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 …

This paper develops techniques which are used to answer a number of questions in the
theory of equivalence relations generated by continuous actions of abelian groups. The …

We give a new short proof of the theorem due to Marquis and Sabok, which states that the
orbit equivalence relation induced by the action of a finitely generated hyperbolic group on …

Let $ X $ be a Polish space with Borel probability measure $\mu, $ and let $ G $ be a Borel
graph on $ X $ with no odd cycles and maximum degree $\Delta (G). $ We show that the …

This thesis comprises two parts, each consisting of three articles. In the first part we will use
techniques inspired by measurable and topological dynamics to solve problems in finite …

In this note, we show that if G is a Borel graph of finite maximum degree, then its Baire
measurable edge chromatic number is at most 1 more than its (discrete) edge chromatic …