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Actions with some degree of hyperbolicity arise naturally in many mathematical contexts. Many natural problems reduce ti the classification of invariant measures or closed invariant sets. For instance, given a manifold equipped with an action by a large (not virtually-cyclic, though not necessarily higher-rank) group, under certain dynamical, geometric, or algebraic criteria on the action, one might hope to classify (1) all stationary or invariant measures and (2) all orbit closures for the action. In a geometrically related setting, given a partially hyperbolic diffeomorphism, one might ask when a u-Gibbs measure is necessarily SRB or when an equivariant foliation is necessarily minimal.
This workshop will bring together experts working in homogeneous dynamics, smooth hyperbolic dynamics, complex and arithmetic dynamics, and group actions to discuss new results and techniques related to the rigidity of invariant measures and orbit closures for hyperbolic group actions.