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Explore the concept of random subgroups in mathematics through this 53-minute lecture by Tsachik Gelander, part of the Measured Group Theory series at the Centre de recherches mathématiques. Delve into the theory of invariant random subgroups (IRS) and its applications to lattices and asymptotic invariants in locally symmetric manifolds and discrete subgroups of Lie groups. Discover how introducing randomness can simplify complex mathematical problems and provide insights into deterministic objects. Learn about the limitations of invariant measures and the potential of stationary random subgroups (SRS) in addressing previously unreachable questions. Gain a foundational understanding of IRS in this first lecture of a three-part series on random subgroups in group theory.
