Gergely Ambrus:

New estimates on convex layer numbers


Abstract: 

Let X be a finite point set in R^d. We introduce the peeling process as follows: in each step, we take our current set (starting with X), and we remove the vertices of its convex hull from it. How many steps are needed to delete the entire set X? This is called the layer number of X. 
Previous studies about layer numbers include determining the layer number of random point sets, and the planar square grid. In this talk, we will study evenly distributed families of sets contained in the unit ball. We determine the sharp lower bound for their layer numbers, and also give an upper bound together with an asymptotically almost matching construction. 
Joint work with Peter Nielsen and  Caledonia Wilson.