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Explore the concepts of Invariant Random Subgroups (IRS) and Uniformly Recurrent Subgroups (URS) in this 28-minute conference talk by Gil Goffer. Delve into these generalizations of normal subgroups that emerge from a group's action on its subgroup space. Examine various contexts where IRS and URS exhibit behavior similar to normal subgroups. Learn about ongoing research projects with Pierre-Emmanuel Caprace, Waltraud Lederle, and Tal Cohen, focusing on compact URS and compact IRS. Gain insights into measured group theory as part of the "Théories des groups mesurée/ Measured Group Theory" conference held in March 2023 at the Centre de recherches mathématiques (CRM).