Andy Zucker, Department of Pure Mathematics, University of Waterloo
"Ultracoproducts of G-flows"
Given a topological group G, a G-flow is a continuous action of G on a compact Hausdorff space X. This talk will discuss a notion of ultracoproduct for G-flows, which arise from considering ultraproducts of commutative G-C*-algebras by Gelfand duality. We apply the construction to develop an understanding of the properties of various classes of subflows of a flow, i.e. minimal, topologically transitive, etc. For groups which are locally Roelcke precompact, ultracoproducts of G-flows lead to a well-behaved notion of weak containment for a wide class of G-flows, and in particular for all G-flows when G is locally compact. In joint work with Gianluca Basso, we apply ultracoproducts of G-flows to achieve a new characterization of those Polish groups G with the property that every minimal flow has a comeager orbit.
MC 5479