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SUMMARY:Pierre Guillon (CNRS/Marseille)
DTSTART:20230418T130000Z
DTEND:20230418T150000Z
DTSTAMP:20260423T041009Z
UID:WienGAGT/34
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WienGAGT/34/
 ">Decidability and symbolic dynamics over groups</a>\nby Pierre Guillon (C
 NRS/Marseille) as part of Vienna Geometry and Analysis on Groups Seminar\n
 \n\nAbstract\nShifts of finite type are sets of biinfinite words (sequence
 s of colors from a finite alphabet indexed in \\(\\mathbb{Z}\\)) that avoi
 d a finite collection of finite patterns. Their dynamical properties are v
 ery well understood thanks to their representation by matrices or finite g
 raphs. When changing \\(\\mathbb{Z}\\) into \\(\\mathbb{Z}^2\\)\, the defi
 nition stays coherent\, but most classical dynamical properties or invaria
 nts become intractable\; one way to understand this is to consider this ob
 ject as a computational model\, capable of some algorithmic behavior. <br 
 /> Now\, when changing \\(\\mathbb{Z}^2\\) into any finitely generated gro
 up\, it is not completely clear when the behavior is close to that of \\(\
 \mathbb{Z}\\) or to that of \\(\\mathbb{Z}^2\\). I will try to give some i
 ntuition on this open problem\, survey what is known\, and sketch some ide
 as that could help approach a solution.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/34/
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