Hypergeometric Groups and their Arithmeticity
Explore the concept of hypergeometric groups and their arithmeticity in this 59-minute lecture by Sandip Singh. Delve into the theory of arithmetic and Zariski-dense subgroups, examining recent progress and applications in algebraic and differential geometry, combinatorics, and related fields. Learn about techniques used to investigate Zariski-dense subgroups, with emphasis on methods from algebraic and analytic number theory. Discover how these approaches have been applied to solve long-standing problems in mathematics and physics. Gain insights into topics such as bounded generation, stability, asymptotic cohomology, and new approaches to Bruhat-Tits theory. Understand the connections between these concepts and their implications for isospectral locally symmetric spaces, pseudo-Riemannian geometry, and the classification of compact space forms.