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

par Sebastián Barbieri (ENS Lyon)

mardi 7 mars 2017, 10:45 → 11:45 Europe/Paris

salle Fokko du Cloux (ICJ, UCBL - La Doua, Bât. Braconnier)

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. This is joint work with Nathalie Aubrun and Stéphan Thomassé.