Do local constraints demand global coordination? I'll address a particularly simple formulation of this question: can the vertices of a graph be assigned random colors in a stationary way, so that neighboring colors always differ, but without long-range dependence? The quest to answer this has led to the discovery of a beautiful yet mysterious new stochastic process that seemingly has no right to exist, while overturning the conventional thinking on a fundamental 49-year old question.
(Joint work with Tom Liggett.)