Speaker: Shira Zerbib
Title: Covering geometrical hypergraphs
Abstract:
The covering number of a family of sets is the minimal number of elements needed to intersect all the sets in the family. Bounding the covering numbers of families F of sets in the Euclidean space, given some local intersection properties of F, is a thriving area of research in discrete geometry. It was initiated by the classical theorem of Helly from 1923, asserting that if in a family F of convex sets in R^d every d+1 sets intersect, then all the sets in F intersect, i.e., F can be covered by one point.
We will discuss old and new results regarding the covering numbers of certain families of sets in the Euclidean space.