Abstract by Kyle Meaker
Chromatic Numbers of the Plane
A coloring of a metric space X is a mapping into a set, which we refer to as the set of colors, such that no two points a fixed distance d apart are the same color. The chromatic number of X is the cardinality of the minimal number of colors required to color X. Our research is centered around the Hadwiger-Nelson problem, which asks for the chromatic number of the plane with the L^2-metric. We will explain how to determine the chromatic number for the plane with the L^1-metric, as well as the known lower and upper bounds of the plane with the L^2-metric.