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Explore the second lecture of a mini-course on Uniform Stability of Higher-rank Groups, presented by Alex Lubotzky and Bharatram Rangarajan. Delve into advanced topics related to Zariski dense subgroups, number theory, and their geometric applications as part of a comprehensive program organized by the International Centre for Theoretical Sciences. 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, and learn about their successful application to long-standing problems in mathematics. Discover how these methods have been used to address issues such as fake projective planes, isospectral and length-commensurable locally symmetric spaces, and expanding graphs. Engage with cutting-edge research on bounded generation, stability, and asymptotic cohomology in the context of linear groups.
