D04 Entropy, orbit equivalence, and dynamical tilings

This project aims to advance the theory of rigidity and classification for Bernoulli actions of general groups with respect to orbit equivalence and its quantitative strengthenings. One overarching problem is to determine the extent to which the boundary between rigid and flexible behaviour is reflected in geometric or analytic properties of the group, and specifically, whether such properties intervene in questions of entropy invariance under Shannon orbit equivalence.