|Time:|| 3:30pm - 4:30 pm
Wean Hall 8220
Department of Mathematical Sciences
Measure-theoretic unfriendly colorings
Given a graph with vertices painted red and blue, we say the coloring is unfriendly if every red vertex has at least as many blue neighbors as red, and vice versa. Every finite graph admits an unfriendly coloring, but (ridiculously) it remains open whether every countable graph does. Rather than tackle that problem, we consider measure-theoretic analogs associated with probability-measure-preserving actions of finitely generated groups. We don't really answer any questions here, either, but we do obtain such colorings up to weak equivalence of actions. Time permitting, we also discuss recent constructions of unfriendly colorings of acyclic hyperfinite graphs. The talk may include joint work with Kechris, Marks, Tucker-Drob, and Unger.