Sofic entropy and surjunctive dynamical systems

Abstract: A dynamical system is a pair \((X,G)\), where \(X\) is a compact metrizable space and \(G\) is a countable group acting by homeomorphisms of \(X\). An endomorphism of \((X,G)\) is a continuous selfmap of \(X\) which commutes with the action of \(G\). A dynamical system \((X, G)\) is said to be surjunctive if every injective endomorphism of \((X,G)\) is surjective. When the group \(G\) is sofic, the combination of suitable dynamical properties (such as expansivity, nonnegative sofic topological entropy, weak specification, and strong topological Markov property) guarantees that (X,G) is surjunctive. I'll explain in detail all notions involved, the motivations, and outline the main ideas of the proof of this result obtained in collaboration with Michel Coornaert and Hanfeng Li.

algebraic topologyfunctional analysisgroup theorygeometric topologyoperator algebras

Audience: researchers in the topic

Vienna Geometry and Analysis on Groups Seminar