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BIRS Workshop Lecture Videos

Proof of a conjecure of Barany, Katchalski and Pach Naszodi, Marton


B\'ar\'any, Katchalski and Pach proved the following quantitative form of Helly's theorem: If the intersection of a family of convex sets in $\mathbb{R}^d$ is of volume one, then the intersection of some subfamily of at most $2d$ members is of volume at most some constant $v(d)$. They gave the bound $v(d)\leq d^{2d2}$, and conjectured that $v(d)\leq d^{cd}$. We confirmed it. We discuss the proof and further results.

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