BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Theorems of Helly and Tverberg without dimension Bárány, Imre


The Helly theorem in the title says the following. Assume $k < d+1$ and $F$ is a finite family of convex bodies, all contained in the Euclidean unit ball of $R^d$ with the property that every $k$-tuple of sets in $F$ has a point in common. Then there is a point $q$ in $R^d$ which is closer than $1/ \sqrt k$ to every set in $F$. This result has several colourful and fractional variants. Similar versions of Tverberg's theorem and some of their extensions are also established. This is joint work with Karim Adiprasito, Nabil Mustafa, and Tamás Terpai.

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