Copenhagen
Groups and Operator Algebras Seminar

Abstract:  Given a finitely generated group G, a non-trivial element g in G, and a minimal action of G on a compact space X, with amenable stabilizers, we prove sufficient conditions in terms of various growth/decay functions for topological freeness of the action of g on X. We apply our results to the case of the (Furstenberg) boundary action of G, to conclude C*-simplicity under (semi)rapid decay conditions. In this context, we also give a description of the support of stationary states on the reduced C*-algebra of G. We further extend these techniques to conclude topological freeness for more general classes of actions under growth assumptions on the C*-algebras generated by unitary representations weakly containing the quasi-regular representations of the stabilizer subgroups.

Abstract:  Since the breakthrough work of Connes on the classification of injective factors, the existence and uniqueness of continuous trace scaling flows on a given II_\infty factor has remained a challenging problem in general. Haagerup's seminal work showed that the unique injective II_\infty factor has a unique such flow. Subsequently, Radulescu showed the existence of such a flow on L(F_\infty) \otimes B(H) (its uniqueness is still open), and Dykema showed that the existence of such a flow on L(F_2) \otimes B(H) implies that all free group factors are isomorphic. In this talk we shall see how some Lie algebraic techniques can be used to compute the number of 'distinct' trace scaling flows on full II_\infty factors whose outer automorphism groups are locally compact. This talk is based on joint work with Sergiu Novac.

Abstract:  The coarse Baum--Connes conjecture is a problem on higher index theory of metric spaces, which has significant application on geometry and topology. In this talk, we explain how decompositions of metric spaces give rise to Mayer–Vietoris arguments in quantitative K-theory. As applications, we discuss free products of metric spaces and relatively hyperbolic groups. This talk is based on joint works with Jintao Deng.

Abstract:  TBA