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 …

In this article we survey the emerging field of descriptive graph combinatorics. This area has
developed in the last two decades or so at the interface of descriptive set theory and graph …

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 …

This book introduces a new research direction in set theory: the study of models of set theory
with respect to their extensional overlap or disagreement. In Part I, the method is applied to …

Extremal aspects of graph and hypergraph decomposition problems. Page 245 Extremal aspects
of graph and hypergraph decomposition problems Stefan Glock Daniela Kühn Deryk Osthus …

Laczkovich proved that if bounded subsets A and B of R^k have the same nonzero
Lebesgue measure and the upper box dimension of the boundary of each set is less than k …

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 …

We extend Følner's amenability criterion to the realm of general topological groups. Building
on this, we show that a topological group is amenable if and only if its left-translation action …

We introduce new types of local algorithms, which we call" ASI Algorithms", and use them to
demonstrate a link between descriptive and computable combinatorics. This allows us to …

We study the relationship between hyperfiniteness and problems in Borel graph
combinatorics by adapting game-theoretic techniques introduced by Marks to the hyperfinite …