Cuauhtemoc Gomez Navarro: A Conjecture of Dolnikov on Colored Convex Sets

Let K be a convex set in the plane. Consider a finite family of translates of K, each colored either blue, red, or green, such that any two sets of different colors intersect. A conjecture of Dolnikov states that there is a color class that can be pierced by three points.

In this talk we present new progress towards this conjecture. We will also discuss a related result in higher dimensions.