Mathematics Colloquium

The Kakeya set conjecture in three dimensions

Joshua Zahl, Department of Mathematics, University of British Columbia,

A Besicovitch set is a compact subset of Rn that contains a unit line segment pointing in every direction. The Kakeya set conjecture asserts that every Besicovitch set in Rn has Minkowski and Hausdorff dimension n. I will discuss some recent progress on this conjecture, leading to the resolution of the Kakeya set conjecture in three dimensions. This is joint work with Hong Wang.

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