# Past Events

Logic Seminar

## 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.

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