Character Rigidity and Ergodic Actions of Non-uniform Higher Rank Lattices

Explore advanced mathematical concepts in this special seminar lecture examining character rigidity and ergodic actions of non-uniform higher rank lattices. Delve into the powerful theory of rigidity for lattices in higher rank semisimple Lie groups, which combines methods from algebra, number theory, geometry, and dynamics. Learn about Margulis' normal subgroup theorem and its implications for understanding normal subgroups of higher rank lattices. Examine Connes' conjecture regarding extremal, positive definite, normalized central functions (characters) defined on lattices, and discover how recent collaborative research has proven this conjecture for non-uniform lattices in products of rank-1 groups over arbitrary local fields of uneven characteristic, as well as Lie groups with infinite center. Understand how these findings, combined with previous work by other researchers, fully establish both Connes' and Stuck-Zimmer's conjectures for all non-uniform lattices, representing a significant advancement in the field of mathematical rigidity theory.