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Covers dynamical techniques inspired by homogeneous dynamics including the use of Margulis functions to establish quantitative recurrence results; the use of random walks, inspired by work of Benoist and Quint, to prove measure rigidity statements; and the use of Zimmer's theory of the algebraic hull to prove finiteness results.","requirements_text":"Graduate/professional standing or declared in Mathematics VISP (graduate or dissertator)"}]