Mathematical Conversations

Originating in the work of Hadamard in the 1890’s on the coding of geodesic flow, symbolic dynamics has become a key tool for studying topological, smooth, and measurable dynamical systems. The automorphism group of a symbolic system capture its symmetries, reflecting the dynamical behavior and the complexity of the system. I will give an overview of relations among dynamical properties of the system, algebraic properties of the automorphism group, and measurable properties of associated systems, all of which quickly lead to open questions.