A one-dimensional subshift of finite type is a set of bi-infinite words defined by a finite set of forbidden subwords. This may represent the inherent constraints of a communication channel (such as the impossibility of sending two consecutive 1-bits). The automorphism group of a subshift of finite type turns out to be mathematically an incredibly rich object, for instance its subgroups show a wide variety of behaviors. The project studies to what extent this purely algebraic object remembers the constraints, aiming at generalizing a famous theorem of Rubin to cover this situation. More generally, the project attempts to shed light on the structure of the automorphism group.

2026

2030