P. Baum and A. Connes have made a deep conjecture about the calculation of the K-theory of certain types of C∗-algebras [1, 2]. In particular, for a discrete group Γ they have conjectured the calculation of K∗(C r (Γ)), the Ktheory of the reduced C∗-algebra of Γ. So far, there is quite little evidence for this conjecture. For example, there is not a single property T group for which it is known...

The discrimination technique for estimating the parameters of Gaussian mixtures that is based on the Extended Baum transformations (EB) has had significant impact on the speech recognition community. The proof that definitively shows that these transformations increase the value of an objective function with iteration (i.e., so-called ”growth transformations”) was presented by the author two ye...

In this work, the continuously controlled techniques developed by Carlsson and Pedersen are used to prove that the Baum-Connes map is a split injection for groups satisfying certain geometric conditions.

Let (1→Nm→Gm→Qm→1)m∈N be a sequence of extensions finite groups such that their coarse disjoint unions have bounded geometry. In this paper, we show if the (Nm)m∈N and (Qm)m∈N are coarsely embeddable into Hilbert space, then Baum–Connes conjecture holds for union (Gm)m∈N. As an application, relative expanders constructed by G. Arzhantseva R. Tessera, special box spaces free discovered T. Delabi...