Uniform Stability of Higher-rank Arithmetic Groups - Lecture 1

Explore the first lecture of a mini-course on Uniform Stability of Higher-rank Arithmetic Groups, presented by Alex Lu and Bharatram R. at the International Centre for Theoretical Sciences. Delve into advanced topics in Zariski dense subgroups, number theory, and geometric applications as part of a comprehensive program featuring experts in algebraic and Lie groups, differential and algebraic geometry. 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. Discover the latest techniques used to investigate Zariski-dense subgroups, with a focus on methods from algebraic and analytic number theory and arithmetic theory of algebraic groups. Learn about recent results on bounded/non-bounded generation, bounded generation by conjugacy classes, and stability and asymptotic cohomology. Engage with new approaches to Bruhat-Tits theory and groups with good reduction. Examine problems related to isospectral locally symmetric spaces and explore the concept of eigenvalue rigidity. Suitable for active researchers at any stage of their academic career in Lie groups, discrete subgroups, algebraic groups, and related areas of algebraic and differential geometry.