New directions in entropy theory

Speaker
Amos Nevo, the Technion
Date
10/03/2019 - 13:00 - 12:00Add to Calendar 2019-03-10 12:00:00 2019-03-10 13:00:00 New directions in entropy theory In recent years, the classical theory of entropy for a dynamical system has been revolutionized by the ground-breaking work of several researchers. Two definitions were proposed and developed for actions of general groups : sofic entropy (initiated by L. Bowen)  and Rokhlin entropy (initiated by B. Seward).  We will start with a very brief account of the latter, and then describe our own recently developed approach to entropy theory for free probability-measure-preserving actions of all countable groups.  We will then formulate our main result, namely that Rokhlin entropy  satisfies a Shannon-McMillan-Breiman pointwise convergence theorem. We will demonstrate the geometric significance of this convergence theorem in the case of actions of free non-Abelian groups     Based on joint work with F. Pogorzelski (Leipzig University).  Department Seminar Room 216/201 אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Department Seminar Room 216/201
Abstract

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

    Based on joint work with F. Pogorzelski (Leipzig University). 

Last Updated Date : 04/03/2019