Deformation, rigidity and classification results for group actions and von Neumann algebras

I will explain a new strategy for studying measure preserving
actions of groups on the probability space and their associated
von Neumann algebras ($II_1$ factors), which can be applied whenever some “mild” deformations and rigidity properties are met. A sample situation is when the action is by Bernoulli shifts and the acting group has infinite normal subgroups with the relative property (T).
Applications include strong rigidity results and precise computations of invariants for the actions and their $II_1$ factors.