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Explore the dynamics of subgroup conjugation in Baumslag-Solitar groups through this 49-minute mathematical lecture. Examine the space of subgroups of infinite countable groups endowed with the Chabauty topology, which forms a closed subspace of the Cantor set with homeomorphic actions given by G-conjugation. Investigate the dynamics induced by this action on closed G-invariant subspaces, focusing particularly on the perfect kernel - the largest closed subspace without isolated points. Discover how this research reveals a fundamentally different situation from the acylindrically hyperbolic context, where Hull, Mynasyan and Osin demonstrated strong mixing properties. Learn about the decomposition of the perfect kernel introduced by Carderi, Gaboriau, Le Maître and Stalder, and understand how conjugation exhibits μ-mixing properties in unimodular Baumslag-Solitar groups. Contrast this with non-unimodular cases, where a continuum of measures μ exists for which the action is μ-mixing only on a single piece of the partition. Gain insights into advanced topics in orbit equivalence, topological dynamics, and measurable dynamics through this specialized mathematical presentation delivered at the Centre International de Rencontres Mathématiques.
