Séminaire Orléans

Entropy theory beyond amenable groups
Amos Nevo (Technion, Haifa)
Thursday 11 April 2019 14:00 -  Orléans -  Salle de Séminaires

Résumé :

In recent years, the classical theory of entropy for a dynamical system has been revolutionized by the ground-breaking work of Lewis Bowen and of Brandon Seward. Two definitions were proposed and developed for actions of general groups : sofic entropy (initiated by Bowen) and Rokhlin entropy (initiated by Seward). We will start with a very brief account of the latter, and then describe our own recently developed approach to entropy theory for probability-measure-preserving free actions of all countable groups. We will then formulate our main result, namely that orbital Rokhlin entropy satisfies a Shannon-McMillan-Breiman pointwise convergence theorem. We will demonstrate the geometric significance of this convergence theorem and its relation to the boundary of the group in the case of actions of free non-Abelian groups.

Liens :

• Indico