What is… Helly's theorem?

Abstract

Helly's Theorem is one of the most famous results of a combinatorial nature about convex sets. It states that if we have n convex sets in R^d, where n>d, and the intersection of every d+1 of these sets is nonempty, then the intersection of all sets is nonempty. In preparation of Gil Kalai's BMS talk, we will see a basic proof of this theorem using (a basic proof of) Radon's Lemma. Hopefully we will also have a look at some application(s).

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