On coarse embeddability into ℓp\ell_p-spaces and a conjecture of Dranishnikov

We show that the Hilbert space is coarsely embeddable into any $\ell_p$ for $1\le p<\infty$. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space.Comment: 5 page

Aperiodic tilings of manifolds of intermediate growth

We give a homological construction of aperiodic tiles for certain open Riemannian surfaces admitting actions of Grigorchuk groups of intermediate growth.Comment: Accepted for publication in Groups, Geometry and Dynamic

Eilenberg swindles and higher large scale homology of products of trees

We show that uniformly finite homology of products of $n$ trees vanishes in all degrees except degree $n$, where it is infinite dimensional. Our method is geometric and applies to several large scale homology theories, including almost equivariant homology and controlled coarse homology. As an application we determine group homology with $\ell_{\infty}$-coefficients of lattices in products of trees. We also show a characterization of amenability in terms of 1-homology and construct aperiodic tilings using higher homology.Comment: Final version, to appear in Groups, Geometry & Dynamic

Hilbert C*-modules and amenable actions

We study actions of discrete groups on Hilbert $C^*$-modules induced from topological actions on compact Hausdorff spaces. We show non-amenability of actions of non-amenable and non-a-T-menable groups, provided there exists a quasi-invariant probability measure which is sufficiently close to being invariant.Comment: Final version, to appear in Studia Mathematic

Expanders are counterexamples to the coarse pp-Baum-Connes conjecture

We show that certain expanders are counterexamples to the coarse $p$-Baum-Connes conjecture.Comment: 19 page