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Explore measure rigidity in higher rank lattice actions through this comprehensive lecture that forms the second part of a three-part mini-course series. 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 contexts. Learn about classical theorems including Margulis' normal subgroup theorem and Margulis' superrigidity theorem, understanding how measure rigidity provides the foundation for proving these landmark 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 interplay between algebraic structures, geometric actions, and measure-theoretic techniques that characterize this active area of research in mathematics. The lecture builds upon foundational concepts while progressing toward contemporary research directions, making it valuable for graduate students and researchers interested in lattice theory, ergodic theory, and geometric group theory.
