Explore a comprehensive lecture on convolution and square operations in Abelian groups presented by Yves Benoist. Delve into advanced mathematical concepts as part of the "Zariski Dense Subgroups, Number Theory and Geometric Applications" program organized by the International Centre for Theoretical Sciences. Gain insights into the theory of arithmetic and Zariski-dense subgroups, their applications in algebraic and differential geometry, and connections to combinatorics. Examine techniques from algebraic and analytic number theory, and discover how these methods have been applied to solve long-standing problems in mathematics. Investigate topics such as fake projective planes, isospectral and length-commensurable locally symmetric spaces, and expanding graphs. Learn about recent developments in bounded generation, stability, and asymptotic cohomology. Engage with new approaches to Bruhat-Tits theory and explore groups with good reduction. Consider geometric problems related to isospectral locally symmetric spaces and their implications for eigenvalue rigidity and pseudo-Riemannian geometry. Read more