A short proof of the existence of strongly aperiodic subshifts over {0,1} in countable groups

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Date(s) - 11/04/2017
11 h 00 min - 12 h 00 min


A Theorem of Gao, Jackson and Seward, originally conjectured to be false by Glasner and Uspenskij, asserts that every countable group admits a strongly aperiodic subshift over a 2-symbol alphabet. Their proof consists of a quite technical construction. We give a shorter proof of their result by using the asymmetrical version of Lovasz Local Lemma which allows us also to prove that this subshift is effectively closed in the case of a finitely generated group with decidable word problem. This will all be preceded by a gentle introduction to symbolic dynamics.


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