We say that a group $ G $ is acylindrically hyperbolic if it admits a non-elementary
acylindrical action on a hyperbolic space. We prove that the class of acylindrically hyperbolic …

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to
have the unique trace property if its reduced C*-algebra has a unique tracial state. A …

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We study actions of countable discrete groups which are amenable in the sense that there
exists a mean on X which is invariant under the action of G. Assuming that G is …

We study percolation on nonamenable groups at the uniqueness threshold $ p_u $, the
critical value that separates the phase in which there are infinitely many infinite clusters from …

Vaughan Jones discovered unexpected connections between Richard Thompson's group
and subfactor theory while attempting to construct conformal field theories (in short CFT) …

We prove a new inequality bounding the probability that the random walk on a group has
small total displacement in terms of the spectral and isoperimetric profiles of the group. This …

We study lattices acting on $\mathrm {CAT}(0) $ spaces via their commensurated
subgroups. To do this we introduce the notions of a graph of lattices and a complex of …

We introduce a class of countable groups by some abstract group-theoretic conditions. This
class includes linear groups with finite amenable radical and finitely generated residually …

We show that the continuous L p-cohomology of locally compact second countable groups is
a quasi-isometric invariant. As an application, we prove partial results supporting a positive …