Tameness, forcing, and the revised Newelski conjecture
The revised Newelski conjecture asserts that for any group definable in an NIP structure, the automorphism group of its definable universal minimal flow is Hausdorff in the so-called "tau-topology." Recently, the countable case of the conjecture was proven by Chernikov, Gannon, and Krupinski using a deep result of Glasner, which provides a structure theorem for minimal metrizable tame flows. With this result, they prove that the Ellis group of a minimal metrizable tame flow (the automorphism group of a related flow) has Hausdorff tau-topology, and the conjecture for groups definable in countable NIP structures follows. We prove the revised Newelski conjecture in full by showing that the Ellis group of any minimal tame flow has Hausdorff tau-topology. To do this, we introduce new set-theoretic methods in topological dynamics which allow us to apply forcing and absoluteness arguments. As a consequence, we obtain a partial version of Glasner's structure theorem for general minimal tame flows. Joint work with Gianluca Basso.