics)
DTSTART:20220525T133000Z
DTEND:20220525T135500Z
DTSTAMP:20260423T011437Z
UID:CANT2022/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/17/
 ">Fuglede's conjecture\, the one dimensional case</a>\nby Gabor Somlai (Eo
 tvos Lorand University and   Alfred Renyi Institute of Mathematics) as par
 t of Combinatorial and additive number theory (CANT 2022)\n\n\nAbstract\nF
 uglede conjectured that a bounded measurable set (in $\\mathbb{R}^n$) is s
 pectral if and only if it is a tile. The conjecture was also confirmed by 
 Fuglede for sets whose tiling complement is lattice and for spectral sets 
 one of whose spectrums is a lattice. \nThe conjecture was disproved by Tao
  by constructing a spectral set in $\\mathbb{Z}_3^5$\, which is not a tile
  and lifted it to the $5$ dimensional Euclidean space. \n\nThe conjecture 
 is open only in dimensions 1 and 2. The 1 dimensional case is directly con
 nected with the one of finite cyclic groups and to the so called Coven-Mey
 erowitz conjecture. One of the main aims of the talk is to present some of
  the methods developed that lead to our recent results.\n
LOCATION:https://researchseminars.org/talk/CANT2022/17/
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