Minicourse: Uniform Stability of Higher-rank Arithmetic Groups - Lecture 3

Explore the third lecture in a minicourse on Uniform Stability of Higher-rank Arithmetic Groups, presented by Alex Lubotzky and Bharatram Rangarajan. Delve into advanced topics related to Zariski dense subgroups, number theory, and their geometric applications as part of a comprehensive program organized by the International Centre for Theoretical Sciences. Gain insights into recent developments in the theory of arithmetic and Zariski-dense subgroups, including applications to algebraic and differential geometry, combinatorics, and other areas. Examine techniques from algebraic and analytic number theory, and learn about their role in solving long-standing problems in mathematics. Discover how these methods contribute to understanding fake projective planes, isospectral and length-commensurable locally symmetric spaces, expanding graphs, and multi-dimensional expanders. Engage with cutting-edge research on bounded generation, stability, and asymptotic cohomology in the context of linear groups.