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Explore the concepts of rigidity and stiffness in arithmetic groups in this 22-minute lecture by Itamar Vigdorovich, part of the "Zariski Dense Subgroups, Number Theory and Geometric Applications" program at the International Centre for Theoretical Sciences. Delve into the latest advancements in the theory of arithmetic and Zariski-dense subgroups, examining their applications in algebraic and differential geometry, combinatorics, and other fields. Gain insights into techniques used to investigate Zariski-dense subgroups, with a focus on methods from algebraic and analytic number theory and arithmetic theory of algebraic groups. Learn about recent developments in bounded generation, stability, and asymptotic cohomology, as well as new approaches to Bruhat-Tits theory and groups with good reduction. Discover how these concepts relate to isospectral locally symmetric spaces and the emerging concept of eigenvalue rigidity.
