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Explore measure rigidity in higher rank lattice actions through this concluding lecture of a three-part mini-course delivered by Homin Lee from Northwestern University at the Institut des Hautes Etudes Scientifiques. Delve into the fundamental definitions and properties of higher rank lattice actions while examining how measures and measure rigidity serve as crucial tools across various mathematical settings. Learn about classical theorems including Margulis' normal subgroup theorem and Margulis' superrigidity theorem, understanding how measure rigidity provides the foundation for these important results. Investigate recent developments in the Zimmer program, focusing on smooth actions of higher rank lattices on manifolds and their geometric implications. Gain insights into the sophisticated interplay between measure theory, group actions, and rigidity phenomena in higher-dimensional settings, building upon concepts introduced in the previous sessions of this comprehensive mathematical series.
