Zoltán Vidnyánszky:
Finite and infinite: connections between distributed computing and Borel combinatorics
Partially motivated by the success of graph theoretic methods in the theory of paradoxical decompositions, in the past decade, the field of Borel combinatorics has gained popularity. In this area, nice (that is, definable) infinite graphs and Borel / measurable / Baire measurable objects are investigated (for example, questions about paradoxical decompositions can be reformulated in terms of the existence of perfect matchings).
In the past two years an exciting new connection has been developed: the behaviour of large (but finite) graphs in the so-called LOCAL model of distributed computing is observed to be similar to the one encountered in the Borel context. Surprisingly, sometimes even transfer theorems can be proved! I will discuss some of the most important results of both fields and the connection between the two worlds.