Noncommutative Ergodic Theory of Higher Rank Lattices

Explore recent advancements in noncommutative ergodic theory of higher rank lattices in this 46-minute lecture by Cyril Houdayer. Delve into the dynamics of positive definite functions and character rigidity of irreducible lattices in higher rank semisimple algebraic groups. Discover applications to ergodic theory, topological dynamics, unitary representation theory, and operator algebras. Examine the noncommutative Nevo–Zimmer theorem for actions on von Neumann algebras, a key operator algebraic innovation for lattices in higher rank simple algebraic groups. Investigate a noncommutative analogue of Margulis' factor theorem and its implications for Connes' rigidity conjecture. Follow the comprehensive syllabus covering topics such as simple algebraic groups, examples of higher rank lattices, dynamics of AP(A), character classification, boundary structures on von Neumann algebras, and more.