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Contemporary Problems in Number Theory
June 11, 2014 12:45, Moscow, Steklov Mathematical Institute, Room 530 (8 Gubkina)
 


Dimension of the set of singular vectors

Nicolas Chevallier
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Nicolas Chevallier


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Abstract: Singular vectors were defined by Khintchin in the twenties. Recently it has been proved by Yitwah Cheung that the Hausdorff dimension of the set of singular couples is $4/3$. In a joint work with Yitwah Cheung, we have proved that the Hausdorff dimension of the set of singular vectors in $\mathbb R^d$ is $\frac{d^2}{d+1}$.
We will explain the proof of this formula with a special emphasis on best Diophantine approximations.
This talk is supported by “Short-time visits of foreign scientists to Russia” of Dynastia Foundation

Language: English

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