Maximally highly proximal flows

Given a Polish group G, the maximally highly proximal flows, or MHP flows, are those flows which do not admit a non-trivial highly proximal extension. Examples of MHP flows include the Samuel compactification, the universal minimal flow, the universal minimal proximal flow, and the Furstenberg boundary. In this talk, we will seek a detailed understanding of topologically transitive MHP flows. In particular, if X is an MHP flow with a comeager orbit, then X is the Samuel compactification of G/H for some closed subgroup H, and in many cases, we can describe H explicitly.