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Subshifts, the emptiness problem and Lovász local lemma

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Authors : Aubrun, Nathalie (Author of the conference)
CIRM (Publisher )

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Abstract : Subshifts are set of colorings of a group by a finite alphabet that respect local constraints, given by some forbidden patterns ode m. The asymmetric version of Lovász local lemma reveals particularly useful to prove the existence of a coloring inside a subshift, i.e. a coloring that avoids all the forbidden patterns. In this talk I will present some sufficient conditions on the set of forbidden patterns to get at least one coloring. Then we will see as an application why every group possesses a strongly aperiodic subshift (joint work with Sebastián Barbieri and Stéphan Thomassé).

Keywords : symbolic dynamics; aperiodicity; Lovász local lemma

MSC Codes :
37B10 - Symbolic dynamics
37B50 - Multi-dimensional shifts of finite type, tiling dynamics
68R99 - None of the above but in this section

Additional resources :
https://www.cirm-math.fr/RepOrga/2696/Slides/slidesAubrun.pdf

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : French
    Available date : 11/04/2022
    Conference Date : 22/03/2022
    Subseries : Research talks
    arXiv category : Dynamical Systems ; Group Theory ; Discrete Mathematics
    Mathematical Area(s) : Combinatorics ; Computer Science
    Format : MP4 (.mp4) - HD
    Video Time : 00:54:36
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-03-22_N_Aubrun.mp4

Information on the Event

Event Title : ALEA Days / Journées ALEA
Event Organizers : Bouttier, Jérémie ; Miermont, Grégory ; Nadeau, Philippe
Dates : 21/03/2022 - 25/03/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2696.html

Citation Data

DOI : 10.24350/CIRM.V.19897403
Cite this video as: Aubrun, Nathalie (2022). Subshifts, the emptiness problem and Lovász local lemma. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19897403
URI : http://dx.doi.org/10.24350/CIRM.V.19897403

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