Entropy and determinants for unitary representations

Understand

Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups.

• These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of the group, and Bowen's sofic entropy for sofic groups.
• In this work we pursue these notions across an analogy between ergodic theory and representation theory.
• We arrive at new quantities associated to unitary representations of groups and representations of other C*-algebras.