Orbit Closures on Homogeneous Spaces and Applications to Number Theory by George Tomanov

Explore a comprehensive lecture on orbit closures in homogeneous spaces and their applications to number theory. Delivered by George Tomanov as part of the "Zariski Dense Subgroups, Number Theory and Geometric Applications" program at the International Centre for Theoretical Sciences. Delve into advanced mathematical concepts, including arithmetic and Zariski-dense subgroups, algebraic and analytic number theory, and the arithmetic theory of algebraic groups. Discover how these techniques have been applied to solve long-standing problems in algebraic and differential geometry, combinatorics, and other areas. Gain insights into recent developments in bounded generation, stability, and asymptotic cohomology. Learn about new approaches to Bruhat-Tits theory and groups with good reduction. Examine the connections between these topics and pseudo-Riemannian geometry, including the classification of compact space forms and eigenvalue rigidity.