Descriptive combinatorics and distributed algorithms

Abstract

This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed algorithms -- a fundamental part of computer science that is becoming increasingly important in the modern era of decentralized computation. In the first part of the article we give a brief introduction to some of the central notions and problems of descriptive combinatorics. The second part is devoted to an overview of some of the results concerning the interactions between descriptive combinatorics and distributed algorithms, as well as a few open problems. The article should be accessible to readers with little to no background in either descriptive set theory or computer science.