The Kakeya conjecture

Описание к видео The Kakeya conjecture

Speaker: Tamás Keleti (ELTE)

Abstract: How large area is needed to rotate a needle? How small a hedgehog can be? Are lines much bigger than line segments? What do these questions have to do with the Kakeya conjecture, which claims that if a compact set in R^n has unit line segments in every direction then the set must have Hausdorff/Minkowski dimension n? Why is this conjecture so important to some of the leading mathematicians? What partial results could they prove? How do I fail to achieve breakthrough?

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