We study connections between distributed local algorithms, finitary factors of iid processes,
and descriptive combinatorics in the context of regular trees. We extend the Borel …

We present an intimate connection among the following fields:(a) distributed local
algorithms: coming from the area of computer science,(b) finitary factors of iid processes …

The theory of definable equivalence relations has been a very active area of research in
descriptive set theory during the last three decades. It serves as a foundation of a theory of …

We provide a gentle introduction, aimed at non-experts, to Borel combinatorics that studies
definable graphs on topological spaces. This is an emerging field on the borderline between …

We show that every free continuous action of a countably infinite elementary amenable
group on a finite-dimensional compact metrizable space is almost finite. As a consequence …

We prove that the homology groups of a principal ample groupoid vanish in dimensions
greater than the dynamic asymptotic dimension of the groupoid (as a side‐effect of our …

We show that a minimal action of a finitely generated group of polynomial growth on a
compact metrizable space has comparison. It follows that if such an action is free and has …

Let $(X,\tau) $ be a Polish space with Borel probability measure $\mu $, and $ G $ a locally
finite one-ended Borel graph on $ X $. We show that $ G $ admits a Borel one-ended …

Asymptotic separation index is a parameter that measures how easily a Borel graph can be
approximated by its subgraphs with finite components. In contrast to the more classical …

We show that a free action G↷ X is almost finite if its restriction to some infinite normal
subgroup of G is almost finite. Consider the class of groups which contains all infinite groups …