A group is boundedly acyclic if its bounded cohomology with trivial real coefficients vanishes
in all positive degrees. Amenable groups are boundedly acyclic, while the first nonamenable …

We prove the vanishing of the bounded cohomology of lamplighter groups for a wide range
of coefficients. This implies the same vanishing for a number of groups with self-similarity …

We prove a general criterion for the vanishing of second bounded cohomology (with trivial
real coefficients) for groups that admit an action satisfying certain mild hypotheses. This …

In recent years, there has been a growing interest in the widespread application of graph
neural networks (GNNs). However, existing GNN frameworks are predominantly designed …

We introduce a set of combinatorial techniques for studying the simplicial bounded
cohomology of semi-simplicial sets, simplicial complexes and posets. We apply these …

We show that a large family of groups is uniformly stable relative to unitary groups equipped
with submultiplicative norms, such as the operator, Frobenius, and Schatten p-norms. These …

A well-known question by Gromov asks whether the vanishing of the simplicial volume of
oriented closed aspherical manifolds implies the vanishing of the Euler characteristic. We …

We prove the vanishing of bounded cohomology with separable dual coefficients for many
groups of interest in geometry, dynamics, and algebra. These include compactly supported …

We provide new vanishing and glueing results for relative simplicial volume, following up on
two current themes in bounded cohomology: The passage from amenable groups to …

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity
properties. In this work, we add another such rigidity property to the list: uniform stability with …