A short proof of the existence of strongly aperiodic subshifts in countable groups
Résumé : 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.