Abstract : Deciding whether two one-dimensional subshifts are conjugate remains one of the most important question in symbolic dynamics. In this talk, we will highlight a new approach, using the diagrammatic calculus approach popular in category theory and especially in categorical quantum mechanics. We will explain how matrices (and subshifts of finite type) can be represented graphically and how this representation may help us find new conjugacy invariants.

Keywords : symbolic dynamics; monoidal categories