Bounded Generation of Linear Groups and Diophantine Approximation - Lecture 3

Explore the third 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 advanced topics in number theory and geometric applications as part of a comprehensive program on Zariski Dense Subgroups. 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, as well as the arithmetic theory of algebraic groups, 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. Learn about bounded and non-bounded generation, diophantine techniques in linear groups, and recent results on stability and asymptotic cohomology. Engage with cutting-edge research and open problems in this 49-minute lecture, which is part of a broader program featuring experts in algebraic and Lie groups, differential and algebraic geometry, and related fields.