BIRS Workshop Lecture Videos
Exact quantitative Helly theorems. Soberón, Pablo
We will discuss several quantitative Helly theorems, where we characterize families of convex sets whose intersection has a large volume or diameter. The Helly numbers we obtain depend on the complexity of a witness set that guarantees that the intersection is large. For example, our Helly numbers characterize families of convex sets that contain ellipsoids with large volume, or zonotopes with large diameter. The methods we describe work for a wide family of functions and witness sets. We will describe which results can be proven with purely geometric methods and which ones require a bit of topology.
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