Entropy for sofic group actions

par Prof. Lewis BOWEN (University of Texas at Austin & IHÉS)

jeudi 10 juil. 2014, 11:00 → 12:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

In 1958, Kolmogorov defined the entropy of a probability measure preserving transformation. Entropy has since been central to the classification theory of measurable dynamics. In the 70s and 80s researchers extended entropy theory to measure preserving actions of amenable groups (Kieffer, Ornstein-Weiss). My recent work generalizes the entropy concept to actions of sofic groups; a class of groups that contains for example, all subgroups of GL(n,C). Applications include the classification of Bernoulli shifts over a free group. This answers a question of Ornstein and Weiss.