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Vector-sum theorems, their relatives and applications


Speaker: Prof. Imre Barany, Hungarian Academy of Science & Univ. College London
Location: 1147
Start time: Mon, Feb 24 2020, 4:10PM

About hundred years ago, while answering a question of Riemann, Steinitz proved the following result:

Let $B$ be the unit ball of the Euclidean norm in $R^d$ and assume that $V \subset B$ is finite and the sum of the elements in $V$ is zero. Then there is an ordering $v_1,\ldots,v_n$ of $V$ such that all partial sums along this ordering have norm smaller than $2d$.

I am going to talk about extensions, generalizations, and applications of this remarkable theorem.

There will be refreshments before the talk