New results on the behaviour of a wide range of cohomological (and homotopical) invariants for infinite groups

I will talk about the behaviour of a wide range of cohomological and homotopical invariants over groups that are locally in Kropholler's hierarchy of groups with the base class being groups of type Phi that were introduced by Olympia Talelli. Many of the new results that we'll discuss are more general in theme. We will show how our results relate to some existing conjectures in the area and discuss the significance and applications of these relations.