D04 Entropy, orbit equivalence, and dynamical tilings

This project will pursue the theme of deformation and rigidity in the context of ergodic theory and operator algebras, first of all by investigating the relationships between entropy, treeability, and orbit equivalence rigidity for actions of general classes of groups, and secondly by establishing tileability results for continuous actions of amenable groups under dimensionality conditions, with applications to the structure and classification theory of C*-algebras.