THERMOGAMAS - Variants of the Mozes Theorem and Graph Subshifts (Léo Paviet Salomon)

Talk given during the THERMOGAMAS Workshop.

Abstract: This talk presents some variations on the "Mozes Theorem" [Mozes, 1989], which can be summarized as "Under mild conditions, substitutive subshifts are sofic". We present the different contexts in which similar statements hold: ℤ^d subshifts, ℝ^d subshifts, some Cayley graphs, Schreier graphs of automata groups... The two main goals of the talk are the following:

First, try to derive a meta-theorem, precising the "mild conditions" under which the theorem holds in all those contexts. We claim that they are mostly of combinatorial nature, and that the different variants of the theorem can then be proven in a very similar way.

Then, try to give another proof of this result, in a new setting: graph subshifts. We continue the work of [Arrighi, Durbec, Guillon, 2023] and try to define a model of substitutions on the relevant class of graphs; we finally obtain a (here stated informally) theorem which generalizes some of the previously known results:

If s is a sufficiently-connected graph-substitution, and X_s is the graph-subshift it generates, then the set of graph-coverings of X_s is sofic.