Graphs and Matroids - James Davies

Title: Non-measurable colourings avoiding large distances

Abstract: "In 1983, F{\"u}rstenberg, Katznelson, and Weiss proved that for every finite measurable colouring of the plane, there exists a $d_0$ such that for every $d \ge d_0$ there is a monochromatic pair of points at distance $d$. In contrast to this, we show that there is a finite colouring avoiding arbitrarily large distances.

Joint work with Rutger Campbell."