The Borel chromatic number of \(\\Z^2\)
Brandon Seward, NYU
Location: HILL 705
Date & time: Monday, 11 December 2017 at 5:00PM - 6:00PM
Abstract: I will discuss joint work with Su Gao, Steve Jackson, and Ed Krohne that proves that \(Z^2\) has Borel chromatic number 3. Specifically, given any standard Borel space X and a free Borel action of \(Z^2\) on X, one constructs a Borel graph on X by laying down a copy of the canonical (unmarked) Cayley graph of \(Z^2\) on each \(Z^2\)-orbit. We prove that this graph always admits a graph-theoretic 3-coloring that is Borel.