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Explore recent advances in the classification of higher-rank semisimple group actions through this mathematical seminar lecture from the Institute for Advanced Study. Delve into Kurt Vinhage's research on partially hyperbolic actions of semisimple Lie groups, building upon Zimmer's foundational work from the 1980s that established rigidity results for associated cocycles in measurable categories. Learn about cutting-edge progress in classifying such actions when uniformly expanding and contracting directions are present, drawing from collaborative research with D. Damjanovic, R. Spatzier, and D. Xu. Gain insights into the intersection of dynamical systems theory and Lie group theory as presented in this joint IAS/Princeton University Groups and Dynamics Seminar, suitable for graduate students and researchers in mathematics focusing on group actions, dynamical systems, and geometric group theory.