Résumé : 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