Uniform Stability of Higher-rank Arithmetic Groups - Lecture 1

Explore the first lecture of a minicourse on Uniform Stability of Higher-rank Arithmetic Groups, delivered by Alex Lubotzky and Bharatram. Delve into advanced topics in number theory and geometric applications as part of the "Zariski Dense Subgroups, Number Theory and Geometric Applications" program. Gain insights into recent developments in the theory of arithmetic and Zariski-dense subgroups, with applications to algebraic and differential geometry, combinatorics, and other areas. Learn about techniques from algebraic and analytic number theory used to address long-standing problems in mathematics. Discover how these methods have been applied to solve issues related to fake projective planes, isospectral and length-commensurable locally symmetric spaces, expanding graphs, and multi-dimensional expanders. Examine recent results on bounded/non-bounded generation, bounded generation by conjugacy classes, and stability and asymptotic cohomology. Engage with experts in algebraic and Lie groups, differential and algebraic geometry, and related fields through this comprehensive lecture series organized by the International Centre for Theoretical Sciences.