Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 1

Explore the first lecture in a series on Bounded Generation of Linear Groups and Diophantine Approximation, delivered by Pietro Corvaja at the International Centre for Theoretical Sciences. Delve into the complex world of Zariski dense subgroups, number theory, and their geometric applications as part of a comprehensive program featuring experts in algebraic and Lie groups, differential and algebraic geometry. Gain insights into recent advancements in the theory of arithmetic and Zariski-dense subgroups, including applications to algebraic and differential geometry, combinatorics, and other areas. Discover the intersection of diophantine techniques in linear groups, bounded generation by conjugacy classes, and new approaches to Bruhat-Tits theory. Engage with cutting-edge research on isospectral locally symmetric spaces, eigenvalue rigidity, and potential applications in pseudo-Riemannian geometry and the classification of compact space forms.